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path: root/apps/recorder/icons.c (follow)
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* Recording: Add AIFF recording to SWCODEC. Note: AIFF playback chokes on ↵Michael Sevakis2006-11-24
| | | | | | sample rates other than 44.1kHz whether recorded or created and saved with an external program. Recorded files will still open in an external editor however. git-svn-id: svn://svn.rockbox.org/rockbox/trunk@11583 a1c6a512-1295-4272-9138-f99709370657
* Big Patch adds primarily: Samplerate and format selection to recording for ↵Michael Sevakis2006-11-06
| | | | | | SWCODEC. Supprort for samplerates changing in playback (just goes with the recording part inseparably). Samplerates to all encoders. Encoders can be configured individually on a menu specific to the encoder in the recording menu. File creation is delayed until flush time to reduce spinups when splitting. Misc: statusbar icons for numbers are individual digits to display any number. Audio buffer was rearranged to maximize memory available to recording and properly reinitialized when trashed. ColdFire PCM stuff moved to target tree to avoid a complicated mess when adding samplerate switching. Some needed API changes and to neaten up growing gap between hardware and software codecs. git-svn-id: svn://svn.rockbox.org/rockbox/trunk@11452 a1c6a512-1295-4272-9138-f99709370657
* Added inner fill option to normal scrollbar and foreground only option. ↵Michael Sevakis2006-10-13
| | | | | | Added a left-pointing cursor for using pointer. Updated color picker and now sliders look very good on color, grayscale and mono screens when using bar selector. Some misc. changes for appearance. git-svn-id: svn://svn.rockbox.org/rockbox/trunk@11210 a1c6a512-1295-4272-9138-f99709370657
* Recording Statusbar: Just shove those icons right by 1 pixelMartin Scarratt2006-09-26
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@11069 a1c6a512-1295-4272-9138-f99709370657
* Recording screen statusbar: Improved channel icon by Paul Louden and ↵Martin Scarratt2006-09-26
| | | | | | improved Q value display for Hardware codec targets git-svn-id: svn://svn.rockbox.org/rockbox/trunk@11062 a1c6a512-1295-4272-9138-f99709370657
* Reverted the recording timer commit, as it has at least 2 major problems. ↵Jens Arnold2006-09-18
| | | | | | (1) It uses the user timer, which interferes e.g. with backlight fading on H1x0 (and potentially other targets). Using the user timer here is a waste, as the required timing lies in the range of seconds to days. A tick task would be sufficient. (2) It draws to the LCD from within an ISR. This must not be done unless there's a mechanism to ensure it doesn't interfere with the main thread's drawing, otherwise garbage might be displayed and LCD updates might stop working. git-svn-id: svn://svn.rockbox.org/rockbox/trunk@10991 a1c6a512-1295-4272-9138-f99709370657
* Recording countdown timer: set timer in recording settings screen (max 1 ↵Martin Scarratt2006-09-18
| | | | | | week countdown), start/pause timer in recording screen by pressing the pause button. If you have a separate record button then this will override the timer and start to record. Icon at bottom right of screen indicates timer is ticking. If you are in the recording screen when the countdown is over, recording will start automatically, if not then the icon will flash to indicate you should return to the recording screen to begin recording. git-svn-id: svn://svn.rockbox.org/rockbox/trunk@10990 a1c6a512-1295-4272-9138-f99709370657
* Save a few bytes on hwcodec targets...Magnus Holmgren2006-09-12
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@10937 a1c6a512-1295-4272-9138-f99709370657
* Improved statusbar icons in recording screen by Davide GentileMartin Scarratt2006-09-12
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@10935 a1c6a512-1295-4272-9138-f99709370657
* Display bitrate (Q value for Archos), samplerate, channels and recording ↵Martin Scarratt2006-09-02
| | | | | | format (M = MP3) in the statusbar in the recording screen. This is all new info for archos targets and I-river targets now have this info on the remote as well as the main screen git-svn-id: svn://svn.rockbox.org/rockbox/trunk@10856 a1c6a512-1295-4272-9138-f99709370657
* New harddisk icon for units (and remotes) without real harddisk LED.Jens Arnold2006-04-16
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@9695 a1c6a512-1295-4272-9138-f99709370657
* Patch #2711 by Alexander Spyridakis with some changes by me: adds load/save ↵Hristo Kovachev2006-04-02
| | | | | | | | | of presets to different files; Also fix the preset menu context menu not working on the remote git-svn-id: svn://svn.rockbox.org/rockbox/trunk@9425 a1c6a512-1295-4272-9138-f99709370657
* Add support for loadable vkeyboard layoutsFrank Dischner2006-03-29
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@9347 a1c6a512-1295-4272-9138-f99709370657
* Initial attempt at using bmp2rb in the build system. Don't forget to re-run ↵Dave Chapman2006-01-22
| | | | | | configure git-svn-id: svn://svn.rockbox.org/rockbox/trunk@8418 a1c6a512-1295-4272-9138-f99709370657
* Fixed disk icon display in remote status bar on iriver. * Rolled back led.c ↵Jens Arnold2005-11-24
| | | | | | changes, introducing a changed #if condition only. Reduces code size on targets with real controllable LED. git-svn-id: svn://svn.rockbox.org/rockbox/trunk@8059 a1c6a512-1295-4272-9138-f99709370657
* Adapted and commited Markus Kaufhold's remote hold icon on statusbar patch ↵Kevin Ferrare2005-11-22
| | | | | | for iriver ; generic logo handler (now it's possible to have a different USB logo on main screen and on remote), made the quickscreen behave as it was before git-svn-id: svn://svn.rockbox.org/rockbox/trunk@8044 a1c6a512-1295-4272-9138-f99709370657
* removed old statusbar and buttonbar codeKevin Ferrare2005-11-20
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@8004 a1c6a512-1295-4272-9138-f99709370657
* new icons for radio statusAnton Oleynikov2005-11-19
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@8002 a1c6a512-1295-4272-9138-f99709370657
* Multi screen support for playlist viewer, some fixes in other gui filesKevin Ferrare2005-11-16
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@7901 a1c6a512-1295-4272-9138-f99709370657
* On popular demand, the arrow cursor is reintroducedLinus Nielsen Feltzing2005-09-01
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@7438 a1c6a512-1295-4272-9138-f99709370657
* Removed the line selector option, it is now always an inverse bar (except ↵Linus Nielsen Feltzing2005-08-30
| | | | | | for the Player/Studio of course) git-svn-id: svn://svn.rockbox.org/rockbox/trunk@7423 a1c6a512-1295-4272-9138-f99709370657
* Icon code cleanup, optimisation & policeing. Removed unused icons. Applied ↵Jens Arnold2005-08-24
| | | | | | uniform icon naming scheme. git-svn-id: svn://svn.rockbox.org/rockbox/trunk@7396 a1c6a512-1295-4272-9138-f99709370657
* Patch #1105616 by Ray Lambert - A-B Repeat for Archos studio/recorder, still ↵Linus Nielsen Feltzing2005-08-21
| | | | | | not 100% complete, but I wanted to commit it before the 2.5 feature freeze git-svn-id: svn://svn.rockbox.org/rockbox/trunk@7380 a1c6a512-1295-4272-9138-f99709370657
* 4-shades greyscale graphics core for iriver H1x0. 4-grey rockbox logo and ↵Jens Arnold2005-07-06
| | | | | | light grey background in splash() boxes. Simplified the splash() box creation as the new graphics core does clipping. Adapted screendump feature and added flexible preprocessing to construct the bmp header. Rockboy now uses 4-grey mode as well. 4-grey support for win32 simulator. Fixed win32 player sim to not use double bitmap conversion via a recorder-like framebuffer, and correctly display double-height text. X11 simulator temporarily adapted. The display won't be distorted, but it still shows b&w only. git-svn-id: svn://svn.rockbox.org/rockbox/trunk@7046 a1c6a512-1295-4272-9138-f99709370657
* Second part of graphics api rework. Bitmap drawing and text output ↵Jens Arnold2005-06-28
| | | | | | converted; some code cleanup and more optimisations. git-svn-id: svn://svn.rockbox.org/rockbox/trunk@6906 a1c6a512-1295-4272-9138-f99709370657
* New feature for units that can be powered or charged from USB (Recorder ↵Jens Arnold2005-06-23
| | | | | | fm/v2, Ondios): USB power mode, based on patch #1110332 by Pieter Bos. This way you can save battery power or even charge the battery (fm/v2) while using your unit near a PC. Hold MODE (Ondio) or F1 (fm/v2) while plugging USB to enter that mode. A tiny USB plug icon will be displayed is the status bar (overridden by the regular power plug icon in case of fm/v2 when the charger is connected). git-svn-id: svn://svn.rockbox.org/rockbox/trunk@6836 a1c6a512-1295-4272-9138-f99709370657
* use the 160 pixels wide logo for wider LCDs too (for now at least)Daniel Stenberg2005-06-15
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@6720 a1c6a512-1295-4272-9138-f99709370657
* Multiple choice LED configuration instead of HAVE_LED. Removes erroneous MMC ↵Jens Arnold2005-06-04
| | | | | | icon display on iriver, and saves some code on Ondio. Removed invert_led() as it is no longer used. git-svn-id: svn://svn.rockbox.org/rockbox/trunk@6568 a1c6a512-1295-4272-9138-f99709370657
* iRiver remote LCD is only 128x64Linus Nielsen Feltzing2005-05-31
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@6542 a1c6a512-1295-4272-9138-f99709370657
* IRiver: show logo on startup at remote lcdChristian Gmeiner2005-04-15
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@6302 a1c6a512-1295-4272-9138-f99709370657
* Ondio activity icon changed to MMC/flash symbol (thanks Jens)Jörg Hohensohn2005-03-01
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@6099 a1c6a512-1295-4272-9138-f99709370657
* Ondio: disk indication in the status bar, to compensate for lacking LEDJörg Hohensohn2005-02-19
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@6012 a1c6a512-1295-4272-9138-f99709370657
* Renamed the config variable for the battery display type to battery_display ↵Jens Arnold2005-01-30
| | | | | | to get it out of the way for the upcoming battery_type setting for the Ondio. Also seems more logical. git-svn-id: svn://svn.rockbox.org/rockbox/trunk@5711 a1c6a512-1295-4272-9138-f99709370657
* Enabled logo display for gmini.Jens Arnold2005-01-25
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@5661 a1c6a512-1295-4272-9138-f99709370657
* bigger Rockbox logo for bigger LCD screenDaniel Stenberg2004-12-20
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@5500 a1c6a512-1295-4272-9138-f99709370657
* slider_bar was obsoleteJens Arnold2004-07-20
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4897 a1c6a512-1295-4272-9138-f99709370657
* Const'ed the logo, the bitmaps and the credits (optimization for running ↵Jens Arnold2004-07-19
| | | | | | from ROM) git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4896 a1c6a512-1295-4272-9138-f99709370657
* Fixed the slow status bar update in bug report #727790.Linus Nielsen Feltzing2004-07-13
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4868 a1c6a512-1295-4272-9138-f99709370657
* The volume icon is now drawn in the original state the very first timeLinus Nielsen Feltzing2004-06-28
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4812 a1c6a512-1295-4272-9138-f99709370657
* The first fix for bug #898145 was incorrectLinus Nielsen Feltzing2004-06-27
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4808 a1c6a512-1295-4272-9138-f99709370657
* Fixed a glitch in the Recorder status bar volume icon display, bug #898145Linus Nielsen Feltzing2004-06-27
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4807 a1c6a512-1295-4272-9138-f99709370657
* removed extra ';'Daniel Stenberg2004-06-16
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4755 a1c6a512-1295-4272-9138-f99709370657
* Plugin/file type association system. Patch #879411 by Henrik BackeBjörn Stenberg2004-05-21
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4677 a1c6a512-1295-4272-9138-f99709370657
* preparation for the JPEG viewerJörg Hohensohn2004-05-12
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4610 a1c6a512-1295-4272-9138-f99709370657
* Added Benjamin Metzlers bookmarking feature (patch #669440)Björn Stenberg2004-01-14
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4227 a1c6a512-1295-4272-9138-f99709370657
* icons for .ch8, .rvfJörg Hohensohn2003-12-22
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4172 a1c6a512-1295-4272-9138-f99709370657
* Battery meter now shows '?' after boot instead of nothing at all.Björn Stenberg2003-12-03
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@4103 a1c6a512-1295-4272-9138-f99709370657
* chip icon for UCL filesJörg Hohensohn2003-07-27
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@3897 a1c6a512-1295-4272-9138-f99709370657
* Added plugin loader. Moved games, demos and the text viewer to loadable ↵Björn Stenberg2003-06-29
| | | | | | plugins. Copy your *.rock files to /.rockbox/rocks/ git-svn-id: svn://svn.rockbox.org/rockbox/trunk@3769 a1c6a512-1295-4272-9138-f99709370657
* Only redraw the status line when info actually changed.Björn Stenberg2003-04-23
| | | | git-svn-id: svn://svn.rockbox.org/rockbox/trunk@3588 a1c6a512-1295-4272-9138-f99709370657
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/*
 * (c) Lambros Lambrou 2008
 *
 * Code for working with general grids, which can be any planar graph
 * with faces, edges and vertices (dots).  Includes generators for a few
 * types of grid, including square, hexagonal, triangular and others.
 */

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <ctype.h>
#include <float.h>
#include <limits.h>
#ifdef NO_TGMATH_H
#  include <math.h>
#else
#  include <tgmath.h>
#endif

#include "puzzles.h"
#include "tree234.h"
#include "grid.h"
#include "penrose-legacy.h"
#include "penrose.h"
#include "hat.h"
#include "spectre.h"

/* Debugging options */

/*
#define DEBUG_GRID
*/

/* ----------------------------------------------------------------------
 * Deallocate or dereference a grid
 */
void grid_free(grid *g)
{
    assert(g->refcount);

    g->refcount--;
    if (g->refcount == 0) {
        int i;
        for (i = 0; i < g->num_faces; i++) {
            sfree(g->faces[i]->dots);
            sfree(g->faces[i]->edges);
            sfree(g->faces[i]);
        }
        for (i = 0; i < g->num_dots; i++) {
            sfree(g->dots[i]->faces);
            sfree(g->dots[i]->edges);
            sfree(g->dots[i]);
        }
        for (i = 0; i < g->num_edges; i++) {
            sfree(g->edges[i]);
        }
        sfree(g->faces);
        sfree(g->edges);
        sfree(g->dots);
        sfree(g);
    }
}

/* Used by the other grid generators.  Create a brand new grid with nothing
 * initialised (all lists are NULL) */
static grid *grid_empty(void)
{
    grid *g = snew(grid);
    g->faces = NULL;
    g->edges = NULL;
    g->dots = NULL;
    g->num_faces = g->num_edges = g->num_dots = 0;
    g->size_faces = g->size_edges = g->size_dots = 0;
    g->refcount = 1;
    g->lowest_x = g->lowest_y = g->highest_x = g->highest_y = 0;
    return g;
}

/* Helper function to calculate perpendicular distance from
 * a point P to a line AB.  A and B mustn't be equal here.
 *
 * Well-known formula for area A of a triangle:
 *                             /  1   1   1 \
 * 2A = determinant of matrix  | px  ax  bx |
 *                             \ py  ay  by /
 *
 * Also well-known: 2A = base * height
 *                     = perpendicular distance * line-length.
 *
 * Combining gives: distance = determinant / line-length(a,b)
 */
static double point_line_distance(long px, long py,
                                  long ax, long ay,
                                  long bx, long by)
{
    long det = ax*by - bx*ay + bx*py - px*by + px*ay - ax*py;
    double len;
    det = max(det, -det);
    len = sqrt(SQ(ax - bx) + SQ(ay - by));
    return det / len;
}

/* Determine nearest edge to where the user clicked.
 * (x, y) is the clicked location, converted to grid coordinates.
 * Returns the nearest edge, or NULL if no edge is reasonably
 * near the position.
 *
 * Just judging edges by perpendicular distance is not quite right -
 * the edge might be "off to one side". So we insist that the triangle
 * with (x,y) has acute angles at the edge's dots.
 *
 *     edge1
 *  *---------*------
 *            |
 *            |      *(x,y)
 *      edge2 |
 *            |   edge2 is OK, but edge1 is not, even though
 *            |   edge1 is perpendicularly closer to (x,y)
 *            *
 *
 */
grid_edge *grid_nearest_edge(grid *g, int x, int y)
{
    grid_edge *best_edge;
    double best_distance = 0;
    int i;

    best_edge = NULL;

    for (i = 0; i < g->num_edges; i++) {
        grid_edge *e = g->edges[i];
        long e2; /* squared length of edge */
        long a2, b2; /* squared lengths of other sides */
        double dist;

        /* See if edge e is eligible - the triangle must have acute angles
         * at the edge's dots.
         * Pythagoras formula h^2 = a^2 + b^2 detects right-angles,
         * so detect acute angles by testing for h^2 < a^2 + b^2 */
        e2 = SQ((long)e->dot1->x - (long)e->dot2->x) + SQ((long)e->dot1->y - (long)e->dot2->y);
        a2 = SQ((long)e->dot1->x - (long)x) + SQ((long)e->dot1->y - (long)y);
        b2 = SQ((long)e->dot2->x - (long)x) + SQ((long)e->dot2->y - (long)y);
        if (a2 >= e2 + b2) continue;
        if (b2 >= e2 + a2) continue;
         
        /* e is eligible so far.  Now check the edge is reasonably close
         * to where the user clicked.  Don't want to toggle an edge if the
         * click was way off the grid.
         * There is room for experimentation here.  We could check the
         * perpendicular distance is within a certain fraction of the length
         * of the edge.  That amounts to testing a rectangular region around
         * the edge.
         * Alternatively, we could check that the angle at the point is obtuse.
         * That would amount to testing a circular region with the edge as
         * diameter. */
        dist = point_line_distance((long)x, (long)y,
                                   (long)e->dot1->x, (long)e->dot1->y,
                                   (long)e->dot2->x, (long)e->dot2->y);
        /* Is dist more than half edge length ? */
        if (4 * SQ(dist) > e2)
            continue;

        if (best_edge == NULL || dist < best_distance) {
            best_edge = e;
            best_distance = dist;
        }
    }
    return best_edge;
}

/* ----------------------------------------------------------------------
 * Grid generation
 */

#ifdef SVG_GRID

#define SVG_DOTS  1
#define SVG_EDGES 2
#define SVG_FACES 4

#define FACE_COLOUR "red"
#define EDGE_COLOUR "blue"
#define DOT_COLOUR "black"

static void grid_output_svg(FILE *fp, grid *g, int which)
{
    int i, j;

    fprintf(fp,"\
<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n\
<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 20010904//EN\"\n\
\"http://www.w3.org/TR/2001/REC-SVG-20010904/DTD/svg10.dtd\">\n\
\n\
<svg xmlns=\"http://www.w3.org/2000/svg\"\n\
xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n\n");

    if (which & SVG_FACES) {
        fprintf(fp, "<g>\n");
        for (i = 0; i < g->num_faces; i++) {
            grid_face *f = g->faces[i];
            fprintf(fp, "<polygon points=\"");
            for (j = 0; j < f->order; j++) {
                grid_dot *d = f->dots[j];
                fprintf(fp, "%s%d,%d", (j == 0) ? "" : " ",
                        d->x, d->y);
            }
            fprintf(fp, "\" style=\"fill: %s; fill-opacity: 0.2; stroke: %s\" />\n",
                    FACE_COLOUR, FACE_COLOUR);
        }
        fprintf(fp, "</g>\n");
    }
    if (which & SVG_EDGES) {
        fprintf(fp, "<g>\n");
        for (i = 0; i < g->num_edges; i++) {
            grid_edge *e = g->edges[i];
            grid_dot *d1 = e->dot1, *d2 = e->dot2;

            fprintf(fp, "<line x1=\"%d\" y1=\"%d\" x2=\"%d\" y2=\"%d\" "
                        "style=\"stroke: %s\" />\n",
                        d1->x, d1->y, d2->x, d2->y, EDGE_COLOUR);
        }
        fprintf(fp, "</g>\n");
    }

    if (which & SVG_DOTS) {
        fprintf(fp, "<g>\n");
        for (i = 0; i < g->num_dots; i++) {
            grid_dot *d = g->dots[i];
            fprintf(fp, "<ellipse cx=\"%d\" cy=\"%d\" rx=\"%d\" ry=\"%d\" fill=\"%s\" />",
                    d->x, d->y, g->tilesize/20, g->tilesize/20, DOT_COLOUR);
        }
        fprintf(fp, "</g>\n");
    }

    fprintf(fp, "</svg>\n");
}
#endif

#ifdef SVG_GRID
#include <errno.h>

static void grid_try_svg(grid *g, int which)
{
    char *svg = getenv("PUZZLES_SVG_GRID");
    if (svg) {
        FILE *svgf = fopen(svg, "w");
        if (svgf) {
            grid_output_svg(svgf, g, which);
            fclose(svgf);
        } else {
            fprintf(stderr, "Unable to open file `%s': %s", svg, strerror(errno));
        }
    }
}
#endif

/* Show the basic grid information, before doing grid_make_consistent */
static void grid_debug_basic(grid *g)
{
    /* TODO: Maybe we should generate an SVG image of the dots and lines
     * of the grid here, before grid_make_consistent.
     * Would help with debugging grid generation. */
#ifdef DEBUG_GRID
    int i;
    printf("--- Basic Grid Data ---\n");
    for (i = 0; i < g->num_dots; i++) {
        grid_dot *d = g->dots[i];
        printf("Dot %d at (%d,%d)\n", i, d->x, d->y);
    }
    for (i = 0; i < g->num_faces; i++) {
        grid_face *f = g->faces[i];
        printf("Face %d: dots[", i);
        int j;
        for (j = 0; j < f->order; j++) {
            grid_dot *d = f->dots[j];
            printf("%s%d", j ? "," : "", (int)(d->index));
        }
        printf("]\n");
    }
#endif
#ifdef SVG_GRID
    grid_try_svg(g, SVG_FACES);
#endif
}

/* Show the derived grid information, computed by grid_make_consistent */
static void grid_debug_derived(grid *g)
{
#ifdef DEBUG_GRID
    /* edges */
    int i;
    printf("--- Derived Grid Data ---\n");
    for (i = 0; i < g->num_edges; i++) {
        grid_edge *e = g->edges[i];
        printf("Edge %d: dots[%d,%d] faces[%d,%d]\n",
            i, (int)(e->dot1->index), (int)(e->dot2->index),
            e->face1 ? (int)(e->face1->index) : -1,
            e->face2 ? (int)(e->face2->index) : -1);
    }
    /* faces */
    for (i = 0; i < g->num_faces; i++) {
        grid_face *f = g->faces[i];
        int j;
        printf("Face %d: faces[", i);
        for (j = 0; j < f->order; j++) {
            grid_edge *e = f->edges[j];
            grid_face *f2 = (e->face1 == f) ? e->face2 : e->face1;
            printf("%s%d", j ? "," : "", f2 ? f2->index : -1);
        }
        printf("]\n");
    }
    /* dots */
    for (i = 0; i < g->num_dots; i++) {
        grid_dot *d = g->dots[i];
        int j;
        printf("Dot %d: dots[", i);
        for (j = 0; j < d->order; j++) {
            grid_edge *e = d->edges[j];
            grid_dot *d2 = (e->dot1 == d) ? e->dot2 : e->dot1;
            printf("%s%d", j ? "," : "", d2->index);
        }
        printf("] faces[");
        for (j = 0; j < d->order; j++) {
            grid_face *f = d->faces[j];
            printf("%s%d", j ? "," : "", f ? f->index : -1);
        }
        printf("]\n");
    }
#endif
#ifdef SVG_GRID
    grid_try_svg(g, SVG_DOTS | SVG_EDGES | SVG_FACES);
#endif
}

/* Helper function for building incomplete-edges list in
 * grid_make_consistent() */
static int grid_edge_bydots_cmpfn(void *v1, void *v2)
{
    grid_edge *a = v1;
    grid_edge *b = v2;
    grid_dot *da, *db;

    /* Edges are not "normalised" - the 2 dots could be stored in any order,
     * so we need to take this into account when comparing edges. */

    /* Compare first dots */
    da = (a->dot1 < a->dot2) ? a->dot1 : a->dot2;
    db = (b->dot1 < b->dot2) ? b->dot1 : b->dot2;
    if (da->index < db->index)
        return -1;
    if (da->index > db->index)
        return +1;
    /* Compare last dots */
    da = (a->dot1 < a->dot2) ? a->dot2 : a->dot1;
    db = (b->dot1 < b->dot2) ? b->dot2 : b->dot1;
    if (da->index < db->index)
        return -1;
    if (da->index > db->index)
        return +1;

    return 0;
}

/*
 * 'Vigorously trim' a grid, by which I mean deleting any isolated or
 * uninteresting faces. By which, in turn, I mean: ensure that the
 * grid is composed solely of faces adjacent to at least one
 * 'landlocked' dot (i.e. one not in contact with the infinite
 * exterior face), and that all those dots are in a single connected
 * component.
 *
 * This function operates on, and returns, a grid satisfying the
 * preconditions to grid_make_consistent() rather than the
 * postconditions. (So call it first.)
 */
static void grid_trim_vigorously(grid *g)
{
    int *dotpairs, *faces, *dots;
    DSF *dsf;
    int i, j, k, size, newfaces, newdots;

    /*
     * First construct a matrix in which each ordered pair of dots is
     * mapped to the index of the face in which those dots occur in
     * that order.
     */
    dotpairs = snewn(g->num_dots * g->num_dots, int);
    for (i = 0; i < g->num_dots; i++)
        for (j = 0; j < g->num_dots; j++)
            dotpairs[i*g->num_dots+j] = -1;
    for (i = 0; i < g->num_faces; i++) {
        grid_face *f = g->faces[i];
        int dot0 = f->dots[f->order-1]->index;
        for (j = 0; j < f->order; j++) {
            int dot1 = f->dots[j]->index;
            dotpairs[dot0 * g->num_dots + dot1] = i;
            dot0 = dot1;
        }
    }

    /*
     * Now we can identify landlocked dots: they're the ones all of
     * whose edges have a mirror-image counterpart in this matrix.
     */
    dots = snewn(g->num_dots, int);
    for (i = 0; i < g->num_dots; i++) {
        dots[i] = 1;
        for (j = 0; j < g->num_dots; j++) {
            if ((dotpairs[i*g->num_dots+j] >= 0) ^
                (dotpairs[j*g->num_dots+i] >= 0))
                dots[i] = 0;    /* non-duplicated edge: coastal dot */
        }
    }

    /*
     * Now identify connected pairs of landlocked dots, and form a dsf
     * unifying them.
     */
    dsf = dsf_new(g->num_dots);
    for (i = 0; i < g->num_dots; i++)
        for (j = 0; j < i; j++)
            if (dots[i] && dots[j] &&
                dotpairs[i*g->num_dots+j] >= 0 &&
                dotpairs[j*g->num_dots+i] >= 0)
                dsf_merge(dsf, i, j);

    /*
     * Now look for the largest component.
     */
    size = 0;
    j = -1;
    for (i = 0; i < g->num_dots; i++) {
        int newsize;
        if (dots[i] && dsf_canonify(dsf, i) == i &&
            (newsize = dsf_size(dsf, i)) > size) {
            j = i;
            size = newsize;
        }
    }

    /*
     * Work out which faces we're going to keep (precisely those with
     * at least one dot in the same connected component as j) and
     * which dots (those required by any face we're keeping).
     *
     * At this point we reuse the 'dots' array to indicate the dots
     * we're keeping, rather than the ones that are landlocked.
     */
    faces = snewn(g->num_faces, int);
    for (i = 0; i < g->num_faces; i++)
        faces[i] = 0;
    for (i = 0; i < g->num_dots; i++)
        dots[i] = 0;
    for (i = 0; i < g->num_faces; i++) {
        grid_face *f = g->faces[i];
        bool keep = false;
        for (k = 0; k < f->order; k++)
            if (dsf_canonify(dsf, f->dots[k]->index) == j)
                keep = true;
        if (keep) {
            faces[i] = 1;
            for (k = 0; k < f->order; k++)
                dots[f->dots[k]->index] = 1;
        }
    }

    /*
     * Compact the faces array, rewriting the faces' indices and
     * freeing the unwanted ones.
     */
    for (i = newfaces = 0; i < g->num_faces; i++) {
        grid_face *f = g->faces[i];
        if (faces[i]) {
            f->index = newfaces++;
            g->faces[f->index] = f;
        } else {
            sfree(f->dots);
            sfree(f);
        }
    }
    g->num_faces = newfaces;

    /*
     * Compact the dots array, similarly.
     */
    for (i = newdots = 0; i < g->num_dots; i++) {
        grid_dot *d = g->dots[i];
        if (dots[i]) {
            d->index = newdots++;
            g->dots[d->index] = d;
        } else {
            sfree(d->edges);
            sfree(d->faces);
            sfree(d);
        }
    }
    g->num_dots = newdots;

    sfree(dotpairs);
    dsf_free(dsf);
    sfree(dots);
    sfree(faces);
}

/* Input: grid has its dots and faces initialised:
 * - dots have (optionally) x and y coordinates, but no edges or faces
 * (pointers are NULL).
 * - edges not initialised at all
 * - faces initialised and know which dots they have (but no edges yet).  The
 * dots around each face are assumed to be clockwise.
 *
 * Output: grid is complete and valid with all relationships defined.
 */
static void grid_make_consistent(grid *g)
{
    int i;
    tree234 *incomplete_edges;

    grid_debug_basic(g);

    /* ====== Stage 1 ======
     * Generate edges
     */

    /* Iterate over faces, and over each face's dots, generating edges as we
     * go.  As we find each new edge, we can immediately fill in the edge's
     * dots, but only one of the edge's faces.  Later on in the iteration, we
     * will find the same edge again (unless it's on the border), but we will
     * know the other face.
     * For efficiency, maintain a list of the incomplete edges, sorted by
     * their dots. */
    incomplete_edges = newtree234(grid_edge_bydots_cmpfn);
    for (i = 0; i < g->num_faces; i++) {
        grid_face *f = g->faces[i];
        int j;
        for (j = 0; j < f->order; j++) {
            grid_edge e; /* fake edge for searching */
            grid_edge *edge_found;
            int j2 = j + 1;
            if (j2 == f->order)
                j2 = 0;
            e.dot1 = f->dots[j];
            e.dot2 = f->dots[j2];
            /* Use del234 instead of find234, because we always want to
             * remove the edge if found */
            edge_found = del234(incomplete_edges, &e);
            if (edge_found) {
                /* This edge already added, so fill out missing face.
                 * Edge is already removed from incomplete_edges. */
                edge_found->face2 = f;
            } else {
                grid_edge *new_edge = snew(grid_edge);
                new_edge->dot1 = e.dot1;
                new_edge->dot2 = e.dot2;
                new_edge->face1 = f;
                new_edge->face2 = NULL; /* potentially infinite face */
                add234(incomplete_edges, new_edge);

                /* And add it to g->edges. */
                if (g->num_edges >= g->size_edges) {
                    int increment = g->num_edges / 4 + 128;
                    g->size_edges = (increment < INT_MAX - g->num_edges ?
                                     g->num_edges + increment : INT_MAX);
                    g->edges = sresize(g->edges, g->size_edges, grid_edge *);
                }
                assert(g->num_edges < INT_MAX);
                new_edge->index = g->num_edges++;
                g->edges[new_edge->index] = new_edge;
            }
        }
    }
    freetree234(incomplete_edges);

    /* ====== Stage 2 ======
     * For each face, build its edge list.
     */

    /* Allocate space for each edge list.  Can do this, because each face's
     * edge-list is the same size as its dot-list. */
    for (i = 0; i < g->num_faces; i++) {
        grid_face *f = g->faces[i];
        int j;
        f->edges = snewn(f->order, grid_edge*);
        /* Preload with NULLs, to help detect potential bugs. */
        for (j = 0; j < f->order; j++)
            f->edges[j] = NULL;
    }
    
    /* Iterate over each edge, and over both its faces.  Add this edge to
     * the face's edge-list, after finding where it should go in the
     * sequence. */
    for (i = 0; i < g->num_edges; i++) {
        grid_edge *e = g->edges[i];
        int j;
        for (j = 0; j < 2; j++) {
            grid_face *f = j ? e->face2 : e->face1;
            int k, k2;
            if (f == NULL) continue;
            /* Find one of the dots around the face */
            for (k = 0; k < f->order; k++) {
                if (f->dots[k] == e->dot1)
                    break; /* found dot1 */
            }
            assert(k != f->order); /* Must find the dot around this face */

            /* Labelling scheme: as we walk clockwise around the face,
             * starting at dot0 (f->dots[0]), we hit:
             * (dot0), edge0, dot1, edge1, dot2,...
             *
             *     0
             *  0-----1
             *        |
             *        |1
             *        |
             *  3-----2
             *     2
             *
             * Therefore, edgeK joins dotK and dot{K+1}
             */
            
            /* Around this face, either the next dot or the previous dot
             * must be e->dot2.  Otherwise the edge is wrong. */
            k2 = k + 1;
            if (k2 == f->order)
                k2 = 0;
            if (f->dots[k2] == e->dot2) {
                /* dot1(k) and dot2(k2) go clockwise around this face, so add
                 * this edge at position k (see diagram). */
                assert(f->edges[k] == NULL);
                f->edges[k] = e;
                continue;
            }
            /* Try previous dot */
            k2 = k - 1;
            if (k2 == -1)
                k2 = f->order - 1;
            if (f->dots[k2] == e->dot2) {
                /* dot1(k) and dot2(k2) go anticlockwise around this face. */
                assert(f->edges[k2] == NULL);
                f->edges[k2] = e;
                continue;
            }
            assert(!"Grid broken: bad edge-face relationship");
        }
    }

    /* ====== Stage 3 ======
     * For each dot, build its edge-list and face-list.
     */

    /* We don't know how many edges/faces go around each dot, so we can't
     * allocate the right space for these lists.  Pre-compute the sizes by
     * iterating over each edge and recording a tally against each dot. */
    for (i = 0; i < g->num_dots; i++) {
        g->dots[i]->order = 0;
    }
    for (i = 0; i < g->num_edges; i++) {
        grid_edge *e = g->edges[i];
        ++(e->dot1->order);
        ++(e->dot2->order);
    }
    /* Now we have the sizes, pre-allocate the edge and face lists. */
    for (i = 0; i < g->num_dots; i++) {
        grid_dot *d = g->dots[i];
        int j;
        assert(d->order >= 2); /* sanity check */
        d->edges = snewn(d->order, grid_edge*);
        d->faces = snewn(d->order, grid_face*);
        for (j = 0; j < d->order; j++) {
            d->edges[j] = NULL;
            d->faces[j] = NULL;
        }
    }
    /* For each dot, need to find a face that touches it, so we can seed
     * the edge-face-edge-face process around each dot. */
    for (i = 0; i < g->num_faces; i++) {
        grid_face *f = g->faces[i];
        int j;
        for (j = 0; j < f->order; j++) {
            grid_dot *d = f->dots[j];
            d->faces[0] = f;
        }
    }
    /* Each dot now has a face in its first slot.  Generate the remaining
     * faces and edges around the dot, by searching both clockwise and
     * anticlockwise from the first face.  Need to do both directions,
     * because of the possibility of hitting the infinite face, which
     * blocks progress.  But there's only one such face, so we will
     * succeed in finding every edge and face this way. */
    for (i = 0; i < g->num_dots; i++) {
        grid_dot *d = g->dots[i];
        int current_face1 = 0; /* ascends clockwise */
        int current_face2 = 0; /* descends anticlockwise */
        
        /* Labelling scheme: as we walk clockwise around the dot, starting
         * at face0 (d->faces[0]), we hit:
         * (face0), edge0, face1, edge1, face2,...
         *
         *       0
         *       |
         *    0  |  1
         *       |
         *  -----d-----1
         *       |
         *       |  2
         *       |
         *       2
         *
         * So, for example, face1 should be joined to edge0 and edge1,
         * and those edges should appear in an anticlockwise sense around
         * that face (see diagram). */
 
        /* clockwise search */
        while (true) {
            grid_face *f = d->faces[current_face1];
            grid_edge *e;
            int j;
            assert(f != NULL);
            /* find dot around this face */
            for (j = 0; j < f->order; j++) {
                if (f->dots[j] == d)
                    break;
            }
            assert(j != f->order); /* must find dot */
            
            /* Around f, required edge is anticlockwise from the dot.  See
             * the other labelling scheme higher up, for why we subtract 1
             * from j. */
            j--;
            if (j == -1)
                j = f->order - 1;
            e = f->edges[j];
            d->edges[current_face1] = e; /* set edge */
            current_face1++;
            if (current_face1 == d->order)
                break;
            else {
                /* set face */
                d->faces[current_face1] =
                    (e->face1 == f) ? e->face2 : e->face1;
                if (d->faces[current_face1] == NULL)
                    break; /* cannot progress beyond infinite face */
            }
        }
        /* If the clockwise search made it all the way round, don't need to
         * bother with the anticlockwise search. */
        if (current_face1 == d->order)
            continue; /* this dot is complete, move on to next dot */
        
        /* anticlockwise search */
        while (true) {
            grid_face *f = d->faces[current_face2];
            grid_edge *e;
            int j;
            assert(f != NULL);
            /* find dot around this face */
            for (j = 0; j < f->order; j++) {
                if (f->dots[j] == d)
                    break;
            }
            assert(j != f->order); /* must find dot */
            
            /* Around f, required edge is clockwise from the dot. */
            e = f->edges[j];
            
            current_face2--;
            if (current_face2 == -1)
                current_face2 = d->order - 1;
            d->edges[current_face2] = e; /* set edge */

            /* set face */
            if (current_face2 == current_face1)
                break;
            d->faces[current_face2] =
                    (e->face1 == f) ? e->face2 : e->face1;
            /* There's only 1 infinite face, so we must get all the way
             * to current_face1 before we hit it. */
            assert(d->faces[current_face2]);
        }
    }

    /* ====== Stage 4 ======
     * Compute other grid settings
     */

    /* Bounding rectangle */
    for (i = 0; i < g->num_dots; i++) {
        grid_dot *d = g->dots[i];
        if (i == 0) {
            g->lowest_x = g->highest_x = d->x;
            g->lowest_y = g->highest_y = d->y;
        } else {
            g->lowest_x = min(g->lowest_x, d->x);
            g->highest_x = max(g->highest_x, d->x);
            g->lowest_y = min(g->lowest_y, d->y);
            g->highest_y = max(g->highest_y, d->y);
        }
    }

    grid_debug_derived(g);
}

/* Helpers for making grid-generation easier.  These functions are only
 * intended for use during grid generation. */

/* Comparison function for the (tree234) sorted dot list */
static int grid_point_cmp_fn(void *v1, void *v2)
{
    grid_dot *p1 = v1;
    grid_dot *p2 = v2;
    if (p1->y != p2->y)
        return p2->y - p1->y;
    else
        return p2->x - p1->x;
}
/* Add a new face to the grid, with its dot list allocated. */
static void grid_face_add_new(grid *g, int face_size)
{
    int i;
    grid_face *new_face = snew(grid_face);
    assert(g->num_faces < INT_MAX);
    if (g->num_faces >= g->size_faces) {
        int increment = g->num_faces / 4 + 128;
        g->size_faces = (increment < INT_MAX - g->num_faces ?
                         g->num_faces + increment : INT_MAX);
        g->faces = sresize(g->faces, g->size_faces, grid_face *);
    }
    new_face->index = g->num_faces++;
    g->faces[new_face->index] = new_face;

    new_face->order = face_size;
    new_face->dots = snewn(face_size, grid_dot*);
    for (i = 0; i < face_size; i++)
        new_face->dots[i] = NULL;
    new_face->edges = NULL;
    new_face->has_incentre = false;
}
static grid_dot *grid_dot_add_new(grid *g, int x, int y)
{
    grid_dot *new_dot = snew(grid_dot);
    if (g->num_dots >= g->size_dots) {
        int increment = g->num_dots / 4 + 128;
        g->size_dots = (increment < INT_MAX - g->num_dots ?
                         g->num_dots + increment : INT_MAX);
        g->dots = sresize(g->dots, g->size_dots, grid_dot *);
    }
    assert(g->num_dots < INT_MAX);
    new_dot->index = g->num_dots++;
    g->dots[new_dot->index] = new_dot;

    new_dot->order = 0;
    new_dot->edges = NULL;
    new_dot->faces = NULL;
    new_dot->x = x;
    new_dot->y = y;

    return new_dot;
}
/* Retrieve a dot with these (x,y) coordinates.  Either return an existing dot
 * in the dot_list, or add a new dot to the grid (and the dot_list) and
 * return that. */
static grid_dot *grid_get_dot(grid *g, tree234 *dot_list, int x, int y)
{
    grid_dot test, *ret;

    test.order = 0;
    test.edges = NULL;
    test.faces = NULL;
    test.x = x;
    test.y = y;
    ret = find234(dot_list, &test, NULL);
    if (ret)
        return ret;

    ret = grid_dot_add_new(g, x, y);
    add234(dot_list, ret);
    return ret;
}

/* Sets the last face of the grid to include this dot, at this position
 * around the face. Assumes num_faces is at least 1 (a new face has
 * previously been added, with the required number of dots allocated) */
static void grid_face_set_dot(grid *g, grid_dot *d, int position)
{
    grid_face *last_face = g->faces[g->num_faces - 1];
    last_face->dots[position] = d;
}

/*
 * Helper routines for grid_find_incentre.
 */
static bool solve_2x2_matrix(double mx[4], double vin[2], double vout[2])
{
    double inv[4];
    double det;
    det = (mx[0]*mx[3] - mx[1]*mx[2]);
    if (det == 0)
        return false;

    inv[0] = mx[3] / det;
    inv[1] = -mx[1] / det;
    inv[2] = -mx[2] / det;
    inv[3] = mx[0] / det;

    vout[0] = inv[0]*vin[0] + inv[1]*vin[1];
    vout[1] = inv[2]*vin[0] + inv[3]*vin[1];

    return true;
}
static bool solve_3x3_matrix(double mx[9], double vin[3], double vout[3])
{
    double inv[9];
    double det;

    det = (mx[0]*mx[4]*mx[8] + mx[1]*mx[5]*mx[6] + mx[2]*mx[3]*mx[7] -
           mx[0]*mx[5]*mx[7] - mx[1]*mx[3]*mx[8] - mx[2]*mx[4]*mx[6]);
    if (det == 0)
        return false;

    inv[0] = (mx[4]*mx[8] - mx[5]*mx[7]) / det;
    inv[1] = (mx[2]*mx[7] - mx[1]*mx[8]) / det;
    inv[2] = (mx[1]*mx[5] - mx[2]*mx[4]) / det;
    inv[3] = (mx[5]*mx[6] - mx[3]*mx[8]) / det;
    inv[4] = (mx[0]*mx[8] - mx[2]*mx[6]) / det;
    inv[5] = (mx[2]*mx[3] - mx[0]*mx[5]) / det;
    inv[6] = (mx[3]*mx[7] - mx[4]*mx[6]) / det;
    inv[7] = (mx[1]*mx[6] - mx[0]*mx[7]) / det;
    inv[8] = (mx[0]*mx[4] - mx[1]*mx[3]) / det;

    vout[0] = inv[0]*vin[0] + inv[1]*vin[1] + inv[2]*vin[2];
    vout[1] = inv[3]*vin[0] + inv[4]*vin[1] + inv[5]*vin[2];
    vout[2] = inv[6]*vin[0] + inv[7]*vin[1] + inv[8]*vin[2];

    return true;
}

void grid_find_incentre(grid_face *f)
{
    double xbest, ybest, bestdist;
    int i, j, k, m;
    grid_dot *edgedot1[3], *edgedot2[3];
    grid_dot *dots[3];
    int nedges, ndots;

    if (f->has_incentre)
        return;

    /*
     * Find the point in the polygon with the maximum distance to any
     * edge or corner.
     *
     * Such a point must exist which is in contact with at least three
     * edges and/or vertices. (Proof: if it's only in contact with two
     * edges and/or vertices, it can't even be at a _local_ maximum -
     * any such circle can always be expanded in some direction.) So
     * we iterate through all 3-subsets of the combined set of edges
     * and vertices; for each subset we generate one or two candidate
     * points that might be the incentre, and then we vet each one to
     * see if it's inside the polygon and what its maximum radius is.
     *
     * (There's one case which this algorithm will get noticeably
     * wrong, and that's when a continuum of equally good answers
     * exists due to parallel edges. Consider a long thin rectangle,
     * for instance, or a parallelogram. This algorithm will pick a
     * point near one end, and choose the end arbitrarily; obviously a
     * nicer point to choose would be in the centre. To fix this I
     * would have to introduce a special-case system which detected
     * parallel edges in advance, set aside all candidate points
     * generated using both edges in a parallel pair, and generated
     * some additional candidate points half way between them. Also,
     * of course, I'd have to cope with rounding error making such a
     * point look worse than one of its endpoints. So I haven't done
     * this for the moment, and will cross it if necessary when I come
     * to it.)
     *
     * We don't actually iterate literally over _edges_, in the sense
     * of grid_edge structures. Instead, we fill in edgedot1[] and
     * edgedot2[] with a pair of dots adjacent in the face's list of
     * vertices. This ensures that we get the edges in consistent
     * orientation, which we could not do from the grid structure
     * alone. (A moment's consideration of an order-3 vertex should
     * make it clear that if a notional arrow was written on each
     * edge, _at least one_ of the three faces bordering that vertex
     * would have to have the two arrows tip-to-tip or tail-to-tail
     * rather than tip-to-tail.)
     */
    nedges = ndots = 0;
    bestdist = 0;
    xbest = ybest = 0;

    for (i = 0; i+2 < 2*f->order; i++) {
        if (i < f->order) {
            edgedot1[nedges] = f->dots[i];
            edgedot2[nedges++] = f->dots[(i+1)%f->order];
        } else
            dots[ndots++] = f->dots[i - f->order];

        for (j = i+1; j+1 < 2*f->order; j++) {
            if (j < f->order) {
                edgedot1[nedges] = f->dots[j];
                edgedot2[nedges++] = f->dots[(j+1)%f->order];
            } else
                dots[ndots++] = f->dots[j - f->order];

            for (k = j+1; k < 2*f->order; k++) {
                double cx[2], cy[2];   /* candidate positions */
                int cn = 0;            /* number of candidates */

                if (k < f->order) {
                    edgedot1[nedges] = f->dots[k];
                    edgedot2[nedges++] = f->dots[(k+1)%f->order];
                } else
                    dots[ndots++] = f->dots[k - f->order];

                /*
                 * Find a point, or pair of points, equidistant from
                 * all the specified edges and/or vertices.
                 */
                if (nedges == 3) {
                    /*
                     * Three edges. This is a linear matrix equation:
                     * each row of the matrix represents the fact that
                     * the point (x,y) we seek is at distance r from
                     * that edge, and we solve three of those
                     * simultaneously to obtain x,y,r. (We ignore r.)
                     */
                    double matrix[9], vector[3], vector2[3];
                    int m;

                    for (m = 0; m < 3; m++) {
                        int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x;
                        int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y;
                        int dx = x2-x1, dy = y2-y1;

                        /*
                         * ((x,y) - (x1,y1)) . (dy,-dx) = r |(dx,dy)|
                         *
                         * => x dy - y dx - r |(dx,dy)| = (x1 dy - y1 dx)
                         */
                        matrix[3*m+0] = dy;
                        matrix[3*m+1] = -dx;
                        matrix[3*m+2] = -sqrt((double)dx*dx+(double)dy*dy);
                        vector[m] = (double)x1*dy - (double)y1*dx;
                    }

                    if (solve_3x3_matrix(matrix, vector, vector2)) {
                        cx[cn] = vector2[0];
                        cy[cn] = vector2[1];
                        cn++;
                    }
                } else if (nedges == 2) {
                    /*
                     * Two edges and a dot. This will end up in a
                     * quadratic equation.
                     *
                     * First, look at the two edges. Having our point
                     * be some distance r from both of them gives rise
                     * to a pair of linear equations in x,y,r of the
                     * form
                     *
                     *   (x-x1) dy - (y-y1) dx = r sqrt(dx^2+dy^2)
                     *
                     * We eliminate r between those equations to give
                     * us a single linear equation in x,y describing
                     * the locus of points equidistant from both lines
                     * - i.e. the angle bisector. 
                     *
                     * We then choose one of x,y to be a parameter t,
                     * and derive linear formulae for x,y,r in terms
                     * of t. This enables us to write down the
                     * circular equation (x-xd)^2+(y-yd)^2=r^2 as a
                     * quadratic in t; solving that and substituting
                     * in for x,y gives us two candidate points.
                     */
                    double eqs[2][4];  /* a,b,c,d : ax+by+cr=d */
                    double eq[3];      /* a,b,c: ax+by=c */
                    double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */
                    double q[3];                /* a,b,c: at^2+bt+c=0 */
                    double disc;

                    /* Find equations of the two input lines. */
                    for (m = 0; m < 2; m++) {
                        int x1 = edgedot1[m]->x, x2 = edgedot2[m]->x;
                        int y1 = edgedot1[m]->y, y2 = edgedot2[m]->y;
                        int dx = x2-x1, dy = y2-y1;

                        eqs[m][0] = dy;
                        eqs[m][1] = -dx;
                        eqs[m][2] = -sqrt(dx*dx+dy*dy);
                        eqs[m][3] = x1*dy - y1*dx;
                    }

                    /* Derive the angle bisector by eliminating r. */
                    eq[0] = eqs[0][0]*eqs[1][2] - eqs[1][0]*eqs[0][2];
                    eq[1] = eqs[0][1]*eqs[1][2] - eqs[1][1]*eqs[0][2];
                    eq[2] = eqs[0][3]*eqs[1][2] - eqs[1][3]*eqs[0][2];

                    /* Parametrise x and y in terms of some t. */
                    if (fabs(eq[0]) < fabs(eq[1])) {
                        /* Parameter is x. */
                        xt[0] = 1; xt[1] = 0;
                        yt[0] = -eq[0]/eq[1]; yt[1] = eq[2]/eq[1];
                    } else {
                        /* Parameter is y. */
                        yt[0] = 1; yt[1] = 0;
                        xt[0] = -eq[1]/eq[0]; xt[1] = eq[2]/eq[0];
                    }

                    /* Find a linear representation of r using eqs[0]. */
                    rt[0] = -(eqs[0][0]*xt[0] + eqs[0][1]*yt[0])/eqs[0][2];
                    rt[1] = (eqs[0][3] - eqs[0][0]*xt[1] -
                             eqs[0][1]*yt[1])/eqs[0][2];

                    /* Construct the quadratic equation. */
                    q[0] = -rt[0]*rt[0];
                    q[1] = -2*rt[0]*rt[1];
                    q[2] = -rt[1]*rt[1];
                    q[0] += xt[0]*xt[0];
                    q[1] += 2*xt[0]*(xt[1]-dots[0]->x);
                    q[2] += (xt[1]-dots[0]->x)*(xt[1]-dots[0]->x);
                    q[0] += yt[0]*yt[0];
                    q[1] += 2*yt[0]*(yt[1]-dots[0]->y);
                    q[2] += (yt[1]-dots[0]->y)*(yt[1]-dots[0]->y);

                    /* And solve it. */
                    disc = q[1]*q[1] - 4*q[0]*q[2];
                    if (disc >= 0) {
                        double t;

                        disc = sqrt(disc);

                        t = (-q[1] + disc) / (2*q[0]);
                        cx[cn] = xt[0]*t + xt[1];
                        cy[cn] = yt[0]*t + yt[1];
                        cn++;

                        t = (-q[1] - disc) / (2*q[0]);
                        cx[cn] = xt[0]*t + xt[1];
                        cy[cn] = yt[0]*t + yt[1];
                        cn++;
                    }
                } else if (nedges == 1) {
                    /*
                     * Two dots and an edge. This one's another
                     * quadratic equation.
                     *
                     * The point we want must lie on the perpendicular
                     * bisector of the two dots; that much is obvious.
                     * So we can construct a parametrisation of that
                     * bisecting line, giving linear formulae for x,y
                     * in terms of t. We can also express the distance
                     * from the edge as such a linear formula.
                     *
                     * Then we set that equal to the radius of the
                     * circle passing through the two points, which is
                     * a Pythagoras exercise; that gives rise to a
                     * quadratic in t, which we solve.
                     */
                    double xt[2], yt[2], rt[2]; /* a,b: {x,y,r}=at+b */
                    double q[3];                /* a,b,c: at^2+bt+c=0 */
                    double disc;
                    double halfsep;

                    /* Find parametric formulae for x,y. */
                    {
                        int x1 = dots[0]->x, x2 = dots[1]->x;
                        int y1 = dots[0]->y, y2 = dots[1]->y;
                        int dx = x2-x1, dy = y2-y1;
                        double d = sqrt((double)dx*dx + (double)dy*dy);

                        xt[1] = (x1+x2)/2.0;
                        yt[1] = (y1+y2)/2.0;
                        /* It's convenient if we have t at standard scale. */
                        xt[0] = -dy/d;
                        yt[0] = dx/d;

                        /* Also note down half the separation between
                         * the dots, for use in computing the circle radius. */
                        halfsep = 0.5*d;
                    }

                    /* Find a parametric formula for r. */
                    {
                        int x1 = edgedot1[0]->x, x2 = edgedot2[0]->x;
                        int y1 = edgedot1[0]->y, y2 = edgedot2[0]->y;
                        int dx = x2-x1, dy = y2-y1;
                        double d = sqrt((double)dx*dx + (double)dy*dy);
                        rt[0] = (xt[0]*dy - yt[0]*dx) / d;
                        rt[1] = ((xt[1]-x1)*dy - (yt[1]-y1)*dx) / d;
                    }

                    /* Construct the quadratic equation. */
                    q[0] = rt[0]*rt[0];
                    q[1] = 2*rt[0]*rt[1];
                    q[2] = rt[1]*rt[1];
                    q[0] -= 1;
                    q[2] -= halfsep*halfsep;

                    /* And solve it. */
                    disc = q[1]*q[1] - 4*q[0]*q[2];
                    if (disc >= 0) {
                        double t;

                        disc = sqrt(disc);

                        t = (-q[1] + disc) / (2*q[0]);
                        cx[cn] = xt[0]*t + xt[1];
                        cy[cn] = yt[0]*t + yt[1];
                        cn++;

                        t = (-q[1] - disc) / (2*q[0]);
                        cx[cn] = xt[0]*t + xt[1];
                        cy[cn] = yt[0]*t + yt[1];
                        cn++;
                    }
                } else if (nedges == 0) {
                    /*
                     * Three dots. This is another linear matrix
                     * equation, this time with each row of the matrix
                     * representing the perpendicular bisector between
                     * two of the points. Of course we only need two
                     * such lines to find their intersection, so we
                     * need only solve a 2x2 matrix equation.
                     */

                    double matrix[4], vector[2], vector2[2];
                    int m;

                    for (m = 0; m < 2; m++) {
                        int x1 = dots[m]->x, x2 = dots[m+1]->x;
                        int y1 = dots[m]->y, y2 = dots[m+1]->y;
                        int dx = x2-x1, dy = y2-y1;

                        /*
                         * ((x,y) - (x1,y1)) . (dx,dy) = 1/2 |(dx,dy)|^2
                         *
                         * => 2x dx + 2y dy = dx^2+dy^2 + (2 x1 dx + 2 y1 dy)
                         */
                        matrix[2*m+0] = 2*dx;
                        matrix[2*m+1] = 2*dy;
                        vector[m] = ((double)dx*dx + (double)dy*dy +
                                     2.0*x1*dx + 2.0*y1*dy);
                    }

                    if (solve_2x2_matrix(matrix, vector, vector2)) {
                        cx[cn] = vector2[0];
                        cy[cn] = vector2[1];
                        cn++;
                    }
                }

                /*
                 * Now go through our candidate points and see if any
                 * of them are better than what we've got so far.
                 */
                for (m = 0; m < cn; m++) {
                    double x = cx[m], y = cy[m];

                    /*
                     * First, disqualify the point if it's not inside
                     * the polygon, which we work out by counting the
                     * edges to the right of the point. (For
                     * tiebreaking purposes when edges start or end on
                     * our y-coordinate or go right through it, we
                     * consider our point to be offset by a small
                     * _positive_ epsilon in both the x- and
                     * y-direction.)
                     */
                    int e;
                    bool in = false;
                    for (e = 0; e < f->order; e++) {
                        int xs = f->edges[e]->dot1->x;
                        int xe = f->edges[e]->dot2->x;
                        int ys = f->edges[e]->dot1->y;
                        int ye = f->edges[e]->dot2->y;
                        if ((y >= ys && y < ye) || (y >= ye && y < ys)) {
                            /*
                             * The line goes past our y-position. Now we need
                             * to know if its x-coordinate when it does so is
                             * to our right.
                             *
                             * The x-coordinate in question is mathematically
                             * (y - ys) * (xe - xs) / (ye - ys), and we want
                             * to know whether (x - xs) >= that. Of course we
                             * avoid the division, so we can work in integers;
                             * to do this we must multiply both sides of the
                             * inequality by ye - ys, which means we must
                             * first check that's not negative.
                             */
                            int num = xe - xs, denom = ye - ys;
                            if (denom < 0) {
                                num = -num;
                                denom = -denom;
                            }
                            if ((x - xs) * denom >= (y - ys) * num)
                                in = !in;
                        }
                    }

                    if (in) {
#ifdef HUGE_VAL
                        double mindist = HUGE_VAL;
#else
#ifdef DBL_MAX
                        double mindist = DBL_MAX;
#else
#error No way to get maximum floating-point number.
#endif
#endif
                        int e, d;

                        /*
                         * This point is inside the polygon, so now we check
                         * its minimum distance to every edge and corner.
                         * First the corners ...
                         */
                        for (d = 0; d < f->order; d++) {
                            int xp = f->dots[d]->x;
                            int yp = f->dots[d]->y;
                            double dx = x - xp, dy = y - yp;
                            double dist = dx*dx + dy*dy;
                            if (mindist > dist)
                                mindist = dist;
                        }

                        /*
                         * ... and now also check the perpendicular distance
                         * to every edge, if the perpendicular lies between
                         * the edge's endpoints.
                         */
                        for (e = 0; e < f->order; e++) {
                            int xs = f->edges[e]->dot1->x;
                            int xe = f->edges[e]->dot2->x;
                            int ys = f->edges[e]->dot1->y;
                            int ye = f->edges[e]->dot2->y;

                            /*
                             * If s and e are our endpoints, and p our
                             * candidate circle centre, the foot of a
                             * perpendicular from p to the line se lies
                             * between s and e if and only if (p-s).(e-s) lies
                             * strictly between 0 and (e-s).(e-s).
                             */
                            int edx = xe - xs, edy = ye - ys;
                            double pdx = x - xs, pdy = y - ys;
                            double pde = pdx * edx + pdy * edy;
                            long ede = (long)edx * edx + (long)edy * edy;
                            if (0 < pde && pde < ede) {
                                /*
                                 * Yes, the nearest point on this edge is
                                 * closer than either endpoint, so we must
                                 * take it into account by measuring the
                                 * perpendicular distance to the edge and
                                 * checking its square against mindist.
                                 */

                                double pdre = pdx * edy - pdy * edx;
                                double sqlen = pdre * pdre / ede;

                                if (mindist > sqlen)
                                    mindist = sqlen;
                            }
                        }

                        /*
                         * Right. Now we know the biggest circle around this
                         * point, so we can check it against bestdist.
                         */
                        if (bestdist < mindist) {
                            bestdist = mindist;
                            xbest = x;
                            ybest = y;
                        }
                    }
                }

                if (k < f->order)
                    nedges--;
                else
                    ndots--;
            }
            if (j < f->order)
                nedges--;
            else
                ndots--;
        }
        if (i < f->order)
            nedges--;
        else
            ndots--;
    }

    assert(bestdist > 0);

    f->has_incentre = true;
    f->ix = xbest + 0.5;               /* round to nearest */
    f->iy = ybest + 0.5;
}

/* ------ Generate various types of grid ------ */

/* General method is to generate faces, by calculating their dot coordinates.
 * As new faces are added, we keep track of all the dots so we can tell when
 * a new face reuses an existing dot.  For example, two squares touching at an
 * edge would generate six unique dots: four dots from the first face, then
 * two additional dots for the second face, because we detect the other two
 * dots have already been taken up.  This list is stored in a tree234
 * called "points".  No extra memory-allocation needed here - we store the
 * actual grid_dot* pointers, which all point into the g->dots list.
 * For this reason, we have to calculate coordinates in such a way as to
 * eliminate any rounding errors, so we can detect when a dot on one
 * face precisely lands on a dot of a different face.  No floating-point
 * arithmetic here!
 */

#define SQUARE_TILESIZE 20

static const char *grid_validate_params_square(int width, int height)
{
    if (width > INT_MAX / SQUARE_TILESIZE ||  /* xextent */
        height > INT_MAX / SQUARE_TILESIZE || /* yextent */
        width + 1 > INT_MAX / (height + 1))   /* max_dots */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_square(int width, int height,
                      int *tilesize, int *xextent, int *yextent)
{
    int a = SQUARE_TILESIZE;

    *tilesize = a;
    *xextent = width * a;
    *yextent = height * a;
}

static grid *grid_new_square(int width, int height, const char *desc)
{
    int x, y;
    /* Side length */
    int a = SQUARE_TILESIZE;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = a;

    points = newtree234(grid_point_cmp_fn);

    /* generate square faces */
    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* face position */
            int px = a * x;
            int py = a * y;

            grid_face_add_new(g, 4);
            d = grid_get_dot(g, points, px, py);
            grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px + a, py);
            grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px + a, py + a);
            grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px, py + a);
            grid_face_set_dot(g, d, 3);
        }
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

#define HONEY_TILESIZE 45
/* Vector for side of hexagon - ratio is close to sqrt(3) */
#define HONEY_A 15
#define HONEY_B 26

static const char *grid_validate_params_honeycomb(int width, int height)
{
    int a = HONEY_A;
    int b = HONEY_B;

    if (width - 1 > (INT_MAX - 4*a) / (3 * a) ||  /* xextent */
        height - 1 > (INT_MAX - 3*b) / (2 * b) || /* yextent */
        width + 1 > INT_MAX / 2 / (height + 1))   /* max_dots */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_honeycomb(int width, int height,
                         int *tilesize, int *xextent, int *yextent)
{
    int a = HONEY_A;
    int b = HONEY_B;

    *tilesize = HONEY_TILESIZE;
    *xextent = (3 * a * (width-1)) + 4*a;
    *yextent = (2 * b * (height-1)) + 3*b;
}

static grid *grid_new_honeycomb(int width, int height, const char *desc)
{
    int x, y;
    int a = HONEY_A;
    int b = HONEY_B;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = HONEY_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    /* generate hexagonal faces */
    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* face centre */
            int cx = 3 * a * x;
            int cy = 2 * b * y;
            if (x % 2)
                cy += b;
            grid_face_add_new(g, 6);

            d = grid_get_dot(g, points, cx - a, cy - b);
            grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, cx + a, cy - b);
            grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, cx + 2*a, cy);
            grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, cx + a, cy + b);
            grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, cx - a, cy + b);
            grid_face_set_dot(g, d, 4);
            d = grid_get_dot(g, points, cx - 2*a, cy);
            grid_face_set_dot(g, d, 5);
        }
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

#define TRIANGLE_TILESIZE 18
/* Vector for side of triangle - ratio is close to sqrt(3) */
#define TRIANGLE_VEC_X 15
#define TRIANGLE_VEC_Y 26

static const char *grid_validate_params_triangular(int width, int height)
{
    int vec_x = TRIANGLE_VEC_X;
    int vec_y = TRIANGLE_VEC_Y;

    if (width > INT_MAX / (2 * vec_x) - 1 ||    /* xextent */
        height > INT_MAX / vec_y ||             /* yextent */
        width + 1 > INT_MAX / 4 / (height + 1)) /* max_dots */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_triangular(int width, int height,
                          int *tilesize, int *xextent, int *yextent)
{
    int vec_x = TRIANGLE_VEC_X;
    int vec_y = TRIANGLE_VEC_Y;

    *tilesize = TRIANGLE_TILESIZE;
    *xextent = (width+1) * 2 * vec_x;
    *yextent = height * vec_y;
}

static const char *grid_validate_desc_triangular(grid_type type, int width,
                                                 int height, const char *desc)
{
    /*
     * Triangular grids: an absent description is valid (indicating
     * the old-style approach which had 'ears', i.e. triangles
     * connected to only one other face, at some grid corners), and so
     * is a description reading just "0" (indicating the new-style
     * approach in which those ears are trimmed off). Anything else is
     * illegal.
     */

    if (!desc || !strcmp(desc, "0"))
        return NULL;

    return "Unrecognised grid description.";
}

/* Doesn't use the previous method of generation, it pre-dates it!
 * A triangular grid is just about simple enough to do by "brute force" */
static grid *grid_new_triangular(int width, int height, const char *desc)
{
    int x,y;
    int version = (desc == NULL ? -1 : atoi(desc));
    
    /* Vector for side of triangle - ratio is close to sqrt(3) */
    int vec_x = TRIANGLE_VEC_X;
    int vec_y = TRIANGLE_VEC_Y;
    
    int index;

    /* convenient alias */
    int w = width + 1;

    grid *g = grid_empty();
    g->tilesize = TRIANGLE_TILESIZE;

    if (version == -1) {
        /*
         * Old-style triangular grid generation, preserved as-is for
         * backwards compatibility with old game ids, in which it's
         * just a little asymmetric and there are 'ears' (faces linked
         * to only one other face) at two grid corners.
         *
         * Example old-style game ids, which should still work, and in
         * which you should see the ears in the TL/BR corners on the
         * first one and in the TL/BL corners on the second:
         *
         *   5x5t1:2c2a1a2a201a1a1a1112a1a2b1211f0b21a2a2a0a
         *   5x6t1:a022a212h1a1d1a12c2b11a012b1a20d1a0a12e
         */

        g->num_faces = g->size_faces = width * height * 2;
        g->num_dots = g->size_dots = (width + 1) * (height + 1);
        g->faces = snewn(g->size_faces, grid_face *);
        g->dots = snewn(g->size_dots, grid_dot *);

        /* generate dots */
        index = 0;
        for (y = 0; y <= height; y++) {
            for (x = 0; x <= width; x++) {
                grid_dot *d = snew(grid_dot);
                d->index = index;
                g->dots[d->index] = d;
                /* odd rows are offset to the right */
                d->order = 0;
                d->edges = NULL;
                d->faces = NULL;
                d->x = x * 2 * vec_x + ((y % 2) ? vec_x : 0);
                d->y = y * vec_y;
                index++;
            }
        }
    
        /* generate faces */
        index = 0;
        for (y = 0; y < height; y++) {
            for (x = 0; x < width; x++) {
                /* initialise two faces for this (x,y) */
                grid_face *f1 = snew(grid_face), *f2 = snew(grid_face);
                f1->index = index;
                f2->index = index + 1;
                g->faces[f1->index] = f1;
                g->faces[f2->index] = f2;
                f1->edges = NULL;
                f1->order = 3;
                f1->dots = snewn(f1->order, grid_dot*);
                f1->has_incentre = false;
                f2->edges = NULL;
                f2->order = 3;
                f2->dots = snewn(f2->order, grid_dot*);
                f2->has_incentre = false;

                /* face descriptions depend on whether the row-number is
                 * odd or even */
                if (y % 2) {
                    f1->dots[0] = g->dots[y       * w + x];
                    f1->dots[1] = g->dots[(y + 1) * w + x + 1];
                    f1->dots[2] = g->dots[(y + 1) * w + x];
                    f2->dots[0] = g->dots[y       * w + x];
                    f2->dots[1] = g->dots[y       * w + x + 1];
                    f2->dots[2] = g->dots[(y + 1) * w + x + 1];
                } else {
                    f1->dots[0] = g->dots[y       * w + x];
                    f1->dots[1] = g->dots[y       * w + x + 1];
                    f1->dots[2] = g->dots[(y + 1) * w + x];
                    f2->dots[0] = g->dots[y       * w + x + 1];
                    f2->dots[1] = g->dots[(y + 1) * w + x + 1];
                    f2->dots[2] = g->dots[(y + 1) * w + x];
                }
                index += 2;
            }
        }
    } else {
        /*
         * New-style approach, in which there are never any 'ears',
         * and if height is even then the grid is nicely 4-way
         * symmetric.
         *
         * Example new-style grids:
         *
         *   5x5t1:0_21120b11a1a01a1a00c1a0b211021c1h1a2a1a0a
         *   5x6t1:0_a1212c22c2a02a2f22a0c12a110d0e1c0c0a101121a1
         */
        tree234 *points = newtree234(grid_point_cmp_fn);

        for (y = 0; y < height; y++) {
            /*
             * Each row contains (width+1) triangles one way up, and
             * (width) triangles the other way up. Which way up is
             * which varies with parity of y. Also, the dots around
             * each face will flip direction with parity of y, so we
             * set up n1 and n2 to cope with that easily.
             */
            int y0, y1, n1, n2;
            y0 = y1 = y * vec_y;
            if (y % 2) {
                y1 += vec_y;
                n1 = 2; n2 = 1;
            } else {
                y0 += vec_y;
                n1 = 1; n2 = 2;
            }

            for (x = 0; x <= width; x++) {
                int x0 = 2*x * vec_x, x1 = x0 + vec_x, x2 = x1 + vec_x;

                /*
                 * If the grid has odd height, then we skip the first
                 * and last triangles on this row, otherwise they'll
                 * end up as ears.
                 */
                if (height % 2 == 1 && y == height-1 && (x == 0 || x == width))
                    continue;

                grid_face_add_new(g, 3);
                grid_face_set_dot(g, grid_get_dot(g, points, x0, y0), 0);
                grid_face_set_dot(g, grid_get_dot(g, points, x1, y1), n1);
                grid_face_set_dot(g, grid_get_dot(g, points, x2, y0), n2);
            }

            for (x = 0; x < width; x++) {
                int x0 = (2*x+1) * vec_x, x1 = x0 + vec_x, x2 = x1 + vec_x;

                grid_face_add_new(g, 3);
                grid_face_set_dot(g, grid_get_dot(g, points, x0, y1), 0);
                grid_face_set_dot(g, grid_get_dot(g, points, x1, y0), n2);
                grid_face_set_dot(g, grid_get_dot(g, points, x2, y1), n1);
            }
        }

        freetree234(points);
    }

    grid_make_consistent(g);
    return g;
}

#define SNUBSQUARE_TILESIZE 18
/* Vector for side of triangle - ratio is close to sqrt(3) */
#define SNUBSQUARE_A 15
#define SNUBSQUARE_B 26

static const char *grid_validate_params_snubsquare(int width, int height)
{
    int a = SNUBSQUARE_A;
    int b = SNUBSQUARE_B;

    if (width-1 > (INT_MAX - (a + b)) / (a+b) || /* xextent */
        height > (INT_MAX - (a + b)) / (a+b) ||  /* yextent */
        width > INT_MAX / 3 / height ||          /* max_faces */
        width + 1 > INT_MAX / 2 / (height + 1))  /* max_dots */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_snubsquare(int width, int height,
                          int *tilesize, int *xextent, int *yextent)
{
    int a = SNUBSQUARE_A;
    int b = SNUBSQUARE_B;

    *tilesize = SNUBSQUARE_TILESIZE;
    *xextent = (a+b) * (width-1) + a + b;
    *yextent = (a+b) * (height-1) + a + b;
}

static grid *grid_new_snubsquare(int width, int height, const char *desc)
{
    int x, y;
    int a = SNUBSQUARE_A;
    int b = SNUBSQUARE_B;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = SNUBSQUARE_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* face position */
            int px = (a + b) * x;
            int py = (a + b) * y;

            /* generate square faces */
            grid_face_add_new(g, 4);
            if ((x + y) % 2) {
                d = grid_get_dot(g, points, px + a, py);
                grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + a + b, py + a);
                grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + b, py + a + b);
                grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px, py + b);
                grid_face_set_dot(g, d, 3);
            } else {
                d = grid_get_dot(g, points, px + b, py);
                grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + a + b, py + b);
                grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + a, py + a + b);
                grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px, py + a);
                grid_face_set_dot(g, d, 3);
            }

            /* generate up/down triangles */
            if (x > 0) {
                grid_face_add_new(g, 3);
                if ((x + y) % 2) {
                    d = grid_get_dot(g, points, px + a, py);
                    grid_face_set_dot(g, d, 0);
                    d = grid_get_dot(g, points, px, py + b);
                    grid_face_set_dot(g, d, 1);
                    d = grid_get_dot(g, points, px - a, py);
                    grid_face_set_dot(g, d, 2);
                } else {
                    d = grid_get_dot(g, points, px, py + a);
                    grid_face_set_dot(g, d, 0);
                    d = grid_get_dot(g, points, px + a, py + a + b);
                    grid_face_set_dot(g, d, 1);
                    d = grid_get_dot(g, points, px - a, py + a + b);
                    grid_face_set_dot(g, d, 2);
                }
            }

            /* generate left/right triangles */
            if (y > 0) {
                grid_face_add_new(g, 3);
                if ((x + y) % 2) {
                    d = grid_get_dot(g, points, px + a, py);
                    grid_face_set_dot(g, d, 0);
                    d = grid_get_dot(g, points, px + a + b, py - a);
                    grid_face_set_dot(g, d, 1);
                    d = grid_get_dot(g, points, px + a + b, py + a);
                    grid_face_set_dot(g, d, 2);
                } else {
                    d = grid_get_dot(g, points, px, py - a);
                    grid_face_set_dot(g, d, 0);
                    d = grid_get_dot(g, points, px + b, py);
                    grid_face_set_dot(g, d, 1);
                    d = grid_get_dot(g, points, px, py + a);
                    grid_face_set_dot(g, d, 2);
                }
            }
        }
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

#define CAIRO_TILESIZE 40
/* Vector for side of pentagon - ratio is close to (4+sqrt(7))/3 */
#define CAIRO_A 14
#define CAIRO_B 31

static const char *grid_validate_params_cairo(int width, int height)
{
    int b = CAIRO_B; /* a unused in determining grid size. */

    if (width - 1 > (INT_MAX - 2*b) / (2*b) ||  /* xextent */
        height - 1 > (INT_MAX - 2*b) / (2*b) || /* yextent */
        width > INT_MAX / 2 / height ||         /* max_faces */
        width + 1 > INT_MAX / 3 / (height + 1)) /* max_dots */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_cairo(int width, int height,
                          int *tilesize, int *xextent, int *yextent)
{
    int b = CAIRO_B; /* a unused in determining grid size. */

    *tilesize = CAIRO_TILESIZE;
    *xextent = 2*b*(width-1) + 2*b;
    *yextent = 2*b*(height-1) + 2*b;
}

static grid *grid_new_cairo(int width, int height, const char *desc)
{
    int x, y;
    int a = CAIRO_A;
    int b = CAIRO_B;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = CAIRO_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* cell position */
            int px = 2 * b * x;
            int py = 2 * b * y;

            /* horizontal pentagons */
            if (y > 0) {
                grid_face_add_new(g, 5);
                if ((x + y) % 2) {
                    d = grid_get_dot(g, points, px + a, py - b);
                    grid_face_set_dot(g, d, 0);
                    d = grid_get_dot(g, points, px + 2*b - a, py - b);
                    grid_face_set_dot(g, d, 1);
                    d = grid_get_dot(g, points, px + 2*b, py);
                    grid_face_set_dot(g, d, 2);
                    d = grid_get_dot(g, points, px + b, py + a);
                    grid_face_set_dot(g, d, 3);
                    d = grid_get_dot(g, points, px, py);
                    grid_face_set_dot(g, d, 4);
                } else {
                    d = grid_get_dot(g, points, px, py);
                    grid_face_set_dot(g, d, 0);
                    d = grid_get_dot(g, points, px + b, py - a);
                    grid_face_set_dot(g, d, 1);
                    d = grid_get_dot(g, points, px + 2*b, py);
                    grid_face_set_dot(g, d, 2);
                    d = grid_get_dot(g, points, px + 2*b - a, py + b);
                    grid_face_set_dot(g, d, 3);
                    d = grid_get_dot(g, points, px + a, py + b);
                    grid_face_set_dot(g, d, 4);
                }
            }
            /* vertical pentagons */
            if (x > 0) {
                grid_face_add_new(g, 5);
                if ((x + y) % 2) {
                    d = grid_get_dot(g, points, px, py);
                    grid_face_set_dot(g, d, 0);
                    d = grid_get_dot(g, points, px + b, py + a);
                    grid_face_set_dot(g, d, 1);
                    d = grid_get_dot(g, points, px + b, py + 2*b - a);
                    grid_face_set_dot(g, d, 2);
                    d = grid_get_dot(g, points, px, py + 2*b);
                    grid_face_set_dot(g, d, 3);
                    d = grid_get_dot(g, points, px - a, py + b);
                    grid_face_set_dot(g, d, 4);
                } else {
                    d = grid_get_dot(g, points, px, py);
                    grid_face_set_dot(g, d, 0);
                    d = grid_get_dot(g, points, px + a, py + b);
                    grid_face_set_dot(g, d, 1);
                    d = grid_get_dot(g, points, px, py + 2*b);
                    grid_face_set_dot(g, d, 2);
                    d = grid_get_dot(g, points, px - b, py + 2*b - a);
                    grid_face_set_dot(g, d, 3);
                    d = grid_get_dot(g, points, px - b, py + a);
                    grid_face_set_dot(g, d, 4);
                }
            }
        }
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

#define GREATHEX_TILESIZE 18
/* Vector for side of triangle - ratio is close to sqrt(3) */
#define GREATHEX_A 15
#define GREATHEX_B 26

static const char *grid_validate_params_greathexagonal(int width, int height)
{
    int a = GREATHEX_A;
    int b = GREATHEX_B;

    if (width-1 > (INT_MAX - 4*a) / (3*a + b) ||          /* xextent */
        height-1 > (INT_MAX - (3*b + a)) / (2*a + 2*b) || /* yextent */
        width + 1 > INT_MAX / 6 / (height + 1))           /* max_faces */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_greathexagonal(int width, int height,
                          int *tilesize, int *xextent, int *yextent)
{
    int a = GREATHEX_A;
    int b = GREATHEX_B;

    *tilesize = GREATHEX_TILESIZE;
    *xextent = (3*a + b) * (width-1) + 4*a;
    *yextent = (2*a + 2*b) * (height-1) + 3*b + a;
}

static grid *grid_new_greathexagonal(int width, int height, const char *desc)
{
    int x, y;
    int a = GREATHEX_A;
    int b = GREATHEX_B;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = GREATHEX_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* centre of hexagon */
            int px = (3*a + b) * x;
            int py = (2*a + 2*b) * y;
            if (x % 2)
                py += a + b;

            /* hexagon */
            grid_face_add_new(g, 6);
            d = grid_get_dot(g, points, px - a, py - b);
            grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px + a, py - b);
            grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px + 2*a, py);
            grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px + a, py + b);
            grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, px - a, py + b);
            grid_face_set_dot(g, d, 4);
            d = grid_get_dot(g, points, px - 2*a, py);
            grid_face_set_dot(g, d, 5);

            /* square below hexagon */
            if (y < height - 1) {
                grid_face_add_new(g, 4);
                d = grid_get_dot(g, points, px - a, py + b);
                grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + a, py + b);
                grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + a, py + 2*a + b);
                grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px - a, py + 2*a + b);
                grid_face_set_dot(g, d, 3);
            }

            /* square below right */
            if ((x < width - 1) && (((x % 2) == 0) || (y < height - 1))) {
                grid_face_add_new(g, 4);
                d = grid_get_dot(g, points, px + 2*a, py);
                grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + 2*a + b, py + a);
                grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + a + b, py + a + b);
                grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px + a, py + b);
                grid_face_set_dot(g, d, 3);
            }

            /* square below left */
            if ((x > 0) && (((x % 2) == 0) || (y < height - 1))) {
                grid_face_add_new(g, 4);
                d = grid_get_dot(g, points, px - 2*a, py);
                grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px - a, py + b);
                grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px - a - b, py + a + b);
                grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px - 2*a - b, py + a);
                grid_face_set_dot(g, d, 3);
            }
           
            /* Triangle below right */
            if ((x < width - 1) && (y < height - 1)) {
                grid_face_add_new(g, 3);
                d = grid_get_dot(g, points, px + a, py + b);
                grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + a + b, py + a + b);
                grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + a, py + 2*a + b);
                grid_face_set_dot(g, d, 2);
            }

            /* Triangle below left */
            if ((x > 0) && (y < height - 1)) {
                grid_face_add_new(g, 3);
                d = grid_get_dot(g, points, px - a, py + b);
                grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px - a, py + 2*a + b);
                grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px - a - b, py + a + b);
                grid_face_set_dot(g, d, 2);
            }
        }
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

#define KAGOME_TILESIZE 18
/* Vector for side of triangle - ratio is close to sqrt(3) */
#define KAGOME_A 15
#define KAGOME_B 26

static const char *grid_validate_params_kagome(int width, int height)
{
    int a = KAGOME_A;
    int b = KAGOME_B;

    if (width-1 > (INT_MAX - 6*a) / (4*a) ||    /* xextent */
        height-1 > (INT_MAX - 2*b) / (2*b) ||   /* yextent */
        width + 1 > INT_MAX / 6 / (height + 1)) /* max_faces */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_kagome(int width, int height,
                             int *tilesize, int *xextent, int *yextent)
{
    int a = KAGOME_A;
    int b = KAGOME_B;

    *tilesize = KAGOME_TILESIZE;
    *xextent = (4*a) * (width-1) + 6*a;
    *yextent = (2*b) * (height-1) + 2*b;
}

static grid *grid_new_kagome(int width, int height, const char *desc)
{
    int x, y;
    int a = KAGOME_A;
    int b = KAGOME_B;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = KAGOME_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* centre of hexagon */
            int px = (4*a) * x;
            int py = (2*b) * y;
            if (y % 2)
                px += 2*a;

            /* hexagon */
            grid_face_add_new(g, 6);
            d = grid_get_dot(g, points, px +   a, py -   b); grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px + 2*a, py      ); grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px +   a, py +   b); grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px -   a, py +   b); grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, px - 2*a, py      ); grid_face_set_dot(g, d, 4);
            d = grid_get_dot(g, points, px -   a, py -   b); grid_face_set_dot(g, d, 5);

            /* Triangle above right */
            if ((x < width - 1) || (!(y % 2) && y)) {
                grid_face_add_new(g, 3);
                d = grid_get_dot(g, points, px + 3*a, py - b); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + 2*a, py    ); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px +   a, py - b); grid_face_set_dot(g, d, 2);
            }

            /* Triangle below right */
            if ((x < width - 1) || (!(y % 2) && (y < height - 1))) {
                grid_face_add_new(g, 3);
                d = grid_get_dot(g, points, px + 3*a, py + b); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px +   a, py + b); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + 2*a, py    ); grid_face_set_dot(g, d, 2);
            }

            /* Left triangles */
            if (!x && (y % 2)) {
                /* Triangle above left */
                grid_face_add_new(g, 3);
                d = grid_get_dot(g, points, px -   a, py - b); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px - 2*a, py    ); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px - 3*a, py - b); grid_face_set_dot(g, d, 2);

                /* Triangle below left */
                if (y < height - 1) {
                    grid_face_add_new(g, 3);
                    d = grid_get_dot(g, points, px -   a, py + b); grid_face_set_dot(g, d, 0);
                    d = grid_get_dot(g, points, px - 3*a, py + b); grid_face_set_dot(g, d, 1);
                    d = grid_get_dot(g, points, px - 2*a, py    ); grid_face_set_dot(g, d, 2);
                }
            }
        }
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

#define OCTAGONAL_TILESIZE 40
/* b/a approx sqrt(2) */
#define OCTAGONAL_A 29
#define OCTAGONAL_B 41

static const char *grid_validate_params_octagonal(int width, int height)
{
    int a = OCTAGONAL_A;
    int b = OCTAGONAL_B;

    if (width > INT_MAX / (2*a + b) ||          /* xextent */
        height > INT_MAX / (2*a + b) ||         /* yextent */
        height + 1 > INT_MAX / 4 / (width + 1)) /* max_dots */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_octagonal(int width, int height,
                          int *tilesize, int *xextent, int *yextent)
{
    int a = OCTAGONAL_A;
    int b = OCTAGONAL_B;

    *tilesize = OCTAGONAL_TILESIZE;
    *xextent = (2*a + b) * width;
    *yextent = (2*a + b) * height;
}

static grid *grid_new_octagonal(int width, int height, const char *desc)
{
    int x, y;
    int a = OCTAGONAL_A;
    int b = OCTAGONAL_B;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = OCTAGONAL_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* cell position */
            int px = (2*a + b) * x;
            int py = (2*a + b) * y;
            /* octagon */
            grid_face_add_new(g, 8);
            d = grid_get_dot(g, points, px + a, py);
            grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px + a + b, py);
            grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px + 2*a + b, py + a);
            grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px + 2*a + b, py + a + b);
            grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, px + a + b, py + 2*a + b);
            grid_face_set_dot(g, d, 4);
            d = grid_get_dot(g, points, px + a, py + 2*a + b);
            grid_face_set_dot(g, d, 5);
            d = grid_get_dot(g, points, px, py + a + b);
            grid_face_set_dot(g, d, 6);
            d = grid_get_dot(g, points, px, py + a);
            grid_face_set_dot(g, d, 7);

            /* diamond */
            if ((x > 0) && (y > 0)) {
                grid_face_add_new(g, 4);
                d = grid_get_dot(g, points, px, py - a);
                grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + a, py);
                grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px, py + a);
                grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px - a, py);
                grid_face_set_dot(g, d, 3);
            }
        }
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

#define KITE_TILESIZE 40
/* b/a approx sqrt(3) */
#define KITE_A 15
#define KITE_B 26

static const char *grid_validate_params_kites(int width, int height)
{
    int a = KITE_A;
    int b = KITE_B;

    if (width > (INT_MAX - 2*b) / (4*b) ||      /* xextent */
        height - 1 > (INT_MAX - 8*a) / (6*a) || /* yextent */
        width + 1 > INT_MAX / 6 / (height + 1)) /* max_dots */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_kites(int width, int height,
                     int *tilesize, int *xextent, int *yextent)
{
    int a = KITE_A;
    int b = KITE_B;

    *tilesize = KITE_TILESIZE;
    *xextent = 4*b * width + 2*b;
    *yextent = 6*a * (height-1) + 8*a;
}

static grid *grid_new_kites(int width, int height, const char *desc)
{
    int x, y;
    int a = KITE_A;
    int b = KITE_B;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = KITE_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* position of order-6 dot */
            int px = 4*b * x;
            int py = 6*a * y;
            if (y % 2)
                px += 2*b;

            /* kite pointing up-left */
            grid_face_add_new(g, 4);
            d = grid_get_dot(g, points, px, py);
            grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px + 2*b, py);
            grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px + 2*b, py + 2*a);
            grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px + b, py + 3*a);
            grid_face_set_dot(g, d, 3);

            /* kite pointing up */
            grid_face_add_new(g, 4);
            d = grid_get_dot(g, points, px, py);
            grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px + b, py + 3*a);
            grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px, py + 4*a);
            grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px - b, py + 3*a);
            grid_face_set_dot(g, d, 3);

            /* kite pointing up-right */
            grid_face_add_new(g, 4);
            d = grid_get_dot(g, points, px, py);
            grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px - b, py + 3*a);
            grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px - 2*b, py + 2*a);
            grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px - 2*b, py);
            grid_face_set_dot(g, d, 3);

            /* kite pointing down-right */
            grid_face_add_new(g, 4);
            d = grid_get_dot(g, points, px, py);
            grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px - 2*b, py);
            grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px - 2*b, py - 2*a);
            grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px - b, py - 3*a);
            grid_face_set_dot(g, d, 3);

            /* kite pointing down */
            grid_face_add_new(g, 4);
            d = grid_get_dot(g, points, px, py);
            grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px - b, py - 3*a);
            grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px, py - 4*a);
            grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px + b, py - 3*a);
            grid_face_set_dot(g, d, 3);

            /* kite pointing down-left */
            grid_face_add_new(g, 4);
            d = grid_get_dot(g, points, px, py);
            grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px + b, py - 3*a);
            grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px + 2*b, py - 2*a);
            grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px + 2*b, py);
            grid_face_set_dot(g, d, 3);
        }
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

#define FLORET_TILESIZE 150
/* -py/px is close to tan(30 - atan(sqrt(3)/9))
 * using py=26 makes everything lean to the left, rather than right
 */
#define FLORET_PX 75
#define FLORET_PY -26

static const char *grid_validate_params_floret(int width, int height)
{
    int px = FLORET_PX, py = FLORET_PY;         /* |( 75, -26)| = 79.43 */
    int qx = 4*px/5, qy = -py*2;                /* |( 60,  52)| = 79.40 */
    int ry = qy-py;
    /* rx unused in determining grid size. */

    if (width - 1 > (INT_MAX - (4*qx + 2*px)) / ((6*px+3*qx)/2) ||/* xextent */
        height - 1 > (INT_MAX - (4*qy + 2*ry)) / (5*qy-4*py) ||   /* yextent */
        width + 1 > INT_MAX / 9 / (height + 1))                  /* max_dots */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_floret(int width, int height,
                          int *tilesize, int *xextent, int *yextent)
{
    int px = FLORET_PX, py = FLORET_PY;         /* |( 75, -26)| = 79.43 */
    int qx = 4*px/5, qy = -py*2;                /* |( 60,  52)| = 79.40 */
    int ry = qy-py;
    /* rx unused in determining grid size. */

    *tilesize = FLORET_TILESIZE;
    *xextent = (6*px+3*qx)/2 * (width-1) + 4*qx + 2*px;
    *yextent = (5*qy-4*py) * (height-1) + 4*qy + 2*ry;
    if (height == 1)
        *yextent += (5*qy-4*py)/2;
}

static grid *grid_new_floret(int width, int height, const char *desc)
{
    int x, y;
    /* Vectors for sides; weird numbers needed to keep puzzle aligned with window
     * -py/px is close to tan(30 - atan(sqrt(3)/9))
     * using py=26 makes everything lean to the left, rather than right
     */
    int px = FLORET_PX, py = FLORET_PY;         /* |( 75, -26)| = 79.43 */
    int qx = 4*px/5, qy = -py*2;                /* |( 60,  52)| = 79.40 */
    int rx = qx-px, ry = qy-py;                 /* |(-15,  78)| = 79.38 */

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = FLORET_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    /* generate pentagonal faces */
    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* face centre */
            int cx = (6*px+3*qx)/2 * x;
            int cy = (4*py-5*qy) * y;
            if (x % 2)
                cy -= (4*py-5*qy)/2;
            else if (y && y == height-1)
                continue; /* make better looking grids?  try 3x3 for instance */

            grid_face_add_new(g, 5);
            d = grid_get_dot(g, points, cx        , cy        ); grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, cx+2*rx   , cy+2*ry   ); grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, cx+2*rx+qx, cy+2*ry+qy); grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, cx+2*qx+rx, cy+2*qy+ry); grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, cx+2*qx   , cy+2*qy   ); grid_face_set_dot(g, d, 4);

            grid_face_add_new(g, 5);
            d = grid_get_dot(g, points, cx        , cy        ); grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, cx+2*qx   , cy+2*qy   ); grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, cx+2*qx+px, cy+2*qy+py); grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, cx+2*px+qx, cy+2*py+qy); grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, cx+2*px   , cy+2*py   ); grid_face_set_dot(g, d, 4);

            grid_face_add_new(g, 5);
            d = grid_get_dot(g, points, cx        , cy        ); grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, cx+2*px   , cy+2*py   ); grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, cx+2*px-rx, cy+2*py-ry); grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, cx-2*rx+px, cy-2*ry+py); grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, cx-2*rx   , cy-2*ry   ); grid_face_set_dot(g, d, 4);

            grid_face_add_new(g, 5);
            d = grid_get_dot(g, points, cx        , cy        ); grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, cx-2*rx   , cy-2*ry   ); grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, cx-2*rx-qx, cy-2*ry-qy); grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, cx-2*qx-rx, cy-2*qy-ry); grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, cx-2*qx   , cy-2*qy   ); grid_face_set_dot(g, d, 4);

            grid_face_add_new(g, 5);
            d = grid_get_dot(g, points, cx        , cy        ); grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, cx-2*qx   , cy-2*qy   ); grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, cx-2*qx-px, cy-2*qy-py); grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, cx-2*px-qx, cy-2*py-qy); grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, cx-2*px   , cy-2*py   ); grid_face_set_dot(g, d, 4);

            grid_face_add_new(g, 5);
            d = grid_get_dot(g, points, cx        , cy        ); grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, cx-2*px   , cy-2*py   ); grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, cx-2*px+rx, cy-2*py+ry); grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, cx+2*rx-px, cy+2*ry-py); grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, cx+2*rx   , cy+2*ry   ); grid_face_set_dot(g, d, 4);
        }
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

/* DODEC_* are used for dodecagonal and great-dodecagonal grids. */
#define DODEC_TILESIZE 26
/* Vector for side of triangle - ratio is close to sqrt(3) */
#define DODEC_A 15
#define DODEC_B 26

static const char *grid_validate_params_dodecagonal(int width, int height)
{
    int a = DODEC_A;
    int b = DODEC_B;

    if (width - 1 > (INT_MAX - 3*(2*a + b)) / (4*a + 2*b) ||  /* xextent */
        height - 1 > (INT_MAX - 2*(2*a + b)) / (3*a + 2*b) || /* yextent */
        width > INT_MAX / 14 / height)                        /* max_dots */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_dodecagonal(int width, int height,
                          int *tilesize, int *xextent, int *yextent)
{
    int a = DODEC_A;
    int b = DODEC_B;

    *tilesize = DODEC_TILESIZE;
    *xextent = (4*a + 2*b) * (width-1) + 3*(2*a + b);
    *yextent = (3*a + 2*b) * (height-1) + 2*(2*a + b);
}

static grid *grid_new_dodecagonal(int width, int height, const char *desc)
{
    int x, y;
    int a = DODEC_A;
    int b = DODEC_B;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = DODEC_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* centre of dodecagon */
            int px = (4*a + 2*b) * x;
            int py = (3*a + 2*b) * y;
            if (y % 2)
                px += 2*a + b;

            /* dodecagon */
            grid_face_add_new(g, 12);
            d = grid_get_dot(g, points, px + (  a    ), py - (2*a + b)); grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px + (  a + b), py - (  a + b)); grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px + (2*a + b), py - (  a    )); grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px + (2*a + b), py + (  a    )); grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, px + (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 4);
            d = grid_get_dot(g, points, px + (  a    ), py + (2*a + b)); grid_face_set_dot(g, d, 5);
            d = grid_get_dot(g, points, px - (  a    ), py + (2*a + b)); grid_face_set_dot(g, d, 6);
            d = grid_get_dot(g, points, px - (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 7);
            d = grid_get_dot(g, points, px - (2*a + b), py + (  a    )); grid_face_set_dot(g, d, 8);
            d = grid_get_dot(g, points, px - (2*a + b), py - (  a    )); grid_face_set_dot(g, d, 9);
            d = grid_get_dot(g, points, px - (  a + b), py - (  a + b)); grid_face_set_dot(g, d, 10);
            d = grid_get_dot(g, points, px - (  a    ), py - (2*a + b)); grid_face_set_dot(g, d, 11);

            /* triangle below dodecagon */
	    if ((y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) {
	      	grid_face_add_new(g, 3);
	      	d = grid_get_dot(g, points, px + a, py + (2*a +   b)); grid_face_set_dot(g, d, 0);
	      	d = grid_get_dot(g, points, px    , py + (2*a + 2*b)); grid_face_set_dot(g, d, 1);
	      	d = grid_get_dot(g, points, px - a, py + (2*a +   b)); grid_face_set_dot(g, d, 2);
	    }

            /* triangle above dodecagon */
	    if ((y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2)))) {
	      	grid_face_add_new(g, 3);
	      	d = grid_get_dot(g, points, px - a, py - (2*a +   b)); grid_face_set_dot(g, d, 0);
	      	d = grid_get_dot(g, points, px    , py - (2*a + 2*b)); grid_face_set_dot(g, d, 1);
	      	d = grid_get_dot(g, points, px + a, py - (2*a +   b)); grid_face_set_dot(g, d, 2);
	    }
	}
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

static const char *grid_validate_params_greatdodecagonal(int width, int height)
{
    int a = DODEC_A;
    int b = DODEC_B;

    if (width - 1 > (INT_MAX - (2*(2*a + b) + 3*a + b)) / (6*a + 2*b) ||
        height - 1 > (INT_MAX - 2*(2*a + b)) / (3*a + 3*b) || /* yextent */
        width > INT_MAX / 200 / height) /* max_dots */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_greatdodecagonal(int width, int height,
                          int *tilesize, int *xextent, int *yextent)
{
    int a = DODEC_A;
    int b = DODEC_B;

    *tilesize = DODEC_TILESIZE;
    *xextent = (6*a + 2*b) * (width-1) + 2*(2*a + b) + 3*a + b;
    *yextent = (3*a + 3*b) * (height-1) + 2*(2*a + b);
}

static grid *grid_new_greatdodecagonal(int width, int height, const char *desc)
{
    int x, y;
    /* Vector for side of triangle - ratio is close to sqrt(3) */
    int a = DODEC_A;
    int b = DODEC_B;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = DODEC_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* centre of dodecagon */
            int px = (6*a + 2*b) * x;
            int py = (3*a + 3*b) * y;
            if (y % 2)
                px += 3*a + b;

            /* dodecagon */
            grid_face_add_new(g, 12);
            d = grid_get_dot(g, points, px + (  a    ), py - (2*a + b)); grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px + (  a + b), py - (  a + b)); grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px + (2*a + b), py - (  a    )); grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px + (2*a + b), py + (  a    )); grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, px + (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 4);
            d = grid_get_dot(g, points, px + (  a    ), py + (2*a + b)); grid_face_set_dot(g, d, 5);
            d = grid_get_dot(g, points, px - (  a    ), py + (2*a + b)); grid_face_set_dot(g, d, 6);
            d = grid_get_dot(g, points, px - (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 7);
            d = grid_get_dot(g, points, px - (2*a + b), py + (  a    )); grid_face_set_dot(g, d, 8);
            d = grid_get_dot(g, points, px - (2*a + b), py - (  a    )); grid_face_set_dot(g, d, 9);
            d = grid_get_dot(g, points, px - (  a + b), py - (  a + b)); grid_face_set_dot(g, d, 10);
            d = grid_get_dot(g, points, px - (  a    ), py - (2*a + b)); grid_face_set_dot(g, d, 11);

            /* hexagon below dodecagon */
	    if (y < height - 1 && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) {
	      	grid_face_add_new(g, 6);
	      	d = grid_get_dot(g, points, px +   a, py + (2*a +   b)); grid_face_set_dot(g, d, 0);
	      	d = grid_get_dot(g, points, px + 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 1);
	      	d = grid_get_dot(g, points, px +   a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 2);
	      	d = grid_get_dot(g, points, px -   a, py + (2*a + 3*b)); grid_face_set_dot(g, d, 3);
	      	d = grid_get_dot(g, points, px - 2*a, py + (2*a + 2*b)); grid_face_set_dot(g, d, 4);
	      	d = grid_get_dot(g, points, px -   a, py + (2*a +   b)); grid_face_set_dot(g, d, 5);
	    }

            /* hexagon above dodecagon */
	    if (y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) {
	      	grid_face_add_new(g, 6);
	      	d = grid_get_dot(g, points, px -   a, py - (2*a +   b)); grid_face_set_dot(g, d, 0);
	      	d = grid_get_dot(g, points, px - 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 1);
	      	d = grid_get_dot(g, points, px -   a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 2);
	      	d = grid_get_dot(g, points, px +   a, py - (2*a + 3*b)); grid_face_set_dot(g, d, 3);
	      	d = grid_get_dot(g, points, px + 2*a, py - (2*a + 2*b)); grid_face_set_dot(g, d, 4);
	      	d = grid_get_dot(g, points, px +   a, py - (2*a +   b)); grid_face_set_dot(g, d, 5);
	    }

            /* square on right of dodecagon */
	    if (x < width - 1) {
	      	grid_face_add_new(g, 4);
	      	d = grid_get_dot(g, points, px + 2*a + b, py - a); grid_face_set_dot(g, d, 0);
	      	d = grid_get_dot(g, points, px + 4*a + b, py - a); grid_face_set_dot(g, d, 1);
	      	d = grid_get_dot(g, points, px + 4*a + b, py + a); grid_face_set_dot(g, d, 2);
	      	d = grid_get_dot(g, points, px + 2*a + b, py + a); grid_face_set_dot(g, d, 3);
	    }

            /* square on top right of dodecagon */
	    if (y && (x < width - 1 || !(y % 2))) {
	      	grid_face_add_new(g, 4);
	      	d = grid_get_dot(g, points, px + (  a    ), py - (2*a +   b)); grid_face_set_dot(g, d, 0);
		d = grid_get_dot(g, points, px + (2*a    ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 1);
		d = grid_get_dot(g, points, px + (2*a + b), py - (  a + 2*b)); grid_face_set_dot(g, d, 2);
		d = grid_get_dot(g, points, px + (  a + b), py - (  a +   b)); grid_face_set_dot(g, d, 3);
	    }

            /* square on top left of dodecagon */
	    if (y && (x || (y % 2))) {
	      	grid_face_add_new(g, 4);
		d = grid_get_dot(g, points, px - (  a + b), py - (  a +   b)); grid_face_set_dot(g, d, 0);
		d = grid_get_dot(g, points, px - (2*a + b), py - (  a + 2*b)); grid_face_set_dot(g, d, 1);
		d = grid_get_dot(g, points, px - (2*a    ), py - (2*a + 2*b)); grid_face_set_dot(g, d, 2);
	      	d = grid_get_dot(g, points, px - (  a    ), py - (2*a +   b)); grid_face_set_dot(g, d, 3);
	    }
	}
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

static const char *grid_validate_params_greatgreatdodecagonal(
    int width, int height)
{
    int a = DODEC_A;
    int b = DODEC_B;

    if (width-1 > (INT_MAX - (2*(2*a + b) + 2*a + 2*b)) / (4*a + 4*b) ||
        height-1 > (INT_MAX - 2*(2*a + b)) / (6*a + 2*b) || /* yextent */
        width > INT_MAX / 300 / height) /* max_dots */
        return "Grid size must not be unreasonably large";
    return NULL;
}

static void grid_size_greatgreatdodecagonal(int width, int height,
                                            int *tilesize, int *xextent, int *yextent)
{
    int a = DODEC_A;
    int b = DODEC_B;

    *tilesize = DODEC_TILESIZE;
    *xextent = (4*a + 4*b) * (width-1) + 2*(2*a + b) + 2*a + 2*b;
    *yextent = (6*a + 2*b) * (height-1) + 2*(2*a + b);
}

static grid *grid_new_greatgreatdodecagonal(int width, int height, const char *desc)
{
    int x, y;
    /* Vector for side of triangle - ratio is close to sqrt(3) */
    int a = DODEC_A;
    int b = DODEC_B;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = DODEC_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* centre of dodecagon */
            int px = (4*a + 4*b) * x;
            int py = (6*a + 2*b) * y;
            if (y % 2)
                px += 2*a + 2*b;

            /* dodecagon */
            grid_face_add_new(g, 12);
            d = grid_get_dot(g, points, px + (  a    ), py - (2*a + b)); grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px + (  a + b), py - (  a + b)); grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px + (2*a + b), py - (  a    )); grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px + (2*a + b), py + (  a    )); grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, px + (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 4);
            d = grid_get_dot(g, points, px + (  a    ), py + (2*a + b)); grid_face_set_dot(g, d, 5);
            d = grid_get_dot(g, points, px - (  a    ), py + (2*a + b)); grid_face_set_dot(g, d, 6);
            d = grid_get_dot(g, points, px - (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 7);
            d = grid_get_dot(g, points, px - (2*a + b), py + (  a    )); grid_face_set_dot(g, d, 8);
            d = grid_get_dot(g, points, px - (2*a + b), py - (  a    )); grid_face_set_dot(g, d, 9);
            d = grid_get_dot(g, points, px - (  a + b), py - (  a + b)); grid_face_set_dot(g, d, 10);
            d = grid_get_dot(g, points, px - (  a    ), py - (2*a + b)); grid_face_set_dot(g, d, 11);

            /* hexagon on top right of dodecagon */
            if (y && (x < width - 1 || !(y % 2))) {
                grid_face_add_new(g, 6);
                d = grid_get_dot(g, points, px + (a + 2*b), py - (4*a + b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (a + 2*b), py - (2*a + b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (a +   b), py - (  a + b)); grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px + (a      ), py - (2*a + b)); grid_face_set_dot(g, d, 3);
                d = grid_get_dot(g, points, px + (a      ), py - (4*a + b)); grid_face_set_dot(g, d, 4);
                d = grid_get_dot(g, points, px + (a +   b), py - (5*a + b)); grid_face_set_dot(g, d, 5);
            }

            /* hexagon on right of dodecagon*/
            if (x < width - 1) {
                grid_face_add_new(g, 6);
                d = grid_get_dot(g, points, px + (2*a + 3*b), py -   a); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (2*a + 3*b), py +   a); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (2*a + 2*b), py + 2*a); grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px + (2*a +   b), py +   a); grid_face_set_dot(g, d, 3);
                d = grid_get_dot(g, points, px + (2*a +   b), py -   a); grid_face_set_dot(g, d, 4);
                d = grid_get_dot(g, points, px + (2*a + 2*b), py - 2*a); grid_face_set_dot(g, d, 5);
            }

            /* hexagon on bottom right of dodecagon */
            if ((y < height - 1) && (x < width - 1 || !(y % 2))) {
                grid_face_add_new(g, 6);
                d = grid_get_dot(g, points, px + (a + 2*b), py + (2*a + b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (a + 2*b), py + (4*a + b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (a +   b), py + (5*a + b)); grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px + (a      ), py + (4*a + b)); grid_face_set_dot(g, d, 3);
                d = grid_get_dot(g, points, px + (a      ), py + (2*a + b)); grid_face_set_dot(g, d, 4);
                d = grid_get_dot(g, points, px + (a +   b), py + (  a + b)); grid_face_set_dot(g, d, 5);
            }

            /* square on top right of dodecagon */
            if (y && (x < width - 1 )) {
                grid_face_add_new(g, 4);
                d = grid_get_dot(g, points, px + (  a + 2*b), py - (2*a +   b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (2*a + 2*b), py - (2*a      )); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (2*a +   b), py - (  a      )); grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px + (  a +   b), py - (  a +   b)); grid_face_set_dot(g, d, 3);
            }

            /* square on bottom right of dodecagon */
            if ((y < height - 1) && (x < width - 1 )) {
                grid_face_add_new(g, 4);
                d = grid_get_dot(g, points, px + (2*a + 2*b), py + (2*a      )); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (  a + 2*b), py + (2*a +   b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (  a +   b), py + (  a +   b)); grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px + (2*a +   b), py + (  a      )); grid_face_set_dot(g, d, 3);
            }

            /* square below dodecagon */
            if ((y < height - 1) && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) {
                grid_face_add_new(g, 4);
                d = grid_get_dot(g, points, px + a, py + (2*a + b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + a, py + (4*a + b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px - a, py + (4*a + b)); grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px - a, py + (2*a + b)); grid_face_set_dot(g, d, 3);
            }

            /* square on bottom left of dodecagon */
            if (x && (y < height - 1)) {
                grid_face_add_new(g, 4);
                d = grid_get_dot(g, points, px - (2*a +   b), py + (  a      )); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px - (  a +   b), py + (  a +   b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px - (  a + 2*b), py + (2*a +   b)); grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px - (2*a + 2*b), py + (2*a      )); grid_face_set_dot(g, d, 3);
            }

            /* square on top left of dodecagon */
            if (x && y) {
                grid_face_add_new(g, 4);
                d = grid_get_dot(g, points, px - (  a +   b), py - (  a +   b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px - (2*a +   b), py - (  a      )); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px - (2*a + 2*b), py - (2*a      )); grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px - (  a + 2*b), py - (2*a +   b)); grid_face_set_dot(g, d, 3);

            }

            /* square above dodecagon */
            if (y && (x < width - 1 || !(y % 2)) && (x > 0 || (y % 2))) {
                grid_face_add_new(g, 4);
                d = grid_get_dot(g, points, px + a, py - (4*a + b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + a, py - (2*a + b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px - a, py - (2*a + b)); grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px - a, py - (4*a + b)); grid_face_set_dot(g, d, 3);
            }

            /* upper triangle (v) */
            if (y && (x < width - 1)) {
                grid_face_add_new(g, 3);
                d = grid_get_dot(g, points, px + (3*a + 2*b), py - (2*a +   b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (2*a + 2*b), py - (2*a      )); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (  a + 2*b), py - (2*a +   b)); grid_face_set_dot(g, d, 2);
            }

            /* lower triangle (^) */
            if ((y < height - 1) && (x < width - 1)) {
                grid_face_add_new(g, 3);
                d = grid_get_dot(g, points, px + (3*a + 2*b), py + (2*a +   b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (  a + 2*b), py + (2*a +   b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (2*a + 2*b), py + (2*a      )); grid_face_set_dot(g, d, 2);
            }
        }
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

static const char *grid_validate_params_compassdodecagonal(
    int width, int height)
{
    int a = DODEC_A;
    int b = DODEC_B;

    if (width > INT_MAX / (4*a + 2*b) ||  /* xextent */
        height > INT_MAX / (4*a + 2*b) || /* yextent */
        width > INT_MAX / 18 / height)    /* max_dots */
        return "Grid must not be unreasonably large";
    return NULL;
}

static void grid_size_compassdodecagonal(int width, int height,
                                         int *tilesize, int *xextent, int *yextent)
{
    int a = DODEC_A;
    int b = DODEC_B;

    *tilesize = DODEC_TILESIZE;
    *xextent = (4*a + 2*b) * width;
    *yextent = (4*a + 2*b) * height;
}

static grid *grid_new_compassdodecagonal(int width, int height, const char *desc)
{
    int x, y;
    /* Vector for side of triangle - ratio is close to sqrt(3) */
    int a = DODEC_A;
    int b = DODEC_B;

    tree234 *points;

    grid *g = grid_empty();
    g->tilesize = DODEC_TILESIZE;

    points = newtree234(grid_point_cmp_fn);

    for (y = 0; y < height; y++) {
        for (x = 0; x < width; x++) {
            grid_dot *d;
            /* centre of dodecagon */
            int px = (4*a + 2*b) * x;
            int py = (4*a + 2*b) * y;

            /* dodecagon */
            grid_face_add_new(g, 12);
            d = grid_get_dot(g, points, px + (  a    ), py - (2*a + b)); grid_face_set_dot(g, d, 0);
            d = grid_get_dot(g, points, px + (  a + b), py - (  a + b)); grid_face_set_dot(g, d, 1);
            d = grid_get_dot(g, points, px + (2*a + b), py - (  a    )); grid_face_set_dot(g, d, 2);
            d = grid_get_dot(g, points, px + (2*a + b), py + (  a    )); grid_face_set_dot(g, d, 3);
            d = grid_get_dot(g, points, px + (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 4);
            d = grid_get_dot(g, points, px + (  a    ), py + (2*a + b)); grid_face_set_dot(g, d, 5);
            d = grid_get_dot(g, points, px - (  a    ), py + (2*a + b)); grid_face_set_dot(g, d, 6);
            d = grid_get_dot(g, points, px - (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 7);
            d = grid_get_dot(g, points, px - (2*a + b), py + (  a    )); grid_face_set_dot(g, d, 8);
            d = grid_get_dot(g, points, px - (2*a + b), py - (  a    )); grid_face_set_dot(g, d, 9);
            d = grid_get_dot(g, points, px - (  a + b), py - (  a + b)); grid_face_set_dot(g, d, 10);
            d = grid_get_dot(g, points, px - (  a    ), py - (2*a + b)); grid_face_set_dot(g, d, 11);

            if (x < width - 1 && y < height - 1) {
                /* north triangle */
                grid_face_add_new(g, 3);
                d = grid_get_dot(g, points, px + (2*a + b), py + (  a    )); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (3*a + b), py + (  a + b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 2);

                /* east triangle */
                grid_face_add_new(g, 3);
                d = grid_get_dot(g, points, px + (3*a + 2*b), py + (2*a + b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (3*a +   b), py + (3*a + b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (3*a +   b), py + (  a + b)); grid_face_set_dot(g, d, 2);

                /* south triangle */
                grid_face_add_new(g, 3);
                d = grid_get_dot(g, points, px + (3*a + b), py + (3*a +   b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (2*a + b), py + (3*a + 2*b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (  a + b), py + (3*a +   b)); grid_face_set_dot(g, d, 2);

                /* west triangle */
                grid_face_add_new(g, 3);
                d = grid_get_dot(g, points, px + (a + b), py + (  a + b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (a + b), py + (3*a + b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (a    ), py + (2*a + b)); grid_face_set_dot(g, d, 2);

                /* square in center */
                grid_face_add_new(g, 4);
                d = grid_get_dot(g, points, px + (3*a + b), py + (  a + b)); grid_face_set_dot(g, d, 0);
                d = grid_get_dot(g, points, px + (3*a + b), py + (3*a + b)); grid_face_set_dot(g, d, 1);
                d = grid_get_dot(g, points, px + (  a + b), py + (3*a + b)); grid_face_set_dot(g, d, 2);
                d = grid_get_dot(g, points, px + (  a + b), py + (  a + b)); grid_face_set_dot(g, d, 3);
            }
        }
    }

    freetree234(points);

    grid_make_consistent(g);
    return g;
}

/*
 * Penrose tilings. For historical reasons, we support two totally
 * different generation algorithms: the legacy one is only supported
 * by grid_new_penrose, for backwards compatibility with game
 * descriptions generated before we switched. New grid generation uses
 * only the new system.
 */

#define PENROSE_TILESIZE 100

static const char *grid_validate_params_penrose(int width, int height)
{
    int l = PENROSE_TILESIZE;

    if (width > INT_MAX / l ||                  /* xextent */
        height > INT_MAX / l ||                 /* yextent */
        width > INT_MAX / (3 * 3 * 4 * height)) /* max_dots */
        return "Grid must not be unreasonably large";
    return NULL;
}

static void grid_size_penrose(int width, int height,
                              int *tilesize, int *xextent, int *yextent)
{
    int l = PENROSE_TILESIZE;

    *tilesize = l;
    *xextent = l * width;
    *yextent = l * height;
}

/*
 * Legacy generation by selecting a patch of tiling from the expansion
 * of a big triangle.
 */

typedef struct penrose_legacy_set_faces_ctx {
    int xmin, xmax, ymin, ymax;

    grid *g;
    tree234 *points;
} penrose_legacy_set_faces_ctx;

static double round_int_nearest_away(double r)
{
    return (r > 0.0) ? floor(r + 0.5) : ceil(r - 0.5);
}

static int penrose_legacy_set_faces(penrose_legacy_state *state, vector *vs,
                                    int n, int depth)
{
    penrose_legacy_set_faces_ctx *sf_ctx =
        (penrose_legacy_set_faces_ctx *)state->ctx;
    int i;
    int xs[4], ys[4];

    if (depth < state->max_depth) return 0;
#ifdef DEBUG_PENROSE
    if (n != 4) return 0; /* triangles are sent as debugging. */
#endif

    for (i = 0; i < n; i++) {
        double tx = penrose_legacy_vx(vs, i), ty = penrose_legacy_vy(vs, i);

        xs[i] = (int)round_int_nearest_away(tx);
        ys[i] = (int)round_int_nearest_away(ty);

        if (xs[i] < sf_ctx->xmin || xs[i] > sf_ctx->xmax) return 0;
        if (ys[i] < sf_ctx->ymin || ys[i] > sf_ctx->ymax) return 0;
    }

    grid_face_add_new(sf_ctx->g, n);
    debug(("penrose: new face l=%f gen=%d...",
           penrose_legacy_side_length(state->start_size, depth), depth));
    for (i = 0; i < n; i++) {
        grid_dot *d = grid_get_dot(sf_ctx->g, sf_ctx->points,
                                   xs[i], ys[i]);
        grid_face_set_dot(sf_ctx->g, d, i);
        debug((" ... dot 0x%x (%d,%d) (was %2.2f,%2.2f)",
               d, d->x, d->y, penrose_legacy_vx(vs, i),
               penrose_legacy_vy(vs, i)));
    }

    return 0;
}

static grid *grid_new_penrose_legacy(int width, int height, int which,
                                     const char *desc);

static const char *grid_validate_desc_penrose_legacy(
    grid_type type, int width, int height, const char *desc)
{
    int tilesize = PENROSE_TILESIZE, startsz, depth, xoff, yoff, aoff, inner_radius;
    double outer_radius;
    int which = (type == GRID_PENROSE_P2 ? PENROSE_P2 : PENROSE_P3);
    grid *g;

    if (!desc)
        return "Missing grid description string.";

    penrose_legacy_calculate_size(which, tilesize, width, height,
                                  &outer_radius, &startsz, &depth);
    inner_radius = (int)(outer_radius - sqrt(width*width + height*height));

    if (sscanf(desc, "G%d,%d,%d", &xoff, &yoff, &aoff) != 3)
        return "Invalid format grid description string.";

    if (sqrt(xoff*xoff + yoff*yoff) > inner_radius)
        return "Patch offset out of bounds.";
    if ((aoff % 36) != 0 || aoff < 0 || aoff >= 360)
        return "Angle offset out of bounds.";

    /*
     * Test-generate to ensure these parameters don't end us up with
     * no grid at all.
     */
    g = grid_new_penrose_legacy(width, height, which, desc);
    if (!g)
        return "Patch coordinates do not identify a usable grid fragment";
    grid_free(g);

    return NULL;
}

static grid *grid_new_penrose_legacy(int width, int height, int which,
                                     const char *desc)
{
    int tilesize = PENROSE_TILESIZE;
    int xsz, ysz, xoff, yoff, aoff;
    double rradius;

    tree234 *points;
    grid *g;

    penrose_legacy_state ps;
    penrose_legacy_set_faces_ctx sf_ctx;

    penrose_legacy_calculate_size(which, tilesize, width, height,
                                  &rradius, &ps.start_size, &ps.max_depth);

    debug(("penrose: w%d h%d, tile size %d, start size %d, depth %d",
           width, height, tilesize, ps.start_size, ps.max_depth));

    ps.new_tile = penrose_legacy_set_faces;
    ps.ctx = &sf_ctx;

    g = grid_empty();
    g->tilesize = tilesize;

    points = newtree234(grid_point_cmp_fn);

    memset(&sf_ctx, 0, sizeof(sf_ctx));
    sf_ctx.g = g;
    sf_ctx.points = points;

    if (desc != NULL) {
        if (sscanf(desc, "G%d,%d,%d", &xoff, &yoff, &aoff) != 3)
            assert(!"Invalid grid description.");
    } else {
        xoff = yoff = aoff = 0;
    }

    xsz = width * tilesize;
    ysz = height * tilesize;

    sf_ctx.xmin = xoff - xsz/2;
    sf_ctx.xmax = xoff + xsz/2;
    sf_ctx.ymin = yoff - ysz/2;
    sf_ctx.ymax = yoff + ysz/2;

    debug(("penrose: centre (%f, %f) xsz %f ysz %f",
           0.0, 0.0, xsz, ysz));
    debug(("penrose: x range (%f --> %f), y range (%f --> %f)",
           sf_ctx.xmin, sf_ctx.xmax, sf_ctx.ymin, sf_ctx.ymax));

    penrose_legacy(&ps, which, aoff);

    freetree234(points);

    debug(("penrose: %d faces total (equivalent to %d wide by %d high)",
           g->num_faces, g->num_faces/height, g->num_faces/width));

    /*
     * Return NULL if we ended up with an empty grid, either because
     * the initial generation was over too small a rectangle to
     * encompass any face or because grid_trim_vigorously ended up
     * removing absolutely everything.
     */
    if (g->num_faces == 0 || g->num_dots == 0) {
        grid_free(g);
        return NULL;
    }
    grid_trim_vigorously(g);
    if (g->num_faces == 0 || g->num_dots == 0) {
        grid_free(g);
        return NULL;
    }

    grid_make_consistent(g);

    /*
     * Centre the grid in its originally promised rectangle.
     */
    g->lowest_x -= ((sf_ctx.xmax - sf_ctx.xmin) -
                    (g->highest_x - g->lowest_x)) / 2;
    g->highest_x = g->lowest_x + (sf_ctx.xmax - sf_ctx.xmin);
    g->lowest_y -= ((sf_ctx.ymax - sf_ctx.ymin) -
                    (g->highest_y - g->lowest_y)) / 2;
    g->highest_y = g->lowest_y + (sf_ctx.ymax - sf_ctx.ymin);

    return g;
}

/*
 * Combinatorial-coordinate generation.
 *
 * We receive coordinates from the generator in the form of x,y pairs
 * each of which is an integer combination of 1 and sqrt(5), but those
 * pairs have different scale units in the x and y directions. The
 * scale units are 1/4 for x and sin(pi/5)/2 for y, which makes their
 * ratio equal to 2 sin(pi/5) ~= 1.1756. We fudge that irrational
 * aspect ratio into a rational approximation, by simply taking a pair
 * of integer scale factors for the x and y dimensions; this distorts
 * the output tiling slightly, but the distortion is consistent, and
 * doesn't accumulate over a large patch of tiling, so it won't make
 * anything end up totally out of place.
 *
 * (However, we compute the subsequent combination of 1 and sqrt(5)
 * exactly, because using an approximation to sqrt(5) _could_ mean
 * that in a sufficiently large patch of tiling two such combinations
 * ended up misordered.)
 *
 * Adding to the confusion, we also flip round the x and y
 * coordinates, because it's slightly nicer to have vertical edges in
 * the tiling rather than horizontal ones. (Both for aesthetics, and
 * also because if two P3 thin rhombs are separated by a horizontal
 * line and both contain numeric clues then the clue numbers look a
 * bit crowded, due to digits being taller than they are wide.)
 *
 * Finally, we have different base unit sizes for the two tiling
 * types, because sensible sizes for the two are actually different.
 * Each of P2 and P3 can be subdivided into the other, via dividing
 * the larger triangle type in two, so that L large and S small become
 * L+S large and L small. In the limit, this means that you expect the
 * number of triangles (hence tiles) to grow by a factor of phi in
 * each of those subdivisions (and hence by a factor of phi^2 in a
 * full subdivision of P2 to a finer P2). So a sensible size ratio
 * between the two tilings is one that makes them fit about the same
 * number of tiles into the same area - and since tile area is
 * proportional to _square_ of length, it follows that the P2 and P3
 * length unit should differ by a factor of sqrt(phi).
 */
#define PENROSE_XUNIT_P2 37
#define PENROSE_YUNIT_P2 44
#define PENROSE_XUNIT_P3 30
#define PENROSE_YUNIT_P3 35

struct size { int w, h; };
static struct size api_size_penrose(int width, int height, int which)
{
    int xunit = (which == PENROSE_P2 ? PENROSE_XUNIT_P2 : PENROSE_XUNIT_P3);
    int yunit = (which == PENROSE_P2 ? PENROSE_YUNIT_P2 : PENROSE_YUNIT_P3);
    struct size size = {
        width * PENROSE_TILESIZE / yunit,
        height * PENROSE_TILESIZE / xunit,
    };
    return size;
}

static grid *grid_new_penrose(int width, int height, int which,
                              const char *desc); /* forward reference */

static char *grid_new_desc_penrose(grid_type type, int width, int height,
                                   random_state *rs)
{
    char *buf;
    struct PenrosePatchParams params;
    int which = (type == GRID_PENROSE_P2 ? PENROSE_P2 : PENROSE_P3);
    struct size size = api_size_penrose(width, height, which);

    penrose_tiling_randomise(&params, which, size.h, size.w, rs);

    buf = snewn(params.ncoords + 3, char);
    buf[0] = '0' + params.orientation;
    buf[1] = '0' + params.start_vertex;
    memcpy(buf + 2, params.coords, params.ncoords);
    buf[2 + params.ncoords] = '\0';

    sfree(params.coords);
    return buf;
}

/* Shared code between validating and reading grid descs.
 * Always allocates params->coords, whether or not it returns an error. */
static const char *grid_desc_to_penrose_params(
    const char *desc, int which, struct PenrosePatchParams *params)
{
    int i;

    if (!*desc)
        return "empty grid description";

    params->ncoords = strlen(desc) - 2;
    params->coords = snewn(params->ncoords, char);

    {
        char c = desc[0];
        if (isdigit((unsigned char)c))
            params->orientation = c - '0';
        else
            return "expected digit at start of grid description";

        c = desc[1];
        if (c >= '0' && c < '3')
            params->start_vertex = c - '0';
        else
            return "expected digit as second char of grid description";
    }

    for (i = 0; i < params->ncoords; i++) {
        char c = desc[i+2];
        if (!penrose_valid_letter(c, which))
            return "expected tile letter in grid description";
        params->coords[i] = c;
    }

    return NULL;
}

static const char *grid_validate_desc_penrose(grid_type type,
                                              int width, int height,
                                              const char *desc)
{
    struct PenrosePatchParams params;
    const char *error = NULL;
    int which = (type == GRID_PENROSE_P2 ? PENROSE_P2 : PENROSE_P3);

    if (!desc)
        return "Missing grid description string.";

    if (*desc == 'G')
        return grid_validate_desc_penrose_legacy(type, width, height, desc);

    error = grid_desc_to_penrose_params(desc, which, &params);
    if (!error)
        error = penrose_tiling_params_invalid(&params, which);

    sfree(params.coords);
    return error;
}

struct penrosecontext {
    grid *g;
    tree234 *points;
    int xunit, yunit;
};

static void grid_penrose_callback(void *vctx, const int *coords)
{
    struct penrosecontext *ctx = (struct penrosecontext *)vctx;
    size_t i;

    grid_face_add_new(ctx->g, 4);
    for (i = 0; i < 4; i++) {
        grid_dot *d = grid_get_dot(
            ctx->g, ctx->points,
            coords[4*i+2] * ctx->yunit + n_times_root_k(
                coords[4*i+3] * ctx->yunit, 5),
            coords[4*i+0] * ctx->xunit + n_times_root_k(
                coords[4*i+1] * ctx->xunit, 5));
        grid_face_set_dot(ctx->g, d, i);
    }
}

static grid *grid_new_penrose(int width, int height, int which,
                              const char *desc)
{
    struct PenrosePatchParams params;
    const char *error = NULL;
    struct penrosecontext ctx[1];
    struct size size;

    if (*desc == 'G')
        return grid_new_penrose_legacy(width, height, which, desc);

    error = grid_desc_to_penrose_params(desc, which, &params);
    assert(error == NULL && "grid_validate_desc_penrose should have failed");

    ctx->g = grid_empty();
    ctx->g->tilesize = PENROSE_TILESIZE;

    ctx->points = newtree234(grid_point_cmp_fn);

    ctx->xunit = (which == PENROSE_P2 ? PENROSE_XUNIT_P2 : PENROSE_XUNIT_P3);
    ctx->yunit = (which == PENROSE_P2 ? PENROSE_YUNIT_P2 : PENROSE_YUNIT_P3);

    size = api_size_penrose(width, height, which);
    penrose_tiling_generate(&params, size.h, size.w,
                            grid_penrose_callback, ctx);

    freetree234(ctx->points);
    sfree(params.coords);

    grid_trim_vigorously(ctx->g);
    grid_make_consistent(ctx->g);

    /*
     * Centre the grid in its originally promised rectangle.
     */
    {
        int w = width * PENROSE_TILESIZE, h = height * PENROSE_TILESIZE;
        ctx->g->lowest_x -= (w - (ctx->g->highest_x - ctx->g->lowest_x))/2;
        ctx->g->lowest_y -= (h - (ctx->g->highest_y - ctx->g->lowest_y))/2;
        ctx->g->highest_x = ctx->g->lowest_x + w;
        ctx->g->highest_y = ctx->g->lowest_y + h;
    }

    return ctx->g;
}

static const char *grid_validate_params_penrose_p2_kite(int width, int height)
{
    return grid_validate_params_penrose(width, height);
}

static const char *grid_validate_params_penrose_p3_thick(int width, int height)
{
    return grid_validate_params_penrose(width, height);
}

static void grid_size_penrose_p2_kite(int width, int height,
                       int *tilesize, int *xextent, int *yextent)
{
    grid_size_penrose(width, height, tilesize, xextent, yextent);
}

static void grid_size_penrose_p3_thick(int width, int height,
                       int *tilesize, int *xextent, int *yextent)
{
    grid_size_penrose(width, height, tilesize, xextent, yextent);
}

static grid *grid_new_penrose_p2_kite(int width, int height, const char *desc)
{
    return grid_new_penrose(width, height, PENROSE_P2, desc);
}

static grid *grid_new_penrose_p3_thick(int width, int height, const char *desc)
{
    return grid_new_penrose(width, height, PENROSE_P3, desc);
}

#define HATS_TILESIZE 32
#define HATS_XSQUARELEN 4
#define HATS_YSQUARELEN 6
#define HATS_XUNIT 14
#define HATS_YUNIT 8

static const char *grid_validate_params_hats(
    int width, int height)
{
    int l = HATS_TILESIZE;

    if (width > INT_MAX / l ||                  /* xextent */
        height > INT_MAX / l ||                 /* yextent */
        width > INT_MAX / (6 * height))         /* max_dots */
        return "Grid must not be unreasonably large";
    return NULL;
}

static void grid_size_hats(int width, int height,
                           int *tilesize, int *xextent, int *yextent)
{
    *tilesize = HATS_TILESIZE;
    *xextent = width * HATS_XUNIT * HATS_XSQUARELEN;
    *yextent = height * HATS_YUNIT * HATS_YSQUARELEN;
}

static char *grid_new_desc_hats(
    grid_type type, int width, int height, random_state *rs)
{
    char *buf, *p;
    size_t bufmax, i;
    struct HatPatchParams hp;

    hat_tiling_randomise(&hp, width, height, rs);

    bufmax = 3 * hp.ncoords + 2;
    buf = snewn(bufmax, char);
    p = buf;
    for (i = 0; i < hp.ncoords; i++) {
        assert(hp.coords[i] < 100);    /* at most 2 digits */
        assert(p - buf <= bufmax-4);   /* room for 2 digits, comma and NUL */
        p += sprintf(p, "%d,", (int)hp.coords[i]);
    }
    assert(p - buf <= bufmax-2);       /* room for final letter and NUL */
    p[0] = hp.final_metatile;
    p[1] = '\0';

    sfree(hp.coords);
    return buf;
}

/* Shared code between validating and reading grid descs.
 * Always allocates hp->coords, whether or not it returns an error. */
static const char *grid_desc_to_hat_params(
    const char *desc, struct HatPatchParams *hp)
{
    size_t maxcoords;
    const char *p = desc;

    maxcoords = (strlen(desc) + 1) / 2;
    hp->coords = snewn(maxcoords, unsigned char);
    hp->ncoords = 0;

    while (isdigit((unsigned char)*p)) {
        const char *p_orig = p;
        int n = atoi(p);
        while (*p && isdigit((unsigned char)*p)) p++;
        if (*p != ',')
            return "expected ',' in grid description";
        if (p - p_orig > 2 || n > 0xFF)
            return "too-large coordinate in grid description";
        p++; /* eat the comma */

        /* This assert should be guaranteed by the way we calculated
         * maxcoords, so a failure of this check is a bug in this
         * function, not an indication of an invalid input string */
        assert(hp->ncoords < maxcoords);
        hp->coords[hp->ncoords++] = n;
    }

    if (*p == 'H' || *p == 'T' || *p == 'P' || *p == 'F')
        hp->final_metatile = *p;
    else
        return "invalid character in grid description";

    return NULL;
}

static const char *grid_validate_desc_hats(
    grid_type type, int width, int height, const char *desc)
{
    struct HatPatchParams hp;
    const char *error = NULL;

    if (!desc)
        return "Missing grid description string.";

    error = grid_desc_to_hat_params(desc, &hp);
    if (!error)
        error = hat_tiling_params_invalid(&hp);

    sfree(hp.coords);
    return error;
}

struct hatcontext {
    grid *g;
    tree234 *points;
};

static void grid_hats_callback(void *vctx, size_t nvertices, int *coords)
{
    struct hatcontext *ctx = (struct hatcontext *)vctx;
    size_t i;

    grid_face_add_new(ctx->g, nvertices);
    for (i = 0; i < nvertices; i++) {
        grid_dot *d = grid_get_dot(
            ctx->g, ctx->points,
            coords[2*i] * HATS_XUNIT,
            coords[2*i+1] * HATS_YUNIT);
        grid_face_set_dot(ctx->g, d, i);
    }
}

static grid *grid_new_hats(int width, int height, const char *desc)
{
    struct HatPatchParams hp;
    const char *error = NULL;

    error = grid_desc_to_hat_params(desc, &hp);
    assert(error == NULL && "grid_validate_desc_hats should have failed");

    struct hatcontext ctx[1];

    ctx->g = grid_empty();
    ctx->g->tilesize = HATS_TILESIZE;

    ctx->points = newtree234(grid_point_cmp_fn);

    hat_tiling_generate(&hp, width, height, grid_hats_callback, ctx);

    freetree234(ctx->points);
    sfree(hp.coords);

    grid_trim_vigorously(ctx->g);
    grid_make_consistent(ctx->g);
    return ctx->g;
}

#define SPECTRE_TILESIZE 32
#define SPECTRE_SQUARELEN 7
#define SPECTRE_UNIT 8

static const char *grid_validate_params_spectres(
    int width, int height)
{
    int l = SPECTRE_UNIT * SPECTRE_SQUARELEN;

    if (width > INT_MAX / l ||                  /* xextent */
        height > INT_MAX / l ||                 /* yextent */
        width > (INT_MAX / SPECTRE_SQUARELEN /
                 SPECTRE_SQUARELEN / height))   /* max_faces */
        return "Grid must not be unreasonably large";
    return NULL;
}

static void grid_size_spectres(int width, int height,
                               int *tilesize, int *xextent, int *yextent)
{
    *tilesize = SPECTRE_TILESIZE;
    *xextent = width * SPECTRE_UNIT * SPECTRE_SQUARELEN;
    *yextent = height * SPECTRE_UNIT * SPECTRE_SQUARELEN;
}

static char *grid_new_desc_spectres(
    grid_type type, int width, int height, random_state *rs)
{
    char *buf;
    size_t i;
    struct SpectrePatchParams sp;

    spectre_tiling_randomise(&sp, width * SPECTRE_SQUARELEN,
                             height * SPECTRE_SQUARELEN, rs);

    buf = snewn(sp.ncoords + 3, char);
    buf[0] = (sp.orientation < 10 ? '0' + sp.orientation :
              'A' + sp.orientation - 10);
    for (i = 0; i < sp.ncoords; i++) {
        assert(sp.coords[i] < 10);    /* all indices are 1 digit */
        buf[i+1] = '0' + sp.coords[i];
    }
    buf[sp.ncoords+1] = sp.final_hex;
    buf[sp.ncoords+2] = '\0';

    sfree(sp.coords);
    return buf;
}

/* Shared code between validating and reading grid descs.
 * Always allocates sp->coords, whether or not it returns an error. */
static const char *grid_desc_to_spectre_params(
    const char *desc, struct SpectrePatchParams *sp)
{
    size_t i;

    if (!*desc)
        return "empty grid description";

    sp->ncoords = strlen(desc) - 2;
    sp->coords = snewn(sp->ncoords, unsigned char);

    {
        char c = desc[0];
        if (isdigit((unsigned char)c))
            sp->orientation = c - '0';
        else if (c == 'A' || c == 'B')
            sp->orientation = 10 + c - 'A';
        else
            return "expected digit or A,B at start of grid description";
    }

    for (i = 0; i < sp->ncoords; i++) {
        char c = desc[i+1];
        if (!isdigit((unsigned char)c))
            return "expected digit in grid description";
        sp->coords[i] = c - '0';
    }

    sp->final_hex = desc[sp->ncoords+1];

    return NULL;
}

static const char *grid_validate_desc_spectres(
    grid_type type, int width, int height, const char *desc)
{
    struct SpectrePatchParams sp;
    const char *error = NULL;

    if (!desc)
        return "Missing grid description string.";

    error = grid_desc_to_spectre_params(desc, &sp);
    if (!error)
        error = spectre_tiling_params_invalid(&sp);

    sfree(sp.coords);
    return error;
}

struct spectrecontext {
    grid *g;
    tree234 *points;
};

static void grid_spectres_callback(void *vctx, const int *coords)
{
    struct spectrecontext *ctx = (struct spectrecontext *)vctx;
    size_t i;

    grid_face_add_new(ctx->g, SPECTRE_NVERTICES);
    for (i = 0; i < SPECTRE_NVERTICES; i++) {
        grid_dot *d = grid_get_dot(
            ctx->g, ctx->points,
            (coords[4*i+0] * SPECTRE_UNIT +
             n_times_root_k(coords[4*i+1] * SPECTRE_UNIT, 3)),
            (coords[4*i+2] * SPECTRE_UNIT +
             n_times_root_k(coords[4*i+3] * SPECTRE_UNIT, 3)));
        grid_face_set_dot(ctx->g, d, i);
    }
}

static grid *grid_new_spectres(int width, int height, const char *desc)
{
    struct SpectrePatchParams sp;
    const char *error = NULL;
    int width2 = width * SPECTRE_SQUARELEN;
    int height2 = height * SPECTRE_SQUARELEN;

    error = grid_desc_to_spectre_params(desc, &sp);
    assert(error == NULL && "grid_validate_desc_spectres should have failed");

    struct spectrecontext ctx[1];

    ctx->g = grid_empty();
    ctx->g->tilesize = SPECTRE_TILESIZE;

    ctx->points = newtree234(grid_point_cmp_fn);

    spectre_tiling_generate(&sp, width2, height2, grid_spectres_callback, ctx);

    freetree234(ctx->points);
    sfree(sp.coords);

    grid_trim_vigorously(ctx->g);
    grid_make_consistent(ctx->g);

    /*
     * As with the Penrose tiling, we're likely to have different
     * sized margins due to the lack of a neat grid that this tiling
     * fits on. So now we know what tiles we're left with, recentre
     * them.
     */
    {
        int w = width2 * SPECTRE_UNIT, h = height2 * SPECTRE_UNIT;
        ctx->g->lowest_x -= (w - (ctx->g->highest_x - ctx->g->lowest_x))/2;
        ctx->g->lowest_y -= (h - (ctx->g->highest_y - ctx->g->lowest_y))/2;
        ctx->g->highest_x = ctx->g->lowest_x + w;
        ctx->g->highest_y = ctx->g->lowest_y + h;
    }

    return ctx->g;
}

/* ----------- End of grid generators ------------- */

#define FNVAL(upper,lower) &grid_validate_params_ ## lower,
#define FNNEW(upper,lower) &grid_new_ ## lower,
#define FNSZ(upper,lower) &grid_size_ ## lower,

static const char *(*(grid_validate_paramses[]))(int, int) =
    { GRIDGEN_LIST(FNVAL) };
static grid *(*(grid_news[]))(int, int, const char*) = { GRIDGEN_LIST(FNNEW) };
static void(*(grid_sizes[]))(int, int, int*, int*, int*) = { GRIDGEN_LIST(FNSZ) };

/* Work out if a grid can be made, and complain if not. */

const char *grid_validate_params(grid_type type, int width, int height)
{
    if (width <= 0 || height <= 0)
        return "Width and height must both be positive";
    return grid_validate_paramses[type](width, height);
}

char *grid_new_desc(grid_type type, int width, int height, random_state *rs)
{
    if (type == GRID_PENROSE_P2 || type == GRID_PENROSE_P3) {
        return grid_new_desc_penrose(type, width, height, rs);
    } else if (type == GRID_HATS) {
        return grid_new_desc_hats(type, width, height, rs);
    } else if (type == GRID_SPECTRES) {
        return grid_new_desc_spectres(type, width, height, rs);
    } else if (type == GRID_TRIANGULAR) {
        return dupstr("0"); /* up-to-date version of triangular grid */
    } else {
        return NULL;
    }
}

const char *grid_validate_desc(grid_type type, int width, int height,
                               const char *desc)
{
    if (type == GRID_PENROSE_P2 || type == GRID_PENROSE_P3) {
        return grid_validate_desc_penrose(type, width, height, desc);
    } else if (type == GRID_HATS) {
        return grid_validate_desc_hats(type, width, height, desc);
    } else if (type == GRID_SPECTRES) {
        return grid_validate_desc_spectres(type, width, height, desc);
    } else if (type == GRID_TRIANGULAR) {
        return grid_validate_desc_triangular(type, width, height, desc);
    } else {
        if (desc != NULL)
            return "Grid description strings not used with this grid type";
        return NULL;
    }
}

grid *grid_new(grid_type type, int width, int height, const char *desc)
{
    const char *err = grid_validate_desc(type, width, height, desc);
    if (err) assert(!"Invalid grid description.");

    return grid_news[type](width, height, desc);
}

void grid_compute_size(grid_type type, int width, int height,
                       int *tilesize, int *xextent, int *yextent)
{
    grid_sizes[type](width, height, tilesize, xextent, yextent);
}

/* ----------- End of grid helpers ------------- */

/* vim: set shiftwidth=4 tabstop=8: */
generated by cgit v1.1 at 2026-04-28 04:08:02 +0000