Generalize to 2-manifolds, refactor, improve

Moves some stuff to libfml

7 files changed, 465 insertions, 62 deletions

diff --git a/CMakeLists.txt b/CMakeLists.txt
index cd5836a..a99d693 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,6 +1,6 @@
 cmake_minimum_required (VERSION 2.6)
 project (fieldviz)
-add_executable(fieldviz src/main.cpp src/curve.cpp)
+add_executable(fieldviz src/main.cpp src/curve.cpp src/surface.cpp)
 
 add_definitions(-std=c++14 -O2 -g)
 
diff --git a/src/curve.cpp b/src/curve.cpp
index 19ce1a8..83bec06 100644
--- a/src/curve.cpp
+++ b/src/curve.cpp
@@ -31,7 +31,7 @@ vec3 Arc::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
 
     //cout << "R = " << r << ", dtheta = " << dtheta << endl;
 
-    quat rot = quat::from_angleaxis(dtheta, normal), crot = rot.conjugate();
+    quat rot = quat::from_angleaxis(dtheta, normal);
 
     //cout << "rot = " << rot << ", crot = " << crot << endl;
 
@@ -46,15 +46,13 @@ vec3 Arc::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
         vec3 ds = this->normal.cross(radius).normalize() * dl;
         sum += integrand(this->center + radius, ds);
 
-        radius = rot * radius * crot;
+        radius = radius.rotateby(rot);
     }
 
     if(l < len)
     {
         dl = len - l;
         dtheta = dl / r;
-        rot = quat::from_angleaxis(dtheta, normal);
-        crot = rot.conjugate();
 
         vec3 ds = this->normal.cross(radius).normalize() * dl;
         sum += integrand(this->center + radius, ds);
@@ -71,7 +69,7 @@ vec3 Spiral::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
 
     //cout << "R = " << r << ", dtheta = " << dtheta << endl;
 
-    quat rot = quat::from_angleaxis(dtheta, normal), crot = rot.conjugate();
+    quat rot = quat::from_angleaxis(dtheta, normal);
 
     //cout << "rot = " << rot << ", crot = " << crot << endl;
 
@@ -94,15 +92,13 @@ vec3 Spiral::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
         sum += integrand(this->origin + axis + radius, ds);
 
         /* rotate by dtheta about normal */
-        radius = rot * radius * crot;
+        radius = radius.rotateby(rot);
     }
 
     if(l < len)
     {
         dl = len - l;
         dtheta = dl / r;
-        rot = quat::from_angleaxis(dtheta, normal);
-        crot = rot.conjugate();
         dp = this->normal * dtheta * pitch / (2 * M_PI);
 
         vec3 ds = this->normal.cross(radius).normalize() * dl + dp;
@@ -137,9 +133,9 @@ vec3 Toroid::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
     vec3 minor_normal = this->major_normal.cross(this->major_radius).normalize();
 
     /* quaternion describing rotation of minor vector */
-    quat minor_rot = quat::from_angleaxis(minor_dtheta, minor_normal), minor_crot = minor_rot.conjugate();
+    quat minor_rot = quat::from_angleaxis(minor_dtheta, minor_normal);
 
-    quat major_rot = quat::from_angleaxis(major_dtheta, major_normal), major_crot = major_rot.conjugate();
+    quat major_rot = quat::from_angleaxis(major_dtheta, major_normal);
 
     vec3 sum = 0;
 
@@ -163,13 +159,12 @@ vec3 Toroid::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
          * radius */
         /* we also need to rotate the minor radius rotation quaternion
          * about the origin */
-        major_radius = major_rot * major_radius * major_crot;
-        minor_normal = major_rot * minor_normal * major_crot;
+        major_radius = major_radius.rotateby(major_rot);
+        minor_normal = minor_normal.rotateby(major_rot);
 
-        minor_radius = minor_rot * minor_radius * minor_crot;
+        minor_radius = minor_radius.rotateby(minor_rot);
 
         minor_rot = quat::from_angleaxis(minor_dtheta, minor_normal);
-        minor_crot = minor_rot.conjugate();
         //minor_rot = major_rot * minor_rot;
         //minor_crot = minor_rot.conjugate();
 
@@ -193,4 +188,3 @@ vec3 Toroid::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
 
     return sum;
 }
-
diff --git a/src/curve.h b/src/curve.h
index 891a6af..a3d743a 100644
--- a/src/curve.h
+++ b/src/curve.h
@@ -4,16 +4,19 @@
 #include <cmath>
 #include <iostream>
 #include <fml/fml.h>
+
+#include "manifold.h"
+
 using namespace fml;
 
-/* All curves inherit this class */
-class Curve {
+/* All curves inherit this class (which is empty because Manifold has
+ * everything we need). */
+class Curve : public Manifold {
 public:
-    virtual vec3 integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar delta) const = 0;
-    virtual const char *name() const = 0;
+    const int dimension() const { return 1; }
 };
 
-class LineSegment : Curve {
+class LineSegment : public Curve {
 private:
     vec3 a, b;
 public:
@@ -28,7 +31,7 @@ public:
 
 std::istream operator>>(std::istream &is, LineSegment &ls);
 
-class Arc : Curve {
+class Arc : public Curve {
 private:
     vec3 center;
 
@@ -50,7 +53,7 @@ public:
 
 std::istream operator>>(std::istream &is, LineSegment &ls);
 
-class Spiral : Curve {
+class Spiral : public Curve {
 private:
     vec3 origin;
 
@@ -75,7 +78,7 @@ public:
 
 std::istream operator>>(std::istream &is, LineSegment &ls);
 
-class Toroid : Curve {
+class Toroid : public Curve {
 private:
     vec3 origin;
 
diff --git a/src/main.cpp b/src/main.cpp
index b6b6c10..f56209f 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -1,11 +1,12 @@
 #include <cmath>
+#include <csignal>
 #include <cstdlib>
 #include <fstream>
 #include <iostream>
+#include <map>
 #include <sstream>
 #include <sys/stat.h>
 #include <sys/types.h>
-#include <vector>
 
 #include <readline/readline.h>
 #include <readline/history.h>
@@ -13,8 +14,12 @@
 #include "gnuplot_i.hpp"
 
 #include "curve.h"
+#include "surface.h"
 #include <fml/fml.h>
 
+// under $HOME
+#define HISTORY_FILE ".fieldviz_history"
+
 using namespace fml;
 using namespace std;
 
@@ -27,7 +32,7 @@ struct Entity {
         scalar I; /* current */
     };
 
-    Curve *path;
+    Manifold *path;
 };
 
 vec3 point;
@@ -56,30 +61,31 @@ vec3 dE(vec3 s, vec3 ds)
     return rnorm * ds.magnitude() / r2;
 }
 
-vector<Entity> entities;
+int ent_counter = 0;
+map<int, Entity> entities;
 
-int add_current(scalar I, Curve *path)
+int add_entity(Entity e)
 {
-    Entity n = { Entity::CURRENT, I, path };
-    entities.push_back(n);
-
-    /* index */
-    return entities.size() - 1;
+    entities[ent_counter] = e;
+    return ent_counter++;
 }
 
-int add_charge(scalar Q_density, Curve *path)
+int add_current(scalar I, Manifold *path)
 {
-    Entity n = { Entity::CHARGE, Q_density, path };
-    entities.push_back(n);
+    return add_entity((Entity){ Entity::CURRENT, I, path });
+}
 
-    return entities.size() - 1;
+int add_charge(scalar Q_density, Manifold *path)
+{
+    return add_entity((Entity){ Entity::CHARGE, Q_density, path });
 }
 
 const scalar U0 = 4e-7 * M_PI;
 const scalar C = 299792458;
 const scalar E0 = 1 / ( U0 * C * C );
 const scalar K_E = 1 / (4 * M_PI * E0);
-const scalar D = 1e-2;
+const scalar DEFAULT_D = 1e-1;
+scalar D = DEFAULT_D;
 
 vec3 calc_Bfield(vec3 x)
 {
@@ -87,10 +93,11 @@ vec3 calc_Bfield(vec3 x)
 
     vec3 B = 0;
 
-    for(int i = 0; i < entities.size(); i++)
+    for(map<int, Entity>::iterator i = entities.begin(); i != entities.end(); i++)
     {
-        if(entities[i].type == Entity::CURRENT)
-            B += entities[i].path->integrate(dB, D) * U0 * entities[i].I;
+        Entity &e = i->second;
+        if(e.type == Entity::CURRENT)
+            B += e.path->integrate(dB, D) * U0 * e.I;
     }
 
     return B;
@@ -102,10 +109,11 @@ vec3 calc_Efield(vec3 x)
 
     vec3 E = 0;
 
-    for(int i = 0; i < entities.size(); i++)
+    for(map<int, Entity>::iterator i = entities.begin(); i != entities.end(); i++)
     {
-        if(entities[i].type == Entity::CHARGE)
-            E += entities[i].path->integrate(dE, D) * K_E * entities[i].Q_density;
+        Entity &e = i->second;
+        if(e.type == Entity::CHARGE)
+            E += e.path->integrate(dE, D) * K_E * e.Q_density;
     }
 
     return E;
@@ -120,20 +128,21 @@ vec3 dump(vec3 s, vec3 ds)
     return 0;
 }
 
-void dump_path(ostream &out, Curve *c)
+void dump_points(ostream &out, Manifold *c)
 {
     dump_ofs = &out;
     c->integrate(dump, D);
 }
 
-int dump_entities(ostream &out, int which, vector<Entity> &e)
+int dump_entities(ostream &out, int which, map<int, Entity> &en)
 {
     int count = 0;
-    for(int i = 0; i < e.size(); i++)
+    for(map<int, Entity>::iterator i = en.begin(); i != en.end(); i++)
     {
-        if(which & e[i].type)
+        Entity &e = i->second;
+        if(which & e.type)
         {
-            dump_path(out, e[i].path);
+            dump_points(out, e.path);
 
             /* two blank lines mark an index in gnuplot */
             out << endl << endl;
@@ -141,6 +150,7 @@ int dump_entities(ostream &out, int which, vector<Entity> &e)
             count++;
         }
     }
+
     return count;
 }
 
@@ -189,8 +199,6 @@ void dump_values(vec3 start, vec3 del, int times)
     point = start;
     while(times--)
     {
-
-
         point += del;
     }
 }
@@ -208,7 +216,7 @@ string itoa(int n)
     return ss.str();
 }
 
-Curve *parse_curve(stringstream &ss)
+Manifold *parse_curve(stringstream &ss)
 {
     string type;
     ss >> type;
@@ -242,6 +250,41 @@ Curve *parse_curve(stringstream &ss)
 
         return (Curve*)new Toroid(origin, maj_radius, maj_normal, maj_angle, min_radius, pitch);
     }
+    else if(type == "plane")
+    {
+        vec3 origin, v1, v2;
+        ss >> origin >> v1 >> v2;
+        return (Surface*)new Plane(origin, v1, v2);
+    }
+    else if(type == "disk")
+    {
+        vec3 center, radius, normal;
+        scalar angle;
+        ss >> center >> radius >> normal >> angle;
+        return (Surface*)new Disk(center, radius, normal, angle);
+    }
+    else if(type == "sphere")
+    {
+        vec3 center;
+        scalar radius;
+        ss >> center >> radius;
+
+        return (Surface*)new Sphere(center, radius);
+    }
+    else if(type == "opencylinder")
+    {
+        vec3 origin, axis;
+        scalar rad;
+        ss >> origin >> axis >> rad;
+        return (Surface*)new OpenCylinder(origin, axis, rad);
+    }
+    else if(type == "closedcylinder")
+    {
+        vec3 origin, axis;
+        scalar rad;
+        ss >> origin >> axis >> rad;
+        return (Surface*)new ClosedCylinder(origin, axis, rad);
+    }
     else throw "unknown curve type (must be line, arc, spiral, or toroid)";
 }
 
@@ -252,13 +295,21 @@ void print_help()
     cout << "Copyright (C) 2019 Franklin Wei" << endl << endl;
 
     cout << "Commands:" << endl;
-    cout << "  add {I CURRENT|Q DENSITY} CURVE" << endl;
-    cout << "    Add an entity of the specified type and the shape CURVE, where CURVE is one" << endl;
+    cout << "  add {I CURRENT|Q DENSITY} MANIFOLD" << endl;
+    cout << "    Add an entity of the specified type and the shape MANIFOLD, which can be:" << endl;
     cout << "    of (<X> is a 3-tuple specifying a vector):" << endl;
+    cout << "     1-manifolds:" << endl;
     cout << "      line <a> <b>" << endl;
     cout << "      arc <center> <radius> <normal> angle" << endl;
     cout << "      solenoid <center> <radius> <normal> angle pitch" << endl;
     cout << "      toroid <center> <radius> <maj_normal> min_radius maj_angle pitch" << endl;
+    cout << "     2-manifolds:" << endl;
+    cout << "      plane <origin> <vec1> <vec2>" << endl;
+    cout << "      disk <center> <radius> <normal> angle" << endl;
+    cout << "      sphere <center> radius" << endl;
+    cout << endl;
+    cout << "  delete [ID..]" << endl;
+    cout << "    Delete an entity by its previously returned identifier." << endl;
     cout << endl;
     cout << "  draw [I|Q] ..." << endl;
     cout << "    Draw the specified current/charge distributions" << endl;
@@ -266,16 +317,51 @@ void print_help()
     cout << "  field [E|B] <lower_corner> <upper_corner> DELTA" << endl;
     cout << "    Plot the E or B field in the rectangular prism bounded by lower and upper." << endl;
     cout << "    DELTA specifies density." << endl;
+    cout << endl;
+    cout << "  newwindow" << endl;
+    cout << "    Make future plots go into a new window" << endl;
+    cout << endl;
+    cout << "  delta D" << endl;
+    cout << "    Set integration fineness to D (smaller is better but slower)" << endl;
+}
+
+vec3 dA(vec3 s, vec3 dA)
+{
+    /* will cast to vec3 */
+    return dA.magnitude();
+}
+
+string hist_path;
+
+void exit_handler()
+{
+    write_history(hist_path.c_str());
+}
+
+void int_handler(int a)
+{
+    (void) a;
+    exit(0);
 }
 
 int main(int argc, char *argv[])
 {
-    Toroid loop(vec3(0, 0, 0), vec3(1, 0, 0), vec3(0, 0, 1), M_PI * 2, .1, 2*M_PI / 10);
-    //add_current(1, (Curve*)&loop);
+    Surface *surf = new Sphere(vec3(0, 0, 1), 1);
+    cout << "Area of 10x10 square = " << surf->integrate(dA, D) << endl;
+
+    hist_path = getenv("HOME");
+    hist_path += "/";
+    hist_path += HISTORY_FILE;
+
+    using_history();
+    read_history(hist_path.c_str());
+    atexit(exit_handler);
+    signal(SIGINT, int_handler);
 
     Gnuplot *gp = NULL;
 
     try {
+        Gnuplot::set_terminal_std("qt");
         gp = new Gnuplot();
     }
     catch(GnuplotException e) {
@@ -288,17 +374,20 @@ int main(int argc, char *argv[])
     cout << "Welcome to fieldviz!" << endl << endl;
     cout << "Type `help' for a command listing." << endl;
 
+    /* will change to replot on subsequent commands */
+    string plot_cmd = "splot";
+
     while(1)
     {
         char *cs = readline("fieldviz> ");
         if(!cs)
             return 0;
         add_history(cs);
-        
+
         string line(cs);
 
         free(cs);
-        
+
         all_lower(line);
 
         /* parse */
@@ -320,9 +409,9 @@ int main(int argc, char *argv[])
                 double val;
                 ss >> val;
 
-                Curve *path = parse_curve(ss);
+                Manifold *path = parse_curve(ss);
 
-                cout << "Curve type: " << path->name() << endl;
+                cout << "Manifold type: " << path->name() << endl;
 
                 int idx;
                 if(type == "i")
@@ -333,6 +422,17 @@ int main(int argc, char *argv[])
 
                 cout << "Index: " << idx << endl;
             }
+            else if(cmd == "delete")
+            {
+                int id;
+                while(ss >> id)
+                {
+                    if(entities.erase(id))
+                        cout << "Deleted " << id << "." << endl;
+                    else
+                        cerr << "No entity " << id << "!" << endl;
+                }
+            }
             else if(cmd == "field")
             {
                 string type;
@@ -354,8 +454,10 @@ int main(int argc, char *argv[])
 
                 out.close();
 
-                string cmd = "splot '" + fname + "' w vectors";
+                string cmd = plot_cmd + " '" + fname + "' w vectors";
                 *gp << cmd;
+
+                plot_cmd = "replot";
             }
             else if(cmd == "draw")
             {
@@ -384,11 +486,28 @@ int main(int argc, char *argv[])
                                       entities);
                 out.close();
 
-                string cmd = "splot for[i = 0:" + itoa(n - 1) + "] '" + fname + "' i i w lines";
+                string cmd = plot_cmd + " for[i = 0:" + itoa(n - 1) + "] '" + fname + "' i i w vectors";
                 *gp << cmd;
+
+                plot_cmd = "replot";
+            }
+            else if(cmd == "delta")
+            {
+                ss >> D;
+                if(D <= 0)
+                {
+                    cerr << "D must be positive and non-zero!" << endl;
+                    D = DEFAULT_D;
+                }
+            }
+            else if(cmd == "newwindow")
+            {
+                plot_cmd = "splot";
             }
             else if(cmd == "help")
                 print_help();
+            else
+                cerr << "invalid" << endl;
         } catch(const char *err) {
             cerr << "parse error: " << err << endl;
         }
diff --git a/src/manifold.h b/src/manifold.h
new file mode 100644
index 0000000..f7fad5b
--- /dev/null
+++ b/src/manifold.h
@@ -0,0 +1,17 @@
+#ifndef MANIFOLD_H
+#define MANIFOLD_H
+
+#include <cmath>
+#include <iostream>
+#include <fml/fml.h>
+using namespace fml;
+
+/* All manifolds inherit this class */
+class Manifold {
+public:
+    virtual vec3 integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar delta) const = 0;
+    virtual const char *name() const = 0;
+    virtual const int dimension() const = 0; // 0 = point, 1 = curve, 2 = surface, 3 = solid
+};
+
+#endif
diff --git a/src/surface.cpp b/src/surface.cpp
new file mode 100644
index 0000000..8ab52d4
--- /dev/null
+++ b/src/surface.cpp
@@ -0,0 +1,149 @@
+#include <iostream>
+#include <cmath>
+#include "surface.h"
+
+vec3 Plane::integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const
+{
+    vec3 sum = 0;
+
+    vec3 dA = (d * this->v1).cross(d * this->v2);
+
+    for(scalar s = 0; s < 1; s += d)
+        for(scalar t = 0; t < 1; t += d)
+        {
+            vec3 p = this->p0 + s * this->v1 + t * this->v2;
+            sum += integrand(p, dA);
+        }
+    return sum;
+}
+
+vec3 Disk::integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar dr) const
+{
+    vec3 sum = 0;
+
+    scalar radius = this->radius.magnitude();
+    vec3 radnorm = this->radius.normalize();
+
+    /* chosen so that the outermost ring will consist of square area
+     * elements */
+    scalar dtheta = dr / radius;
+
+    quat rot = quat::from_angleaxis(dtheta, this->normal);
+
+    for(scalar r = 0; r < radius; r += dr)
+    {
+        vec3 s = this->center + radnorm * r;
+
+        /* area element is constant for given r */
+        vec3 dA = this->normal * r * dr * dtheta;
+
+        for(scalar theta = 0; theta < this->angle; theta += dtheta)
+        {
+            sum += integrand(s, dA);
+
+            s = s.rotateby(rot);
+        }
+    }
+
+    return sum;
+}
+
+vec3 Sphere::integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const
+{
+    vec3 sum = 0;
+    /*
+     * Coordinate reference (right-handed):
+     *
+     *  ^ z
+     *  |
+     *  |    ^ y
+     *  |   /
+     *  |  /
+     *  | /
+     *  |/
+     *  O---------> x
+     *
+     */
+
+    /* we will rotate this unit vector clockwise in the X-Z plane by d
+     * each outer loop (scale and offset later) */
+    vec3 rad = vec3(0, 0, 1.0);
+
+    scalar r_sq = this->radius * this->radius;
+
+    quat roty = quat::from_angleaxis(d, vec3(0, 1, 0));
+    quat rotz = quat::from_angleaxis(d, vec3(0, 0, 1));
+
+    for(scalar phi = 0; phi < M_PI; phi += d)
+    {
+        /* operate on a copy to avoid accumulating roundoff error */
+        vec3 rad2 = rad;
+
+        /* from Jacobian: dA = r^2 * sin(phi) * dphi * dtheta */
+        scalar dA = r_sq * sin(phi) * d * d;
+
+        for(scalar theta = 0; theta < 2*M_PI; theta += d)
+        {
+            sum += integrand(this->center + this->radius * rad2, dA * rad2);
+
+            /* rotate rad2 around the z axis */
+            rad2 = rad2.rotateby(rotz);
+        }
+
+        /* rotate radius clockwise around y */
+        rad = rad.rotateby(roty);
+    }
+
+    return sum;
+}
+
+vec3 OpenCylinder::integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const
+{
+    /*
+     * We loop along the axis length, rotating a vector around it as
+     * we go.
+     *
+     * Offset is trivial.
+     *
+     *        rad/v
+     *          ^       x
+     *         .|x     . x
+     *        . | x   .   x
+     *    O-------x-------------> axis
+     *    x   .   x   .   x   .
+     *     x .     x .     x .
+     *      x       x       x
+     *
+     */
+
+    /* TODO: normalize d so all integrals run in 1/d^n time? */
+
+    vec3 v = vec3::any_unit_normal(this->axis);
+    quat rot = quat::from_angleaxis(d, this->axis);
+
+    scalar axis_len = this->axis.magnitude();
+    vec3 norm_axis = this->axis.normalize();
+
+    vec3 sum = 0;
+
+    for(scalar l = 0; l < axis_len; l += d)
+    {
+        vec3 rad = v;
+        for(scalar theta = 0; theta < 2*M_PI; theta += d)
+        {
+            sum += integrand(this->origin + l * norm_axis + this->radius * rad, rad);
+            rad = rad.rotateby(rot);
+        }
+    }
+
+    return sum;
+}
+
+vec3 ClosedCylinder::integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const
+{
+    vec3 sum = OpenCylinder::integrate(integrand, d);
+
+    sum += cap1.integrate(integrand, d) + cap2.integrate(integrand, d);
+
+    return sum;
+}
diff --git a/src/surface.h b/src/surface.h
new file mode 100644
index 0000000..4726521
--- /dev/null
+++ b/src/surface.h
@@ -0,0 +1,121 @@
+#ifndef SURFACE_H
+#define SURFACE_H
+
+#include <fml/fml.h>
+#include "manifold.h"
+
+using namespace fml;
+
+/* All surfaces inherit this class */
+/* The exact meaning of d is surface-dependent (see class
+ * definitions below); the limit of the calculated integral must
+ * approach its true value as d->0. d must be > 0. */
+class Surface : public Manifold {
+public:
+    const int dimension() const { return 2; }
+};
+
+class Plane : public Surface {
+private:
+    /* The surface is specified by all points p = p0 + s v1 + t v2,
+     * such that 0 <= {s, t} < 1
+     *
+     * v1 and v2 must NOT be parallel.
+     *
+     * v1 and v2 should (but do not have to be) be normal (this is
+     * motivated primarily by usability; if the two vectors are indeed
+     * normal, then m1 and m2 have the nice geometric meaning of side
+     * length).
+     *
+     * d = ds = dt.
+     * dA will be in the direction of v1 x v2.
+     */
+    vec3 p0, v1, v2;
+
+public:
+    Plane(vec3 p, vec3 _v1, vec3 _v2) : p0(p), v1(_v1), v2(_v2) {};
+
+    vec3 integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const;
+    const char *name() const { return "Plane"; }
+};
+
+/* Flat, circular disk (of varying extent) */
+class Disk : public Surface {
+private:
+    /* This represents a (possibly incomplete) circular disk in space,
+     * with a center, radius, and normal vector as specified.
+     *
+     * `angle' specifies the extent of the disk; angle=2pi for a full
+     * circle.
+     *
+     * We use:
+     * d = dr.
+     * d_theta = d / r.
+     *
+     * This makes it so that differential area elements on the edge of
+     * the disk are square.
+     *
+     * dA will be in the direction of normal.
+     */
+    vec3 center, radius, normal;
+    scalar angle;
+
+public:
+    Disk(vec3 c, vec3 r, vec3 n, scalar a) : center(c), radius(r), normal(n), angle(a) {};
+
+    vec3 integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const;
+    const char *name() const { return "Disk"; }
+};
+
+/* Hollow, spherical shell */
+class Sphere : public Surface {
+private:
+    /* d = dtheta = dphi */
+
+    vec3 center;
+    scalar radius;
+
+public:
+    Sphere(vec3 c, scalar r) : center(c), radius(r) {};
+
+    vec3 integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const;
+    const char *name() const { return "Sphere"; }
+};
+
+/* Cylinder without end caps */
+class OpenCylinder : public Surface {
+private:
+    /* Like this:
+     *
+     *         ___________________
+     *        / \                 \
+     *       origin ---------------> axis
+     *        \_/_________________/
+     *
+     */
+
+    vec3 origin, axis;
+    scalar radius;
+
+public:
+    OpenCylinder(vec3 o, vec3 a, scalar r) : origin(o), axis(a), radius(r) {}
+
+    vec3 integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const;
+    const char *name() const { return "OpenCylinder"; }
+};
+
+/* Capped cylinder */
+class ClosedCylinder : public OpenCylinder {
+private:
+    Disk cap1, cap2;
+
+public:
+    ClosedCylinder(vec3 o, vec3 a, scalar r) : OpenCylinder(o, a, r),
+                                               cap1(o, vec3::any_unit_normal(a), -a.normalize(), 2*M_PI),
+                                               cap2(o + a, vec3::any_unit_normal(a), a.normalize(), 2*M_PI) {}
+
+    vec3 integrate(vec3 (*integrand)(vec3 s, vec3 dA), scalar d) const;
+    const char *name() const { return "ClosedCylinder"; }
+};
+
+#endif