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-rw-r--r--src/curve.cpp192
-rw-r--r--src/surface.cpp151
2 files changed, 343 insertions, 0 deletions
diff --git a/src/curve.cpp b/src/curve.cpp
new file mode 100644
index 0000000..0b49bef
--- /dev/null
+++ b/src/curve.cpp
@@ -0,0 +1,192 @@
+#include <iostream>
+#include <cmath>
+#include <fml/curve.h>
+
+using namespace std;
+
+namespace fml {
+ vec3 LineSegment::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
+ {
+ vec3 diff = this->b - this->a, sum = 0;
+
+ scalar len = diff.magnitude();
+
+ vec3 diffnorm = diff / len, s = this->a, ds = diffnorm * dl;
+
+ scalar l;
+
+ for(l = 0; l < len; l += dl, s += ds)
+ sum += integrand(s, ds);
+
+ if(l < len)
+ sum += integrand(s, diffnorm * (len - l));
+
+ return sum;
+ }
+
+ vec3 Arc::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
+ {
+ //cout << "Integrating loop of length " << this->angle << " radians" << endl;
+
+ scalar r = this->radius.magnitude(), dtheta = dl / r;
+
+ //cout << "R = " << r << ", dtheta = " << dtheta << endl;
+
+ quat rot = quat::from_angleaxis(dtheta, normal);
+
+ //cout << "rot = " << rot << ", crot = " << crot << endl;
+
+ scalar len = this->angle * r, l;
+
+ vec3 sum = 0;
+
+ quat radius = this->radius;
+
+ for(l = 0; l < len; l += dl)
+ {
+ vec3 ds = this->normal.cross(radius).normalize() * dl;
+ sum += integrand(this->center + radius, ds);
+
+ radius = radius.rotateby(rot);
+ }
+
+ if(l < len)
+ {
+ dl = len - l;
+ dtheta = dl / r;
+
+ vec3 ds = this->normal.cross(radius).normalize() * dl;
+ sum += integrand(this->center + radius, ds);
+ }
+
+ return sum;
+ }
+
+ vec3 Spiral::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
+ {
+ //cout << "Integrating loop of length " << this->angle << " radians" << endl;
+
+ scalar r = this->radius.magnitude(), dtheta = dl / r;
+
+ //cout << "R = " << r << ", dtheta = " << dtheta << endl;
+
+ quat rot = quat::from_angleaxis(dtheta, normal);
+
+ //cout << "rot = " << rot << ", crot = " << crot << endl;
+
+ /* only flat (doesn't include stretched length) */
+ scalar len = this->angle * r, l;
+
+ vec3 sum = 0;
+
+ quat radius = this->radius;
+
+ /* how far along the axis we've moved */
+ vec3 axis = 0;
+
+ /* we add this axial component each iteration */
+ vec3 dp = this->normal * dtheta * pitch / (2 * M_PI);
+
+ for(l = 0; l < len; l += dl, axis += dp)
+ {
+ vec3 ds = this->normal.cross(radius).normalize() * dl + dp;
+ sum += integrand(this->origin + axis + radius, ds);
+
+ /* rotate by dtheta about normal */
+ radius = radius.rotateby(rot);
+ }
+
+ if(l < len)
+ {
+ dl = len - l;
+ dtheta = dl / r;
+ dp = this->normal * dtheta * pitch / (2 * M_PI);
+
+ vec3 ds = this->normal.cross(radius).normalize() * dl + dp;
+ sum += integrand(this->origin + axis + radius, ds);
+ }
+
+ return sum;
+ }
+
+ vec3 Toroid::integrate(vec3 (*integrand)(vec3 s, vec3 ds), scalar dl) const
+ {
+ /* this applies to the minor rotation */
+ scalar minor_r = this->minor_r;
+
+ scalar major_r = this->major_radius.magnitude();
+
+ /* how far parallel to the major median each dl takes us */
+ scalar pitch_length = this->pitch * major_r;
+
+ scalar dpar = this->pitch * dl / (2 * M_PI * sqrt(minor_r * minor_r + pitch_length * pitch_length)) * major_r;
+
+ /* how far each dl rotates the major vector */
+ scalar major_dtheta = dpar / major_r;
+
+ /* how long perpendicular to the major median each dl takes us (from
+ * Pythagoras) */
+ scalar dper = sqrt(dl * dl - dpar * dpar);
+
+ scalar minor_dtheta = dper / minor_r;
+
+ /* minor normal is binormal to major normal and radius */
+ 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);
+
+ quat major_rot = quat::from_angleaxis(major_dtheta, major_normal);
+
+ vec3 sum = 0;
+
+ quat major_radius = this->major_radius;
+ quat minor_radius = this->major_radius.normalize() * this->minor_r;
+
+ //cout << "minor_dtheta = " << minor_dtheta << endl;
+ //cout << "minor_dper = " << dper << endl;
+ //cout << "dl = " << dl << endl;
+ //cout << "dpar = " << dpar << endl;
+ //cout << "pitch = " << this->pitch << endl;
+
+ for(scalar theta = 0; theta < this->major_angle; theta += major_dtheta)
+ {
+ vec3 dpar_vec = minor_normal * dpar;
+ vec3 ds = minor_normal.cross(minor_radius).normalize() * dper + dpar_vec;
+ sum += integrand(this->origin + major_radius + minor_radius, ds);
+
+ /* we need to rotate some vectors: first the major radius and
+ * minor normal about the major normal, and then the minor
+ * radius */
+ /* we also need to rotate the minor radius rotation quaternion
+ * about the origin */
+ major_radius = major_radius.rotateby(major_rot);
+ minor_normal = minor_normal.rotateby(major_rot);
+
+ minor_radius = minor_radius.rotateby(minor_rot);
+
+ minor_rot = quat::from_angleaxis(minor_dtheta, minor_normal);
+ //minor_rot = major_rot * minor_rot;
+ //minor_crot = minor_rot.conjugate();
+
+ //cout << "Minor radius is " << minor_radius << endl;
+ //cout << "Minor rot quat is " << minor_rot << endl;
+ }
+
+#if 0
+ 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;
+ sum += integrand(this->origin + axis + radius, ds);
+ }
+#endif
+
+ return sum;
+ }
+}
diff --git a/src/surface.cpp b/src/surface.cpp
new file mode 100644
index 0000000..e3fb061
--- /dev/null
+++ b/src/surface.cpp
@@ -0,0 +1,151 @@
+#include <iostream>
+#include <cmath>
+#include <fml/surface.h>
+
+namespace fml {
+ 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;
+ }
+}
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