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authorTavian Barnes <tavianator@tavianator.com>2014-08-19 17:10:03 -0400
committerTavian Barnes <tavianator@tavianator.com>2015-10-25 11:03:56 -0400
commit7b09710392d35fb55b52031d447a542d99fc6b4b (patch)
tree270eb927ee8c52ceeb99926ebf4843704775a610 /libdimension/torus.c
parent200c86b91ea7063d35be3bffc11c5da53c054653 (diff)
downloaddimension-7b09710392d35fb55b52031d447a542d99fc6b4b.tar.xz
Modularize the libdimension codebase.
Diffstat (limited to 'libdimension/torus.c')
-rw-r--r--libdimension/torus.c172
1 files changed, 0 insertions, 172 deletions
diff --git a/libdimension/torus.c b/libdimension/torus.c
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-/*************************************************************************
- * Copyright (C) 2010-2014 Tavian Barnes <tavianator@tavianator.com> *
- * *
- * This file is part of The Dimension Library. *
- * *
- * The Dimension Library is free software; you can redistribute it and/ *
- * or modify it under the terms of the GNU Lesser General Public License *
- * as published by the Free Software Foundation; either version 3 of the *
- * License, or (at your option) any later version. *
- * *
- * The Dimension Library is distributed in the hope that it will be *
- * useful, but WITHOUT ANY WARRANTY; without even the implied warranty *
- * of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
- * Lesser General Public License for more details. *
- * *
- * You should have received a copy of the GNU Lesser General Public *
- * License along with this program. If not, see *
- * <http://www.gnu.org/licenses/>. *
- *************************************************************************/
-
-/**
- * @file
- * Torii. A special case of a quartic.
- */
-
-#include "dimension.h"
-
-/// Torus type.
-typedef struct {
- dmnsn_object object;
- double major, minor;
-} dmnsn_torus;
-
-/// Bound the torus in a cylindrical shell.
-static inline bool
-dmnsn_torus_bound_intersection(const dmnsn_torus *torus, dmnsn_line l)
-{
- double R = torus->major, r = torus->minor;
- double rmax = R + r, rmin = R - r;
- double rmax2 = rmax*rmax, rmin2 = rmin*rmin;
-
- // Try the caps first
- double tlower = (-r - l.x0.y)/l.n.y;
- double tupper = (+r - l.x0.y)/l.n.y;
- dmnsn_vector lower = dmnsn_line_point(l, tlower);
- dmnsn_vector upper = dmnsn_line_point(l, tupper);
- double ldist2 = lower.x*lower.x + lower.z*lower.z;
- double udist2 = upper.x*upper.x + upper.z*upper.z;
- if ((ldist2 < rmin2 || ldist2 > rmax2) && (udist2 < rmin2 || udist2 > rmax2)) {
- // No valid intersection with the caps, try the cylinder walls
- double dist2 = l.x0.x*l.x0.x + l.x0.z*l.x0.z;
- double bigcyl[3], smallcyl[3];
- bigcyl[2] = smallcyl[2] = l.n.x*l.n.x + l.n.z*l.n.z;
- bigcyl[1] = smallcyl[1] = 2.0*(l.n.x*l.x0.x + l.n.z*l.x0.z);
- bigcyl[0] = dist2 - rmax2;
- smallcyl[0] = dist2 - rmin2;
-
- double x[4];
- size_t n = dmnsn_polynomial_solve(bigcyl, 2, x);
- n += dmnsn_polynomial_solve(smallcyl, 2, x + n);
-
- size_t i;
- for (i = 0; i < n; ++i) {
- dmnsn_vector p = dmnsn_line_point(l, x[i]);
- if (p.y >= -r && p.y <= r)
- break;
- }
-
- if (i == n) {
- // No valid intersection found
- return false;
- }
- }
-
- return true;
-}
-
-/// Torus intersection callback.
-static bool
-dmnsn_torus_intersection_fn(const dmnsn_object *object, dmnsn_line l,
- dmnsn_intersection *intersection)
-{
- const dmnsn_torus *torus = (const dmnsn_torus *)object;
- double R = torus->major, r = torus->minor;
- double RR = R*R, rr = r*r;
-
- if (!dmnsn_torus_bound_intersection(torus, l)) {
- return false;
- }
-
- // This bit of algebra here is correct
- dmnsn_vector x0mod = dmnsn_new_vector(l.x0.x, -l.x0.y, l.x0.z);
- dmnsn_vector nmod = dmnsn_new_vector(l.n.x, -l.n.y, l.n.z);
- double nn = dmnsn_vector_dot(l.n, l.n);
- double nx0 = dmnsn_vector_dot(l.n, l.x0);
- double x0x0 = dmnsn_vector_dot(l.x0, l.x0);
- double x0x0mod = dmnsn_vector_dot(l.x0, x0mod);
- double nx0mod = dmnsn_vector_dot(l.n, x0mod);
- double nnmod = dmnsn_vector_dot(l.n, nmod);
-
- double poly[5];
- poly[4] = nn*nn;
- poly[3] = 4*nn*nx0;
- poly[2] = 2.0*(nn*(x0x0 - rr) + 2.0*nx0*nx0 - RR*nnmod);
- poly[1] = 4.0*(nx0*(x0x0 - rr) - RR*nx0mod);
- poly[0] = x0x0*x0x0 + RR*(RR - 2.0*x0x0mod) - rr*(2.0*(RR + x0x0) - rr);
-
- double x[4];
- size_t n = dmnsn_polynomial_solve(poly, 4, x);
- if (n == 0)
- return false;
-
- double t = x[0];
- for (size_t i = 1; i < n; ++i) {
- t = dmnsn_min(t, x[i]);
- }
-
- if (t < 0.0) {
- return false;
- }
-
- dmnsn_vector p = dmnsn_line_point(l, t);
- dmnsn_vector center = dmnsn_vector_mul(
- R,
- dmnsn_vector_normalized(dmnsn_new_vector(p.x, 0.0, p.z))
- );
- dmnsn_vector normal = dmnsn_vector_sub(p, center);
-
- intersection->t = t;
- intersection->normal = normal;
- return true;
-}
-
-/// Torus inside callback.
-static bool
-dmnsn_torus_inside_fn(const dmnsn_object *object, dmnsn_vector point)
-{
- const dmnsn_torus *torus = (const dmnsn_torus *)object;
- double dmajor = torus->major - sqrt(point.x*point.x + point.z*point.z);
- return dmajor*dmajor + point.y*point.y < torus->minor*torus->minor;
-}
-
-/// Torus bounding callback.
-static dmnsn_bounding_box
-dmnsn_torus_bounding_fn(const dmnsn_object *object, dmnsn_matrix trans)
-{
- const dmnsn_torus *torus = (const dmnsn_torus *)object;
-
- double extent = torus->major + torus->minor;
- dmnsn_bounding_box box = dmnsn_symmetric_bounding_box(dmnsn_new_vector(extent, torus->minor, extent));
- return dmnsn_transform_bounding_box(trans, box);
-}
-
-/// Torus vtable.
-static const dmnsn_object_vtable dmnsn_torus_vtable = {
- .intersection_fn = dmnsn_torus_intersection_fn,
- .inside_fn = dmnsn_torus_inside_fn,
- .bounding_fn = dmnsn_torus_bounding_fn,
-};
-
-dmnsn_object *
-dmnsn_new_torus(dmnsn_pool *pool, double major, double minor)
-{
- dmnsn_torus *torus = DMNSN_PALLOC(pool, dmnsn_torus);
- torus->major = major;
- torus->minor = minor;
-
- dmnsn_object *object = &torus->object;
- dmnsn_init_object(object);
- object->vtable = &dmnsn_torus_vtable;
- return object;
-}