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+/*************************************************************************
+ * Copyright (C) 2009-2010 Tavian Barnes <tavianator@gmail.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/>. *
+ *************************************************************************/
+
+#include "dimension.h"
+
+/*
+ * Torus - special case of a quartic
+ */
+
+/* Torus object callbacks */
+
+static bool dmnsn_torus_intersection_fn(const dmnsn_object *torus,
+ dmnsn_line line,
+ dmnsn_intersection *intersection);
+static bool dmnsn_torus_inside_fn(const dmnsn_object *torus,
+ dmnsn_vector point);
+
+/* Payload type */
+typedef struct dmnsn_torus_payload {
+ double major, minor;
+} dmnsn_torus_payload;
+
+/* Allocate a new torus */
+dmnsn_object *
+dmnsn_new_torus(double major, double minor)
+{
+ dmnsn_object *torus = dmnsn_new_object();
+ torus->intersection_fn = &dmnsn_torus_intersection_fn;
+ torus->inside_fn = &dmnsn_torus_inside_fn;
+ torus->bounding_box.min = dmnsn_new_vector(-(major + minor),
+ -minor,
+ -(major + minor));
+ torus->bounding_box.max = dmnsn_new_vector(major + minor,
+ minor,
+ major + minor);
+
+ dmnsn_torus_payload *payload = dmnsn_malloc(sizeof(dmnsn_torus_payload));
+ payload->major = major;
+ payload->minor = minor;
+ torus->ptr = payload;
+ torus->free_fn = &dmnsn_free;
+ return torus;
+}
+
+/* Returns the closest intersection of `line' with `torus' */
+static bool
+dmnsn_torus_intersection_fn(const dmnsn_object *torus, dmnsn_line line,
+ dmnsn_intersection *intersection)
+{
+ dmnsn_line l = dmnsn_transform_line(torus->trans_inv, line);
+ const dmnsn_torus_payload *payload = torus->ptr;
+ double R2 = payload->major*payload->major, r2 = payload->minor*payload->minor;
+
+ /* This bit of algebra here is correct, and can be verified with a CAS */
+ 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 - r2) + 2.0*nx0*nx0 - R2*nnmod);
+ poly[1] = 4.0*(nx0*(x0x0 - r2) - R2*nx0mod);
+ poly[0] = x0x0*x0x0 + R2*(R2 - 2.0*x0x0mod) - r2*(2.0*(R2 + x0x0) - r2);
+
+ double x[4];
+ size_t n = dmnsn_solve_polynomial(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(
+ payload->major,
+ dmnsn_vector_normalize(dmnsn_new_vector(p.x, 0.0, p.z))
+ );
+ dmnsn_vector normal = dmnsn_vector_normalize(dmnsn_vector_sub(p, center));
+ intersection->ray = line;
+ intersection->t = t;
+ intersection->normal = dmnsn_transform_normal(torus->trans, normal);
+ intersection->texture = torus->texture;
+ intersection->interior = torus->interior;
+ return true;
+}
+
+/* Return whether a point is inside a torus */
+static bool
+dmnsn_torus_inside_fn(const dmnsn_object *torus, dmnsn_vector point)
+{
+ point = dmnsn_transform_vector(torus->trans_inv, point);
+ const dmnsn_torus_payload *payload = torus->ptr;
+ double dmajor = payload->major - sqrt(point.x*point.x + point.z*point.z);
+ return dmajor*dmajor + point.y*point.y < payload->minor*payload->minor;
+}