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Diffstat (limited to 'libdimension/torus.c')
| -rw-r--r-- | libdimension/torus.c | 123 |
1 files changed, 123 insertions, 0 deletions
diff --git a/libdimension/torus.c b/libdimension/torus.c new file mode 100644 index 0000000..8e53f99 --- /dev/null +++ b/libdimension/torus.c @@ -0,0 +1,123 @@ +/************************************************************************* + * 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; +} |