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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;
}
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