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/*************************************************************************
* Copyright (C) 2010-2011 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 payload type. */
typedef struct dmnsn_torus_payload {
double major, minor;
} dmnsn_torus_payload;
/** Bound the torus in a cylindrical shell. */
static inline bool
dmnsn_torus_bound_intersection(const dmnsn_torus_payload *payload, dmnsn_line l)
{
double R = payload->major, r = payload->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_solve_polynomial(bigcyl, 2, x);
n += dmnsn_solve_polynomial(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 *torus, dmnsn_line l,
dmnsn_intersection *intersection)
{
const dmnsn_torus_payload *payload = torus->ptr;
double R = payload->major, r = payload->minor;
double R2 = R*R, r2 = r*r;
if (!dmnsn_torus_bound_intersection(payload, 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 - 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_normalized(dmnsn_new_vector(p.x, 0.0, p.z))
);
dmnsn_vector normal = dmnsn_vector_normalized(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 *torus, dmnsn_vector 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;
}
/* 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;
}
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