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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;
}
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