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/*************************************************************************
* Copyright (C) 2009-2014 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
* Spheres.
*/
#include "dimension-internal.h"
/// Sphere intersection callback.
static bool
dmnsn_sphere_intersection_fn(const dmnsn_object *sphere, dmnsn_line l,
dmnsn_intersection *intersection)
{
// Solve (x0 + nx*t)^2 + (y0 + ny*t)^2 + (z0 + nz*t)^2 == 1
double poly[3], x[2];
poly[2] = dmnsn_vector_dot(l.n, l.n);
poly[1] = 2.0*dmnsn_vector_dot(l.n, l.x0);
poly[0] = dmnsn_vector_dot(l.x0, l.x0) - 1.0;
size_t n = dmnsn_polynomial_solve(poly, 2, x);
if (n == 0) {
return false;
}
double t = x[0];
// Optimize for the case where we're outside the sphere
if (dmnsn_likely(n == 2)) {
t = dmnsn_min(t, x[1]);
}
intersection->t = t;
intersection->normal = dmnsn_line_point(l, t);
return true;
}
/// Sphere inside callback.
static bool
dmnsn_sphere_inside_fn(const dmnsn_object *sphere, dmnsn_vector point)
{
return point.x*point.x + point.y*point.y + point.z*point.z < 1.0;
}
/// Sphere bounding callback.
static dmnsn_bounding_box
dmnsn_sphere_bounding_fn(const dmnsn_object *object, dmnsn_matrix trans)
{
// Get a tight bound using the conic representation of a sphere:
//
// S = [ 1 0 0 0 ]
// [ 0 1 0 0 ]
// [ 0 0 1 0 ]
// [ 0 0 0 -1 ].
//
// The surface is defined by
// p^T * S * p = 0,
// and the tangent planes are defined by
// q * S^-1 * q^T = 0.
// Note that S = S^-1.
//
// The symmetric matrix R, defined by
// R = M * S^-1 * M^T,
// characterizes the tangent planes. Specifically,
// min.x = (R[0,3] - sqrt(R[0,3]^2 - R[0,0]*R[3,3]))/R[3,3]
// max.x = (R[0,3] + sqrt(R[0,3]^2 - R[0,0]*R[3,3]))/R[3,3]
// min.y = (R[1,3] - sqrt(R[1,3]^2 - R[1,1]*R[3,3]))/R[3,3]
// max.y = (R[1,3] + sqrt(R[1,3]^2 - R[1,1]*R[3,3]))/R[3,3]
// min.z = (R[2,3] - sqrt(R[2,3]^2 - R[2,2]*R[3,3]))/R[3,3]
// max.z = (R[2,3] + sqrt(R[2,3]^2 - R[2,2]*R[3,3]))/R[3,3]
//
// Unfortunately, we can't use dmnsn_matrix because the matrices are not
// affine
// MS = M * S^-1 = M * S
// Last row is [ 0 0 0 -1 ] implicitly
double MS[3][4];
for (int i = 0; i < 3; ++i) {
for (int j = 0; j < 3; ++j) {
MS[i][j] = trans.n[i][j];
}
MS[i][3] = -trans.n[i][3];
}
// R = MS * M^T
// We only compute the upper triangular portion
// R[3][3] is implicitly -1
double R[4][4];
for (int i = 0; i < 3; ++i) {
for (int j = i; j < 3; ++j) {
R[i][j] = 0.0;
for (int k = 0; k < 4; ++k) {
R[i][j] += MS[i][k]*trans.n[j][k];
}
}
R[i][3] = MS[i][3];
}
dmnsn_bounding_box box;
double dx = sqrt(R[0][3]*R[0][3] + R[0][0]);
box.min.x = -R[0][3] - dx;
box.max.x = -R[0][3] + dx;
double dy = sqrt(R[1][3]*R[1][3] + R[1][1]);
box.min.y = -R[1][3] - dy;
box.max.y = -R[1][3] + dy;
double dz = sqrt(R[2][3]*R[2][3] + R[2][2]);
box.min.z = -R[2][3] - dz;
box.max.z = -R[2][3] + dz;
return box;
}
/// Sphere vtable.
static const dmnsn_object_vtable dmnsn_sphere_vtable = {
.intersection_fn = dmnsn_sphere_intersection_fn,
.inside_fn = dmnsn_sphere_inside_fn,
.bounding_fn = dmnsn_sphere_bounding_fn,
};
dmnsn_object *
dmnsn_new_sphere(dmnsn_pool *pool)
{
dmnsn_object *sphere = dmnsn_new_object(pool);
sphere->vtable = &dmnsn_sphere_vtable;
return sphere;
}
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