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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 "internal.h"
#include "internal/polynomial.h"
#include "dimension/model.h"
/// Sphere intersection callback.
static bool
dmnsn_sphere_intersection_fn(const dmnsn_object *sphere, dmnsn_ray 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_ray_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;
}
/// Helper for sphere bounding box calculation.
static inline double
dmnsn_implicit_dot(double row[4])
{
double ret = 0.0;
for (int i = 0; i < 3; ++i) {
ret += row[i]*row[i];
}
return ret;
}
/// Sphere bounding callback.
static dmnsn_aabb
dmnsn_sphere_bounding_fn(const dmnsn_object *object, dmnsn_matrix trans)
{
// Get a tight bound using the quadric representation of a sphere. For
// details, see
// http://tavianator.com/2014/06/exact-bounding-boxes-for-spheres-ellipsoids
dmnsn_aabb box;
double cx = trans.n[0][3];
double dx = sqrt(dmnsn_implicit_dot(trans.n[0]));
box.min.x = cx - dx;
box.max.x = cx + dx;
double cy = trans.n[1][3];
double dy = sqrt(dmnsn_implicit_dot(trans.n[1]));
box.min.y = cy - dy;
box.max.y = cy + dy;
double cz = trans.n[2][3];
double dz = sqrt(dmnsn_implicit_dot(trans.n[2]));
box.min.z = cz - dz;
box.max.z = cz + 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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