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/*************************************************************************
* Copyright (C) 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
* Triangle fans. See
* http://tavianator.com/2014/05/a-beautiful-raymesh-intersection-algorithm/
* for a description of the intersection algorithm.
*/
#include "dimension.h"
/** Triangle fan type. */
typedef struct {
dmnsn_object object;
size_t ncoeffs;
double coeffs[][6];
} dmnsn_triangle_fan;
/** Change basis from one triangle to the next. */
static inline dmnsn_vector
dmnsn_change_basis(const double coeffs[6], dmnsn_vector v)
{
return dmnsn_new_vector(
coeffs[0]*v.x + coeffs[1]*v.z + v.y,
coeffs[2]*v.x + coeffs[3]*v.z,
coeffs[4]*v.x + coeffs[5]*v.z
);
}
/** Change basis from one triangle to the next for a normal vector. */
static inline dmnsn_vector
dmnsn_change_normal_basis(const double coeffs[6], dmnsn_vector n)
{
return dmnsn_new_vector(
coeffs[0]*n.x + coeffs[2]*n.y + coeffs[4]*n.z,
n.x,
coeffs[1]*n.x + coeffs[3]*n.y + coeffs[5]*n.z
);
}
/** Triangle intersection callback. */
static bool
dmnsn_triangle_fan_intersection_fn(const dmnsn_object *object, dmnsn_line l, dmnsn_intersection *intersection)
{
const dmnsn_triangle_fan *fan = (const dmnsn_triangle_fan *)object;
double t = -l.x0.z/l.n.z;
double u = l.x0.x + t*l.n.x;
double v = l.x0.y + t*l.n.y;
double best_t = INFINITY;
if (t >= 0.0 && u >= 0.0 && v >= 0.0 && u + v <= 1.0) {
best_t = t;
}
dmnsn_vector normal = dmnsn_z;
dmnsn_vector best_normal = normal;
for (size_t i = 0; i < fan->ncoeffs; ++i) {
const double *coeffs = fan->coeffs[i];
l = dmnsn_new_line(dmnsn_change_basis(coeffs, l.x0), dmnsn_change_basis(coeffs, l.n));
normal = dmnsn_change_normal_basis(coeffs, normal);
t = -l.x0.z/l.n.z;
u = l.x0.x + t*l.n.x;
v = l.x0.y + t*l.n.y;
if (t >= 0.0 && t < best_t && u >= 0.0 && v >= 0.0 && u + v <= 1.0) {
best_t = t;
best_normal = normal;
}
}
if (!isinf(best_t)) {
intersection->t = t;
intersection->normal = best_normal;
return true;
}
return false;
}
/** Triangle fan inside callback. */
static bool
dmnsn_triangle_fan_inside_fn(const dmnsn_object *object, dmnsn_vector point)
{
return false;
}
/** Triangle fan bounding callback. */
static dmnsn_bounding_box
dmnsn_triangle_fan_bounding_fn(const dmnsn_object *object, dmnsn_matrix trans)
{
const dmnsn_triangle_fan *fan = (const dmnsn_triangle_fan *)object;
dmnsn_vector a = dmnsn_transform_point(trans, dmnsn_zero);
dmnsn_vector b = dmnsn_transform_point(trans, dmnsn_x);
dmnsn_vector c = dmnsn_transform_point(trans, dmnsn_y);
dmnsn_bounding_box box = dmnsn_new_bounding_box(a, a);
box = dmnsn_bounding_box_swallow(box, b);
box = dmnsn_bounding_box_swallow(box, c);
dmnsn_matrix P = trans;
for (size_t i = 0; i < fan->ncoeffs; ++i) {
const double *coeffs = fan->coeffs[i];
dmnsn_matrix incremental = dmnsn_new_matrix(coeffs[0], 1.0, coeffs[1], 0.0,
coeffs[2], 0.0, coeffs[3], 0.0,
coeffs[4], 0.0, coeffs[5], 0.0);
P = dmnsn_matrix_mul(P, dmnsn_matrix_inverse(incremental));
dmnsn_vector d = dmnsn_transform_point(P, dmnsn_y);
box = dmnsn_bounding_box_swallow(box, d);
}
return box;
}
/** Triangle fan vtable. */
static dmnsn_object_vtable dmnsn_triangle_fan_vtable = {
.intersection_fn = dmnsn_triangle_fan_intersection_fn,
.inside_fn = dmnsn_triangle_fan_inside_fn,
.bounding_fn = dmnsn_triangle_fan_bounding_fn,
};
dmnsn_object *
dmnsn_new_triangle_fan(dmnsn_pool *pool, dmnsn_vector vertices[], size_t nvertices)
{
dmnsn_assert(nvertices >= 3, "Not enough vertices for one triangle");
size_t ncoeffs = nvertices - 3;
dmnsn_triangle_fan *fan = dmnsn_palloc(pool, sizeof(dmnsn_triangle_fan) + ncoeffs*sizeof(double[6]));
fan->ncoeffs = ncoeffs;
dmnsn_object *object = &fan->object;
dmnsn_init_object(object);
object->vtable = &dmnsn_triangle_fan_vtable;
object->bounding_box.min = dmnsn_zero;
object->bounding_box.max = dmnsn_new_vector(1.0, 1.0, 0.0);
/* Compute the initial matrix and the coefficients */
dmnsn_vector a = vertices[0];
dmnsn_vector ab = dmnsn_vector_sub(vertices[1], a);
dmnsn_vector ac = dmnsn_vector_sub(vertices[2], a);
dmnsn_vector normal = dmnsn_vector_cross(ab, ac);
dmnsn_matrix P = dmnsn_new_matrix4(ab, ac, normal, a);
object->intrinsic_trans = P;
for (size_t i = 0; i < ncoeffs; ++i) {
ab = ac;
ac = dmnsn_vector_sub(vertices[i + 3], a);
normal = dmnsn_vector_cross(ab, ac);
dmnsn_matrix newP = dmnsn_new_matrix4(ab, ac, normal, a);
dmnsn_matrix incremental = dmnsn_matrix_mul(dmnsn_matrix_inverse(newP), P);
double *coeffs = fan->coeffs[i];
coeffs[0] = incremental.n[0][0];
coeffs[1] = incremental.n[0][2];
coeffs[2] = incremental.n[1][0];
coeffs[3] = incremental.n[1][2];
coeffs[4] = incremental.n[2][0];
coeffs[5] = incremental.n[2][2];
P = newP;
}
return object;
}
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