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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
* Affine transformation matrices.
*/
#ifndef DMNSN_MATH_H
#error "Please include <dimension/math.h> instead of this header directly."
#endif
/** A 4x4 affine transformation matrix, with implied [0 0 0 1] bottom row. */
typedef struct dmnsn_matrix {
double n[3][4]; /**< The matrix elements in row-major order. */
} dmnsn_matrix;
/** A standard format string for matricies. */
#define DMNSN_MATRIX_FORMAT \
"[%g\t%g\t%g\t%g]\n" \
"[%g\t%g\t%g\t%g]\n" \
"[%g\t%g\t%g\t%g]\n" \
"[%g\t%g\t%g\t%g]"
/** The appropriate arguements to printf() a matrix. */
#define DMNSN_MATRIX_PRINTF(M) \
(M).n[0][0], (M).n[0][1], (M).n[0][2], (M).n[0][3], \
(M).n[1][0], (M).n[1][1], (M).n[1][2], (M).n[1][3], \
(M).n[2][0], (M).n[2][1], (M).n[2][2], (M).n[2][3], \
0.0, 0.0, 0.0, 1.0
/** Create a transformation matrix. */
DMNSN_INLINE dmnsn_matrix
dmnsn_new_matrix(double a0, double b0, double c0, double d0,
double a1, double b1, double c1, double d1,
double a2, double b2, double c2, double d2)
{
dmnsn_matrix M = {
{
{ a0, b0, c0, d0 },
{ a1, b1, c1, d1 },
{ a2, b2, c2, d2 }
}
};
return M;
}
/** Create a transformation matrix from column vectors. */
DMNSN_INLINE dmnsn_matrix
dmnsn_new_matrix4(dmnsn_vector a, dmnsn_vector b, dmnsn_vector c, dmnsn_vector d)
{
dmnsn_matrix M;
unsigned int i;
for (i = 0; i < 3; ++i) {
M.n[i][0] = a.n[i];
}
for (i = 0; i < 3; ++i) {
M.n[i][1] = b.n[i];
}
for (i = 0; i < 3; ++i) {
M.n[i][2] = c.n[i];
}
for (i = 0; i < 3; ++i) {
M.n[i][3] = d.n[i];
}
return M;
}
/** Extract column vectors from a matrix. */
DMNSN_INLINE dmnsn_vector
dmnsn_matrix_column(dmnsn_matrix M, unsigned int i)
{
dmnsn_vector v;
unsigned int j;
for (j = 0; j < 3; ++j) {
v.n[j] = M.n[j][i];
}
return v;
}
/** Return the identity matrix. */
DMNSN_INLINE dmnsn_matrix
dmnsn_identity_matrix(void)
{
return dmnsn_new_matrix(
1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0
);
}
/**
* Return a scale transformation.
* @param[in] s A vector with components representing the scaling factor in
* each axis.
*/
DMNSN_INLINE dmnsn_matrix
dmnsn_scale_matrix(dmnsn_vector s)
{
return dmnsn_new_matrix(
s.n[0], 0.0, 0.0, 0.0,
0.0, s.n[1], 0.0, 0.0,
0.0, 0.0, s.n[2], 0.0
);
}
/**
* Set \p M to a translation matrix.
* @param[in] d The vector to translate by.
*/
DMNSN_INLINE dmnsn_matrix
dmnsn_translation_matrix(dmnsn_vector d)
{
return dmnsn_new_matrix(
1.0, 0.0, 0.0, d.n[0],
0.0, 1.0, 0.0, d.n[1],
0.0, 0.0, 1.0, d.n[2]
);
}
/**
* Return a rotation matrix.
* @param[in] theta A vector representing an axis and angle.
* @f$ axis = \vec{\theta}/|\vec{\theta}| @f$,
* @f$ angle = |\vec{\theta}| @f$
*/
dmnsn_matrix dmnsn_rotation_matrix(dmnsn_vector theta);
/**
* Return an alignment matrix.
* @param[in] from The initial vector.
* @param[in] to The desired direction.
* @param[in] axis1 The first axis about which to rotate.
* @param[in] axis2 The second axis about which to rotate.
*/
dmnsn_matrix dmnsn_alignment_matrix(dmnsn_vector from, dmnsn_vector to, dmnsn_vector axis1, dmnsn_vector axis2);
/** Invert a matrix. */
dmnsn_matrix dmnsn_matrix_inverse(dmnsn_matrix M);
/** Multiply two matricies. */
DMNSN_INLINE dmnsn_matrix dmnsn_matrix_mul(dmnsn_matrix lhs, dmnsn_matrix rhs)
{
dmnsn_matrix M;
unsigned int i, j, k;
for (i = 0; i < 3; ++i) {
for (j = 0; j < 3; ++j) {
M.n[i][j] = 0.0;
for (k = 0; k < 3; ++k) {
M.n[i][j] += lhs.n[i][k]*rhs.n[k][j];
}
}
M.n[i][3] = lhs.n[i][3];
for (k = 0; k < 3; ++k) {
M.n[i][3] += lhs.n[i][k]*rhs.n[k][3];
}
}
return M;
}
/** Transform a point by a matrix. */
DMNSN_INLINE dmnsn_vector
dmnsn_transform_point(dmnsn_matrix M, dmnsn_vector v)
{
dmnsn_vector r;
unsigned int i, j;
for (i = 0; i < 3; ++i) {
r.n[i] = M.n[i][3];
for (j = 0; j < 3; ++j) {
r.n[i] += M.n[i][j]*v.n[j];
}
}
return r;
}
/** Transform a direction by a matrix. */
DMNSN_INLINE dmnsn_vector
dmnsn_transform_direction(dmnsn_matrix M, dmnsn_vector v)
{
dmnsn_vector r;
unsigned int i, j;
for (i = 0; i < 3; ++i) {
r.n[i] = 0.0;
for (j = 0; j < 3; ++j) {
r.n[i] += M.n[i][j]*v.n[j];
}
}
return r;
}
/**
* Transform a pseudovector by a matrix.
* @param[in] Minv The inverse of the transformation matrix.
* @param[in] v The pseudovector to transform.
* @return The transformed pseudovector.
*/
DMNSN_INLINE dmnsn_vector
dmnsn_transform_normal(dmnsn_matrix Minv, dmnsn_vector v)
{
/* Multiply by the transpose of the inverse */
dmnsn_vector r;
unsigned int i, j;
for (i = 0; i < 3; ++i) {
r.n[i] = 0.0;
for (j = 0; j < 3; ++j) {
r.n[i] += Minv.n[j][i]*v.n[j];
}
}
return r;
}
/** Transform a ray by a matrix. */
DMNSN_INLINE dmnsn_ray
dmnsn_transform_ray(dmnsn_matrix M, dmnsn_ray l)
{
dmnsn_ray ret;
ret.x0 = dmnsn_transform_point(M, l.x0);
ret.n = dmnsn_transform_direction(M, l.n);
return ret;
}
/** Transform a bounding box by a matrix. */
dmnsn_aabb dmnsn_transform_aabb(dmnsn_matrix M, dmnsn_aabb box);
/** Return whether a matrix contains any NaN components. */
DMNSN_INLINE bool
dmnsn_matrix_isnan(dmnsn_matrix M)
{
unsigned int i, j;
for (i = 0; i < 3; ++i) {
for (j = 0; j < 4; ++j) {
if (dmnsn_isnan(M.n[i][j])) {
return true;
}
}
}
return false;
}
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