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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
/** Construct a new transformation matrix. */
DMNSN_INLINE dmnsn_matrix
dmnsn_new_matrix(double a0, double a1, double a2, double a3,
double b0, double b1, double b2, double b3,
double c0, double c1, double c2, double c3)
{
dmnsn_matrix m = { { { a0, a1, a2, a3 },
{ b0, b1, b2, b3 },
{ c0, c1, c2, c3 } } };
return m;
}
/** Construct a new 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 = { { { a.x, b.x, c.x, d.x },
{ a.y, b.y, c.y, d.y },
{ a.z, b.z, c.z, d.z } } };
return m;
}
/** Extract column vectors from a matrix. */
DMNSN_INLINE dmnsn_vector
dmnsn_matrix_column(dmnsn_matrix M, unsigned int i)
{
return dmnsn_new_vector(M.n[0][i], M.n[1][i], M.n[2][i]);
}
/** Return the identity matrix. */
dmnsn_matrix dmnsn_identity_matrix(void);
/**
* A scale transformation.
* @param[in] s A vector with components representing the scaling factor in
* each axis.
* @return The transformation matrix.
*/
dmnsn_matrix dmnsn_scale_matrix(dmnsn_vector s);
/**
* A translation.
* @param[in] d The vector to translate by.
* @return The transformation matrix.
*/
dmnsn_matrix dmnsn_translation_matrix(dmnsn_vector d);
/**
* A left-handed rotation.
* @param[in] theta A vector representing an axis and angle.
* @f$ axis = \vec{\theta}/|\vec{\theta}| @f$,
* @f$ angle = |\vec{\theta}| @f$
* @return The transformation matrix.
*/
dmnsn_matrix dmnsn_rotation_matrix(dmnsn_vector theta);
/**
* 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.
* @return A transformation matrix that will rotate \p from to \p to.
*/
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 A);
/** Multiply two matricies. */
dmnsn_matrix dmnsn_matrix_mul(dmnsn_matrix lhs, dmnsn_matrix rhs);
/** Transform a point by a matrix. */
DMNSN_INLINE dmnsn_vector
dmnsn_transform_point(dmnsn_matrix T, dmnsn_vector v)
{
/* 9 multiplications, 9 additions */
dmnsn_vector r;
r.x = T.n[0][0]*v.x + T.n[0][1]*v.y + T.n[0][2]*v.z + T.n[0][3];
r.y = T.n[1][0]*v.x + T.n[1][1]*v.y + T.n[1][2]*v.z + T.n[1][3];
r.z = T.n[2][0]*v.x + T.n[2][1]*v.y + T.n[2][2]*v.z + T.n[2][3];
return r;
}
/** Transform a direction by a matrix. */
DMNSN_INLINE dmnsn_vector
dmnsn_transform_direction(dmnsn_matrix T, dmnsn_vector v)
{
/* 9 multiplications, 6 additions */
dmnsn_vector r;
r.x = T.n[0][0]*v.x + T.n[0][1]*v.y + T.n[0][2]*v.z;
r.y = T.n[1][0]*v.x + T.n[1][1]*v.y + T.n[1][2]*v.z;
r.z = T.n[2][0]*v.x + T.n[2][1]*v.y + T.n[2][2]*v.z;
return r;
}
/**
* Transform a pseudovector by a matrix.
* @param[in] Tinv 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 Tinv, dmnsn_vector v)
{
/* Multiply by the transpose of the inverse
(9 multiplications, 6 additions) */
dmnsn_vector r;
r.x = Tinv.n[0][0]*v.x + Tinv.n[1][0]*v.y + Tinv.n[2][0]*v.z;
r.y = Tinv.n[0][1]*v.x + Tinv.n[1][1]*v.y + Tinv.n[2][1]*v.z;
r.z = Tinv.n[0][2]*v.x + Tinv.n[1][2]*v.y + Tinv.n[2][2]*v.z;
return r;
}
/**
* Transform a ray by a matrix.
* \f$ n' = T(l.\vec{x_0} + l.\vec{n}) - T(l.\vec{x_0}) \f$,
* \f$ \vec{x_0}' = T(l.\vec{x_0}) \f$
*/
DMNSN_INLINE dmnsn_ray
dmnsn_transform_ray(dmnsn_matrix T, dmnsn_ray l)
{
/* 18 multiplications, 15 additions */
dmnsn_ray ret;
ret.x0 = dmnsn_transform_point(T, l.x0);
ret.n = dmnsn_transform_direction(T, l.n);
return ret;
}
/** Transform a bounding box by a matrix. */
dmnsn_aabb dmnsn_transform_aabb(dmnsn_matrix T, dmnsn_aabb box);
/** Return whether a matrix contains any NaN components. */
DMNSN_INLINE bool
dmnsn_matrix_isnan(dmnsn_matrix m)
{
size_t 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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