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/*
* Mesa 3-D graphics library
*
* Copyright (C) 1999-2005 Brian Paul All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining a
* copy of this software and associated documentation files (the "Software"),
* to deal in the Software without restriction, including without limitation
* the rights to use, copy, modify, merge, publish, distribute, sublicense,
* and/or sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included
* in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR
* OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
* OTHER DEALINGS IN THE SOFTWARE.
*/
/**
* \file m_matrix.c
* Matrix operations.
*
* \note
* -# 4x4 transformation matrices are stored in memory in column major order.
* -# Points/vertices are to be thought of as column vectors.
* -# Transformation of a point p by a matrix M is: p' = M * p
*/
#include <stddef.h>
#include <math.h>
#include "main/errors.h"
#include "util/glheader.h"
#include "main/macros.h"
#include "m_matrix.h"
#include "util/u_memory.h"
/**
* \defgroup MatFlags MAT_FLAG_XXX-flags
*
* Bitmasks to indicate different kinds of 4x4 matrices in GLmatrix::flags
*/
/*@{*/
#define MAT_FLAG_IDENTITY 0 /**< is an identity matrix flag.
* (Not actually used - the identity
* matrix is identified by the absence
* of all other flags.)
*/
#define MAT_FLAG_GENERAL 0x1 /**< is a general matrix flag */
#define MAT_FLAG_ROTATION 0x2 /**< is a rotation matrix flag */
#define MAT_FLAG_TRANSLATION 0x4 /**< is a translation matrix flag */
#define MAT_FLAG_UNIFORM_SCALE 0x8 /**< is an uniform scaling matrix flag */
#define MAT_FLAG_GENERAL_SCALE 0x10 /**< is a general scaling matrix flag */
#define MAT_FLAG_GENERAL_3D 0x20 /**< general 3D matrix flag */
#define MAT_FLAG_PERSPECTIVE 0x40 /**< is a perspective proj matrix flag */
#define MAT_FLAG_SINGULAR 0x80 /**< is a singular matrix flag */
#define MAT_DIRTY_TYPE 0x100 /**< matrix type is dirty */
#define MAT_DIRTY_FLAGS 0x200 /**< matrix flags are dirty */
#define MAT_DIRTY_INVERSE 0x400 /**< matrix inverse is dirty */
/** angle preserving matrix flags mask */
#define MAT_FLAGS_ANGLE_PRESERVING (MAT_FLAG_ROTATION | \
MAT_FLAG_TRANSLATION | \
MAT_FLAG_UNIFORM_SCALE)
/** geometry related matrix flags mask */
#define MAT_FLAGS_GEOMETRY (MAT_FLAG_GENERAL | \
MAT_FLAG_ROTATION | \
MAT_FLAG_TRANSLATION | \
MAT_FLAG_UNIFORM_SCALE | \
MAT_FLAG_GENERAL_SCALE | \
MAT_FLAG_GENERAL_3D | \
MAT_FLAG_PERSPECTIVE | \
MAT_FLAG_SINGULAR)
/** length preserving matrix flags mask */
#define MAT_FLAGS_LENGTH_PRESERVING (MAT_FLAG_ROTATION | \
MAT_FLAG_TRANSLATION)
/** 3D (non-perspective) matrix flags mask */
#define MAT_FLAGS_3D (MAT_FLAG_ROTATION | \
MAT_FLAG_TRANSLATION | \
MAT_FLAG_UNIFORM_SCALE | \
MAT_FLAG_GENERAL_SCALE | \
MAT_FLAG_GENERAL_3D)
/** dirty matrix flags mask */
#define MAT_DIRTY (MAT_DIRTY_TYPE | \
MAT_DIRTY_FLAGS | \
MAT_DIRTY_INVERSE)
/*@}*/
/**
* Test geometry related matrix flags.
*
* \param mat a pointer to a GLmatrix structure.
* \param a flags mask.
*
* \returns non-zero if all geometry related matrix flags are contained within
* the mask, or zero otherwise.
*/
#define TEST_MAT_FLAGS(mat, a) \
((MAT_FLAGS_GEOMETRY & (~(a)) & ((mat)->flags) ) == 0)
/**********************************************************************/
/** \name Matrix multiplication */
/*@{*/
#define A(row,col) a[(col<<2)+row]
#define B(row,col) b[(col<<2)+row]
#define P(row,col) product[(col<<2)+row]
/**
* Perform a full 4x4 matrix multiplication.
*
* \param a matrix.
* \param b matrix.
* \param product will receive the product of \p a and \p b.
*
* \warning Is assumed that \p product != \p b. \p product == \p a is allowed.
*
* \note KW: 4*16 = 64 multiplications
*
* \author This \c matmul was contributed by Thomas Malik
*/
static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b )
{
GLint i;
for (i = 0; i < 4; i++) {
const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3);
P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3);
}
}
/**
* Multiply two matrices known to occupy only the top three rows, such
* as typical model matrices, and orthogonal matrices.
*
* \param a matrix.
* \param b matrix.
* \param product will receive the product of \p a and \p b.
*/
static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b )
{
GLint i;
for (i = 0; i < 3; i++) {
const GLfloat ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3);
P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0);
P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1);
P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2);
P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3;
}
P(3,0) = 0;
P(3,1) = 0;
P(3,2) = 0;
P(3,3) = 1;
}
#undef A
#undef B
#undef P
/* "m" must be a 4x4 matrix. Set it to the identity matrix. */
static void
matrix_set_identity(GLfloat *m)
{
m[0] = m[5] = m[10] = m[15] = 1;
m[1] = m[2] = m[3] = m[4] = m[6] = m[7] = 0;
m[8] = m[9] = m[11] = m[12] = m[13] = m[14] = 0;
}
/**
* Multiply a matrix by an array of floats with known properties.
*
* \param mat pointer to a GLmatrix structure containing the left multiplication
* matrix, and that will receive the product result.
* \param m right multiplication matrix array.
* \param flags flags of the matrix \p m.
*
* Joins both flags and marks the type and inverse as dirty. Calls matmul34()
* if both matrices are 3D, or matmul4() otherwise.
*/
static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags )
{
mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D))
matmul34( mat->m, mat->m, m );
else
matmul4( mat->m, mat->m, m );
}
/**
* Matrix multiplication.
*
* \param dest destination matrix.
* \param a left matrix.
* \param b right matrix.
*
* Joins both flags and marks the type and inverse as dirty. Calls matmul34()
* if both matrices are 3D, or matmul4() otherwise.
*/
void
_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b )
{
dest->flags = (a->flags |
b->flags |
MAT_DIRTY_TYPE |
MAT_DIRTY_INVERSE);
if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D))
matmul34( dest->m, a->m, b->m );
else
matmul4( dest->m, a->m, b->m );
}
/**
* Matrix multiplication.
*
* \param dest left and destination matrix.
* \param m right matrix array.
*
* Marks the matrix flags with general flag, and type and inverse dirty flags.
* Calls matmul4() for the multiplication.
*/
void
_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m )
{
dest->flags |= (MAT_FLAG_GENERAL |
MAT_DIRTY_TYPE |
MAT_DIRTY_INVERSE |
MAT_DIRTY_FLAGS);
matmul4( dest->m, dest->m, m );
}
/*@}*/
/**
* References an element of 4x4 matrix.
*
* \param m matrix array.
* \param c column of the desired element.
* \param r row of the desired element.
*
* \return value of the desired element.
*
* Calculate the linear storage index of the element and references it.
*/
#define MAT(m,r,c) (m)[(c)*4+(r)]
/**********************************************************************/
/** \name Matrix inversion */
/*@{*/
/**
* Compute inverse of 4x4 transformation matrix.
*
* \param mat pointer to a GLmatrix structure. The matrix inverse will be
* stored in the GLmatrix::inv attribute.
*
* \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
*
* \author
* Code contributed by Jacques Leroy jle@star.be
*
* Calculates the inverse matrix by performing the gaussian matrix reduction
* with partial pivoting followed by back/substitution with the loops manually
* unrolled.
*/
static GLboolean invert_matrix_general( GLmatrix *mat )
{
return util_invert_mat4x4(mat->inv, mat->m);
}
/**
* Compute inverse of a general 3d transformation matrix.
*
* \param mat pointer to a GLmatrix structure. The matrix inverse will be
* stored in the GLmatrix::inv attribute.
*
* \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
*
* \author Adapted from graphics gems II.
*
* Calculates the inverse of the upper left by first calculating its
* determinant and multiplying it to the symmetric adjust matrix of each
* element. Finally deals with the translation part by transforming the
* original translation vector using by the calculated submatrix inverse.
*/
static GLboolean invert_matrix_3d_general( GLmatrix *mat )
{
const GLfloat *in = mat->m;
GLfloat *out = mat->inv;
GLfloat pos, neg, t;
GLfloat det;
/* Calculate the determinant of upper left 3x3 submatrix and
* determine if the matrix is singular.
*/
pos = neg = 0.0;
t = MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2);
if (t >= 0.0F) pos += t; else neg += t;
t = MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2);
if (t >= 0.0F) pos += t; else neg += t;
t = MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2);
if (t >= 0.0F) pos += t; else neg += t;
t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2);
if (t >= 0.0F) pos += t; else neg += t;
t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2);
if (t >= 0.0F) pos += t; else neg += t;
t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2);
if (t >= 0.0F) pos += t; else neg += t;
det = pos + neg;
if (fabsf(det) < 1e-25F)
return GL_FALSE;
det = 1.0F / det;
MAT(out,0,0) = ( (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det);
MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det);
MAT(out,0,2) = ( (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det);
MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det);
MAT(out,1,1) = ( (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det);
MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det);
MAT(out,2,0) = ( (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det);
MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det);
MAT(out,2,2) = ( (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det);
/* Do the translation part */
MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
MAT(in,1,3) * MAT(out,0,1) +
MAT(in,2,3) * MAT(out,0,2) );
MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
MAT(in,1,3) * MAT(out,1,1) +
MAT(in,2,3) * MAT(out,1,2) );
MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
MAT(in,1,3) * MAT(out,2,1) +
MAT(in,2,3) * MAT(out,2,2) );
return GL_TRUE;
}
/**
* Compute inverse of a 3d transformation matrix.
*
* \param mat pointer to a GLmatrix structure. The matrix inverse will be
* stored in the GLmatrix::inv attribute.
*
* \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
*
* If the matrix is not an angle preserving matrix then calls
* invert_matrix_3d_general for the actual calculation. Otherwise calculates
* the inverse matrix analyzing and inverting each of the scaling, rotation and
* translation parts.
*/
static GLboolean invert_matrix_3d( GLmatrix *mat )
{
const GLfloat *in = mat->m;
GLfloat *out = mat->inv;
if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) {
return invert_matrix_3d_general( mat );
}
if (mat->flags & MAT_FLAG_UNIFORM_SCALE) {
GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) +
MAT(in,0,1) * MAT(in,0,1) +
MAT(in,0,2) * MAT(in,0,2));
if (scale == 0.0F)
return GL_FALSE;
scale = 1.0F / scale;
/* Transpose and scale the 3 by 3 upper-left submatrix. */
MAT(out,0,0) = scale * MAT(in,0,0);
MAT(out,1,0) = scale * MAT(in,0,1);
MAT(out,2,0) = scale * MAT(in,0,2);
MAT(out,0,1) = scale * MAT(in,1,0);
MAT(out,1,1) = scale * MAT(in,1,1);
MAT(out,2,1) = scale * MAT(in,1,2);
MAT(out,0,2) = scale * MAT(in,2,0);
MAT(out,1,2) = scale * MAT(in,2,1);
MAT(out,2,2) = scale * MAT(in,2,2);
}
else if (mat->flags & MAT_FLAG_ROTATION) {
/* Transpose the 3 by 3 upper-left submatrix. */
MAT(out,0,0) = MAT(in,0,0);
MAT(out,1,0) = MAT(in,0,1);
MAT(out,2,0) = MAT(in,0,2);
MAT(out,0,1) = MAT(in,1,0);
MAT(out,1,1) = MAT(in,1,1);
MAT(out,2,1) = MAT(in,1,2);
MAT(out,0,2) = MAT(in,2,0);
MAT(out,1,2) = MAT(in,2,1);
MAT(out,2,2) = MAT(in,2,2);
}
else {
/* pure translation */
matrix_set_identity(out);
MAT(out,0,3) = - MAT(in,0,3);
MAT(out,1,3) = - MAT(in,1,3);
MAT(out,2,3) = - MAT(in,2,3);
return GL_TRUE;
}
if (mat->flags & MAT_FLAG_TRANSLATION) {
/* Do the translation part */
MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
MAT(in,1,3) * MAT(out,0,1) +
MAT(in,2,3) * MAT(out,0,2) );
MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
MAT(in,1,3) * MAT(out,1,1) +
MAT(in,2,3) * MAT(out,1,2) );
MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
MAT(in,1,3) * MAT(out,2,1) +
MAT(in,2,3) * MAT(out,2,2) );
}
else {
MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0;
}
return GL_TRUE;
}
/**
* Compute inverse of an identity transformation matrix.
*
* \param mat pointer to a GLmatrix structure. The matrix inverse will be
* stored in the GLmatrix::inv attribute.
*
* \return always GL_TRUE.
*
* Simply copies Identity into GLmatrix::inv.
*/
static GLboolean invert_matrix_identity( GLmatrix *mat )
{
matrix_set_identity(mat->inv);
return GL_TRUE;
}
/**
* Compute inverse of a no-rotation 3d transformation matrix.
*
* \param mat pointer to a GLmatrix structure. The matrix inverse will be
* stored in the GLmatrix::inv attribute.
*
* \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
*
* Calculates the
*/
static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat )
{
const GLfloat *in = mat->m;
GLfloat *out = mat->inv;
if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 )
return GL_FALSE;
matrix_set_identity(out);
MAT(out,0,0) = 1.0F / MAT(in,0,0);
MAT(out,1,1) = 1.0F / MAT(in,1,1);
MAT(out,2,2) = 1.0F / MAT(in,2,2);
if (mat->flags & MAT_FLAG_TRANSLATION) {
MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2));
}
return GL_TRUE;
}
/**
* Compute inverse of a no-rotation 2d transformation matrix.
*
* \param mat pointer to a GLmatrix structure. The matrix inverse will be
* stored in the GLmatrix::inv attribute.
*
* \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
*
* Calculates the inverse matrix by applying the inverse scaling and
* translation to the identity matrix.
*/
static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat )
{
const GLfloat *in = mat->m;
GLfloat *out = mat->inv;
if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0)
return GL_FALSE;
matrix_set_identity(out);
MAT(out,0,0) = 1.0F / MAT(in,0,0);
MAT(out,1,1) = 1.0F / MAT(in,1,1);
if (mat->flags & MAT_FLAG_TRANSLATION) {
MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
}
return GL_TRUE;
}
/**
* Matrix inversion function pointer type.
*/
typedef GLboolean (*inv_mat_func)( GLmatrix *mat );
/**
* Table of the matrix inversion functions according to the matrix type.
*/
static inv_mat_func inv_mat_tab[7] = {
invert_matrix_general,
invert_matrix_identity,
invert_matrix_3d_no_rot,
invert_matrix_general,
invert_matrix_3d, /* lazy! */
invert_matrix_2d_no_rot,
invert_matrix_3d
};
/**
* Compute inverse of a transformation matrix.
*
* \param mat pointer to a GLmatrix structure. The matrix inverse will be
* stored in the GLmatrix::inv attribute.
*
* \return GL_TRUE for success, GL_FALSE for failure (\p singular matrix).
*
* Calls the matrix inversion function in inv_mat_tab corresponding to the
* given matrix type. In case of failure, updates the MAT_FLAG_SINGULAR flag,
* and copies the identity matrix into GLmatrix::inv.
*/
static GLboolean matrix_invert( GLmatrix *mat )
{
if (inv_mat_tab[mat->type](mat)) {
mat->flags &= ~MAT_FLAG_SINGULAR;
return GL_TRUE;
} else {
mat->flags |= MAT_FLAG_SINGULAR;
matrix_set_identity(mat->inv);
return GL_FALSE;
}
}
/*@}*/
/**********************************************************************/
/** \name Matrix generation */
/*@{*/
/**
* Generate a 4x4 transformation matrix from glRotate parameters, and
* post-multiply the input matrix by it.
*
* \author
* This function was contributed by Erich Boleyn (erich@uruk.org).
* Optimizations contributed by Rudolf Opalla (rudi@khm.de).
*/
void
_math_matrix_rotate( GLmatrix *mat,
GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
{
GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
GLfloat m[16];
GLboolean optimized;
s = sinf( angle * M_PI / 180.0 );
c = cosf( angle * M_PI / 180.0 );
matrix_set_identity(m);
optimized = GL_FALSE;
#define M(row,col) m[col*4+row]
if (x == 0.0F) {
if (y == 0.0F) {
if (z != 0.0F) {
optimized = GL_TRUE;
/* rotate only around z-axis */
M(0,0) = c;
M(1,1) = c;
if (z < 0.0F) {
M(0,1) = s;
M(1,0) = -s;
}
else {
M(0,1) = -s;
M(1,0) = s;
}
}
}
else if (z == 0.0F) {
optimized = GL_TRUE;
/* rotate only around y-axis */
M(0,0) = c;
M(2,2) = c;
if (y < 0.0F) {
M(0,2) = -s;
M(2,0) = s;
}
else {
M(0,2) = s;
M(2,0) = -s;
}
}
}
else if (y == 0.0F) {
if (z == 0.0F) {
optimized = GL_TRUE;
/* rotate only around x-axis */
M(1,1) = c;
M(2,2) = c;
if (x < 0.0F) {
M(1,2) = s;
M(2,1) = -s;
}
else {
M(1,2) = -s;
M(2,1) = s;
}
}
}
if (!optimized) {
const GLfloat mag = sqrtf(x * x + y * y + z * z);
if (mag <= 1.0e-4F) {
/* no rotation, leave mat as-is */
return;
}
x /= mag;
y /= mag;
z /= mag;
/*
* Arbitrary axis rotation matrix.
*
* This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
* like so: Rz * Ry * T * Ry' * Rz'. T is the final rotation
* (which is about the X-axis), and the two composite transforms
* Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
* from the arbitrary axis to the X-axis then back. They are
* all elementary rotations.
*
* Rz' is a rotation about the Z-axis, to bring the axis vector
* into the x-z plane. Then Ry' is applied, rotating about the
* Y-axis to bring the axis vector parallel with the X-axis. The
* rotation about the X-axis is then performed. Ry and Rz are
* simply the respective inverse transforms to bring the arbitrary
* axis back to its original orientation. The first transforms
* Rz' and Ry' are considered inverses, since the data from the
* arbitrary axis gives you info on how to get to it, not how
* to get away from it, and an inverse must be applied.
*
* The basic calculation used is to recognize that the arbitrary
* axis vector (x, y, z), since it is of unit length, actually
* represents the sines and cosines of the angles to rotate the
* X-axis to the same orientation, with theta being the angle about
* Z and phi the angle about Y (in the order described above)
* as follows:
*
* cos ( theta ) = x / sqrt ( 1 - z^2 )
* sin ( theta ) = y / sqrt ( 1 - z^2 )
*
* cos ( phi ) = sqrt ( 1 - z^2 )
* sin ( phi ) = z
*
* Note that cos ( phi ) can further be inserted to the above
* formulas:
*
* cos ( theta ) = x / cos ( phi )
* sin ( theta ) = y / sin ( phi )
*
* ...etc. Because of those relations and the standard trigonometric
* relations, it is pssible to reduce the transforms down to what
* is used below. It may be that any primary axis chosen will give the
* same results (modulo a sign convention) using thie method.
*
* Particularly nice is to notice that all divisions that might
* have caused trouble when parallel to certain planes or
* axis go away with care paid to reducing the expressions.
* After checking, it does perform correctly under all cases, since
* in all the cases of division where the denominator would have
* been zero, the numerator would have been zero as well, giving
* the expected result.
*/
xx = x * x;
yy = y * y;
zz = z * z;
xy = x * y;
yz = y * z;
zx = z * x;
xs = x * s;
ys = y * s;
zs = z * s;
one_c = 1.0F - c;
/* We already hold the identity-matrix so we can skip some statements */
M(0,0) = (one_c * xx) + c;
M(0,1) = (one_c * xy) - zs;
M(0,2) = (one_c * zx) + ys;
/* M(0,3) = 0.0F; */
M(1,0) = (one_c * xy) + zs;
M(1,1) = (one_c * yy) + c;
M(1,2) = (one_c * yz) - xs;
/* M(1,3) = 0.0F; */
M(2,0) = (one_c * zx) - ys;
M(2,1) = (one_c * yz) + xs;
M(2,2) = (one_c * zz) + c;
/* M(2,3) = 0.0F; */
/*
M(3,0) = 0.0F;
M(3,1) = 0.0F;
M(3,2) = 0.0F;
M(3,3) = 1.0F;
*/
}
#undef M
matrix_multf( mat, m, MAT_FLAG_ROTATION );
}
/**
* Apply a perspective projection matrix.
*
* \param mat matrix to apply the projection.
* \param left left clipping plane coordinate.
* \param right right clipping plane coordinate.
* \param bottom bottom clipping plane coordinate.
* \param top top clipping plane coordinate.
* \param nearval distance to the near clipping plane.
* \param farval distance to the far clipping plane.
*
* Creates the projection matrix and multiplies it with \p mat, marking the
* MAT_FLAG_PERSPECTIVE flag.
*/
void
_math_matrix_frustum( GLmatrix *mat,
GLfloat left, GLfloat right,
GLfloat bottom, GLfloat top,
GLfloat nearval, GLfloat farval )
{
GLfloat x, y, a, b, c, d;
GLfloat m[16];
x = (2.0F*nearval) / (right-left);
y = (2.0F*nearval) / (top-bottom);
a = (right+left) / (right-left);
b = (top+bottom) / (top-bottom);
c = -(farval+nearval) / ( farval-nearval);
d = -(2.0F*farval*nearval) / (farval-nearval); /* error? */
#define M(row,col) m[col*4+row]
M(0,0) = x; M(0,1) = 0.0F; M(0,2) = a; M(0,3) = 0.0F;
M(1,0) = 0.0F; M(1,1) = y; M(1,2) = b; M(1,3) = 0.0F;
M(2,0) = 0.0F; M(2,1) = 0.0F; M(2,2) = c; M(2,3) = d;
M(3,0) = 0.0F; M(3,1) = 0.0F; M(3,2) = -1.0F; M(3,3) = 0.0F;
#undef M
matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE );
}
/**
* Create an orthographic projection matrix.
*
* \param m float array in which to store the project matrix
* \param left left clipping plane coordinate.
* \param right right clipping plane coordinate.
* \param bottom bottom clipping plane coordinate.
* \param top top clipping plane coordinate.
* \param nearval distance to the near clipping plane.
* \param farval distance to the far clipping plane.
*
* Creates the projection matrix and stored the values in \p m. As with other
* OpenGL matrices, the data is stored in column-major ordering.
*/
void
_math_float_ortho(float *m,
float left, float right,
float bottom, float top,
float nearval, float farval)
{
#define M(row,col) m[col*4+row]
M(0,0) = 2.0F / (right-left);
M(0,1) = 0.0F;
M(0,2) = 0.0F;
M(0,3) = -(right+left) / (right-left);
M(1,0) = 0.0F;
M(1,1) = 2.0F / (top-bottom);
M(1,2) = 0.0F;
M(1,3) = -(top+bottom) / (top-bottom);
M(2,0) = 0.0F;
M(2,1) = 0.0F;
M(2,2) = -2.0F / (farval-nearval);
M(2,3) = -(farval+nearval) / (farval-nearval);
M(3,0) = 0.0F;
M(3,1) = 0.0F;
M(3,2) = 0.0F;
M(3,3) = 1.0F;
#undef M
}
/**
* Apply an orthographic projection matrix.
*
* \param mat matrix to apply the projection.
* \param left left clipping plane coordinate.
* \param right right clipping plane coordinate.
* \param bottom bottom clipping plane coordinate.
* \param top top clipping plane coordinate.
* \param nearval distance to the near clipping plane.
* \param farval distance to the far clipping plane.
*
* Creates the projection matrix and multiplies it with \p mat, marking the
* MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
*/
void
_math_matrix_ortho( GLmatrix *mat,
GLfloat left, GLfloat right,
GLfloat bottom, GLfloat top,
GLfloat nearval, GLfloat farval )
{
GLfloat m[16];
_math_float_ortho(m, left, right, bottom, top, nearval, farval);
matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION));
}
/**
* Multiply a matrix with a general scaling matrix.
*
* \param mat matrix.
* \param x x axis scale factor.
* \param y y axis scale factor.
* \param z z axis scale factor.
*
* Multiplies in-place the elements of \p mat by the scale factors. Checks if
* the scales factors are roughly the same, marking the MAT_FLAG_UNIFORM_SCALE
* flag, or MAT_FLAG_GENERAL_SCALE. Marks the MAT_DIRTY_TYPE and
* MAT_DIRTY_INVERSE dirty flags.
*/
void
_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
{
GLfloat *m = mat->m;
m[0] *= x; m[4] *= y; m[8] *= z;
m[1] *= x; m[5] *= y; m[9] *= z;
m[2] *= x; m[6] *= y; m[10] *= z;
m[3] *= x; m[7] *= y; m[11] *= z;
if (fabsf(x - y) < 1e-8F && fabsf(x - z) < 1e-8F)
mat->flags |= MAT_FLAG_UNIFORM_SCALE;
else
mat->flags |= MAT_FLAG_GENERAL_SCALE;
mat->flags |= (MAT_DIRTY_TYPE |
MAT_DIRTY_INVERSE);
}
/**
* Multiply a matrix with a translation matrix.
*
* \param mat matrix.
* \param x translation vector x coordinate.
* \param y translation vector y coordinate.
* \param z translation vector z coordinate.
*
* Adds the translation coordinates to the elements of \p mat in-place. Marks
* the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
* dirty flags.
*/
void
_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
{
GLfloat *m = mat->m;
m[12] = m[0] * x + m[4] * y + m[8] * z + m[12];
m[13] = m[1] * x + m[5] * y + m[9] * z + m[13];
m[14] = m[2] * x + m[6] * y + m[10] * z + m[14];
m[15] = m[3] * x + m[7] * y + m[11] * z + m[15];
mat->flags |= (MAT_FLAG_TRANSLATION |
MAT_DIRTY_TYPE |
MAT_DIRTY_INVERSE);
}
/**
* Set matrix to do viewport and depthrange mapping.
* Transforms Normalized Device Coords to window/Z values.
*/
void
_math_matrix_viewport(GLmatrix *m, const float scale[3],
const float translate[3], double depthMax)
{
m->m[0] = scale[0];
m->m[5] = scale[1];
m->m[10] = depthMax*scale[2];
m->m[12] = translate[0];
m->m[13] = translate[1];
m->m[14] = depthMax*translate[2];
m->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION;
m->type = MATRIX_3D_NO_ROT;
}
/**
* Set a matrix to the identity matrix.
*
* \param mat matrix.
*
* Copies ::Identity into \p GLmatrix::m, and into GLmatrix::inv if not NULL.
* Sets the matrix type to identity, and clear the dirty flags.
*/
void
_math_matrix_set_identity( GLmatrix *mat )
{
matrix_set_identity(mat->m);
matrix_set_identity(mat->inv);
mat->type = MATRIX_IDENTITY;
mat->flags &= ~(MAT_DIRTY_FLAGS|
MAT_DIRTY_TYPE|
MAT_DIRTY_INVERSE);
}
/*@}*/
/**********************************************************************/
/** \name Matrix analysis */
/*@{*/
#define ZERO(x) (1<<x)
#define ONE(x) (1<<(x+16))
#define MASK_NO_TRX (ZERO(12) | ZERO(13) | ZERO(14))
#define MASK_NO_2D_SCALE ( ONE(0) | ONE(5))
#define MASK_IDENTITY ( ONE(0) | ZERO(4) | ZERO(8) | ZERO(12) |\
ZERO(1) | ONE(5) | ZERO(9) | ZERO(13) |\
ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
#define MASK_2D_NO_ROT ( ZERO(4) | ZERO(8) | \
ZERO(1) | ZERO(9) | \
ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
#define MASK_2D ( ZERO(8) | \
ZERO(9) | \
ZERO(2) | ZERO(6) | ONE(10) | ZERO(14) |\
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
#define MASK_3D_NO_ROT ( ZERO(4) | ZERO(8) | \
ZERO(1) | ZERO(9) | \
ZERO(2) | ZERO(6) | \
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
#define MASK_3D ( \
\
\
ZERO(3) | ZERO(7) | ZERO(11) | ONE(15) )
#define MASK_PERSPECTIVE ( ZERO(4) | ZERO(12) |\
ZERO(1) | ZERO(13) |\
ZERO(2) | ZERO(6) | \
ZERO(3) | ZERO(7) | ZERO(15) )
#define SQ(x) ((x)*(x))
/**
* Determine type and flags from scratch.
*
* \param mat matrix.
*
* This is expensive enough to only want to do it once.
*/
static void analyse_from_scratch( GLmatrix *mat )
{
const GLfloat *m = mat->m;
GLuint mask = 0;
GLuint i;
for (i = 0 ; i < 16 ; i++) {
if (m[i] == 0.0F) mask |= (1<<i);
}
if (m[0] == 1.0F) mask |= (1<<16);
if (m[5] == 1.0F) mask |= (1<<21);
if (m[10] == 1.0F) mask |= (1<<26);
if (m[15] == 1.0F) mask |= (1<<31);
mat->flags &= ~MAT_FLAGS_GEOMETRY;
/* Check for translation - no-one really cares
*/
if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
mat->flags |= MAT_FLAG_TRANSLATION;
/* Do the real work
*/
if (mask == (GLuint) MASK_IDENTITY) {
mat->type = MATRIX_IDENTITY;
}
else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) {
mat->type = MATRIX_2D_NO_ROT;
if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE)
mat->flags |= MAT_FLAG_GENERAL_SCALE;
}
else if ((mask & MASK_2D) == (GLuint) MASK_2D) {
GLfloat mm = DOT2(m, m);
GLfloat m4m4 = DOT2(m+4,m+4);
GLfloat mm4 = DOT2(m,m+4);
mat->type = MATRIX_2D;
/* Check for scale */
if (SQ(mm-1) > SQ(1e-6F) ||
SQ(m4m4-1) > SQ(1e-6F))
mat->flags |= MAT_FLAG_GENERAL_SCALE;
/* Check for rotation */
if (SQ(mm4) > SQ(1e-6F))
mat->flags |= MAT_FLAG_GENERAL_3D;
else
mat->flags |= MAT_FLAG_ROTATION;
}
else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) {
mat->type = MATRIX_3D_NO_ROT;
/* Check for scale */
if (SQ(m[0]-m[5]) < SQ(1e-6F) &&
SQ(m[0]-m[10]) < SQ(1e-6F)) {
if (SQ(m[0]-1.0F) > SQ(1e-6F)) {
mat->flags |= MAT_FLAG_UNIFORM_SCALE;
}
}
else {
mat->flags |= MAT_FLAG_GENERAL_SCALE;
}
}
else if ((mask & MASK_3D) == (GLuint) MASK_3D) {
GLfloat c1 = DOT3(m,m);
GLfloat c2 = DOT3(m+4,m+4);
GLfloat c3 = DOT3(m+8,m+8);
GLfloat d1 = DOT3(m, m+4);
GLfloat cp[3];
mat->type = MATRIX_3D;
/* Check for scale */
if (SQ(c1-c2) < SQ(1e-6F) && SQ(c1-c3) < SQ(1e-6F)) {
if (SQ(c1-1.0F) > SQ(1e-6F))
mat->flags |= MAT_FLAG_UNIFORM_SCALE;
/* else no scale at all */
}
else {
mat->flags |= MAT_FLAG_GENERAL_SCALE;
}
/* Check for rotation */
if (SQ(d1) < SQ(1e-6F)) {
CROSS3( cp, m, m+4 );
SUB_3V( cp, cp, (m+8) );
if (LEN_SQUARED_3FV(cp) < SQ(1e-6F))
mat->flags |= MAT_FLAG_ROTATION;
else
mat->flags |= MAT_FLAG_GENERAL_3D;
}
else {
mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */
}
}
else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) {
mat->type = MATRIX_PERSPECTIVE;
mat->flags |= MAT_FLAG_GENERAL;
}
else {
mat->type = MATRIX_GENERAL;
mat->flags |= MAT_FLAG_GENERAL;
}
}
/**
* Analyze a matrix given that its flags are accurate.
*
* This is the more common operation, hopefully.
*/
static void analyse_from_flags( GLmatrix *mat )
{
const GLfloat *m = mat->m;
if (TEST_MAT_FLAGS(mat, 0)) {
mat->type = MATRIX_IDENTITY;
}
else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION |
MAT_FLAG_UNIFORM_SCALE |
MAT_FLAG_GENERAL_SCALE))) {
if ( m[10]==1.0F && m[14]==0.0F ) {
mat->type = MATRIX_2D_NO_ROT;
}
else {
mat->type = MATRIX_3D_NO_ROT;
}
}
else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) {
if ( m[ 8]==0.0F
&& m[ 9]==0.0F
&& m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) {
mat->type = MATRIX_2D;
}
else {
mat->type = MATRIX_3D;
}
}
else if ( m[4]==0.0F && m[12]==0.0F
&& m[1]==0.0F && m[13]==0.0F
&& m[2]==0.0F && m[6]==0.0F
&& m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) {
mat->type = MATRIX_PERSPECTIVE;
}
else {
mat->type = MATRIX_GENERAL;
}
}
/**
* Analyze and update a matrix.
*
* \param mat matrix.
*
* If the matrix type is dirty then calls either analyse_from_scratch() or
* analyse_from_flags() to determine its type, according to whether the flags
* are dirty or not, respectively. If the matrix has an inverse and it's dirty
* then calls matrix_invert(). Finally clears the dirty flags.
*/
void
_math_matrix_analyse( GLmatrix *mat )
{
if (mat->flags & MAT_DIRTY_TYPE) {
if (mat->flags & MAT_DIRTY_FLAGS)
analyse_from_scratch( mat );
else
analyse_from_flags( mat );
}
if (mat->flags & MAT_DIRTY_INVERSE) {
matrix_invert( mat );
mat->flags &= ~MAT_DIRTY_INVERSE;
}
mat->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE);
}
/*@}*/
/**
* Test if the given matrix preserves vector lengths.
*/
GLboolean
_math_matrix_is_length_preserving( const GLmatrix *m )
{
return TEST_MAT_FLAGS( m, MAT_FLAGS_LENGTH_PRESERVING);
}
GLboolean
_math_matrix_is_dirty( const GLmatrix *m )
{
return (m->flags & MAT_DIRTY) ? GL_TRUE : GL_FALSE;
}
/**********************************************************************/
/** \name Matrix setup */
/*@{*/
/**
* Copy a matrix.
*
* \param to destination matrix.
* \param from source matrix.
*
* Copies all fields in GLmatrix, creating an inverse array if necessary.
*/
void
_math_matrix_copy( GLmatrix *to, const GLmatrix *from )
{
memcpy(to->m, from->m, 16 * sizeof(GLfloat));
memcpy(to->inv, from->inv, 16 * sizeof(GLfloat));
to->flags = from->flags;
to->type = from->type;
}
/**
* Copy a matrix as part of glPushMatrix.
*
* The makes the source matrix canonical (inverse and flags are up-to-date),
* so that later glPopMatrix is evaluated as a no-op if there is no state
* change.
*
* It this wasn't done, a draw call would canonicalize the matrix, which
* would make it different from the pushed one and so glPopMatrix wouldn't be
* recognized as a no-op.
*/
void
_math_matrix_push_copy(GLmatrix *to, GLmatrix *from)
{
if (from->flags & MAT_DIRTY)
_math_matrix_analyse(from);
_math_matrix_copy(to, from);
}
/**
* Loads a matrix array into GLmatrix.
*
* \param m matrix array.
* \param mat matrix.
*
* Copies \p m into GLmatrix::m and marks the MAT_FLAG_GENERAL and MAT_DIRTY
* flags.
*/
void
_math_matrix_loadf( GLmatrix *mat, const GLfloat *m )
{
memcpy( mat->m, m, 16*sizeof(GLfloat) );
mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);
}
/**
* Matrix constructor.
*
* \param m matrix.
*
* Initialize the GLmatrix fields.
*/
void
_math_matrix_ctr( GLmatrix *m )
{
memset(m, 0, sizeof(*m));
matrix_set_identity(m->m);
matrix_set_identity(m->inv);
m->type = MATRIX_IDENTITY;
m->flags = 0;
}
/*@}*/
/**********************************************************************/
/** \name Matrix transpose */
/*@{*/
/**
* Transpose a GLfloat matrix.
*
* \param to destination array.
* \param from source array.
*/
void
_math_transposef( GLfloat to[16], const GLfloat from[16] )
{
to[0] = from[0];
to[1] = from[4];
to[2] = from[8];
to[3] = from[12];
to[4] = from[1];
to[5] = from[5];
to[6] = from[9];
to[7] = from[13];
to[8] = from[2];
to[9] = from[6];
to[10] = from[10];
to[11] = from[14];
to[12] = from[3];
to[13] = from[7];
to[14] = from[11];
to[15] = from[15];
}
/**
* Transpose a GLdouble matrix.
*
* \param to destination array.
* \param from source array.
*/
void
_math_transposed( GLdouble to[16], const GLdouble from[16] )
{
to[0] = from[0];
to[1] = from[4];
to[2] = from[8];
to[3] = from[12];
to[4] = from[1];
to[5] = from[5];
to[6] = from[9];
to[7] = from[13];
to[8] = from[2];
to[9] = from[6];
to[10] = from[10];
to[11] = from[14];
to[12] = from[3];
to[13] = from[7];
to[14] = from[11];
to[15] = from[15];
}
/**
* Transpose a GLdouble matrix and convert to GLfloat.
*
* \param to destination array.
* \param from source array.
*/
void
_math_transposefd( GLfloat to[16], const GLdouble from[16] )
{
to[0] = (GLfloat) from[0];
to[1] = (GLfloat) from[4];
to[2] = (GLfloat) from[8];
to[3] = (GLfloat) from[12];
to[4] = (GLfloat) from[1];
to[5] = (GLfloat) from[5];
to[6] = (GLfloat) from[9];
to[7] = (GLfloat) from[13];
to[8] = (GLfloat) from[2];
to[9] = (GLfloat) from[6];
to[10] = (GLfloat) from[10];
to[11] = (GLfloat) from[14];
to[12] = (GLfloat) from[3];
to[13] = (GLfloat) from[7];
to[14] = (GLfloat) from[11];
to[15] = (GLfloat) from[15];
}
/*@}*/
/**
* Transform a 4-element row vector (1x4 matrix) by a 4x4 matrix. This
* function is used for transforming clipping plane equations and spotlight
* directions.
* Mathematically, u = v * m.
* Input: v - input vector
* m - transformation matrix
* Output: u - transformed vector
*/
void
_mesa_transform_vector( GLfloat u[4], const GLfloat v[4], const GLfloat m[16] )
{
const GLfloat v0 = v[0], v1 = v[1], v2 = v[2], v3 = v[3];
#define M(row,col) m[row + col*4]
u[0] = v0 * M(0,0) + v1 * M(1,0) + v2 * M(2,0) + v3 * M(3,0);
u[1] = v0 * M(0,1) + v1 * M(1,1) + v2 * M(2,1) + v3 * M(3,1);
u[2] = v0 * M(0,2) + v1 * M(1,2) + v2 * M(2,2) + v3 * M(3,2);
u[3] = v0 * M(0,3) + v1 * M(1,3) + v2 * M(2,3) + v3 * M(3,3);
#undef M
}
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