/cogl/cogl-matrix.c
C | 1659 lines | 1042 code | 188 blank | 429 comment | 170 complexity | d11f21eab356638b55e595e0efac5062 MD5 | raw file
- /*
- * Cogl
- *
- * An object oriented GL/GLES Abstraction/Utility Layer
- *
- * Copyright (C) 2009,2010,2011 Intel Corporation.
- *
- * This 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 2 of the License, or (at your option) any later version.
- *
- * This 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 library. If not, see <http://www.gnu.org/licenses/>.
- *
- * Authors:
- * Robert Bragg <robert@linux.intel.com>
- */
- /*
- * 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
- * BRIAN PAUL 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.
- */
- /*
- * Note: a lot of this code is based on code that was taken from Mesa.
- *
- * Changes compared to the original code from Mesa:
- *
- * - instead of allocating matrix->m and matrix->inv using malloc, our
- * public CoglMatrix typedef is large enough to directly contain the
- * matrix, its inverse, a type and a set of flags.
- * - instead of having a _cogl_matrix_analyse which updates the type,
- * flags and inverse, we have _cogl_matrix_update_inverse which
- * essentially does the same thing (internally making use of
- * _cogl_matrix_update_type_and_flags()) but with additional guards in
- * place to bail out when the inverse matrix is still valid.
- * - when initializing a matrix with the identity matrix we don't
- * immediately initialize the inverse matrix; rather we just set the
- * dirty flag for the inverse (since it's likely the user won't request
- * the inverse of the identity matrix)
- */
- #ifdef HAVE_CONFIG_H
- #include "config.h"
- #endif
- #include <cogl.h>
- #include <cogl-util.h>
- #include <cogl-debug.h>
- #include <cogl-quaternion.h>
- #include <cogl-quaternion-private.h>
- #include <cogl-matrix.h>
- #include <cogl-matrix-private.h>
- #include <cogl-quaternion-private.h>
- #include <glib.h>
- #include <math.h>
- #include <string.h>
- #ifdef _COGL_SUPPORTS_GTYPE_INTEGRATION
- #include <cogl-gtype-private.h>
- COGL_GTYPE_DEFINE_BOXED ("Matrix", matrix,
- cogl_matrix_copy,
- cogl_matrix_free);
- #endif
- /*
- * Symbolic names to some of the entries in the matrix
- *
- * These are handy for the viewport mapping, which is expressed as a matrix.
- */
- #define MAT_SX 0
- #define MAT_SY 5
- #define MAT_SZ 10
- #define MAT_TX 12
- #define MAT_TY 13
- #define MAT_TZ 14
- /*
- * These identify different kinds of 4x4 transformation matrices and we use
- * this information to find fast-paths when available.
- */
- enum CoglMatrixType {
- COGL_MATRIX_TYPE_GENERAL, /**< general 4x4 matrix */
- COGL_MATRIX_TYPE_IDENTITY, /**< identity matrix */
- COGL_MATRIX_TYPE_3D_NO_ROT, /**< orthogonal projection and others... */
- COGL_MATRIX_TYPE_PERSPECTIVE, /**< perspective projection matrix */
- COGL_MATRIX_TYPE_2D, /**< 2-D transformation */
- COGL_MATRIX_TYPE_2D_NO_ROT, /**< 2-D scale & translate only */
- COGL_MATRIX_TYPE_3D, /**< 3-D transformation */
- COGL_MATRIX_N_TYPES
- } ;
- #define DEG2RAD (G_PI/180.0)
- /* Dot product of two 2-element vectors */
- #define DOT2(A,B) ( (A)[0]*(B)[0] + (A)[1]*(B)[1] )
- /* Dot product of two 3-element vectors */
- #define DOT3(A,B) ( (A)[0]*(B)[0] + (A)[1]*(B)[1] + (A)[2]*(B)[2] )
- #define CROSS3(N, U, V) \
- do { \
- (N)[0] = (U)[1]*(V)[2] - (U)[2]*(V)[1]; \
- (N)[1] = (U)[2]*(V)[0] - (U)[0]*(V)[2]; \
- (N)[2] = (U)[0]*(V)[1] - (U)[1]*(V)[0]; \
- } while (0)
- #define SUB_3V(DST, SRCA, SRCB) \
- do { \
- (DST)[0] = (SRCA)[0] - (SRCB)[0]; \
- (DST)[1] = (SRCA)[1] - (SRCB)[1]; \
- (DST)[2] = (SRCA)[2] - (SRCB)[2]; \
- } while (0)
- #define LEN_SQUARED_3FV( V ) ((V)[0]*(V)[0]+(V)[1]*(V)[1]+(V)[2]*(V)[2])
- /*
- * \defgroup MatFlags MAT_FLAG_XXX-flags
- *
- * Bitmasks to indicate different kinds of 4x4 matrices in CoglMatrix::flags
- */
- #define MAT_FLAG_IDENTITY 0 /*< is an identity matrix flag.
- * (Not actually used - the identity
- * matrix is identified by the absense
- * 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_ALL (MAT_DIRTY_TYPE | \
- MAT_DIRTY_FLAGS | \
- MAT_DIRTY_INVERSE)
- /*
- * Test geometry related matrix flags.
- *
- * @mat a pointer to a CoglMatrix structure.
- * @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)
- /*
- * Names of the corresponding CoglMatrixType values.
- */
- static const char *types[] = {
- "COGL_MATRIX_TYPE_GENERAL",
- "COGL_MATRIX_TYPE_IDENTITY",
- "COGL_MATRIX_TYPE_3D_NO_ROT",
- "COGL_MATRIX_TYPE_PERSPECTIVE",
- "COGL_MATRIX_TYPE_2D",
- "COGL_MATRIX_TYPE_2D_NO_ROT",
- "COGL_MATRIX_TYPE_3D"
- };
- /*
- * Identity matrix.
- */
- static float identity[16] = {
- 1.0, 0.0, 0.0, 0.0,
- 0.0, 1.0, 0.0, 0.0,
- 0.0, 0.0, 1.0, 0.0,
- 0.0, 0.0, 0.0, 1.0
- };
- #define A(row,col) a[(col<<2)+row]
- #define B(row,col) b[(col<<2)+row]
- #define R(row,col) result[(col<<2)+row]
- /*
- * Perform a full 4x4 matrix multiplication.
- *
- * <note>It's assumed that @result != @b. @product == @a is allowed.</note>
- *
- * <note>KW: 4*16 = 64 multiplications</note>
- */
- static void
- matrix_multiply4x4 (float *result, const float *a, const float *b)
- {
- int i;
- for (i = 0; i < 4; i++)
- {
- const float ai0 = A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3);
- R(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
- R(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
- R(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
- R(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.
- *
- * @a matrix.
- * @b matrix.
- * @product will receive the product of \p a and \p b.
- */
- static void
- matrix_multiply3x4 (float *result, const float *a, const float *b)
- {
- int i;
- for (i = 0; i < 3; i++)
- {
- const float ai0 = A(i,0), ai1 = A(i,1), ai2 = A(i,2), ai3 = A(i,3);
- R(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0);
- R(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1);
- R(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2);
- R(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3;
- }
- R(3,0) = 0;
- R(3,1) = 0;
- R(3,2) = 0;
- R(3,3) = 1;
- }
- #undef A
- #undef B
- #undef R
- /*
- * Multiply a matrix by an array of floats with known properties.
- *
- * @mat pointer to a CoglMatrix structure containing the left multiplication
- * matrix, and that will receive the product result.
- * @m right multiplication matrix array.
- * @flags flags of the matrix \p m.
- *
- * Joins both flags and marks the type and inverse as dirty. Calls
- * matrix_multiply3x4() if both matrices are 3D, or matrix_multiply4x4()
- * otherwise.
- */
- static void
- matrix_multiply_array_with_flags (CoglMatrix *result,
- const float *array,
- unsigned int flags)
- {
- result->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
- if (TEST_MAT_FLAGS (result, MAT_FLAGS_3D))
- matrix_multiply3x4 ((float *)result, (float *)result, array);
- else
- matrix_multiply4x4 ((float *)result, (float *)result, array);
- }
- /* Joins both flags and marks the type and inverse as dirty. Calls
- * matrix_multiply3x4() if both matrices are 3D, or matrix_multiply4x4()
- * otherwise.
- */
- static void
- _cogl_matrix_multiply (CoglMatrix *result,
- const CoglMatrix *a,
- const CoglMatrix *b)
- {
- result->flags = (a->flags |
- b->flags |
- MAT_DIRTY_TYPE |
- MAT_DIRTY_INVERSE);
- if (TEST_MAT_FLAGS(result, MAT_FLAGS_3D))
- matrix_multiply3x4 ((float *)result, (float *)a, (float *)b);
- else
- matrix_multiply4x4 ((float *)result, (float *)a, (float *)b);
- }
- void
- cogl_matrix_multiply (CoglMatrix *result,
- const CoglMatrix *a,
- const CoglMatrix *b)
- {
- _cogl_matrix_multiply (result, a, b);
- _COGL_MATRIX_DEBUG_PRINT (result);
- }
- #if 0
- /* Marks the matrix flags with general flag, and type and inverse dirty flags.
- * Calls matrix_multiply4x4() for the multiplication.
- */
- static void
- _cogl_matrix_multiply_array (CoglMatrix *result, const float *array)
- {
- result->flags |= (MAT_FLAG_GENERAL |
- MAT_DIRTY_TYPE |
- MAT_DIRTY_INVERSE |
- MAT_DIRTY_FLAGS);
- matrix_multiply4x4 ((float *)result, (float *)result, (float *)array);
- }
- #endif
- /*
- * Print a matrix array.
- *
- * Called by _cogl_matrix_print() to print a matrix or its inverse.
- */
- static void
- print_matrix_floats (const float m[16])
- {
- int i;
- for (i = 0;i < 4; i++)
- g_print ("\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
- }
- /*
- * Dumps the contents of a CoglMatrix structure.
- */
- void
- _cogl_matrix_print (const CoglMatrix *matrix)
- {
- if (!(matrix->flags & MAT_DIRTY_TYPE))
- {
- _COGL_RETURN_IF_FAIL (matrix->type < COGL_MATRIX_N_TYPES);
- g_print ("Matrix type: %s, flags: %x\n",
- types[matrix->type], (int)matrix->flags);
- }
- else
- g_print ("Matrix type: DIRTY, flags: %x\n", (int)matrix->flags);
- print_matrix_floats ((float *)matrix);
- g_print ("Inverse: \n");
- if (!(matrix->flags & MAT_DIRTY_INVERSE))
- {
- float prod[16];
- print_matrix_floats (matrix->inv);
- matrix_multiply4x4 (prod, (float *)matrix, matrix->inv);
- g_print ("Mat * Inverse:\n");
- print_matrix_floats (prod);
- }
- else
- g_print (" - not available\n");
- }
- /*
- * References an element of 4x4 matrix.
- *
- * @m matrix array.
- * @c column of the desired element.
- * @r row of the desired element.
- *
- * Returns: 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)]
- /*
- * Swaps the values of two floating pointer variables.
- *
- * Used by invert_matrix_general() to swap the row pointers.
- */
- #define SWAP_ROWS(a, b) { float *_tmp = a; (a)=(b); (b)=_tmp; }
- /*
- * Compute inverse of 4x4 transformation matrix.
- *
- * @mat pointer to a CoglMatrix structure. The matrix inverse will be
- * stored in the CoglMatrix::inv attribute.
- *
- * Returns: %TRUE for success, %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 gboolean
- invert_matrix_general (CoglMatrix *matrix)
- {
- const float *m = (float *)matrix;
- float *out = matrix->inv;
- float wtmp[4][8];
- float m0, m1, m2, m3, s;
- float *r0, *r1, *r2, *r3;
- r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
- r0[0] = MAT (m, 0, 0), r0[1] = MAT (m, 0, 1),
- r0[2] = MAT (m, 0, 2), r0[3] = MAT (m, 0, 3),
- r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
- r1[0] = MAT (m, 1, 0), r1[1] = MAT (m, 1, 1),
- r1[2] = MAT (m, 1, 2), r1[3] = MAT (m, 1, 3),
- r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
- r2[0] = MAT (m, 2, 0), r2[1] = MAT (m, 2, 1),
- r2[2] = MAT (m, 2, 2), r2[3] = MAT (m, 2, 3),
- r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
- r3[0] = MAT (m, 3, 0), r3[1] = MAT (m, 3, 1),
- r3[2] = MAT (m, 3, 2), r3[3] = MAT (m, 3, 3),
- r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
- /* choose pivot - or die */
- if (fabsf (r3[0]) > fabsf (r2[0]))
- SWAP_ROWS (r3, r2);
- if (fabsf (r2[0]) > fabsf (r1[0]))
- SWAP_ROWS (r2, r1);
- if (fabsf (r1[0]) > fabsf (r0[0]))
- SWAP_ROWS (r1, r0);
- if (0.0 == r0[0])
- return FALSE;
- /* eliminate first variable */
- m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0];
- s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
- s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
- s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
- s = r0[4];
- if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
- s = r0[5];
- if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
- s = r0[6];
- if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
- s = r0[7];
- if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
- /* choose pivot - or die */
- if (fabsf (r3[1]) > fabsf (r2[1]))
- SWAP_ROWS (r3, r2);
- if (fabsf (r2[1]) > fabsf (r1[1]))
- SWAP_ROWS (r2, r1);
- if (0.0 == r1[1])
- return FALSE;
- /* eliminate second variable */
- m2 = r2[1] / r1[1]; m3 = r3[1] / r1[1];
- r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2];
- r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3];
- s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
- s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
- s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
- s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }
- /* choose pivot - or die */
- if (fabsf (r3[2]) > fabsf (r2[2]))
- SWAP_ROWS (r3, r2);
- if (0.0 == r2[2])
- return FALSE;
- /* eliminate third variable */
- m3 = r3[2] / r2[2];
- r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
- r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6],
- r3[7] -= m3 * r2[7];
- /* last check */
- if (0.0 == r3[3])
- return FALSE;
- s = 1.0f / r3[3]; /* now back substitute row 3 */
- r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s;
- m2 = r2[3]; /* now back substitute row 2 */
- s = 1.0f / r2[2];
- r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
- r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
- m1 = r1[3];
- r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
- r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
- m0 = r0[3];
- r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
- r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
- m1 = r1[2]; /* now back substitute row 1 */
- s = 1.0f / r1[1];
- r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
- r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
- m0 = r0[2];
- r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
- r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
- m0 = r0[1]; /* now back substitute row 0 */
- s = 1.0f / r0[0];
- r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
- r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
- MAT (out, 0, 0) = r0[4]; MAT (out, 0, 1) = r0[5],
- MAT (out, 0, 2) = r0[6]; MAT (out, 0, 3) = r0[7],
- MAT (out, 1, 0) = r1[4]; MAT (out, 1, 1) = r1[5],
- MAT (out, 1, 2) = r1[6]; MAT (out, 1, 3) = r1[7],
- MAT (out, 2, 0) = r2[4]; MAT (out, 2, 1) = r2[5],
- MAT (out, 2, 2) = r2[6]; MAT (out, 2, 3) = r2[7],
- MAT (out, 3, 0) = r3[4]; MAT (out, 3, 1) = r3[5],
- MAT (out, 3, 2) = r3[6]; MAT (out, 3, 3) = r3[7];
- return TRUE;
- }
- #undef SWAP_ROWS
- /*
- * Compute inverse of a general 3d transformation matrix.
- *
- * @mat pointer to a CoglMatrix structure. The matrix inverse will be
- * stored in the CoglMatrix::inv attribute.
- *
- * Returns: %TRUE for success, %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 gboolean
- invert_matrix_3d_general (CoglMatrix *matrix)
- {
- const float *in = (float *)matrix;
- float *out = matrix->inv;
- float pos, neg, t;
- float 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 >= 0.0) pos += t; else neg += t;
- t = MAT (in,1,0) * MAT (in,2,1) * MAT (in,0,2);
- if (t >= 0.0) pos += t; else neg += t;
- t = MAT (in,2,0) * MAT (in,0,1) * MAT (in,1,2);
- if (t >= 0.0) pos += t; else neg += t;
- t = -MAT (in,2,0) * MAT (in,1,1) * MAT (in,0,2);
- if (t >= 0.0) pos += t; else neg += t;
- t = -MAT (in,1,0) * MAT (in,0,1) * MAT (in,2,2);
- if (t >= 0.0) pos += t; else neg += t;
- t = -MAT (in,0,0) * MAT (in,2,1) * MAT (in,1,2);
- if (t >= 0.0) pos += t; else neg += t;
- det = pos + neg;
- if (det*det < 1e-25)
- return 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 TRUE;
- }
- /*
- * Compute inverse of a 3d transformation matrix.
- *
- * @mat pointer to a CoglMatrix structure. The matrix inverse will be
- * stored in the CoglMatrix::inv attribute.
- *
- * Returns: %TRUE for success, %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 gboolean
- invert_matrix_3d (CoglMatrix *matrix)
- {
- const float *in = (float *)matrix;
- float *out = matrix->inv;
- if (!TEST_MAT_FLAGS(matrix, MAT_FLAGS_ANGLE_PRESERVING))
- return invert_matrix_3d_general (matrix);
- if (matrix->flags & MAT_FLAG_UNIFORM_SCALE)
- {
- float 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 == 0.0)
- return 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 (matrix->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 */
- memcpy (out, identity, 16 * sizeof (float));
- 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 TRUE;
- }
- if (matrix->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 TRUE;
- }
- /*
- * Compute inverse of an identity transformation matrix.
- *
- * @mat pointer to a CoglMatrix structure. The matrix inverse will be
- * stored in the CoglMatrix::inv attribute.
- *
- * Returns: always %TRUE.
- *
- * Simply copies identity into CoglMatrix::inv.
- */
- static gboolean
- invert_matrix_identity (CoglMatrix *matrix)
- {
- memcpy (matrix->inv, identity, 16 * sizeof (float));
- return TRUE;
- }
- /*
- * Compute inverse of a no-rotation 3d transformation matrix.
- *
- * @mat pointer to a CoglMatrix structure. The matrix inverse will be
- * stored in the CoglMatrix::inv attribute.
- *
- * Returns: %TRUE for success, %FALSE for failure (\p singular matrix).
- *
- * Calculates the
- */
- static gboolean
- invert_matrix_3d_no_rotation (CoglMatrix *matrix)
- {
- const float *in = (float *)matrix;
- float *out = matrix->inv;
- if (MAT (in,0,0) == 0 || MAT (in,1,1) == 0 || MAT (in,2,2) == 0)
- return FALSE;
- memcpy (out, identity, 16 * sizeof (float));
- 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 (matrix->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 TRUE;
- }
- /*
- * Compute inverse of a no-rotation 2d transformation matrix.
- *
- * @mat pointer to a CoglMatrix structure. The matrix inverse will be
- * stored in the CoglMatrix::inv attribute.
- *
- * Returns: %TRUE for success, %FALSE for failure (\p singular matrix).
- *
- * Calculates the inverse matrix by applying the inverse scaling and
- * translation to the identity matrix.
- */
- static gboolean
- invert_matrix_2d_no_rotation (CoglMatrix *matrix)
- {
- const float *in = (float *)matrix;
- float *out = matrix->inv;
- if (MAT (in, 0, 0) == 0 || MAT (in, 1, 1) == 0)
- return FALSE;
- memcpy (out, identity, 16 * sizeof (float));
- MAT (out, 0, 0) = 1.0f / MAT (in, 0, 0);
- MAT (out, 1, 1) = 1.0f / MAT (in, 1, 1);
- if (matrix->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 TRUE;
- }
- #if 0
- /* broken */
- static gboolean
- invert_matrix_perspective (CoglMatrix *matrix)
- {
- const float *in = matrix;
- float *out = matrix->inv;
- if (MAT (in,2,3) == 0)
- return FALSE;
- memcpy( out, identity, 16 * sizeof(float) );
- MAT (out, 0, 0) = 1.0f / MAT (in, 0, 0);
- MAT (out, 1, 1) = 1.0f / MAT (in, 1, 1);
- MAT (out, 0, 3) = MAT (in, 0, 2);
- MAT (out, 1, 3) = MAT (in, 1, 2);
- MAT (out,2,2) = 0;
- MAT (out,2,3) = -1;
- MAT (out,3,2) = 1.0f / MAT (in,2,3);
- MAT (out,3,3) = MAT (in,2,2) * MAT (out,3,2);
- return TRUE;
- }
- #endif
- /*
- * Matrix inversion function pointer type.
- */
- typedef gboolean (*inv_mat_func)(CoglMatrix *matrix);
- /*
- * 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_rotation,
- #if 0
- /* Don't use this function for now - it fails when the projection matrix
- * is premultiplied by a translation (ala Chromium's tilesort SPU).
- */
- invert_matrix_perspective,
- #else
- invert_matrix_general,
- #endif
- invert_matrix_3d, /* lazy! */
- invert_matrix_2d_no_rotation,
- invert_matrix_3d
- };
- #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.
- *
- * This is expensive enough to only want to do it once.
- */
- static void
- analyse_from_scratch (CoglMatrix *matrix)
- {
- const float *m = (float *)matrix;
- unsigned int mask = 0;
- unsigned int i;
- for (i = 0 ; i < 16 ; i++)
- {
- if (m[i] == 0.0) 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);
- matrix->flags &= ~MAT_FLAGS_GEOMETRY;
- /* Check for translation - no-one really cares
- */
- if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
- matrix->flags |= MAT_FLAG_TRANSLATION;
- /* Do the real work
- */
- if (mask == (unsigned int) MASK_IDENTITY)
- matrix->type = COGL_MATRIX_TYPE_IDENTITY;
- else if ((mask & MASK_2D_NO_ROT) == (unsigned int) MASK_2D_NO_ROT)
- {
- matrix->type = COGL_MATRIX_TYPE_2D_NO_ROT;
- if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE)
- matrix->flags |= MAT_FLAG_GENERAL_SCALE;
- }
- else if ((mask & MASK_2D) == (unsigned int) MASK_2D)
- {
- float mm = DOT2 (m, m);
- float m4m4 = DOT2 (m+4,m+4);
- float mm4 = DOT2 (m,m+4);
- matrix->type = COGL_MATRIX_TYPE_2D;
- /* Check for scale */
- if (SQ (mm-1) > SQ (1e-6) ||
- SQ (m4m4-1) > SQ (1e-6))
- matrix->flags |= MAT_FLAG_GENERAL_SCALE;
- /* Check for rotation */
- if (SQ (mm4) > SQ (1e-6))
- matrix->flags |= MAT_FLAG_GENERAL_3D;
- else
- matrix->flags |= MAT_FLAG_ROTATION;
- }
- else if ((mask & MASK_3D_NO_ROT) == (unsigned int) MASK_3D_NO_ROT)
- {
- matrix->type = COGL_MATRIX_TYPE_3D_NO_ROT;
- /* Check for scale */
- if (SQ (m[0]-m[5]) < SQ (1e-6) &&
- SQ (m[0]-m[10]) < SQ (1e-6))
- {
- if (SQ (m[0]-1.0) > SQ (1e-6))
- matrix->flags |= MAT_FLAG_UNIFORM_SCALE;
- }
- else
- matrix->flags |= MAT_FLAG_GENERAL_SCALE;
- }
- else if ((mask & MASK_3D) == (unsigned int) MASK_3D)
- {
- float c1 = DOT3 (m,m);
- float c2 = DOT3 (m+4,m+4);
- float c3 = DOT3 (m+8,m+8);
- float d1 = DOT3 (m, m+4);
- float cp[3];
- matrix->type = COGL_MATRIX_TYPE_3D;
- /* Check for scale */
- if (SQ (c1-c2) < SQ (1e-6) && SQ (c1-c3) < SQ (1e-6))
- {
- if (SQ (c1-1.0) > SQ (1e-6))
- matrix->flags |= MAT_FLAG_UNIFORM_SCALE;
- /* else no scale at all */
- }
- else
- matrix->flags |= MAT_FLAG_GENERAL_SCALE;
- /* Check for rotation */
- if (SQ (d1) < SQ (1e-6))
- {
- CROSS3 ( cp, m, m+4);
- SUB_3V ( cp, cp, (m+8));
- if (LEN_SQUARED_3FV(cp) < SQ(1e-6))
- matrix->flags |= MAT_FLAG_ROTATION;
- else
- matrix->flags |= MAT_FLAG_GENERAL_3D;
- }
- else
- matrix->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */
- }
- else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0f)
- {
- matrix->type = COGL_MATRIX_TYPE_PERSPECTIVE;
- matrix->flags |= MAT_FLAG_GENERAL;
- }
- else
- {
- matrix->type = COGL_MATRIX_TYPE_GENERAL;
- matrix->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 (CoglMatrix *matrix)
- {
- const float *m = (float *)matrix;
- if (TEST_MAT_FLAGS(matrix, 0))
- matrix->type = COGL_MATRIX_TYPE_IDENTITY;
- else if (TEST_MAT_FLAGS(matrix, (MAT_FLAG_TRANSLATION |
- MAT_FLAG_UNIFORM_SCALE |
- MAT_FLAG_GENERAL_SCALE)))
- {
- if ( m[10] == 1.0f && m[14] == 0.0f )
- matrix->type = COGL_MATRIX_TYPE_2D_NO_ROT;
- else
- matrix->type = COGL_MATRIX_TYPE_3D_NO_ROT;
- }
- else if (TEST_MAT_FLAGS (matrix, 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)
- {
- matrix->type = COGL_MATRIX_TYPE_2D;
- }
- else
- matrix->type = COGL_MATRIX_TYPE_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)
- {
- matrix->type = COGL_MATRIX_TYPE_PERSPECTIVE;
- }
- else
- matrix->type = COGL_MATRIX_TYPE_GENERAL;
- }
- /*
- * Analyze and update the type and flags of a 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.
- */
- static void
- _cogl_matrix_update_type_and_flags (CoglMatrix *matrix)
- {
- if (matrix->flags & MAT_DIRTY_TYPE)
- {
- if (matrix->flags & MAT_DIRTY_FLAGS)
- analyse_from_scratch (matrix);
- else
- analyse_from_flags (matrix);
- }
- matrix->flags &= ~(MAT_DIRTY_FLAGS | MAT_DIRTY_TYPE);
- }
- /*
- * Compute inverse of a transformation matrix.
- *
- * @mat pointer to a CoglMatrix structure. The matrix inverse will be
- * stored in the CoglMatrix::inv attribute.
- *
- * Returns: %TRUE for success, %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 CoglMatrix::inv.
- */
- static gboolean
- _cogl_matrix_update_inverse (CoglMatrix *matrix)
- {
- if (matrix->flags & MAT_DIRTY_FLAGS ||
- matrix->flags & MAT_DIRTY_INVERSE)
- {
- _cogl_matrix_update_type_and_flags (matrix);
- if (inv_mat_tab[matrix->type](matrix))
- matrix->flags &= ~MAT_FLAG_SINGULAR;
- else
- {
- matrix->flags |= MAT_FLAG_SINGULAR;
- memcpy (matrix->inv, identity, 16 * sizeof (float));
- }
- matrix->flags &= ~MAT_DIRTY_INVERSE;
- }
- if (matrix->flags & MAT_FLAG_SINGULAR)
- return FALSE;
- else
- return TRUE;
- }
- gboolean
- cogl_matrix_get_inverse (const CoglMatrix *matrix, CoglMatrix *inverse)
- {
- if (_cogl_matrix_update_inverse ((CoglMatrix *)matrix))
- {
- cogl_matrix_init_from_array (inverse, matrix->inv);
- return TRUE;
- }
- else
- {
- cogl_matrix_init_identity (inverse);
- return FALSE;
- }
- }
- /*
- * 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).
- */
- static void
- _cogl_matrix_rotate (CoglMatrix *matrix,
- float angle,
- float x,
- float y,
- float z)
- {
- float xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
- float m[16];
- gboolean optimized;
- s = sinf (angle * DEG2RAD);
- c = cosf (angle * DEG2RAD);
- memcpy (m, identity, 16 * sizeof (float));
- optimized = FALSE;
- #define M(row,col) m[col*4+row]
- if (x == 0.0f)
- {
- if (y == 0.0f)
- {
- if (z != 0.0f)
- {
- optimized = 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 = 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 = 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 float mag = sqrtf (x * x + y * y + z * z);
- if (mag <= 1.0e-4)
- {
- /* 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 it's 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_multiply_array_with_flags (matrix, m, MAT_FLAG_ROTATION);
- }
- void
- cogl_matrix_rotate (CoglMatrix *matrix,
- float angle,
- float x,
- float y,
- float z)
- {
- _cogl_matrix_rotate (matrix, angle, x, y, z);
- _COGL_MATRIX_DEBUG_PRINT (matrix);
- }
- /*
- * Apply a perspective projection matrix.
- *
- * Creates the projection matrix and multiplies it with matrix, marking the
- * MAT_FLAG_PERSPECTIVE flag.
- */
- static void
- _cogl_matrix_frustum (CoglMatrix *matrix,
- float left,
- float right,
- float bottom,
- float top,
- float nearval,
- float farval)
- {
- float x, y, a, b, c, d;
- float 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_multiply_array_with_flags (matrix, m, MAT_FLAG_PERSPECTIVE);
- }
- void
- cogl_matrix_frustum (CoglMatrix *matrix,
- float left,
- float right,
- float bottom,
- float top,
- float z_near,
- float z_far)
- {
- _cogl_matrix_frustum (matrix, left, right, bottom, top, z_near, z_far);
- _COGL_MATRIX_DEBUG_PRINT (matrix);
- }
- void
- cogl_matrix_perspective (CoglMatrix *matrix,
- float fov_y,
- float aspect,
- float z_near,
- float z_far)
- {
- float ymax = z_near * tan (fov_y * G_PI / 360.0);
- cogl_matrix_frustum (matrix,
- -ymax * aspect, /* left */
- ymax * aspect, /* right */
- -ymax, /* bottom */
- ymax, /* top */
- z_near,
- z_far);
- _COGL_MATRIX_DEBUG_PRINT (matrix);
- }
- /*
- * Apply an orthographic projection matrix.
- *
- * Creates the projection matrix and multiplies it with matrix, marking the
- * MAT_FLAG_GENERAL_SCALE and MAT_FLAG_TRANSLATION flags.
- */
- static void
- _cogl_matrix_orthographic (CoglMatrix *matrix,
- float x_1,
- float y_1,
- float x_2,
- float y_2,
- float nearval,
- float farval)
- {
- float m[16];
- #define M(row, col) m[col * 4 + row]
- M (0,0) = 2.0f / (x_2 - x_1);
- M (0,1) = 0.0f;
- M (0,2) = 0.0f;
- M (0,3) = -(x_2 + x_1) / (x_2 - x_1);
- M (1,0) = 0.0f;
- M (1,1) = 2.0f / (y_1 - y_2);
- M (1,2) = 0.0f;
- M (1,3) = -(y_1 + y_2) / (y_1 - y_2);
- 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
- matrix_multiply_array_with_flags (matrix, m,
- (MAT_FLAG_GENERAL_SCALE |
- MAT_FLAG_TRANSLATION));
- }
- void
- cogl_matrix_ortho (CoglMatrix *matrix,
- float left,
- float right,
- float bottom,
- float top,
- float near,
- float far)
- {
- _cogl_matrix_orthographic (matrix, left, top, right, bottom, near, far);
- _COGL_MATRIX_DEBUG_PRINT (matrix);
- }
- void
- cogl_matrix_orthographic (CoglMatrix *matrix,
- float x_1,
- float y_1,
- float x_2,
- float y_2,
- float near,
- float far)
- {
- _cogl_matrix_orthographic (matrix, x_1, y_1, x_2, y_2, near, far);
- _COGL_MATRIX_DEBUG_PRINT (matrix);
- }
- /*
- * Multiply a matrix with a general scaling matrix.
- *
- * Multiplies in-place the elements of matrix 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.
- */
- static void
- _cogl_matrix_scale (CoglMatrix *matrix, float x, float y, float z)
- {
- float *m = (float *)matrix;
- 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-8 && fabsf (x - z) < 1e-8)
- matrix->flags |= MAT_FLAG_UNIFORM_SCALE;
- else
- matrix->flags |= MAT_FLAG_GENERAL_SCALE;
- matrix->flags |= (MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);
- }
- void
- cogl_matrix_scale (CoglMatrix *matrix,
- float sx,
- float sy,
- float sz)
- {
- _cogl_matrix_scale (matrix, sx, sy, sz);
- _COGL_MATRIX_DEBUG_PRINT (matrix);
- }
- /*
- * Multiply a matrix with a translation matrix.
- *
- * Adds the translation coordinates to the elements of matrix in-place. Marks
- * the MAT_FLAG_TRANSLATION flag, and the MAT_DIRTY_TYPE and MAT_DIRTY_INVERSE
- * dirty flags.
- */
- static void
- _cogl_matrix_translate (CoglMatrix *matrix, float x, float y, float z)
- {
- float *m = (float *)matrix;
- 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];
- matrix->flags |= (MAT_FLAG_TRANSLATION |
- MAT_DIRTY_TYPE |
- MAT_DIRTY_INVERSE);
- }
- void
- cogl_matrix_translate (CoglMatrix *matrix,
- float x,
- float y,
- float z)
- {
- _cogl_matrix_translate (matrix, x, y, z);
- _COGL_MATRIX_DEBUG_PRINT (matrix);
- }
- #if 0
- /*
- * Set matrix to do viewport and depthrange mapping.
- * Transforms Normalized Device Coords to window/Z values.
- */
- static void
- _cogl_matrix_viewport (CoglMatrix *matrix,
- float x, float y,
- float width, float height,
- float zNear, float zFar, float depthMax)
- {
- float *m = (float *)matrix;
- m[MAT_SX] = width / 2.0f;
- m[MAT_TX] = m[MAT_SX] + x;
- m[MAT_SY] = height / 2.0f;
- m[MAT_TY] = m[MAT_SY] + y;
- m[MAT_SZ] = depthMax * ((zFar - zNear) / 2.0f);
- m[MAT_TZ] = depthMax * ((zFar - zNear) / 2.0f + zNear);
- matrix->flags = MAT_FLAG_GENERAL_SCALE | MAT_FLAG_TRANSLATION;
- matrix->type = COGL_MATRIX_TYPE_3D_NO_ROT;
- }
- #endif
- /*
- * Set a matrix to the identity matrix.
- *
- * @mat matrix.
- *
- * Copies ::identity into \p CoglMatrix::m, and into CoglMatrix::inv if
- * not NULL. Sets the matrix type to identity, resets the flags. It
- * doesn't initialize the inverse matrix, it just marks it dirty.
- */
- static void
- _cogl_matrix_init_identity (CoglMatrix *matrix)
- {
- memcpy (matrix, identity, 16 * sizeof (float));
- matrix->type = COGL_MATRIX_TYPE_IDENTITY;
- matrix->flags = MAT_DIRTY_INVERSE;
- }
- void
- cogl_matrix_init_identity (CoglMatrix *matrix)
- {
- _cogl_matrix_init_identity (matrix);
- _COGL_MATRIX_DEBUG_PRINT (matrix);
- }
- #if 0
- /*
- * Test if the given matrix preserves vector lengths.
- */
- static gboolean
- _cogl_matrix_is_length_preserving (const CoglMatrix *m)
- {
- return TEST_MAT_FLAGS (m, MAT_FLAGS_LENGTH_PRESERVING);
- }
- /*
- * Test if the given matrix does any rotation.
- * (or perhaps if the upper-left 3x3 is non-identity)
- */
- static gboolean
- _cogl_matrix_has_rotation (const CoglMatrix *matrix)
- {
- if (matrix->flags & (MAT_FLAG_GENERAL |
- MAT_FLAG_ROTATION |
- MAT_FLAG_GENERAL_3D |
- MAT_FLAG_PERSPECTIVE))
- return TRUE;
- else
- return FALSE;
- }
- static gboolean
- _cogl_matrix_is_general_scale (const CoglMatrix *matrix)
- {
- return (matrix->flags & MAT_FLAG_GENERAL_SCALE) ? TRUE : FALSE;
- }
- static gboolean
- _cogl_matrix_is_dirty (const CoglMatrix *matrix)
- {
- return (matrix->flags & MAT_DIRTY_ALL) ? TRUE : FALSE;
- }
- #endif
- /*
- * Loads a matrix array into CoglMatrix.
- *
- * @m matrix array.
- * @mat matrix.
- *
- * Copies \p m into CoglMatrix::m and marks the MAT_FLAG_GENERAL and
- * MAT_DIRTY_ALL
- * flags.
- */
- static void
- _cogl_matrix_init_from_array (CoglMatrix *matrix, const float *array)
- {
- memcpy (matrix, array, 16 * sizeof (float));
- matrix->flags = (MAT_FLAG_GENERAL | MAT_DIRTY_ALL);
- }
- void
- cogl_matrix_init_from_array (CoglMatrix *matrix, const float *array)
- {
- _cogl_matrix_init_from_array (matrix