2 * Mesa 3-D graphics library
5 * Copyright (C) 1999-2005 Brian Paul All Rights Reserved.
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27 * \file math/m_matrix.h
28 * Defines basic structures for matrix-handling.
37 * \name Symbolic names to some of the entries in the matrix
39 * These are handy for the viewport mapping, which is expressed as a matrix.
52 * Different kinds of 4x4 transformation matrices.
53 * We use these to select specific optimized vertex transformation routines.
56 MATRIX_GENERAL
, /**< general 4x4 matrix */
57 MATRIX_IDENTITY
, /**< identity matrix */
58 MATRIX_3D_NO_ROT
, /**< orthogonal projection and others... */
59 MATRIX_PERSPECTIVE
, /**< perspective projection matrix */
60 MATRIX_2D
, /**< 2-D transformation */
61 MATRIX_2D_NO_ROT
, /**< 2-D scale & translate only */
62 MATRIX_3D
/**< 3-D transformation */
66 * Matrix type to represent 4x4 transformation matrices.
69 GLfloat
*m
; /**< 16 matrix elements (16-byte aligned) */
70 GLfloat
*inv
; /**< optional 16-element inverse (16-byte aligned) */
71 GLuint flags
; /**< possible values determined by (of \link
72 * MatFlags MAT_FLAG_* flags\endlink)
74 enum GLmatrixtype type
;
81 _math_matrix_ctr( GLmatrix
*m
);
84 _math_matrix_dtr( GLmatrix
*m
);
87 _math_matrix_alloc_inv( GLmatrix
*m
);
90 _math_matrix_mul_matrix( GLmatrix
*dest
, const GLmatrix
*a
, const GLmatrix
*b
);
93 _math_matrix_mul_floats( GLmatrix
*dest
, const GLfloat
*b
);
96 _math_matrix_loadf( GLmatrix
*mat
, const GLfloat
*m
);
99 _math_matrix_translate( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
);
102 _math_matrix_rotate( GLmatrix
*m
, GLfloat angle
,
103 GLfloat x
, GLfloat y
, GLfloat z
);
106 _math_matrix_scale( GLmatrix
*mat
, GLfloat x
, GLfloat y
, GLfloat z
);
109 _math_matrix_ortho( GLmatrix
*mat
,
110 GLfloat left
, GLfloat right
,
111 GLfloat bottom
, GLfloat top
,
112 GLfloat nearval
, GLfloat farval
);
115 _math_matrix_frustum( GLmatrix
*mat
,
116 GLfloat left
, GLfloat right
,
117 GLfloat bottom
, GLfloat top
,
118 GLfloat nearval
, GLfloat farval
);
121 _math_matrix_viewport(GLmatrix
*m
, GLint x
, GLint y
, GLint width
, GLint height
,
122 GLfloat zNear
, GLfloat zFar
, GLfloat depthMax
);
125 _math_matrix_set_identity( GLmatrix
*dest
);
128 _math_matrix_copy( GLmatrix
*to
, const GLmatrix
*from
);
131 _math_matrix_analyse( GLmatrix
*mat
);
134 _math_matrix_print( const GLmatrix
*m
);
137 _math_matrix_is_length_preserving( const GLmatrix
*m
);
140 _math_matrix_has_rotation( const GLmatrix
*m
);
143 _math_matrix_is_general_scale( const GLmatrix
*m
);
146 _math_matrix_is_dirty( const GLmatrix
*m
);
150 * \name Related functions that don't actually operate on GLmatrix structs
155 _math_transposef( GLfloat to
[16], const GLfloat from
[16] );
158 _math_transposed( GLdouble to
[16], const GLdouble from
[16] );
161 _math_transposefd( GLfloat to
[16], const GLdouble from
[16] );
165 * Transform a point (column vector) by a matrix: Q = M * P
167 #define TRANSFORM_POINT( Q, M, P ) \
168 Q[0] = M[0] * P[0] + M[4] * P[1] + M[8] * P[2] + M[12] * P[3]; \
169 Q[1] = M[1] * P[0] + M[5] * P[1] + M[9] * P[2] + M[13] * P[3]; \
170 Q[2] = M[2] * P[0] + M[6] * P[1] + M[10] * P[2] + M[14] * P[3]; \
171 Q[3] = M[3] * P[0] + M[7] * P[1] + M[11] * P[2] + M[15] * P[3];
174 #define TRANSFORM_POINT3( Q, M, P ) \
175 Q[0] = M[0] * P[0] + M[4] * P[1] + M[8] * P[2] + M[12]; \
176 Q[1] = M[1] * P[0] + M[5] * P[1] + M[9] * P[2] + M[13]; \
177 Q[2] = M[2] * P[0] + M[6] * P[1] + M[10] * P[2] + M[14]; \
178 Q[3] = M[3] * P[0] + M[7] * P[1] + M[11] * P[2] + M[15];
182 * Transform a normal (row vector) by a matrix: [NX NY NZ] = N * MAT
184 #define TRANSFORM_NORMAL( TO, N, MAT ) \
186 TO[0] = N[0] * MAT[0] + N[1] * MAT[1] + N[2] * MAT[2]; \
187 TO[1] = N[0] * MAT[4] + N[1] * MAT[5] + N[2] * MAT[6]; \
188 TO[2] = N[0] * MAT[8] + N[1] * MAT[9] + N[2] * MAT[10]; \
193 * Transform a direction by a matrix.
195 #define TRANSFORM_DIRECTION( TO, DIR, MAT ) \
197 TO[0] = DIR[0] * MAT[0] + DIR[1] * MAT[4] + DIR[2] * MAT[8]; \
198 TO[1] = DIR[0] * MAT[1] + DIR[1] * MAT[5] + DIR[2] * MAT[9]; \
199 TO[2] = DIR[0] * MAT[2] + DIR[1] * MAT[6] + DIR[2] * MAT[10];\
204 _mesa_transform_vector(GLfloat u
[4], const GLfloat v
[4], const GLfloat m
[16]);