matrix.c

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/* $Id: matrix.c,v 1.23 1997/12/29 23:48:53 brianp Exp $ */
 
/*
 * Mesa 3-D graphics library
 * Version:  2.6
 * Copyright (C) 1995-1997  Brian Paul
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Library 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
 * Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public
 * License along with this library; if not, write to the Free
 * Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */
 
 
/*
 * $Log: matrix.c,v $
 * Revision 1.23  1997/12/29 23:48:53  brianp
 * call Driver.NearFar() in gl_LoadMatrixf() for projection matrix
 *
 * Revision 1.22  1997/10/16 23:37:23  brianp
 * fixed scotter's email address
 *
 * Revision 1.21  1997/08/13 01:54:34  brianp
 * new matrix invert code from Scott McCaskill
 *
 * Revision 1.20  1997/07/24 01:23:16  brianp
 * changed precompiled header symbol from PCH to PC_HEADER
 *
 * Revision 1.19  1997/05/30 02:21:43  brianp
 * gl_PopMatrix() set ctx->New*Matrix flag incorrectly
 *
 * Revision 1.18  1997/05/28 04:06:03  brianp
 * implemented projection near/far value stack for Driver.NearFar() function
 *
 * Revision 1.17  1997/05/28 03:25:43  brianp
 * added precompiled header (PCH) support
 *
 * Revision 1.16  1997/05/01 01:39:40  brianp
 * replace sqrt() with GL_SQRT()
 *
 * Revision 1.15  1997/04/21 01:20:41  brianp
 * added MATRIX_2D_NO_ROT
 *
 * Revision 1.14  1997/04/20 20:28:49  brianp
 * replaced abort() with gl_problem()
 *
 * Revision 1.13  1997/04/20 16:31:08  brianp
 * added NearFar device driver function
 *
 * Revision 1.12  1997/04/20 16:18:15  brianp
 * added glOrtho and glFrustum API pointers
 *
 * Revision 1.11  1997/04/01 04:23:53  brianp
 * added gl_analyze_*_matrix() functions
 *
 * Revision 1.10  1997/02/10 19:47:53  brianp
 * moved buffer resize code out of gl_Viewport() into gl_ResizeBuffersMESA()
 *
 * Revision 1.9  1997/01/31 23:32:40  brianp
 * now clear depth buffer after reallocation due to window resize
 *
 * Revision 1.8  1997/01/29 19:06:04  brianp
 * removed extra, local definition of Identity[] matrix
 *
 * Revision 1.7  1997/01/28 22:19:17  brianp
 * new matrix inversion code from Stephane Rehel
 *
 * Revision 1.6  1996/12/22 17:53:11  brianp
 * faster invert_matrix() function from scotter@iname.com
 *
 * Revision 1.5  1996/12/02 18:58:34  brianp
 * gl_rotation_matrix() now returns identity matrix if given a 0 rotation axis
 *
 * Revision 1.4  1996/09/27 01:29:05  brianp
 * added missing default cases to switches
 *
 * Revision 1.3  1996/09/15 14:18:37  brianp
 * now use GLframebuffer and GLvisual
 *
 * Revision 1.2  1996/09/14 06:46:04  brianp
 * better matmul() from Jacques Leroy
 *
 * Revision 1.1  1996/09/13 01:38:16  brianp
 * Initial revision
 *
 */
 
 
/*
 * Matrix operations
 *
 *
 * NOTES:
 * 1. 4x4 transformation matrices are stored in memory in column major order.
 * 2. Points/vertices are to be thought of as column vectors.
 * 3. Transformation of a point p by a matrix M is: p' = M * p
 *
 */
 
 
#ifdef PC_HEADER
#include "all.h"
#else
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "context.h"
#include "dlist.h"
#include "macros.h"
#include "matrix.h"
#include "mmath.h"
#include "types.h"
#endif
 
 
 
static GLfloat 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
};
 
 
#if 0
static void print_matrix( const GLfloat m[16] )
{
   int i;
 
   for (i=0;i<4;i++) {
      printf("%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
   }
}
#endif
 
 
/*
 * Perform a 4x4 matrix multiplication  (product = a x b).
 * Input:  a, b - matrices to multiply
 * Output:  product - product of a and b
 * WARNING: (product != b) assumed
 * NOTE:    (product == a) allowed    
 */
static void matmul( GLfloat *product, const GLfloat *a, const GLfloat *b )
{
   /* This matmul was contributed by Thomas Malik */
   GLint i;
 
#define A(row,col)  a[(col<<2)+row]
#define B(row,col)  b[(col<<2)+row]
#define P(row,col)  product[(col<<2)+row]
 
   /* i-te Zeile */
   for (i = 0; i < 4; i++) {
      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);
   }
 
#undef A
#undef B
#undef P
}
 
 
 
/*
 * Compute the inverse of a 4x4 matrix.
 *
 * From an algorithm by V. Strassen, 1969, _Numerishe Mathematik_, vol. 13,
 * pp. 354-356.
 * 60 multiplies, 24 additions, 10 subtractions, 8 negations, 2 divisions,
 * 48 assignments, _0_ branches
 *
 * This implementation by Scott McCaskill
 */
 
typedef GLfloat Mat2[2][2];
 
enum {
    M00 = 0, M01 = 4, M02 = 8, M03 = 12,
    M10 = 1, M11 = 5, M12 = 9, M13 = 13,
    M20 = 2, M21 = 6, M22 = 10,M23 = 14,
    M30 = 3, M31 = 7, M32 = 11,M33 = 15
};
 
static void invert_matrix_general( const GLfloat *m, GLfloat *out )
{
   Mat2 r1, r2, r3, r4, r5, r6, r7;
   const GLfloat * A = m;
   GLfloat *       C = out;
   GLfloat one_over_det;
 
   /*
    * A is the 4x4 source matrix (to be inverted).
    * C is the 4x4 destination matrix
    * a11 is the 2x2 matrix in the upper left quadrant of A
    * a12 is the 2x2 matrix in the upper right quadrant of A
    * a21 is the 2x2 matrix in the lower left quadrant of A
    * a22 is the 2x2 matrix in the lower right quadrant of A
    * similarly, cXX are the 2x2 quadrants of the destination matrix
    */
 
   /* R1 = inverse( a11 ) */
   one_over_det = 1.0f / ( ( A[M00] * A[M11] ) - ( A[M10] * A[M01] ) );
   r1[0][0] = one_over_det * A[M11];
   r1[0][1] = one_over_det * -A[M01];
   r1[1][0] = one_over_det * -A[M10];
   r1[1][1] = one_over_det * A[M00];
 
   /* R2 = a21 x R1 */
   r2[0][0] = A[M20] * r1[0][0] + A[M21] * r1[1][0];
   r2[0][1] = A[M20] * r1[0][1] + A[M21] * r1[1][1];
   r2[1][0] = A[M30] * r1[0][0] + A[M31] * r1[1][0];
   r2[1][1] = A[M30] * r1[0][1] + A[M31] * r1[1][1];
 
   /* R3 = R1 x a12 */
   r3[0][0] = r1[0][0] * A[M02] + r1[0][1] * A[M12];
   r3[0][1] = r1[0][0] * A[M03] + r1[0][1] * A[M13];
   r3[1][0] = r1[1][0] * A[M02] + r1[1][1] * A[M12];
   r3[1][1] = r1[1][0] * A[M03] + r1[1][1] * A[M13];
 
   /* R4 = a21 x R3 */
   r4[0][0] = A[M20] * r3[0][0] + A[M21] * r3[1][0];
   r4[0][1] = A[M20] * r3[0][1] + A[M21] * r3[1][1];
   r4[1][0] = A[M30] * r3[0][0] + A[M31] * r3[1][0];
   r4[1][1] = A[M30] * r3[0][1] + A[M31] * r3[1][1];
 
   /* R5 = R4 - a22 */
   r5[0][0] = r4[0][0] - A[M22];
   r5[0][1] = r4[0][1] - A[M23];
   r5[1][0] = r4[1][0] - A[M32];
   r5[1][1] = r4[1][1] - A[M33];
 
   /* R6 = inverse( R5 ) */
   one_over_det = 1.0f / ( ( r5[0][0] * r5[1][1] ) - ( r5[1][0] * r5[0][1] ) );
   r6[0][0] = one_over_det * r5[1][1];
   r6[0][1] = one_over_det * -r5[0][1];
   r6[1][0] = one_over_det * -r5[1][0];
   r6[1][1] = one_over_det * r5[0][0];
 
   /* c12 = R3 x R6 */
   C[M02] = r3[0][0] * r6[0][0] + r3[0][1] * r6[1][0];
   C[M03] = r3[0][0] * r6[0][1] + r3[0][1] * r6[1][1];
   C[M12] = r3[1][0] * r6[0][0] + r3[1][1] * r6[1][0];
   C[M13] = r3[1][0] * r6[0][1] + r3[1][1] * r6[1][1];
 
   /* c21 = R6 x R2 */
   C[M20] = r6[0][0] * r2[0][0] + r6[0][1] * r2[1][0];
   C[M21] = r6[0][0] * r2[0][1] + r6[0][1] * r2[1][1];
   C[M30] = r6[1][0] * r2[0][0] + r6[1][1] * r2[1][0];
   C[M31] = r6[1][0] * r2[0][1] + r6[1][1] * r2[1][1];
 
   /* R7 = R3 x c21 */
   r7[0][0] = r3[0][0] * C[M20] + r3[0][1] * C[M30];
   r7[0][1] = r3[0][0] * C[M21] + r3[0][1] * C[M31];
   r7[1][0] = r3[1][0] * C[M20] + r3[1][1] * C[M30];
   r7[1][1] = r3[1][0] * C[M21] + r3[1][1] * C[M31];
 
   /* c11 = R1 - R7 */
   C[M00] = r1[0][0] - r7[0][0];
   C[M01] = r1[0][1] - r7[0][1];
   C[M10] = r1[1][0] - r7[1][0];
   C[M11] = r1[1][1] - r7[1][1];
 
   /* c22 = -R6 */
   C[M22] = -r6[0][0];
   C[M23] = -r6[0][1];
   C[M32] = -r6[1][0];
   C[M33] = -r6[1][1];
}
 
 
/*
 * Invert matrix m.  This algorithm contributed by Stephane Rehel
 * <rehel@worldnet.fr>
 */
static void invert_matrix( const GLfloat *m, GLfloat *out )
{
/* NB. OpenGL Matrices are COLUMN major. */
#define MAT(m,r,c) (m)[(c)*4+(r)]
 
/* Here's some shorthand converting standard (row,column) to index. */
#define m11 MAT(m,0,0)
#define m12 MAT(m,0,1)
#define m13 MAT(m,0,2)
#define m14 MAT(m,0,3)
#define m21 MAT(m,1,0)
#define m22 MAT(m,1,1)
#define m23 MAT(m,1,2)
#define m24 MAT(m,1,3)
#define m31 MAT(m,2,0)
#define m32 MAT(m,2,1)
#define m33 MAT(m,2,2)
#define m34 MAT(m,2,3)
#define m41 MAT(m,3,0)
#define m42 MAT(m,3,1)
#define m43 MAT(m,3,2)
#define m44 MAT(m,3,3)
 
   register GLfloat det;
   GLfloat tmp[16]; /* Allow out == in. */
 
   if( m41 != 0. || m42 != 0. || m43 != 0. || m44 != 1. ) {
      invert_matrix_general(m, out);
      return;
   }
 
   /* Inverse = adjoint / det. (See linear algebra texts.)*/
 
   tmp[0]= m22 * m33 - m23 * m32;
   tmp[1]= m23 * m31 - m21 * m33;
   tmp[2]= m21 * m32 - m22 * m31;
 
   /* Compute determinant as early as possible using these cofactors. */
   det= m11 * tmp[0] + m12 * tmp[1] + m13 * tmp[2];
 
   /* Run singularity test. */
   if (det == 0.0F) {
      /* printf("invert_matrix: Warning: Singular matrix.\n"); */
      MEMCPY( out, Identity, 16*sizeof(GLfloat) );
   }
   else {
      GLfloat d12, d13, d23, d24, d34, d41;
      register GLfloat im11, im12, im13, im14;
 
      det= 1. / det;
 
      /* Compute rest of inverse. */
      tmp[0] *= det;
      tmp[1] *= det;
      tmp[2] *= det;
      tmp[3]  = 0.;
 
      im11= m11 * det;
      im12= m12 * det;
      im13= m13 * det;
      im14= m14 * det;
      tmp[4] = im13 * m32 - im12 * m33;
      tmp[5] = im11 * m33 - im13 * m31;
      tmp[6] = im12 * m31 - im11 * m32;
      tmp[7] = 0.;
 
      /* Pre-compute 2x2 dets for first two rows when computing */
      /* cofactors of last two rows. */
      d12 = im11*m22 - m21*im12;
      d13 = im11*m23 - m21*im13;
      d23 = im12*m23 - m22*im13;
      d24 = im12*m24 - m22*im14;
      d34 = im13*m24 - m23*im14;
      d41 = im14*m21 - m24*im11;
 
      tmp[8] =  d23;
      tmp[9] = -d13;
      tmp[10] = d12;
      tmp[11] = 0.;
 
      tmp[12] = -(m32 * d34 - m33 * d24 + m34 * d23);
      tmp[13] =  (m31 * d34 + m33 * d41 + m34 * d13);
      tmp[14] = -(m31 * d24 + m32 * d41 + m34 * d12);
      tmp[15] =  1.;
 
      MEMCPY(out, tmp, 16*sizeof(GLfloat));
  }
 
#undef m11
#undef m12
#undef m13
#undef m14
#undef m21
#undef m22
#undef m23
#undef m24
#undef m31
#undef m32
#undef m33
#undef m34
#undef m41
#undef m42
#undef m43
#undef m44
#undef MAT
}
 
 
 
/*
 * Determine if the given matrix is the identity matrix.
 */
static GLboolean is_identity( const GLfloat m[16] )
{
   if (   m[0]==1.0F && m[4]==0.0F && m[ 8]==0.0F && m[12]==0.0F
       && m[1]==0.0F && m[5]==1.0F && m[ 9]==0.0F && m[13]==0.0F
       && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F
       && m[3]==0.0F && m[7]==0.0F && m[11]==0.0F && m[15]==1.0F) {
      return GL_TRUE;
   }
   else {
      return GL_FALSE;
   }
}
 
 
/*
 * Examine the current modelview matrix to determine its type.
 * Later we use the matrix type to optimize vertex transformations.
 */
void gl_analyze_modelview_matrix( GLcontext *ctx )
{
   const GLfloat *m = ctx->ModelViewMatrix;
   if (is_identity(m)) {
      ctx->ModelViewMatrixType = MATRIX_IDENTITY;
   }
   else if (                 m[4]==0.0F && m[ 8]==0.0F               
            && m[1]==0.0F               && m[ 9]==0.0F
            && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F
            && m[3]==0.0F && m[7]==0.0F && m[11]==0.0F && m[15]==1.0F) {
      ctx->ModelViewMatrixType = MATRIX_2D_NO_ROT;
   }
   else 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
            && m[3]==0.0F && m[7]==0.0F && m[11]==0.0F && m[15]==1.0F) {
      ctx->ModelViewMatrixType = MATRIX_2D;
   }
   else if (m[3]==0.0F && m[7]==0.0F && m[11]==0.0F && m[15]==1.0F) {
      ctx->ModelViewMatrixType = MATRIX_3D;
   }
   else {
      ctx->ModelViewMatrixType = MATRIX_GENERAL;
   }
 
   invert_matrix( ctx->ModelViewMatrix, ctx->ModelViewInv );
   ctx->NewModelViewMatrix = GL_FALSE;
}
 
 
 
/*
 * Examine the current projection matrix to determine its type.
 * Later we use the matrix type to optimize vertex transformations.
 */
void gl_analyze_projection_matrix( GLcontext *ctx )
{
   /* look for common-case ortho and perspective matrices */
   const GLfloat *m = ctx->ProjectionMatrix;
   if (is_identity(m)) {
      ctx->ProjectionMatrixType = MATRIX_IDENTITY;
   }
   else if (                 m[4]==0.0F && m[8] ==0.0F
            && m[1]==0.0F               && m[9] ==0.0F
            && m[2]==0.0F && m[6]==0.0F
            && m[3]==0.0F && m[7]==0.0F && m[11]==0.0F && m[15]==1.0F) {
      ctx->ProjectionMatrixType = MATRIX_ORTHO;
   }
   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) {
      ctx->ProjectionMatrixType = MATRIX_PERSPECTIVE;
   }
   else {
      ctx->ProjectionMatrixType = MATRIX_GENERAL;
   }
 
   ctx->NewProjectionMatrix = GL_FALSE;
}
 
 
 
/*
 * Examine the current texture matrix to determine its type.
 * Later we use the matrix type to optimize texture coordinate transformations.
 */
void gl_analyze_texture_matrix( GLcontext *ctx )
{
   const GLfloat *m = ctx->TextureMatrix;
   if (is_identity(m)) {
      ctx->TextureMatrixType = MATRIX_IDENTITY;
   }
   else 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
            && m[3]==0.0F && m[7]==0.0F && m[11]==0.0F && m[15]==1.0F) {
      ctx->TextureMatrixType = MATRIX_2D;
   }
   else if (m[3]==0.0F && m[7]==0.0F && m[11]==0.0F && m[15]==1.0F) {
      ctx->TextureMatrixType = MATRIX_3D;
   }
   else {
      ctx->TextureMatrixType = MATRIX_GENERAL;
   }
 
   ctx->NewTextureMatrix = GL_FALSE;
}
 
 
 
void gl_Frustum( GLcontext *ctx,
                 GLdouble left, GLdouble right,
         GLdouble bottom, GLdouble top,
         GLdouble nearval, GLdouble farval )
{
   GLfloat x, y, a, b, c, d;
   GLfloat m[16];
 
   if (nearval<=0.0 || farval<=0.0) {
      gl_error( ctx,  GL_INVALID_VALUE, "glFrustum(near or far)" );
   }
 
   x = (2.0*nearval) / (right-left);
   y = (2.0*nearval) / (top-bottom);
   a = (right+left) / (right-left);
   b = (top+bottom) / (top-bottom);
   c = -(farval+nearval) / ( farval-nearval);
   d = -(2.0*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
 
   gl_MultMatrixf( ctx, m );
 
 
   /* Need to keep a stack of near/far values in case the user push/pops
    * the projection matrix stack so that we can call Driver.NearFar()
    * after a pop.
    */
   ctx->NearFarStack[ctx->ProjectionStackDepth][0] = nearval;
   ctx->NearFarStack[ctx->ProjectionStackDepth][1] = farval;
 
   if (ctx->Driver.NearFar) {
      (*ctx->Driver.NearFar)( ctx, nearval, farval );
   }
}
 
 
void gl_Ortho( GLcontext *ctx,
               GLdouble left, GLdouble right,
               GLdouble bottom, GLdouble top,
               GLdouble nearval, GLdouble farval )
{
   GLfloat x, y, z;
   GLfloat tx, ty, tz;
   GLfloat m[16];
 
   x = 2.0 / (right-left);
   y = 2.0 / (top-bottom);
   z = -2.0 / (farval-nearval);
   tx = -(right+left) / (right-left);
   ty = -(top+bottom) / (top-bottom);
   tz = -(farval+nearval) / (farval-nearval);
 
#define M(row,col)  m[col*4+row]
   M(0,0) = x;     M(0,1) = 0.0F;  M(0,2) = 0.0F;  M(0,3) = tx;
   M(1,0) = 0.0F;  M(1,1) = y;     M(1,2) = 0.0F;  M(1,3) = ty;
   M(2,0) = 0.0F;  M(2,1) = 0.0F;  M(2,2) = z;     M(2,3) = tz;
   M(3,0) = 0.0F;  M(3,1) = 0.0F;  M(3,2) = 0.0F;  M(3,3) = 1.0F;
#undef M
 
   gl_MultMatrixf( ctx, m );
 
   if (ctx->Driver.NearFar) {
      (*ctx->Driver.NearFar)( ctx, nearval, farval );
   }
}
 
 
void gl_MatrixMode( GLcontext *ctx, GLenum mode )
{
   if (INSIDE_BEGIN_END(ctx)) {
      gl_error( ctx,  GL_INVALID_OPERATION, "glMatrixMode" );
      return;
   }
   switch (mode) {
      case GL_MODELVIEW:
      case GL_PROJECTION:
      case GL_TEXTURE:
         ctx->Transform.MatrixMode = mode;
         break;
      default:
         gl_error( ctx,  GL_INVALID_ENUM, "glMatrixMode" );
   }
}
 
 
 
void gl_PushMatrix( GLcontext *ctx )
{
   if (INSIDE_BEGIN_END(ctx)) {
      gl_error( ctx,  GL_INVALID_OPERATION, "glPushMatrix" );
      return;
   }
   switch (ctx->Transform.MatrixMode) {
      case GL_MODELVIEW:
         if (ctx->ModelViewStackDepth>=MAX_MODELVIEW_STACK_DEPTH-1) {
            gl_error( ctx,  GL_STACK_OVERFLOW, "glPushMatrix");
            return;
         }
         MEMCPY( ctx->ModelViewStack[ctx->ModelViewStackDepth],
                 ctx->ModelViewMatrix,
                 16*sizeof(GLfloat) );
         ctx->ModelViewStackDepth++;
         break;
      case GL_PROJECTION:
         if (ctx->ProjectionStackDepth>=MAX_PROJECTION_STACK_DEPTH) {
            gl_error( ctx,  GL_STACK_OVERFLOW, "glPushMatrix");
            return;
         }
         MEMCPY( ctx->ProjectionStack[ctx->ProjectionStackDepth],
                 ctx->ProjectionMatrix,
                 16*sizeof(GLfloat) );
         ctx->ProjectionStackDepth++;
 
         /* Save near and far projection values */
         ctx->NearFarStack[ctx->ProjectionStackDepth][0]
            = ctx->NearFarStack[ctx->ProjectionStackDepth-1][0];
         ctx->NearFarStack[ctx->ProjectionStackDepth][1]
            = ctx->NearFarStack[ctx->ProjectionStackDepth-1][1];
         break;
      case GL_TEXTURE:
         if (ctx->TextureStackDepth>=MAX_TEXTURE_STACK_DEPTH) {
            gl_error( ctx,  GL_STACK_OVERFLOW, "glPushMatrix");
            return;
         }
         MEMCPY( ctx->TextureStack[ctx->TextureStackDepth],
                 ctx->TextureMatrix,
                 16*sizeof(GLfloat) );
         ctx->TextureStackDepth++;
         break;
      default:
         gl_problem(ctx, "Bad matrix mode in gl_PushMatrix");
   }
}
 
 
 
void gl_PopMatrix( GLcontext *ctx )
{
   if (INSIDE_BEGIN_END(ctx)) {
      gl_error( ctx,  GL_INVALID_OPERATION, "glPopMatrix" );
      return;
   }
   switch (ctx->Transform.MatrixMode) {
      case GL_MODELVIEW:
         if (ctx->ModelViewStackDepth==0) {
            gl_error( ctx,  GL_STACK_UNDERFLOW, "glPopMatrix");
            return;
         }
         ctx->ModelViewStackDepth--;
         MEMCPY( ctx->ModelViewMatrix,
                 ctx->ModelViewStack[ctx->ModelViewStackDepth],
                 16*sizeof(GLfloat) );
         ctx->NewModelViewMatrix = GL_TRUE;
         break;
      case GL_PROJECTION:
         if (ctx->ProjectionStackDepth==0) {
            gl_error( ctx,  GL_STACK_UNDERFLOW, "glPopMatrix");
            return;
         }
         ctx->ProjectionStackDepth--;
         MEMCPY( ctx->ProjectionMatrix,
                 ctx->ProjectionStack[ctx->ProjectionStackDepth],
                 16*sizeof(GLfloat) );
         ctx->NewProjectionMatrix = GL_TRUE;
 
         /* Device driver near/far values */
         {
            GLfloat nearVal = ctx->NearFarStack[ctx->ProjectionStackDepth][0];
            GLfloat farVal  = ctx->NearFarStack[ctx->ProjectionStackDepth][1];
            if (ctx->Driver.NearFar) {
               (*ctx->Driver.NearFar)( ctx, nearVal, farVal );
            }
         }
         break;
      case GL_TEXTURE:
         if (ctx->TextureStackDepth==0) {
            gl_error( ctx,  GL_STACK_UNDERFLOW, "glPopMatrix");
            return;
         }
         ctx->TextureStackDepth--;
         MEMCPY( ctx->TextureMatrix,
                 ctx->TextureStack[ctx->TextureStackDepth],
                 16*sizeof(GLfloat) );
         ctx->NewTextureMatrix = GL_TRUE;
         break;
      default:
         gl_problem(ctx, "Bad matrix mode in gl_PopMatrix");
   }
}
 
 
 
void gl_LoadIdentity( GLcontext *ctx )
{
   if (INSIDE_BEGIN_END(ctx)) {
      gl_error( ctx,  GL_INVALID_OPERATION, "glLoadIdentity" );
      return;
   }
   switch (ctx->Transform.MatrixMode) {
      case GL_MODELVIEW:
         MEMCPY( ctx->ModelViewMatrix, Identity, 16*sizeof(GLfloat) );
         MEMCPY( ctx->ModelViewInv, Identity, 16*sizeof(GLfloat) );
         ctx->ModelViewMatrixType = MATRIX_IDENTITY;
     ctx->NewModelViewMatrix = GL_FALSE;
     break;
      case GL_PROJECTION:
     MEMCPY( ctx->ProjectionMatrix, Identity, 16*sizeof(GLfloat) );
         ctx->ProjectionMatrixType = MATRIX_IDENTITY;
     ctx->NewProjectionMatrix = GL_FALSE;
     break;
      case GL_TEXTURE:
     MEMCPY( ctx->TextureMatrix, Identity, 16*sizeof(GLfloat) );
         ctx->TextureMatrixType = MATRIX_IDENTITY;
     ctx->NewTextureMatrix = GL_FALSE;
     break;
      default:
         gl_problem(ctx, "Bad matrix mode in gl_LoadIdentity");
   }
}
 
 
void gl_LoadMatrixf( GLcontext *ctx, const GLfloat *m )
{
   if (INSIDE_BEGIN_END(ctx)) {
      gl_error( ctx,  GL_INVALID_OPERATION, "glLoadMatrix" );
      return;
   }
   switch (ctx->Transform.MatrixMode) {
      case GL_MODELVIEW:
         MEMCPY( ctx->ModelViewMatrix, m, 16*sizeof(GLfloat) );
     ctx->NewModelViewMatrix = GL_TRUE;
     break;
      case GL_PROJECTION:
     MEMCPY( ctx->ProjectionMatrix, m, 16*sizeof(GLfloat) );
     ctx->NewProjectionMatrix = GL_TRUE;
         {
            float n,f,c,d;
 
#define M(row,col)  m[col*4+row]
            c = M(2,2);
            d = M(2,3);
#undef M
            n = d / (c-1);
            f = d / (c+1);
 
            /* Need to keep a stack of near/far values in case the user
             * push/pops the projection matrix stack so that we can call
             * Driver.NearFar() after a pop.
             */
            ctx->NearFarStack[ctx->ProjectionStackDepth][0] = n;
            ctx->NearFarStack[ctx->ProjectionStackDepth][1] = f;
 
            if (ctx->Driver.NearFar) {
               (*ctx->Driver.NearFar)( ctx, n, f );
            }
         }
     break;
      case GL_TEXTURE:
     MEMCPY( ctx->TextureMatrix, m, 16*sizeof(GLfloat) );
     ctx->NewTextureMatrix = GL_TRUE;
     break;
      default:
         gl_problem(ctx, "Bad matrix mode in gl_LoadMatrixf");
   }
}
 
 
 
void gl_MultMatrixf( GLcontext *ctx, const GLfloat *m )
{
   if (INSIDE_BEGIN_END(ctx)) {
      gl_error( ctx,  GL_INVALID_OPERATION, "glMultMatrix" );
      return;
   }
   switch (ctx->Transform.MatrixMode) {
      case GL_MODELVIEW:
         matmul( ctx->ModelViewMatrix, ctx->ModelViewMatrix, m );
     ctx->NewModelViewMatrix = GL_TRUE;
     break;
      case GL_PROJECTION:
     matmul( ctx->ProjectionMatrix, ctx->ProjectionMatrix, m );
     ctx->NewProjectionMatrix = GL_TRUE;
     break;
      case GL_TEXTURE:
     matmul( ctx->TextureMatrix, ctx->TextureMatrix, m );
     ctx->NewTextureMatrix = GL_TRUE;
     break;
      default:
         gl_problem(ctx, "Bad matrix mode in gl_MultMatrixf");
   }
}
 
 
 
/*
 * Generate a 4x4 transformation matrix from glRotate parameters.
 */
void gl_rotation_matrix( GLfloat angle, GLfloat x, GLfloat y, GLfloat z,
                         GLfloat m[] )
{
   /* This function contributed by Erich Boleyn (erich@uruk.org) */
   GLfloat mag, s, c;
   GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c;
 
   s = sin( angle * DEG2RAD );
   c = cos( angle * DEG2RAD );
 
   mag = GL_SQRT( x*x + y*y + z*z );
 
   if (mag == 0.0) {
      /* generate an identity matrix and return */
      MEMCPY(m, Identity, sizeof(GLfloat)*16);
      return;
   }
 
   x /= mag;
   y /= mag;
   z /= mag;
 
#define M(row,col)  m[col*4+row]
 
   /*
    *     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;
 
   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
}
 
 
 
void gl_Rotatef( GLcontext *ctx,
                 GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
{
   GLfloat m[16];
   gl_rotation_matrix( angle, x, y, z, m );
   gl_MultMatrixf( ctx, m );
}
 
 
 
/*
 * Execute a glScale call
 */
void gl_Scalef( GLcontext *ctx, GLfloat x, GLfloat y, GLfloat z )
{
   GLfloat *m;
 
   if (INSIDE_BEGIN_END(ctx)) {
      gl_error( ctx,  GL_INVALID_OPERATION, "glScale" );
      return;
   }
   switch (ctx->Transform.MatrixMode) {
      case GL_MODELVIEW:
         m = ctx->ModelViewMatrix;
     ctx->NewModelViewMatrix = GL_TRUE;
     break;
      case GL_PROJECTION:
         m = ctx->ProjectionMatrix;
     ctx->NewProjectionMatrix = GL_TRUE;
     break;
      case GL_TEXTURE:
         m = ctx->TextureMatrix;
     ctx->NewTextureMatrix = GL_TRUE;
     break;
      default:
         gl_problem(ctx, "Bad matrix mode in gl_Scalef");
         return;
   }
   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;
}
 
 
 
/*
 * Execute a glTranslate call
 */
void gl_Translatef( GLcontext *ctx, GLfloat x, GLfloat y, GLfloat z )
{
   GLfloat *m;
   if (INSIDE_BEGIN_END(ctx)) {
      gl_error( ctx, GL_INVALID_OPERATION, "glTranslate" );
      return;
   }
   switch (ctx->Transform.MatrixMode) {
      case GL_MODELVIEW:
         m = ctx->ModelViewMatrix;
     ctx->NewModelViewMatrix = GL_TRUE;
     break;
      case GL_PROJECTION:
         m = ctx->ProjectionMatrix;
     ctx->NewProjectionMatrix = GL_TRUE;
     break;
      case GL_TEXTURE:
         m = ctx->TextureMatrix;
     ctx->NewTextureMatrix = GL_TRUE;
     break;
      default:
         gl_problem(ctx, "Bad matrix mode in gl_Translatef");
         return;
   }
 
   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];
}
 
 
 
 
/*
 * Define a new viewport and reallocate auxillary buffers if the size of
 * the window (color buffer) has changed.
 */
void gl_Viewport( GLcontext *ctx,
                  GLint x, GLint y, GLsizei width, GLsizei height )
{
   if (width<0 || height<0) {
      gl_error( ctx,  GL_INVALID_VALUE, "glViewport" );
      return;
   }
   if (INSIDE_BEGIN_END(ctx)) {
      gl_error( ctx,  GL_INVALID_OPERATION, "glViewport" );
      return;
   }
 
   /* clamp width, and height to implementation dependent range */
   width  = CLAMP( width,  1, MAX_WIDTH );
   height = CLAMP( height, 1, MAX_HEIGHT );
 
   /* Save viewport */
   ctx->Viewport.X = x;
   ctx->Viewport.Width = width;
   ctx->Viewport.Y = y;
   ctx->Viewport.Height = height;
 
   /* compute scale and bias values */
   ctx->Viewport.Sx = (GLfloat) width / 2.0F;
   ctx->Viewport.Tx = ctx->Viewport.Sx + x;
   ctx->Viewport.Sy = (GLfloat) height / 2.0F;
   ctx->Viewport.Ty = ctx->Viewport.Sy + y;
 
   ctx->NewState |= NEW_ALL;   /* just to be safe */
 
   /* Check if window/buffer has been resized and if so, reallocate the
    * ancillary buffers.
    */
   gl_ResizeBuffersMESA(ctx);
}