m_matrix.c

mesa-6.5-minigui源码

   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 == 0.0)
         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 */
      MEMCPY( out, Identity, sizeof(Identity) );
      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 )
{
   MEMCPY( mat->inv, Identity, sizeof(Identity) );
   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;

   MEMCPY( out, Identity, 16 * sizeof(GLfloat) );
   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;

   MEMCPY( out, Identity, 16 * sizeof(GLfloat) );
   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;
}

#if 0
/* broken */
static GLboolean invert_matrix_perspective( GLmatrix *mat )
{
   const GLfloat *in = mat->m;
   GLfloat *out = mat->inv;

   if (MAT(in,2,3) == 0)
      return GL_FALSE;

   MEMCPY( out, Identity, 16 * sizeof(GLfloat) );

   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 GL_TRUE;
}
#endif

/**
 * 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,
#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_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;
      MEMCPY( mat->inv, Identity, sizeof(Identity) );
      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 ([e-mail]).
 * Optimizations contributed by Rudolf Opalla ([e-mail]).
 */
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 = (GLfloat) _mesa_sin( angle * DEG2RAD );
   c = (GLfloat) _mesa_cos( angle * DEG2RAD );

   MEMCPY(m, Identity, sizeof(GLfloat)*16);
   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-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_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 );
}

/**
 * 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];

#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

   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-8 && FABSF(x - z) < 1e-8)
      mat->flags |= MAT_FLAG_UNIFORM_SCALE;
   else
      mat->flags |= MAT_FLAG_GENERAL_SCALE;