-/* $Id: m_matrix.c,v 1.12 2002/06/29 19:48:17 brianp Exp $ */
+/* $Id: m_matrix.c,v 1.13 2002/09/12 16:26:04 brianp Exp $ */
/*
* Mesa 3-D graphics library
- * Version: 4.0.2
+ * Version: 4.1
*
* Copyright (C) 1999-2002 Brian Paul All Rights Reserved.
*
/*
* Generate a 4x4 transformation matrix from glRotate parameters, and
* postmultiply the input matrix by it.
+ * This function contributed by Erich Boleyn (erich@uruk.org).
+ * Optimizatios contributed by Rudolf Opalla (rudi@khm.de).
*/
void
_math_matrix_rotate( GLmatrix *mat,
GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
{
- /* 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;
+ GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
GLfloat m[16];
+ GLboolean optimized;
s = (GLfloat) sin( angle * DEG2RAD );
c = (GLfloat) cos( angle * DEG2RAD );
- mag = (GLfloat) GL_SQRT( x*x + y*y + z*z );
+ MEMCPY(m, Identity, sizeof(GLfloat)*16);
+ optimized = GL_FALSE;
- if (mag <= 1.0e-4) {
- /* generate an identity matrix and return */
- MEMCPY(m, Identity, sizeof(GLfloat)*16);
- return;
- }
+#define M(row,col) m[col*4+row]
- x /= mag;
- y /= mag;
- z /= mag;
+ 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 (y < 0.0F) {
+ M(1,2) = s;
+ M(2,1) = -s;
+ }
+ else {
+ M(1,2) = -s;
+ M(2,1) = s;
+ }
+ }
+ }
-#define M(row,col) m[col*4+row]
+ if (!optimized) {
+ const GLfloat mag = (GLfloat) GL_SQRT(x * x + y * y + z * z);
- /*
- * 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.
- */
+ if (mag <= 1.0e-4) {
+ /* no rotation, leave mat as-is */
+ return;
+ }
- 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;
+ 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 );
}
+
void
_math_matrix_frustum( GLmatrix *mat,
GLfloat left, GLfloat right,
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