[matrix] Adds cogl_matrix_get_inverse API

This new API takes advantage of the recently imported Mesa code to support
inverse matrix calculation.  The matrix code keeps track (via internal
flags) of the transformations a matrix represents so that it can select an
optimized inversion function.

Note: although other aspects of the Cogl matrix API have followed a similar
style to Cairo's matrix API we haven't added a cogl_matrix_invert API
because the inverse of a CoglMatrix is actually cached as part of the
CoglMatrix structure meaning a destructive API like cogl_matrix_invert
doesn't let users take advantage of this caching design.

clutter/cogl/cogl/cogl-context.h

@@ -61,9 +61,6 @@ typedef struct
   CoglMatrixMode    flushed_matrix_mode;
   GList            *texture_units;
 
-  /* Cache of inverse projection matrix */
-  float            inverse_projection[16];
-
   /* Materials */
   CoglHandle        default_material;
   CoglHandle	    source_material;

clutter/cogl/cogl/cogl-matrix-stack.c

@@ -348,6 +348,17 @@ _cogl_matrix_stack_ortho (CoglMatrixStack *stack,
   state->is_identity = FALSE;
 }
 
+gboolean
+_cogl_matrix_stack_get_inverse (CoglMatrixStack *stack,
+                                CoglMatrix      *inverse)
+{
+  CoglMatrixState *state;
+
+  state = _cogl_matrix_stack_top_mutable (stack, TRUE);
+
+  return cogl_matrix_get_inverse (&state->matrix, inverse);
+}
+
 void
 _cogl_matrix_stack_get (CoglMatrixStack *stack,
                         CoglMatrix      *matrix)

clutter/cogl/cogl/cogl-matrix-stack.h

@@ -71,6 +71,9 @@ void             _cogl_matrix_stack_ortho         (CoglMatrixStack  *stack,
                                                    float             top,
                                                    float             z_near,
                                                    float             z_far);
+
+gboolean         _cogl_matrix_stack_get_inverse   (CoglMatrixStack  *stack,
+                                                   CoglMatrix       *inverse);
 void             _cogl_matrix_stack_get           (CoglMatrixStack  *stack,
                                                    CoglMatrix       *matrix);
 void             _cogl_matrix_stack_set           (CoglMatrixStack  *stack,

clutter/cogl/cogl/cogl-matrix.c

@@ -183,18 +183,6 @@ cogl_matrix_scale (CoglMatrix *matrix,
   _COGL_MATRIX_DEBUG_PRINT (matrix);
 }
 
-#if 0
-gboolean
-cogl_matrix_invert (CoglMatrix *matrix)
-{
-  /* TODO */
-  /* Note: It might be nice to also use the flag based tricks that mesa does
-   * to alow it to track the type of transformations a matrix represents
-   * so it can use various assumptions to optimise the inversion.
-   */
-}
-#endif
-
 void
 cogl_matrix_frustum (CoglMatrix *matrix,
                      float       left,
@@ -321,6 +309,27 @@ cogl_matrix_get_array (const CoglMatrix *matrix)
   return (float *)matrix;
 }
 
+gboolean
+cogl_matrix_get_inverse (const CoglMatrix *matrix, CoglMatrix *inverse)
+{
+#ifndef USE_MESA_MATRIX_API
+#warning "cogl_matrix_get_inverse not supported without Mesa matrix API"
+  cogl_matrix_init_identity (inverse);
+  return FALSE;
+#else
+  if (_math_matrix_update_inverse ((CoglMatrix *)matrix))
+    {
+      cogl_matrix_init_from_array (inverse, matrix->inv);
+      return TRUE;
+    }
+  else
+    {
+      cogl_matrix_init_identity (inverse);
+      return FALSE;
+    }
+#endif
+}
+
 void
 cogl_matrix_transform_point (const CoglMatrix *matrix,
                              float *x,

clutter/cogl/cogl/cogl-matrix.h

@@ -266,6 +266,27 @@ void cogl_matrix_init_from_array (CoglMatrix *matrix, const float *array);
  */
 G_CONST_RETURN float *cogl_matrix_get_array (const CoglMatrix *matrix);
 
+/**
+ * cogl_matrix_get_inverse:
+ * @matrix: A 4x4 transformation matrix
+ * @inverse: The destination for a 4x4 inverse transformation matrix
+ *
+ * This gets the inverse transform of a given matrix and uses it to initialize
+ * a new CoglMatrix.
+ *
+ * Note: that although the first parameter is annotated as const to indicate
+ * that the transform it represents isn't modified this function may
+ * technically save a copy of the inverse transform within the given CoglMatrix
+ * so that subsequent requests for the inverse transform may avoid costly
+ * inversion calculations.
+ *
+ * Returns TRUE if the inverse was successfully calculated or FALSE for
+ * degenerate transformations that can't be inverted (in this case the matrix
+ * will simply be initialized with the identity matrix)
+ */
+gboolean
+cogl_matrix_get_inverse (const CoglMatrix *matrix, CoglMatrix *inverse);
+
 /**
  * cogl_matrix_transform_point:
  * @matrix: A 4x4 transformation matrix

clutter/cogl/cogl/cogl.c

@@ -368,13 +368,17 @@ set_clip_plane (GLint plane_num,
   GLdouble plane[4];
 #endif
   GLfloat angle;
-  CoglMatrix inverse_projection;
   CoglHandle draw_buffer = _cogl_get_draw_buffer ();
   CoglMatrixStack *modelview_stack =
     _cogl_draw_buffer_get_modelview_stack (draw_buffer);
+  CoglMatrixStack *projection_stack =
+    _cogl_draw_buffer_get_projection_stack (draw_buffer);
+  CoglMatrix inverse_projection;
 
   _COGL_GET_CONTEXT (ctx, NO_RETVAL);
 
+  _cogl_matrix_stack_get_inverse (projection_stack, &inverse_projection);
+
   /* Calculate the angle between the axes and the line crossing the
      two points */
   angle = atan2f (vertex_b[1] - vertex_a[1],
@@ -382,13 +386,10 @@ set_clip_plane (GLint plane_num,
 
   _cogl_matrix_stack_push (modelview_stack);
 
-  /* Load the identity matrix and multiply by the reverse of the
-     projection matrix so we can specify the plane in screen
-     coordinates */
-  _cogl_matrix_stack_load_identity (modelview_stack);
-  cogl_matrix_init_from_array (&inverse_projection,
-                               ctx->inverse_projection);
-  _cogl_matrix_stack_multiply (modelview_stack, &inverse_projection);
+  /* Load the inverse of the projection matrix so we can specify the plane
+   * in screen coordinates */
+  _cogl_matrix_stack_set (modelview_stack, &inverse_projection);
+
   /* Rotate about point a */
   _cogl_matrix_stack_translate (modelview_stack,
                                 vertex_a[0], vertex_a[1], vertex_a[2]);
@@ -1095,7 +1096,6 @@ cogl_frustum (float        left,
 	      float        z_near,
 	      float        z_far)
 {
-  float c, d;
   CoglMatrixStack *projection_stack =
     _cogl_draw_buffer_get_projection_stack (_cogl_get_draw_buffer ());
 
@@ -1110,22 +1110,6 @@ cogl_frustum (float        left,
                               top,
                               z_near,
                               z_far);
-
-  /* Calculate and store the inverse of the matrix */
-  memset (ctx->inverse_projection, 0, sizeof (float) * 16);
-
-  c = - (z_far + z_near) /  (z_far - z_near);
-  d = - (2 * (z_far * z_near)) /  (z_far - z_near);
-
-#define M(row,col)  ctx->inverse_projection[col*4+row]
-  M(0,0) =  (right - left) /  (2 * z_near);
-  M(0,3) =  (right + left) /  (2 * z_near);
-  M(1,1) =  (top - bottom) /  (2 * z_near);
-  M(1,3) =  (top + bottom) /  (2 * z_near);
-  M(2,3) = -1.0;
-  M(3,2) = 1.0 / d;
-  M(3,3) = c / d;
-#undef M
 }
 
 void
@@ -1145,19 +1129,6 @@ cogl_ortho (float left,
   cogl_matrix_init_identity (&ortho);
   cogl_matrix_ortho (&ortho, left, right, bottom, top, z_near, z_far);
   _cogl_matrix_stack_set (projection_stack, &ortho);
-
-  /* Calculate and store the inverse of the matrix */
-  memset (ctx->inverse_projection, 0, sizeof (float) * 16);
-
-#define M(row,col)  ctx->inverse_projection[col*4+row]
-  M(0,0) =  1.0 / ortho.xx;
-  M(0,3) =  -ortho.xw;
-  M(1,1) =  1.0 / ortho.yy;
-  M(1,3) =  -ortho.yw;
-  M(2,2) =  1.0 / ortho.zz;
-  M(2,3) =  -ortho.zw;
-  M(3,3) =  1.0;
-#undef M
 }
 
 void