static void
quaternion_matrix_to_from (mutest_spec_t *spec)
{
graphene_quaternion_t *q1, *q2;
graphene_matrix_t *m;
m = graphene_matrix_init_identity (graphene_matrix_alloc ());
q1 = graphene_quaternion_init_from_matrix (graphene_quaternion_alloc (), m);
q2 = graphene_quaternion_init_identity (graphene_quaternion_alloc ());
mutest_expect ("initializing from an identity matrix yields an identity quaternion",
mutest_bool_value (graphene_quaternion_equal (q1, q2)),
mutest_to_be_true,
NULL);
graphene_matrix_rotate_x (m, 30.f);
graphene_matrix_rotate_y (m, 45.f);
graphene_matrix_rotate_z (m, -135.f);
graphene_quaternion_init_from_matrix (q1, m);
mutest_expect ("initializing from a rotation matrix does not yield an identity quaternion",
mutest_bool_value (graphene_quaternion_equal (q1, q2)),
mutest_to_be_false,
NULL);
graphene_matrix_init_identity (m);
graphene_matrix_rotate_quaternion (m, q1);
graphene_quaternion_init_from_matrix (q2, m);
mutest_expect ("rotating a matrix with a quaternion yields the same quaternion",
mutest_bool_value (graphene_quaternion_equal (q1, q2)),
mutest_to_be_true,
NULL);
graphene_quaternion_free (q2);
graphene_quaternion_free (q1);
graphene_matrix_free (m);
}
static gboolean
matrix_decompose_3d (const graphene_matrix_t *m,
graphene_point3d_t *scale_r,
float shear_r[3],
graphene_quaternion_t *rotate_r,
graphene_point3d_t *translate_r,
graphene_vec4_t *perspective_r)
{
graphene_matrix_t local, perspective;
float shear_xy, shear_xz, shear_yz;
float scale_x, scale_y, scale_z;
graphene_simd4f_t dot, cross;
if (graphene_matrix_get_value (m, 3, 3) == 0.f)
return FALSE;
local = *m;
/* normalize the matrix */
graphene_matrix_normalize (&local, &local);
/* perspective is used to solve for the perspective component,
* but it also provides an easy way to test for singularity of
* the upper 3x3 component
*/
perspective = local;
perspective.value.w = graphene_simd4f_init (0.f, 0.f, 0.f, 1.f);
if (graphene_matrix_determinant (&perspective) == 0.f)
return FALSE;
/* isolate the perspective */
if (graphene_simd4f_is_zero3 (local.value.w))
{
graphene_matrix_t tmp;
/* perspective_r is the right hand side of the equation */
perspective_r->value = local.value.w;
/* solve the equation by inverting perspective and multiplying
* the inverse with the perspective vector
*/
graphene_matrix_inverse (&perspective, &tmp);
graphene_matrix_transpose_transform_vec4 (&tmp, perspective_r, perspective_r);
/* clear the perspective partition */
local.value.w = graphene_simd4f_init (0.f, 0.f, 0.f, 1.f);
}
else
graphene_vec4_init (perspective_r, 0.f, 0.f, 0.f, 1.f);
/* next, take care of the translation partition */
translate_r->x = graphene_simd4f_get_x (local.value.w);
translate_r->y = graphene_simd4f_get_y (local.value.w);
translate_r->z = graphene_simd4f_get_z (local.value.w);
local.value.w = graphene_simd4f_init (0.f, 0.f, 0.f, graphene_simd4f_get_w (local.value.w));
/* now get scale and shear */
/* compute the X scale factor and normalize the first row */
scale_x = graphene_simd4f_get_x (graphene_simd4f_length4 (local.value.x));
local.value.x = graphene_simd4f_div (local.value.x, graphene_simd4f_splat (scale_x));
/* compute XY shear factor and the second row orthogonal to the first */
shear_xy = graphene_simd4f_get_x (graphene_simd4f_dot4 (local.value.x, local.value.y));
local.value.y = graphene_simd4f_sub (local.value.y, graphene_simd4f_mul (local.value.x, graphene_simd4f_splat (shear_xy)));
/* now, compute the Y scale factor and normalize the second row */
scale_y = graphene_simd4f_get_x (graphene_simd4f_length4 (local.value.y));
local.value.y = graphene_simd4f_div (local.value.y, graphene_simd4f_splat (scale_y));
shear_xy /= scale_y;
/* compute XZ and YZ shears, make the third row orthogonal */
shear_xz = graphene_simd4f_get_x (graphene_simd4f_dot4 (local.value.x, local.value.z));
local.value.z = graphene_simd4f_sub (local.value.z, graphene_simd4f_mul (local.value.x, graphene_simd4f_splat (shear_xz)));
shear_yz = graphene_simd4f_get_x (graphene_simd4f_dot4 (local.value.y, local.value.z));
local.value.z = graphene_simd4f_sub (local.value.z, graphene_simd4f_mul (local.value.y, graphene_simd4f_splat (shear_yz)));
/* next, get the Z scale and normalize the third row */
scale_z = graphene_simd4f_get_x (graphene_simd4f_length4 (local.value.z));
local.value.z = graphene_simd4f_div (local.value.z, graphene_simd4f_splat (scale_z));
shear_xz /= scale_z;
shear_yz /= scale_z;
shear_r[XY_SHEAR] = shear_xy;
shear_r[XZ_SHEAR] = shear_xz;
shear_r[YZ_SHEAR] = shear_yz;
/* at this point, the matrix is orthonormal. we check for a
* coordinate system flip. if the determinant is -1, then
* negate the matrix and the scaling factors
*/
dot = graphene_simd4f_cross3 (local.value.y, local.value.z);
cross = graphene_simd4f_dot4 (local.value.x, dot);
if (graphene_simd4f_get_x (cross) < 0.f)
{
scale_x *= -1.f;
scale_y *= -1.f;
scale_z *= -1.f;
graphene_simd4f_mul (local.value.x, graphene_simd4f_splat (-1.f));
graphene_simd4f_mul (local.value.y, graphene_simd4f_splat (-1.f));
graphene_simd4f_mul (local.value.z, graphene_simd4f_splat (-1.f));
}
graphene_point3d_init (scale_r, scale_x, scale_y, scale_z);
/* get the rotations out */
graphene_quaternion_init_from_matrix (rotate_r, &local);
return TRUE;
}