/**
* graphene_quaternion_init_from_matrix:
* @q: a #graphene_quaternion_t
* @m: a #graphene_matrix_t
*
* Initializes a #graphene_quaternion_t using the rotation components
* of a transformation matrix.
*
* Returns: (transfer none): the initialized quaternion
*
* Since: 1.0
*/
graphene_quaternion_t *
graphene_quaternion_init_from_matrix (graphene_quaternion_t *q,
const graphene_matrix_t *m)
{
float xx, yy, zz;
xx = graphene_matrix_get_value (m, 0, 0);
yy = graphene_matrix_get_value (m, 1, 1);
zz = graphene_matrix_get_value (m, 2, 2);
q->w = 0.5f * sqrtf (MAX (1 + xx + yy + zz, 0.f));
q->x = 0.5f * sqrtf (MAX (1 + xx - yy - zz, 0.f));
q->y = 0.5f * sqrtf (MAX (1 - xx + yy - zz, 0.f));
q->z = 0.5f * sqrtf (MAX (1 - xx - yy + zz, 0.f));
if (graphene_matrix_get_value (m, 2, 1) > graphene_matrix_get_value (m, 1, 2))
q->x = -q->x;
if (graphene_matrix_get_value (m, 0, 2) > graphene_matrix_get_value (m, 2, 0))
q->y = -q->y;
if (graphene_matrix_get_value (m, 1, 0) > graphene_matrix_get_value (m, 0, 1))
q->z = -q->z;
return q;
}
/**
* graphene_matrix_print:
* @m: The matrix to print
*
* Prints the contents of a matrix.
*
* Since: 1.0
*/
void
graphene_matrix_print (const graphene_matrix_t *m)
{
int i;
for (i = 0; i < 4; i++)
{
fprintf (stderr,
"%.5f %.5f %.5f %.5f\n",
graphene_matrix_get_value (m, i, 0),
graphene_matrix_get_value (m, i, 1),
graphene_matrix_get_value (m, i, 2),
graphene_matrix_get_value (m, i, 3));
}
}
static void
extract_matrix_metadata (const graphene_matrix_t *m,
OpsMatrixMetadata *md)
{
switch (md->category)
{
case GSK_TRANSFORM_CATEGORY_IDENTITY:
md->scale_x = 1;
md->scale_y = 1;
break;
case GSK_TRANSFORM_CATEGORY_2D_TRANSLATE:
md->translate_x = graphene_matrix_get_value (m, 3, 0);
md->translate_y = graphene_matrix_get_value (m, 3, 1);
md->scale_x = 1;
md->scale_y = 1;
break;
case GSK_TRANSFORM_CATEGORY_UNKNOWN:
case GSK_TRANSFORM_CATEGORY_ANY:
case GSK_TRANSFORM_CATEGORY_3D:
case GSK_TRANSFORM_CATEGORY_2D:
case GSK_TRANSFORM_CATEGORY_2D_AFFINE:
{
graphene_vec3_t col1;
graphene_vec3_t col2;
md->translate_x = graphene_matrix_get_value (m, 3, 0);
md->translate_y = graphene_matrix_get_value (m, 3, 1);
graphene_vec3_init (&col1,
graphene_matrix_get_value (m, 0, 0),
graphene_matrix_get_value (m, 1, 0),
graphene_matrix_get_value (m, 2, 0));
graphene_vec3_init (&col2,
graphene_matrix_get_value (m, 0, 1),
graphene_matrix_get_value (m, 1, 1),
graphene_matrix_get_value (m, 2, 1));
md->scale_x = graphene_vec3_length (&col1);
md->scale_y = graphene_vec3_length (&col2);
}
break;
default:
{}
}
}
/**
* graphene_matrix_is_backface_visible:
* @m: a #graphene_matrix_t
*
* Checks whether a #graphene_matrix_t has a visible back face.
*
* Returns: %true if the back face of the matrix is visible
*
* Since: 1.0
*/
bool
graphene_matrix_is_backface_visible (const graphene_matrix_t *m)
{
graphene_matrix_t tmp;
graphene_matrix_inverse (m, &tmp);
/* inverse.zz < 0 */
return graphene_matrix_get_value (&tmp, 2, 2) < 0.f;
}
gboolean
graphene_matrix_is_backface_visible (const graphene_matrix_t *m)
{
graphene_matrix_t tmp;
g_return_val_if_fail (m != NULL, FALSE);
graphene_matrix_inverse (m, &tmp);
/* inverse.zz < 0 */
return graphene_matrix_get_value (&tmp, 2, 2) < 0.f;
}
/**
* graphene_matrix_to_2d:
* @m: a #graphene_matrix_t
* @xx: (out): return location for the xx member
* @yx: (out): return location for the yx member
* @xy: (out): return location for the xy member
* @yy: (out): return location for the yy member
* @x_0: (out): return location for the x0 member
* @y_0: (out): return location for the y0 member
*
* Converts a #graphene_matrix_t to an affine transformation
* matrix, if the given matrix is compatible.
*
* The returned values have the following layout:
*
* |[
* | xx yx | | a b 0 |
* | xy yy | = | c d 0 |
* | x0 y0 | | tx ty 1 |
* ]|
*
* This function can be used to convert between a #graphene_matrix_t
* and a matrix type from other libraries.
*
* Returns: %true if the matrix is compatible with an affine
* transformation matrix
*
* Since: 1.0
*/
bool
graphene_matrix_to_2d (const graphene_matrix_t *m,
double *xx,
double *yx,
double *xy,
double *yy,
double *x_0,
double *y_0)
{
if (!graphene_simd4x4f_is_2d (&m->value))
return false;
if (xx != NULL)
*xx = graphene_matrix_get_value (m, 0, 0);
if (yx != NULL)
*yx = graphene_matrix_get_value (m, 0, 1);
if (xy != NULL)
*xy = graphene_matrix_get_value (m, 1, 0);
if (yy != NULL)
*yy = graphene_matrix_get_value (m, 1, 1);
if (x_0 != NULL)
*x_0 = graphene_matrix_get_value (m, 3, 0);
if (y_0 != NULL)
*y_0 = graphene_matrix_get_value (m, 3, 1);
return true;
}
/**
* graphene_matrix_normalize:
* @m: a #graphene_matrix_t
* @res: (out caller-allocates): return location for the normalized matrix
*
* Normalizes the given #graphene_matrix_t.
*
* Since: 1.0
*/
void
graphene_matrix_normalize (const graphene_matrix_t *m,
graphene_matrix_t *res)
{
graphene_simd4f_t n;
float ww;
ww = graphene_matrix_get_value (m, 3, 3);
n = graphene_simd4f_splat (ww);
res->value.x = graphene_simd4f_div (m->value.x, n);
res->value.y = graphene_simd4f_div (m->value.y, n);
res->value.z = graphene_simd4f_div (m->value.z, n);
res->value.w = graphene_simd4f_div (m->value.w, n);
}
static gboolean
matrix_decompose_2d (const graphene_matrix_t *m,
graphene_point3d_t *scale_r,
float shear_r[3],
graphene_quaternion_t *rotate_r,
graphene_point3d_t *translate_r)
{
float A = graphene_matrix_get_value (m, 0, 0);
float B = graphene_matrix_get_value (m, 1, 0);
float C = graphene_matrix_get_value (m, 0, 1);
float D = graphene_matrix_get_value (m, 1, 1);
float scale_x, scale_y;
float shear_xy;
float rotate;
if (A * D == B * C)
return FALSE;
scale_x = sqrtf (A * A + B * B);
A /= scale_x;
B /= scale_x;
shear_xy = A * C + B * D;
C -= A * shear_xy;
D -= B * shear_xy;
scale_y = sqrtf (C * C + D * D);
C /= scale_y;
D /= scale_y;
shear_xy /= scale_y;
if (A * D < B * C)
{
A = -A;
B = -B;
C = -C;
D = -D;
shear_xy = -shear_xy;
scale_x = -scale_x;
}
rotate = atan2f (B, A);
graphene_quaternion_init (rotate_r, 0.f, 0.f, sin (rotate / 2.f), cos (rotate / 2.f));
shear_r[XY_SHEAR] = shear_xy;
graphene_point3d_init (scale_r, scale_x, scale_y, 1.f);
graphene_point3d_init (translate_r,
graphene_matrix_get_value (m, 3, 0),
graphene_matrix_get_value (m, 3, 1),
0.f);
return TRUE;
}
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;
}
