/**
* graphene_quaternion_slerp:
* @a: a #graphene_quaternion_t
* @b: a #graphene_quaternion_t
* @factor: the linear interpolation factor
* @res: (out caller-allocates): return location for the interpolated
* quaternion
*
* Interpolates between the two given quaternions using a spherical
* linear interpolation, or [SLERP](http://en.wikipedia.org/wiki/Slerp),
* using the given interpolation @factor.
*
* Since: 1.0
*/
void
graphene_quaternion_slerp (const graphene_quaternion_t *a,
const graphene_quaternion_t *b,
float factor,
graphene_quaternion_t *res)
{
float theta, r_sin_theta, right_v, left_v, dot;
graphene_simd4f_t v_a, v_b, left, right, sum;
v_a = graphene_simd4f_init (a->x, a->y, a->z, a->w);
v_b = graphene_simd4f_init (b->x, b->y, b->z, b->w);
dot = CLAMP (graphene_simd4f_get_x (graphene_simd4f_dot4 (v_a, v_b)), -1.f, 1.f);
if (dot == 1.f)
{
*res = *a;
return;
}
theta = acos (dot);
r_sin_theta = 1.f / sqrtf (1.f - dot * dot);
right_v = sinf (factor * theta) * r_sin_theta;
left_v = cosf (factor * theta) - dot * right_v;
left = graphene_simd4f_init (a->x, a->y, a->z, a->w);
right = graphene_simd4f_init (b->x, b->y, b->z, b->w);
left = graphene_simd4f_mul (left, graphene_simd4f_splat (left_v));
right = graphene_simd4f_mul (right, graphene_simd4f_splat (right_v));
sum = graphene_simd4f_add (left, right);
graphene_quaternion_init_from_simd4f (res, sum);
}
/**
* graphene_vec3_scale:
* @v: a #graphene_vec3_t
* @factor: the scalar factor
* @res: (out caller-allocates): return location for the result vector
*
* Multiplies all components of the given vector with the given scalar @factor.
*
* Since: 1.2
*/
void
graphene_vec3_scale (const graphene_vec3_t *v,
float factor,
graphene_vec3_t *res)
{
res->value = graphene_simd4f_mul (v->value, graphene_simd4f_splat (factor));
}
static void
init_static_vec4_once (void)
{
static_vec4[VEC4_ZERO].value = graphene_simd4f_init_zero ();
static_vec4[VEC4_ONE].value = graphene_simd4f_splat (1.f);
static_vec4[VEC4_X_AXIS].value = graphene_simd4f_init (1.f, 0.f, 0.f, 0.f);
static_vec4[VEC4_Y_AXIS].value = graphene_simd4f_init (0.f, 1.f, 0.f, 0.f);
static_vec4[VEC4_Z_AXIS].value = graphene_simd4f_init (0.f, 0.f, 1.f, 0.f);
static_vec4[VEC4_W_AXIS].value = graphene_simd4f_init (0.f, 0.f, 0.f, 1.f);
}
/**
* graphene_matrix_skew_yz:
* @m: a #graphene_matrix_t
* @factor: skew factor
*
* Adds a skew of @factor on the Y and Z axis to the given matrix.
*
* Since: 1.0
*/
void
graphene_matrix_skew_yz (graphene_matrix_t *m,
float factor)
{
graphene_simd4f_t m_y, m_z;
m_y = m->value.y;
m_z = m->value.z;
m->value.z = graphene_simd4f_add (m_z, graphene_simd4f_mul (m_y, graphene_simd4f_splat (factor)));
}
/**
* graphene_matrix_skew_xy:
* @m: a #graphene_matrix_t
* @factor: skew factor
*
* Adds a skew of @factor on the X and Y axis to the given matrix.
*
* Since: 1.0
*/
void
graphene_matrix_skew_xy (graphene_matrix_t *m,
float factor)
{
graphene_simd4f_t m_x, m_y;
m_x = m->value.x;
m_y = m->value.y;
m->value.y = graphene_simd4f_add (m_y, graphene_simd4f_mul (m_x, graphene_simd4f_splat (factor)));
}
void
graphene_matrix_skew_xz (graphene_matrix_t *m,
float factor)
{
graphene_simd4f_t m_x, m_z;
g_return_if_fail (m != NULL);
m_x = m->value.x;
m_z = m->value.z;
m->value.z = graphene_simd4f_add (m_z, graphene_simd4f_mul (m_x, graphene_simd4f_splat (factor)));
}
/**
* 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);
}
/**
* graphene_quaternion_init_from_angle_vec3:
* @q: a #graphene_quaternion_t
* @angle: the rotation on a given axis, in degrees
* @axis: the axis of rotation, expressed as a vector
*
* Initializes a #graphene_quaternion_t using an @angle on a
* specific @axis.
*
* Returns: (transfer none): the initialized quaternion
*
* Since: 1.0
*/
graphene_quaternion_t *
graphene_quaternion_init_from_angle_vec3 (graphene_quaternion_t *q,
float angle,
const graphene_vec3_t *axis)
{
float rad, sin_a, cos_a;
graphene_simd4f_t axis_n;
rad = GRAPHENE_DEG_TO_RAD (angle);
sin_a = sinf (rad / 2.f);
cos_a = cosf (rad / 2.f);
axis_n = graphene_simd4f_mul (graphene_simd4f_normalize3 (axis->value),
graphene_simd4f_splat (sin_a));
q->x = graphene_simd4f_get_x (axis_n);
q->y = graphene_simd4f_get_y (axis_n);
q->z = graphene_simd4f_get_z (axis_n);
q->w = cos_a;
return q;
}
/**
* graphene_simd4f_splat:
* @v: a floating point value
*
* Sets all the components of a new #graphene_simd4f_t to the
* same value @v:
*
* |[<!-- language="plain" -->
* {
* .x = v,
* .y = v,
* .z = v,
* .w = v
* };
* ]|
*
* Returns: the initialized #graphene_simd4f_t
*
* Since: 1.0
*/
graphene_simd4f_t
(graphene_simd4f_splat) (float v)
{
return graphene_simd4f_splat (v);
}
graphene_simd4f_t
(graphene_simd4f_dot3) (const graphene_simd4f_t a,
const graphene_simd4f_t b)
{
return graphene_simd4f_splat (graphene_simd4f_dot3_scalar (a, b));
}
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;
}
