/**
* equivalent to ``shell_angle_to_dist(angle_normalized_v2v2(a, b))``
*/
MINLINE float shell_v2v2_normalized_to_dist(const float a[2], const float b[2])
{
const float angle_cos = fabsf(dot_v2v2(a, b));
BLI_ASSERT_UNIT_V2(a);
BLI_ASSERT_UNIT_V2(b);
return (UNLIKELY(angle_cos < SMALL_NUMBER)) ? 1.0f : (1.0f / angle_cos);
}
/**
* equivalent to ``shell_angle_to_dist(angle_normalized_v2v2(a, b) / 2)``
*/
MINLINE float shell_v2v2_mid_normalized_to_dist(const float a[2], const float b[2])
{
float angle_cos;
float ab[2];
BLI_ASSERT_UNIT_V2(a);
BLI_ASSERT_UNIT_V2(b);
add_v2_v2v2(ab, a, b);
angle_cos = (normalize_v2(ab) != 0.0f) ? fabsf(dot_v2v2(a, ab)) : 0.0f;
return (UNLIKELY(angle_cos < SMALL_NUMBER)) ? 1.0f : (1.0f / angle_cos);
}
float angle_normalized_v2v2(const float v1[2], const float v2[2])
{
/* double check they are normalized */
BLI_ASSERT_UNIT_V2(v1);
BLI_ASSERT_UNIT_V2(v2);
/* this is the same as acos(dot_v3v3(v1, v2)), but more accurate */
if (dot_v2v2(v1, v2) >= 0.0f) {
return 2.0f * saasin(len_v2v2(v1, v2) / 2.0f);
}
else {
float v2_n[2];
negate_v2_v2(v2_n, v2);
return (float)M_PI - 2.0f * saasin(len_v2v2(v1, v2_n) / 2.0f);
}
}
float angle_normalized_v2v2(const float v1[2], const float v2[2])
{
/* double check they are normalized */
BLI_ASSERT_UNIT_V2(v1);
BLI_ASSERT_UNIT_V2(v2);
/* this is the same as acos(dot_v3v3(v1, v2)), but more accurate */
if (dot_v2v2(v1, v2) < 0.0f) {
float vec[2];
vec[0] = -v2[0];
vec[1] = -v2[1];
return (float)M_PI - 2.0f * saasin(len_v2v2(vec, v1) / 2.0f);
}
else
return 2.0f * (float)saasin(len_v2v2(v2, v1) / 2.0f);
}
bool interp_v2_v2v2_slerp(float target[2], const float a[2], const float b[2], const float t)
{
float cosom, w[2];
BLI_ASSERT_UNIT_V2(a);
BLI_ASSERT_UNIT_V2(b);
cosom = dot_v2v2(a, b);
/* direct opposites */
if (UNLIKELY(cosom < (1.0f + FLT_EPSILON))) {
return false;
}
interp_dot_slerp(t, cosom, w);
target[0] = w[0] * a[0] + w[1] * b[0];
target[1] = w[0] * a[1] + w[1] * b[1];
return true;
}
