const float l = hypotf(x, y);
if (l <= 1.f) {
- const float phi = atan2f(x, y);
- const float theta = 2.f * asinf(l);
+ const float z = 2.f * l * sqrtf(1.f - l * l);
- const float sin_phi = sinf(phi);
- const float cos_phi = cosf(phi);
- const float sin_theta = sinf(theta);
- const float cos_theta = cosf(theta);
-
- vec[0] = sin_theta * sin_phi;
- vec[1] = -sin_theta * cos_phi;
- vec[2] = -cos_theta;
+ vec[0] = z * x / (l > 0.f ? l : 1.f);
+ vec[1] = -z * y / (l > 0.f ? l : 1.f);
+ vec[2] = -1.f + 2.f * l * l;
} else {
vec[0] = 0.f;
vec[1] = -1.f;