Sampling Visible GGX Normals with Spherical Caps

SampleVndf_GGX.cpp

// Helper function: sample the visible hemisphere from a spherical cap
vec3 SampleVndf_Hemisphere(vec2 u, vec3 wi)
{
	// sample a spherical cap in (-wi.z, 1]
	float phi = 2.0f * M_PI * u.x;
	float z = fma((1.0f - u.y), (1.0f + wi.z), -wi.z);
	float sinTheta = sqrt(clamp(1.0f - z * z, 0.0f, 1.0f));
	float x = sinTheta * cos(phi);
	float y = sinTheta * sin(phi);
	vec3 c = vec3(x, y, z);
	// compute halfway direction;
	vec3 h = c + wi;
	// return without normalization as this is done later (see line 25)
	return h;
}

// Sample the GGX VNDF
vec3 SampleVndf_GGX(vec2 u, vec3 wi, vec2 alpha)
{
    // warp to the hemisphere configuration
    vec3 wiStd = normalize(vec3(wi.xy * alpha, wi.z));
    // sample the hemisphere
    vec3 wmStd = SampleVndf_Hemisphere(u, wiStd);
    // warp back to the ellipsoid configuration
    vec3 wm = normalize(vec3(wmStd.xy * alpha, wmStd.z));
    // return final normal
    return wm;
}