getConeSample.hlsl

// Returns a random direction vector inside a cone
// Angle defined in radians
// Example: direction=(0,1,0) and angle=pi returns ([-1,1],[0,1],[-1,1])
float3 getConeSample(inout uint randSeed, float3 direction, float coneAngle) {
    float cosAngle = cos(coneAngle);

    // Generate points on the spherical cap around the north pole [1].
    // [1] See https://math.stackexchange.com/a/205589/81266
    float z = nextRand(randSeed) * (1.0f - cosAngle) + cosAngle;
    float phi = nextRand(randSeed) * 2.0f * PI;

    float x = sqrt(1.0f - z * z) * cos(phi);
    float y = sqrt(1.0f - z * z) * sin(phi);
    float3 north = float3(0.f, 0.f, 1.f);

    // Find the rotation axis `u` and rotation angle `rot` [1]
    float3 axis = normalize(cross(north, normalize(direction)));
    float angle = acos(dot(normalize(direction), north));

    // Convert rotation axis and angle to 3x3 rotation matrix [2]
    float3x3 R = angleAxis3x3(angle, axis);

    return mul(R, float3(x, y, z));
}