static void getSphereUV(const point3& p, double& u, double& v) {
    // p: a given point on the sphere of radius one, centered at the origin.
    // u: returned value [0,1] of angle around the Y axis from X=-1.
    // v: returned value [0,1] of angle from Y=-1 to Y=+1.
    //     <1 0 0> yields <0.50 0.50>       <-1  0  0> yields <0.00 0.50>
    //     <0 1 0> yields <0.50 1.00>       < 0 -1  0> yields <0.50 0.00>
    //     <0 0 1> yields <0.25 0.50>       < 0  0 -1> yields <0.75 0.50>
    auto theta = acos(-p.y());
    auto phi = atan2(-p.z(), p.x()) + pi;

    u = phi / (2*pi);
    v = theta / pi;
}