Implement texture coordinate for spheres

sphere.h

@@ -18,6 +18,21 @@ class sphere : public hittable {
             return centre1 + time * centreVec;
         }
 
+        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;
+        }
+
     public: 
         // Stationary sphere. 
         sphere(const point3& centre, double radius, shared_ptr<material> mat) : centre1(centre), radius(fmax(0, radius)), mat(mat), isMoving(false) {
@@ -63,6 +78,7 @@ class sphere : public hittable {
             rec.p = r.at(rec.t);
             vec3 outwardNormal = (rec.p - centre) / radius;
             rec.setFaceNormal(r, outwardNormal);
+            getSphereUV(outwardNormal, rec.u, rec.v);
             rec.mat = mat;
 
             return true;