Implement Sphere::RandomPointOnSurface() RandomPointInside()

include/J3ML/Geometry/Sphere.h

@@ -24,6 +24,28 @@ namespace J3ML::Geometry
         Sphere() {}
         Sphere(const Vector3& pos, float radius) : Position(pos), Radius(radius) {}
 
+        /// Generates a random point on the surface of this sphere
+        /** The points are distributed uniformly.
+            This function uses the rejection method to generate a uniform distribution of points on the surface.
+            Therefore, it is assumed that this sphere is not degenerate, i.e. it has a positive radius.
+            A fixed number of 1000 tries is performed, after which a fixed point on the surface is returned as a fallback.
+            @param rng A pre-seeded random number generator object that is to be used by this function to generate random vlaues.
+            @see class RNG, RandomPointInside(), IsDegenerate()
+            @todo Add Sphere::PointOnSurface(polarYaw, polarPitch). */
+        Vector3 RandomPointOnSurface(RNG& rng) const;
+        static Vector3 RandomPointOnSurface(RNG& rng, const Vector3& center, float radius);
+
+        /// Generates a random point inside this sphere.
+        /** The points are distributed uniformly.
+            This function uses the rejection method to generate a uniform distribution of points inside a sphere.
+            Therefore, it is assumed that this sphere is not degenerate, i.e. it has a positive radius.
+            A fixed number of 1000 tries is performed, after which the sphere center position is returned as a fallback.
+            @param rng A pre-seeded random number generator object that is to be used by this function to generate random values.
+            @see class RNG, RandomPointOnSurface(), IsDegenerate().
+            @todo Add Sphere::Point(polarYaw, polarPitch, radius). */
+        Vector3 RandomPointInside(RNG& rng);
+        static Vector3 RandomPointInside(RNG& rng, const Vector3& center, float radius);
+    public:
         /// Quickly returns an arbitrary point inside this Sphere. Used in GJK intersection test.
         Vector3 AnyPointFast() const { return Position; }
         /// Computes the extreme point of this Sphere in the given direction.

src/J3ML/Geometry/Sphere.cpp

@@ -25,4 +25,47 @@ namespace J3ML::Geometry
         projectionDistance = extremePoint.Dot(direction);
         return extremePoint;
     }
+
+    Vector3 Sphere::RandomPointOnSurface(RNG &rng) const {
+        Vector3 v = Vector3::Zero;
+        // Rejection sampling analysis: The unit sphere fills ~52.4% of the volume of its enclosing box,
+        // so this loop is expected to take only very few iterations before succeeding.
+        for (int i = 0; i < 1000; ++i)
+        {
+            v.x = rng.FloatNeg1_1();
+            v.y = rng.FloatNeg1_1();
+            v.z = rng.FloatNeg1_1();
+            float lenSq = v.LengthSquared();
+            if (lenSq >= 1e-6f && lenSq <= 1.f)
+                return Position + (Radius / std::sqrt(lenSq)) * v;
+        }
+        // Astronomically small probability to reach here, and if we do so, the provided RNG must have been in a bad state.
+        assert(false && "Sphere::RandomPointOnSurface failed!");
+
+        // Failed to generate a point inside this sphere. Return an arbitrary point on the surface as fallback.
+        return Position + Vector3(Radius, 0, 0);
+    }
+
+    Vector3 Sphere::RandomPointInside(RNG &rng) {
+        assert(Radius > 1e-3f);
+        Vector3 v = Vector3::Zero;
+
+        // Rejection sampling analysis: The unit sphere fills ~52.4% of the volume of its enclosing box
+        // so this loop is expected to take only very few iterations before succeeding.
+        for (int i = 0; i < 1000; ++i)
+        {
+            v.x = rng.Float(-Radius, Radius);
+            v.y = rng.Float(-Radius, Radius);
+            v.z = rng.Float(-Radius, Radius);
+
+            if (v.LengthSquared() <= Radius*Radius)
+                return Position + v;
+        }
+        assert(false && "Sphere::RandomPointInside failed!");
+
+        // Failed to generate a point inside this sphere. Return the sphere center as fallback.
+        return Position;
+    }
+
+
 }