public class Sphere {

	int M, N; // sphereMesh dimensions

	double sphereMesh[][][];

	public Sphere(int m, int n) {
		M = m;
		N = n;
		sphereMesh = new double[M][N][3];
		fillMesh();
	}

	public double[][][] transformedBy(Matrix3D t) {
		
		double[][][] transformed = new double[M][N][3];
		
		for (int i = 0; i < transformed.length; i++)
			for (int j = 0; j < transformed[i].length; j++) {
				transformed[i][j] = t.transform(sphereMesh[i][j]);
			}
			
		return transformed;
	}

	private void fillMesh() {
		for (int i = 0; i < M; i++)
			for (int j = 0; j < N; j++) {
				double u = i / (M - 1.0);
				double v = j / (N - 1.0);

				sphereMesh[i][j][0] = x(u, v);
				sphereMesh[i][j][1] = y(u, v);
				sphereMesh[i][j][2] = z(u, v);
			}
	}

	private double x(double u, double v) {
		return (
			Math.cos(2 * Math.PI * u) * Math.cos(Math.PI * v - (Math.PI / 2)));
	}

	private double y(double u, double v) {
		return (Math.sin(Math.PI * v - (Math.PI / 2)));
	}

	private double z(double u, double v) {
		return (
			-1
				* Math.sin(2 * Math.PI * u)
				* Math.cos(Math.PI * v - (Math.PI / 2)));
	}

}