import java.lang.Math;

public class Vector3D {

	public float [] v = new float[3];

	public Vector3D() {
		v[0] = v[1] = v[2] = 0;
	}

	public Vector3D( float x, float y, float z ) {
		v[0] = x;
		v[1] = y;
		v[2] = z;
	}

	public Vector3D( Point3D P ) {
		v[0] = P.p[0];
		v[1] = P.p[1];
		v[2] = P.p[2];
	}

	public void copy( Vector3D V ) {
		v[0] = V.v[0];
		v[1] = V.v[1];
		v[2] = V.v[2];
	}

	public float x() { return v[0]; }
	public float y() { return v[1]; }
	public float z() { return v[2]; }

	public float lengthSquared() {
		return x()*x() + y()*y() + z()*z();
	}
	public float length() {
		return (float)Math.sqrt( lengthSquared() );
	}

	public Vector3D negated() {
		return new Vector3D(-x(),-y(),-z());
	}

	public Vector3D normalized() {
		float l = length();
		if ( l > 0 ) {
			float k = 1/l; // scale factor
			return new Vector3D(k*x(),k*y(),k*z());
		}
		else return new Vector3D(x(),y(),z());
	}

	// returns the dot-product of the given vectors
	static public float dot( Vector3D a, Vector3D b ) {
		return a.x()*b.x() + a.y()*b.y() + a.z()*b.z();
	}

	// returns the cross-product of the given vectors
	static public Vector3D cross( Vector3D a, Vector3D b ) {
		return new Vector3D(
			a.y()*b.z() - a.z()*b.y(),
			a.z()*b.x() - a.x()*b.z(),
			a.x()*b.y() - a.y()*b.x()
		);
	}

	// returns the sum of the given vectors
	static public Vector3D sum( Vector3D a, Vector3D b ) {
		return new Vector3D( a.x()+b.x(), a.y()+b.y(), a.z()+b.z() );
	}

	// returns the difference of the given vectors
	static public Vector3D diff( Vector3D a, Vector3D b ) {
		return new Vector3D( a.x()-b.x(), a.y()-b.y(), a.z()-b.z() );
	}

	// returns the product of the given vector and scalar
	static public Vector3D mult( Vector3D a, float b ) {
		return new Vector3D( a.x()*b, a.y()*b, a.z()*b );
	}

}