/**
* Find the normalized version of the given vector.
* @param <Vector> v
* @return <Vector>
*/
public static Vector Norm(Vector v)
{
double mag = Mag(v);
double div = mag == 0 ? double.PositiveInfinity : 1 / mag;
return Scale(v,div);
}
/**
* Find the magnitude of the given vector.
* @param <Vector> v
* @return <double>
*/
public static double Mag(Vector v)
{
return Math.Sqrt(Dot(v, v));
}
/**
* Subtract one vector from another.
* @param <Vector> v1
* @param <Vector> v2
* @return <Vector>
*/
public static Vector Minus(Vector v1, Vector v2)
{
return new Vector(v1.X - v2.X, v1.Y - v2.Y, v1.Z - v2.Z);
}
/**
* Find the dot-product of two vectors.
* @param <Vector> v1
* @param <Vector> v2
* @return <double>
*/
public static double Dot(Vector v1, Vector v2)
{
return (v1.X * v2.X) + (v1.Y * v2.Y) + (v1.Z * v2.Z);
}
/**
* Determine if two vectors are equivalent.
* @param <Vector> v1
* @param <Vector> v2
* @return <bool>
*/
public static bool Equals(Vector v1, Vector v2)
{
return (v1.X == v2.X) && (v1.Y == v2.Y) && (v1.Z == v2.Z);
}
/**
* Find the cross product of two vectors.
* @param <Vector> v1
* @param <Vector> v2
* @return <Vector>
*/
public static Vector Cross(Vector v1, Vector v2)
{
return new Vector(((v1.Y * v2.Z) - (v1.Z * v2.Y)), ((v1.Z * v2.X) - (v1.X * v2.Z)), ((v1.X * v2.Y) - (v1.Y * v2.X)));
}
/**
* Scale a vector
* @param <Vector> v
* @param <double> x
* @return <Vector>
*/
public static Vector Scale(Vector v, double x)
{
return new Vector(v.X *x, v.Y*x,v.Z*x);
}
/**
* Add two vectors together.
* @param <Vector> v1
* @param <Vector> v2
* @return <Vector>
*/
public static Vector Plus(Vector v1, Vector v2)
{
return new Vector(v1.X + v2.X, v1.Y + v2.Y, v1.Z + v2.Z);
}
/**
* Find the normal vector of the sphere at the given position.
* @param <Vector> pos
* @return <Vector>
*/
public override Vector Normal(Vector pos)
{
return Vector.Norm(Vector.Minus(pos, Center));
}
public abstract Vector Normal(Vector pos);