} // End Function Schnittpunktli
// https://en.wikipedia.org/wiki/Determinant
// | a b |
// | c d |
private static T Determinant2d(T a, T b, T c, T d)
{
T f1 = Arithmetics <T> .Multiply(a, d);
T f2 = Arithmetics <T> .Multiply(b, c);
T result = Arithmetics <T> .Subtract(f1, f2);
return(result);
} // End Function Determinant2d
} // End Operator *
public static MyVector2D <T> operator *(MyVector2D <T> a, T b)
{
MyVector2D <T> v = a.Clone();
v.X = Arithmetics <T> .Multiply(v.X, b);
v.Y = Arithmetics <T> .Multiply(v.Y, b);
return(v);
} // End Operator *
} // End function CrossP
// The dot product (also called the scalar product) is the magnitude of
// vector b multiplied by the size of the projection of a onto b.
// The size of the projection is a cosθ (where θ is the angle between the 2 vectors).
// https://coderwall.com/p/icvt-g/2d-vector-dot-product
// where theta is the angle between u and v, given by the dot product
// cos(theta) = u dotp v
public static T DotP(MyVector2D <T> a, MyVector2D <T> b)
{
T s1 = Arithmetics <T> .Multiply(a.X, b.X);
T s2 = Arithmetics <T> .Multiply(a.Y, b.Y);
//A * B = ax*bx+ay*by+az*bz
T retValue = Arithmetics <T> .Add(s1, s2);
return(retValue);
} // End function DotP
} // End Property NormalVector
// http://mathworld.wolfram.com/CrossProduct.html
// the cross product is a vector that is perpendicular to both
// a and b and thus normal to the plane containing them
// |u x v| = |u| x |v| * sin(phi)
public static T CrossP(MyVector2D <T> a, MyVector2D <T> b)
{
// crossp = det(a,b) = a.X*b.Y- a.Y*b.X
T s1 = Arithmetics <T> .Multiply(a.X, b.Y);
T s2 = Arithmetics <T> .Multiply(a.Y, b.X);
T retValue = Arithmetics <T> .Subtract(s1, s2);
return(retValue);
} // End function CrossP
} // End Function ToString
/// <summary>
/// Returns a new Vector that is the linear blend of the 2 given Vectors
/// </summary>
/// <param name="a">First input vector</param>
/// <param name="b">Second input vector</param>
/// <param name="blend">The blend factor. a when blend=0, b when blend=1.</param>
/// <returns>a when blend=0, b when blend=1, and a linear combination otherwise</returns>
public static MyPoint2D <T> Lerp(MyPoint2D <T> a, MyPoint2D <T> b, T blend)
{
T bxax = Arithmetics <T> .Subtract(b.X, a.X);
T byay = Arithmetics <T> .Subtract(b.Y, a.Y);
T f1 = Arithmetics <T> .Multiply(blend, bxax);
T f2 = Arithmetics <T> .Multiply(blend, byay);
T x = Arithmetics <T> .Add(f1, a.X);
T y = Arithmetics <T> .Add(f2, a.Y);
return(new MyPoint2D <T>(x, y));
} // End Function Lerp
} // End Function ToString
/// <summary>
/// Returns a new Vector that is the linear blend of the 2 given Vectors
/// </summary>
/// <param name="a">First input vector</param>
/// <param name="b">Second input vector</param>
/// <param name="blend">The blend factor. a when blend=0, b when blend=1.</param>
/// <returns>a when blend=0, b when blend=1, and a linear combination otherwise</returns>
public static MyVector3D <T> Lerp(MyVector3D <T> a, MyVector3D <T> b, T blend)
{
T bxax = Arithmetics <T> .Subtract(b.X, a.X);
T byay = Arithmetics <T> .Subtract(b.Y, a.Y);
T bzaz = Arithmetics <T> .Subtract(b.Z, a.Z);
T f1 = Arithmetics <T> .Multiply(blend, bxax);
T f2 = Arithmetics <T> .Multiply(blend, byay);
T f3 = Arithmetics <T> .Multiply(blend, bzaz);
T x = Arithmetics <T> .Add(f1, a.X);
T y = Arithmetics <T> .Add(f2, a.Y);
T z = Arithmetics <T> .Add(f3, a.Z);
return(new MyVector3D <T>(x, y, z));
} // End Function Lerp
} // End function DotP
public static T Angle_Rad(MyVector2D <T> a, MyVector2D <T> b)
{
T axbx = Arithmetics <T> .Multiply(a.X, b.X);
T ayby = Arithmetics <T> .Multiply(a.Y, b.Y);
T azbz = Arithmetics <T> .ZERO;
T sumAB = Arithmetics <T> .Sum(axbx, ayby, azbz);
T ax2 = Arithmetics <T> .Pow(a.X, 2);
T ay2 = Arithmetics <T> .Pow(a.Y, 2);
T az2 = Arithmetics <T> .ZERO;
T bx2 = Arithmetics <T> .Pow(b.X, 2);
T by2 = Arithmetics <T> .Pow(b.Y, 2);
T bz2 = Arithmetics <T> .ZERO;
T aSquare = Arithmetics <T> .Sum(ax2, ay2, az2);
T bSquare = Arithmetics <T> .Sum(bx2, by2, bz2);
T val = Arithmetics <T> .Divide(sumAB,
(
Arithmetics <T> .Multiply(Arithmetics <T> .Sqrt(aSquare), Arithmetics <T> .Sqrt(bSquare))
)
);
T nReturnValue = Arithmetics <T> .Acos(val);
return(nReturnValue);
} // End function Angle_Rad
} // End Function GetNormalVector
/// <summary>
/// Returns the CrossProduct.
/// </summary>
/// <returns>Vector<T> containing the value of the CrossProduct.</returns>
public static MyVector3D <T> CrossP(MyVector3D <T> a, MyVector3D <T> b)
{
T x1 = Arithmetics <T> .Multiply(a.Y, b.Z);
T x2 = Arithmetics <T> .Multiply(a.Z, b.Y);
T y1 = Arithmetics <T> .Multiply(a.Z, b.X);
T y2 = Arithmetics <T> .Multiply(a.X, b.Z);
T z1 = Arithmetics <T> .Multiply(a.X, b.Y);
T z2 = Arithmetics <T> .Multiply(a.Y, b.X);
//A × B = [(ay*bz-az*by),(az*bx-ax*bz),(ax*by-ay*bx)]
MyVector3D <T> vecReturnValue = new MyVector3D <T>(
Arithmetics <T> .Subtract(x1, x2)
, Arithmetics <T> .Subtract(y1, y2)
, Arithmetics <T> .Subtract(z1, z2)
);
return(vecReturnValue);
} // End function CrossP
public void TestMethod1()
{
Arithmetics a = new Arithmetics();
Assert.AreEqual(5, a.Multiply(2, 2));
}