/// <summary>
/// Create a 2-dimensional line of type T.
/// </summary>
/// <param name="Pixel">A pixel of type T.</param>
/// <param name="X">The x-component.</param>
/// <param name="Y">The y-component.</param>
public Line2D(IPixel <T> Pixel, T X, T Y)
{
#region Initial Checks
if (Pixel == null)
{
throw new ArgumentNullException("The given pixel must not be null!");
}
if (X == null)
{
throw new ArgumentNullException("The given x-component must not be null!");
}
if (Y == null)
{
throw new ArgumentNullException("The given y-component must not be null!");
}
#endregion
this.Math = MathsFactory <T> .Instance;
this.X1 = Pixel.X;
this.Y1 = Pixel.Y;
this.X2 = Math.Add(Pixel.X, X);
this.Y2 = Math.Add(Pixel.Y, Y);
this.Pixel1 = new Pixel <T>(X1, Y1);
this.Pixel2 = new Pixel <T>(X2, Y2);
this.Length = Pixel1.DistanceTo(Pixel2);
}
/// <summary>
/// Create a rectangle of type T.
/// </summary>
/// <param name="Pixel">A pixel of type T in the upper left corner of the rectangle.</param>
/// <param name="Width">The width of the rectangle.</param>
/// <param name="Height">The height of the rectangle.</param>
public Rectangle(IPixel <T> Pixel, T Width, T Height)
{
#region Initial Checks
if (Pixel == null)
{
throw new ArgumentNullException("The given pixel must not be null!");
}
if (Width == null || Width.Equals(Math.Zero))
{
throw new ArgumentNullException("The given width must not be null or zero!");
}
if (Height == null || Height.Equals(Math.Zero))
{
throw new ArgumentNullException("The given height must not be null or zero!");
}
#endregion
this.Math = MathsFactory <T> .Instance;
this.Left = Pixel.X;
this.Top = Pixel.Y;
this.Right = Math.Add(Pixel.X, Width);
this.Bottom = Math.Add(Pixel.Y, Height);
this.Pixel1 = new Pixel <T>(Left, Top);
this.Pixel2 = new Pixel <T>(Right, Bottom);
this.Width = Math.Distance(Left, Right);
this.Height = Math.Distance(Top, Bottom);
this.Diameter = Pixel1.DistanceTo(Pixel2);
}
/// <summary>
/// A method to calculate the distance between this
/// voxel and the given coordinates of type T.
/// </summary>
/// <param name="x">A x-coordinate of type T</param>
/// <param name="y">A y-coordinate of type T</param>
/// <param name="z">A z-coordinate of type T</param>
/// <returns>The distance between this voxel and the given coordinates.</returns>
public T DistanceTo(T x, T y, T z)
{
#region Initial Checks
if (x == null)
{
throw new ArgumentNullException("The given x-coordinate must not be null!");
}
if (y == null)
{
throw new ArgumentNullException("The given y-coordinate must not be null!");
}
if (z == null)
{
throw new ArgumentNullException("The given z-coordinate must not be null!");
}
#endregion
var dX = Math.Distance(X, x);
var dY = Math.Distance(Y, y);
var dZ = Math.Distance(Z, z);
return(Math.Sqrt(Math.Add(Math.Mul(dX, dX), Math.Mul(dY, dY), Math.Mul(dZ, dZ))));
}
/// <summary>
/// Create a cube of type T.
/// </summary>
/// <param name="Voxel">A Voxel of type T in the upper left front corner of the cube.</param>
/// <param name="Width">The width of the cube.</param>
/// <param name="Height">The height of the cube.</param>
/// <param name="Depth">The depth of the cube.</param>
public Cube(Voxel <T> Voxel, T Width, T Height, T Depth)
{
#region Initial Checks
if (Voxel == null)
{
throw new ArgumentNullException("The given voxel must not be null!");
}
if (Width == null)
{
throw new ArgumentNullException("The given width must not be null!");
}
if (Height == null)
{
throw new ArgumentNullException("The given height must not be null!");
}
if (Depth == null)
{
throw new ArgumentNullException("The given depth must not be null!");
}
#endregion
this.Math = MathsFactory <T> .Instance;
#region Math Checks
if (Math.Distance(Left, Right).Equals(Math.Zero))
{
throw new ArgumentException("The resulting width must not be zero!");
}
if (Math.Distance(Top, Bottom).Equals(Math.Zero))
{
throw new ArgumentException("The resulting height must not be zero!");
}
if (Math.Distance(Front, Behind).Equals(Math.Zero))
{
throw new ArgumentException("The resulting depth must not be zero!");
}
#endregion
this.Left = Voxel.X;
this.Top = Voxel.Y;
this.Front = Voxel.Z;
this.Right = Math.Add(Voxel.X, Width);
this.Bottom = Math.Add(Voxel.Y, Height);
this.Behind = Math.Add(Voxel.Z, Depth);
}
/// <summary>
/// Checks if the given pixel is located on this line.
/// </summary>
/// <param name="Pixel">A pixel of type T.</param>
/// <returns>True if the pixel is located on this line; False otherwise.</returns>
public Boolean Contains(IPixel <T> Pixel)
{
#region Initial Checks
if (Pixel == null)
{
throw new ArgumentNullException("The given pixel must not be null!");
}
#endregion
#region Check line bounds
if (Pixel.X.IsLessThan(X1) && Pixel.X.IsLessThan(X2))
{
return(false);
}
if (Pixel.X.IsLargerThan(X1) && Pixel.X.IsLargerThan(X2))
{
return(false);
}
if (Pixel.Y.IsLessThan(Y1) && Pixel.Y.IsLessThan(Y2))
{
return(false);
}
if (Pixel.Y.IsLargerThan(Y1) && Pixel.Y.IsLargerThan(Y2))
{
return(false);
}
#endregion
// Check equation: Pixel.Y = m*Pixel.X + t
return(Pixel.Y.Equals(Math.Add(Math.Mul(Gradient, Pixel.X), YIntercept)));
}
/// <summary>
/// A method to add vectors.
/// </summary>
/// <param name="Summands">An array of vectors.</param>
/// <returns>The addition of all summands: v1 + v2 + ...</returns>
public IVector2D <T> Add(params IVector2D <T>[] Summands)
{
if (Summands == null || Summands.Length == 0)
{
throw new ArgumentException("The given summands must not be null!");
}
if (Summands.Length == 1)
{
return(Summands[0]);
}
var _X = Summands[0].X;
var _Y = Summands[0].Y;
for (var i = Summands.Length - 1; i >= 1; i--)
{
_X = Math.Add(_X, Summands[i].X);
_Y = Math.Add(_Y, Summands[i].Y);
}
return(new Vector2D <T>(Math.Zero, Math.Zero, _X, _Y));
}
/// <summary>
/// Checks if the given circle shares some
/// area with this circle.
/// </summary>
/// <param name="Circle">A circle of type T.</param>
/// <returns>True if the circle shares some area with this circle; False otherwise.</returns>
public Boolean Overlaps(ICircle <T> Circle)
{
#region Initial Checks
if (Circle == null)
{
throw new ArgumentNullException("The given circle must not be null!");
}
#endregion
if (Center.DistanceTo(Circle.Center).IsLessThanOrEquals(Math.Add(Radius, Circle.Radius)))
{
return(true);
}
return(true);
}
public double GetInterest(double principalAmount, int Year, double rate, int n) => Maths.Multiply(principalAmount, Math.Pow(Maths.Add(1, Maths.Divide(rate, n)), Maths.Multiply(n, Year)));