/// <summary> /// Calculates whether this box contains another box /// </summary> /// <param name="other">The box.</param> /// <returns>True if this box contains the given box; False otherwise.</returns> /// <remarks>This does consider a box that touches the edge contained.</remarks> public bool Contains(Box3D <T> other) => Scalar.GreaterThanOrEqual(other.Min.X, this.Min.X) && Scalar.GreaterThanOrEqual(other.Min.Y, this.Min.Y) && Scalar.GreaterThanOrEqual(other.Min.Z, this.Min.Z) && Scalar.LessThanOrEqual(other.Max.X, this.Max.X) && Scalar.LessThanOrEqual(other.Max.Y, this.Max.Y) && Scalar.LessThanOrEqual(other.Max.Z, this.Max.Z);
/// <summary>
/// Calculates the distance to the nearest edge from the point.
/// </summary>
/// <param name="point">The point.</param>
/// <returns>The distance.</returns>
public T GetDistanceToNearestEdge(Vector3D <T> point)
{
var dx = Scalar.Max(Scalar.Max(Scalar.Subtract(Min.X, point.X), Scalar <T> .Zero), Scalar.Subtract(point.X, Max.X));
var dy = Scalar.Max(Scalar.Max(Scalar.Subtract(Min.Y, point.Y), Scalar <T> .Zero), Scalar.Subtract(point.Y, Max.Y));
var dz = Scalar.Max(Scalar.Max(Scalar.Subtract(Min.Z, point.Z), Scalar <T> .Zero), Scalar.Subtract(point.Z, Max.Z));
return(Scalar.Sqrt(Scalar.Add(Scalar.Add(Scalar.Multiply(dx, dx), Scalar.Multiply(dy, dy)), Scalar.Multiply(dz, dz))));
}
/// <summary> /// Calculates whether this box contains another box /// </summary> /// <param name="other">The box.</param> /// <returns>True if this box contains the given box; False otherwise.</returns> /// <remarks>This does consider a box that touches the edge contained.</remarks> public bool Contains(Box2D <T> other) => Scalar.GreaterThanOrEqual(other.Min.X, Min.X) && Scalar.GreaterThanOrEqual(other.Min.Y, Min.Y) && Scalar.LessThanOrEqual(other.Max.X, Max.X) && Scalar.LessThanOrEqual(other.Max.Y, Max.Y);
/// <summary> /// Calculates whether this box contains a point. /// </summary> /// <param name="point">The point.</param> /// <returns>True if this box contains the point; False otherwise.</returns> /// <remarks>This does consider a point on the edge contained.</remarks> public bool Contains(Vector3D <T> point) => Scalar.GreaterThanOrEqual(point.X, Min.X) && Scalar.GreaterThanOrEqual(point.Y, Min.Y) && Scalar.GreaterThanOrEqual(point.Z, Min.Z) && Scalar.LessThanOrEqual(point.X, Max.X) && Scalar.LessThanOrEqual(point.Y, Max.Y) && Scalar.LessThanOrEqual(point.Z, Max.Z);
/// <summary>
/// Calculates whether this rectangle contains another rectangle
/// </summary>
/// <param name="other">The rectangle.</param>
/// <returns>True if this rectangle contains the given rectangle; False otherwise.</returns>
/// <remarks>This does consider a rectangle that touches the edge contained.</remarks>
public bool Contains(Rectangle <T> other)
{
var tMax = this.Max;
var oMax = other.Max;
return(Scalar.GreaterThanOrEqual(other.Origin.X, this.Origin.X) && Scalar.GreaterThanOrEqual
(other.Origin.Y, this.Origin.Y) && Scalar.LessThanOrEqual(oMax.X, tMax.X) && Scalar.LessThanOrEqual
(oMax.Y, tMax.Y));
}
/// <summary>
/// Calculates the distance to the nearest edge from the point.
/// </summary>
/// <param name="point">The point.</param>
/// <returns>The distance.</returns>
public T GetDistanceToNearestEdge(Vector2D <T> point)
{
var max = Max;
var dx = Scalar.Max(Scalar.Max(Scalar.Subtract(Origin.X, point.X), Scalar <T> .Zero), Scalar.Subtract(point.X, max.X));
var dy = Scalar.Max(Scalar.Max(Scalar.Subtract(Origin.Y, point.Y), Scalar <T> .Zero), Scalar.Subtract(point.Y, max.Y));
return(Scalar.Sqrt(Scalar.Add(Scalar.Multiply(dx, dx), Scalar.Multiply(dy, dy))));
}
public readonly bool Equals(Plane <T> other)
{
return(Normal.Equals(other.Normal) && Scalar.Equal(Distance, other.Distance));
}
/// <summary>
/// Calculates whether this rectangle contains a point.
/// </summary>
/// <param name="point">The point.</param>
/// <returns>True if this rectangle contains the point; False otherwise.</returns>
/// <remarks>This does consider a point on the edge contained.</remarks>
public bool Contains(Vector2D <T> point)
{
var max = Max;
return(Scalar.GreaterThanOrEqual(point.X, Origin.X) && Scalar.GreaterThanOrEqual
(point.Y, Origin.Y) && Scalar.LessThanOrEqual(point.X, max.X) && Scalar.LessThanOrEqual(point.Y, max.Y));
}
/// <summary>Creates a matrix that rotates around an arbitrary vector.</summary>
/// <param name="axis">The axis to rotate around.</param>
/// <param name="angle">The angle to rotate around the given axis, in radians.</param>
/// <returns>The rotation matrix.</returns>
public static Matrix2X3 <T> CreateFromAxisAngle <T>(Vector3D <T> axis, T angle)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
// a: angle
// x, y, z: unit vector for axis.
//
// Rotation matrix M can compute by using below equation.
//
// T T
// M = uu + (cos a)( I-uu ) + (sin a)S
//
// Where:
//
// u = ( x, y, z )
//
// [ 0 -z y ]
// S = [ z 0 -x ]
// [ -y x 0 ]
//
// [ 1 0 0 ]
// I = [ 0 1 0 ]
// [ 0 0 1 ]
//
//
// [ xx+cosa*(1-xx) yx-cosa*yx-sina*z zx-cosa*xz+sina*y ]
// M = [ xy-cosa*yx+sina*z yy+cosa(1-yy) yz-cosa*yz-sina*x ]
// [ zx-cosa*zx-sina*y zy-cosa*zy+sina*x zz+cosa*(1-zz) ]
//
T x = axis.X, y = axis.Y, z = axis.Z;
T sa = Scalar.Sin(angle), ca = Scalar.Cos(angle);
T xx = Scalar.Multiply(x, x), yy = Scalar.Multiply(y, y), zz = Scalar.Multiply(z, z);
T xy = Scalar.Multiply(x, y), xz = Scalar.Multiply(x, z), yz = Scalar.Multiply(y, z);
Matrix2X3 <T> result = Matrix2X3 <T> .Identity;
result.M11 = Scalar.Add(xx, Scalar.Multiply(ca, Scalar.Subtract(Scalar <T> .One, xx)));
result.M12 = Scalar.Add(Scalar.Subtract(xy, Scalar.Multiply(ca, xy)), Scalar.Multiply(sa, z));
result.M13 = Scalar.Subtract(Scalar.Subtract(xz, Scalar.Multiply(ca, xz)), Scalar.Multiply(sa, y));
result.M21 = Scalar.Subtract(Scalar.Subtract(xy, Scalar.Multiply(ca, xy)), Scalar.Multiply(sa, z));
result.M22 = Scalar.Add(yy, Scalar.Multiply(ca, Scalar.Subtract(Scalar <T> .One, yy)));
result.M23 = Scalar.Add(Scalar.Subtract(yz, Scalar.Multiply(ca, yz)), Scalar.Multiply(sa, x));
return(result);
}
public static bool operator ==(Plane <T> value1, Plane <T> value2) => value1.Normal == value2.Normal && Scalar.Equal(value1.Distance, value2.Distance);
/// <summary>Creates a rotation matrix from the given Quaternion rotation value.</summary>
/// <param name="quaternion">The source Quaternion.</param>
/// <returns>The rotation matrix.</returns>
public static Matrix2X3 <T> CreateFromQuaternion <T>(Quaternion <T> quaternion)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
Matrix2X3 <T> result = Matrix2X3 <T> .Identity;
T xx = Scalar.Multiply(quaternion.X, quaternion.X);
T yy = Scalar.Multiply(quaternion.Y, quaternion.Y);
T zz = Scalar.Multiply(quaternion.Z, quaternion.Z);
T xy = Scalar.Multiply(quaternion.X, quaternion.Y);
T wz = Scalar.Multiply(quaternion.Z, quaternion.W);
T xz = Scalar.Multiply(quaternion.Z, quaternion.X);
T wy = Scalar.Multiply(quaternion.Y, quaternion.W);
T yz = Scalar.Multiply(quaternion.Y, quaternion.Z);
T wx = Scalar.Multiply(quaternion.X, quaternion.W);
result.M11 = Scalar.Subtract(Scalar <T> .One, Scalar.Multiply(Scalar <T> .Two, Scalar.Add(yy, zz)));
result.M12 = Scalar.Multiply(Scalar <T> .Two, Scalar.Add(xy, wz));
result.M13 = Scalar.Multiply(Scalar <T> .Two, Scalar.Subtract(xz, wy));
result.M21 = Scalar.Multiply(Scalar <T> .Two, Scalar.Subtract(xy, wz));
result.M22 = Scalar.Subtract(Scalar <T> .One, Scalar.Multiply(Scalar <T> .Two, Scalar.Add(zz, xx)));
result.M23 = Scalar.Multiply(Scalar <T> .Two, Scalar.Add(yz, wx));
return(result);
}
/// <summary>
/// Calculates the squared distance to the nearest edge from the point.
/// </summary>
/// <param name="point">The point.</param>
/// <returns>The distance squared.</returns>
public T GetDistanceToNearestEdgeSquared(Vector3D <T> point)
{
return(Scalar.Subtract(Vector3D.DistanceSquared(Center, point), SquaredRadius));
}
/// <summary>
/// Calculates whether this sphere contains a point.
/// </summary>
/// <param name="point">The point.</param>
/// <returns>True if this sphere contains the point; False otherwise.</returns>
/// <remarks>This does consider a point on the edge contained.</remarks>
public bool Contains(Vector3D <T> point)
{
return(Scalar.LessThanOrEqual(Vector3D.DistanceSquared(point, Center), Radius));
}
/// <summary>
/// Returns this sphere casted to <typeparamref name="TOther"></typeparamref>
/// </summary>
/// <typeparam name="TOther">The type to cast to</typeparam>
/// <returns>The casted sphere</returns>
public Sphere <TOther> As <TOther>() where TOther : unmanaged, IFormattable, IEquatable <TOther>, IComparable <TOther>
{
return(new(Center.As <TOther>(), Scalar.As <T, TOther>(Radius)));
}
/// <summary> /// Calculates the distance to the nearest edge from the point. /// </summary> /// <param name="point">The point.</param> /// <returns>The distance.</returns> public T GetDistanceToNearestEdge(Vector3D <T> point) => Scalar.Sqrt(GetDistanceToNearestEdgeSquared(point));