public static T Dot <T>(Plane <T> plane, Vector4D <T> value)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
=> Scalar.Add(
Scalar.Add(
Scalar.Add(Scalar.Multiply(plane.Normal.X, value.X),
Scalar.Multiply(plane.Normal.Y, value.Y)), Scalar.Multiply(plane.Normal.Z, value.Z)),
Scalar.Multiply(plane.Distance, value.W));
/// <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 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));
return(Scalar.Sqrt(Scalar.Add(Scalar.Multiply(dx, dx), Scalar.Multiply(dy, dy))));
}
/// <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 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 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));
var dz = Scalar.Max(Scalar.Max(Scalar.Subtract(Origin.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))));
}
public static Plane <T> Transform <T>(Plane <T> plane, Matrix4X4 <T> matrix)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
Matrix4X4.Invert(matrix, out Matrix4X4 <T> m);
T x = plane.Normal.X, y = plane.Normal.Y, z = plane.Normal.Z, w = plane.Distance;
return(new(
Scalar.Add(Scalar.Add(Scalar.Add(Scalar.Multiply(x, m.M11), Scalar.Multiply(y, m.M12)), Scalar.Multiply(z, m.M13)), Scalar.Multiply(w, m.M14)),
Scalar.Add(Scalar.Add(Scalar.Add(Scalar.Multiply(x, m.M21), Scalar.Multiply(y, m.M22)), Scalar.Multiply(z, m.M23)), Scalar.Multiply(w, m.M24)),
Scalar.Add(Scalar.Add(Scalar.Add(Scalar.Multiply(x, m.M31), Scalar.Multiply(y, m.M32)), Scalar.Multiply(z, m.M33)), Scalar.Multiply(w, m.M34)),
Scalar.Add(Scalar.Add(Scalar.Add(Scalar.Multiply(x, m.M41), Scalar.Multiply(y, m.M42)), Scalar.Multiply(z, m.M43)), Scalar.Multiply(w, m.M44))));
}
/// <summary>Linearly interpolates between the corresponding values of two matrices.</summary>
/// <param name="matrix1">The first source matrix.</param>
/// <param name="matrix2">The second source matrix.</param>
/// <param name="amount">The relative weight of the second source matrix.</param>
/// <returns>The interpolated matrix.</returns>
public static unsafe Matrix2X2<T> Lerp<T>(Matrix2X2<T> matrix1, Matrix2X2<T> matrix2, T amount) where T : unmanaged, IFormattable, IEquatable<T>, IComparable<T>
{
Matrix2X2<T> result = default;
// First row
result.M11 = Scalar.Add(matrix1.M11, Scalar.Multiply(Scalar.Subtract(matrix2.M11, matrix1.M11), amount));
result.M12 = Scalar.Add(matrix1.M12, Scalar.Multiply(Scalar.Subtract(matrix2.M12, matrix1.M12), amount));
// Second row
result.M21 = Scalar.Add(matrix1.M21, Scalar.Multiply(Scalar.Subtract(matrix2.M21, matrix1.M21), amount));
result.M22 = Scalar.Add(matrix1.M22, Scalar.Multiply(Scalar.Subtract(matrix2.M22, matrix1.M22), amount));
return result;
}
/// <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 Matrix3X3 <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);
Matrix3X3 <T> result = Matrix3X3 <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));
result.M31 = Scalar.Add(Scalar.Subtract(xz, Scalar.Multiply(ca, xz)), Scalar.Multiply(sa, y));
result.M32 = Scalar.Subtract(Scalar.Subtract(yz, Scalar.Multiply(ca, yz)), Scalar.Multiply(sa, x));
result.M33 = Scalar.Add(zz, Scalar.Multiply(ca, Scalar.Subtract(Scalar <T> .One, zz)));
return(result);
}
public static Plane <T> Transform <T>(Plane <T> plane, Quaternion <T> rotation)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
// Compute rotation matrix.
T x2 = Scalar.Add(rotation.X, rotation.X);
T y2 = Scalar.Add(rotation.Y, rotation.Y);
T z2 = Scalar.Add(rotation.Z, rotation.Z);
T wx2 = Scalar.Multiply(rotation.W, x2);
T wy2 = Scalar.Multiply(rotation.W, y2);
T wz2 = Scalar.Multiply(rotation.W, z2);
T xx2 = Scalar.Multiply(rotation.X, x2);
T xy2 = Scalar.Multiply(rotation.X, y2);
T xz2 = Scalar.Multiply(rotation.X, z2);
T yy2 = Scalar.Multiply(rotation.Y, y2);
T yz2 = Scalar.Multiply(rotation.Y, z2);
T zz2 = Scalar.Multiply(rotation.Z, z2);
T m11 = Scalar.Subtract(Scalar.Subtract(Scalar <T> .One, yy2), zz2);
T m21 = Scalar.Subtract(xy2, wz2);
T m31 = Scalar.Add(xz2, wy2);
T m12 = Scalar.Add(xy2, wz2);
T m22 = Scalar.Subtract(Scalar.Subtract(Scalar <T> .One, xx2), zz2);
T m32 = Scalar.Subtract(yz2, wx2);
T m13 = Scalar.Subtract(xz2, wy2);
T m23 = Scalar.Add(yz2, wx2);
T m33 = Scalar.Subtract(Scalar.Subtract(Scalar <T> .One, xx2), yy2);
T x = plane.Normal.X, y = plane.Normal.Y, z = plane.Normal.Z;
return(new(
Scalar.Add(Scalar.Add(Scalar.Multiply(x, m11), Scalar.Multiply(y, m21)), Scalar.Multiply(z, m31)),
Scalar.Add(Scalar.Add(Scalar.Multiply(x, m12), Scalar.Multiply(y, m22)), Scalar.Multiply(z, m32)),
Scalar.Add(Scalar.Add(Scalar.Multiply(x, m13), Scalar.Multiply(y, m23)), Scalar.Multiply(z, m33)),
plane.Distance));
}
public static Plane <T> Normalize <T>(Plane <T> value)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
/*if (Vector.IsHardwareAccelerated)
* {
* T normalLengthSquared = value.Normal.LengthSquared();
* if (MathF.Abs(normalLengthSquared - 1.0f) < NormalizeEpsilon)
* {
* // It already normalized, so we don't need to farther process.
* return value;
* }
* T normalLength = MathF.Sqrt(normalLengthSquared);
* return new Plane(
* value.Normal / normalLength,
* value.D / normalLength);
* }
* else*/
{
T f = Scalar.Add(
Scalar.Add(Scalar.Multiply(value.Normal.X, value.Normal.X),
Scalar.Multiply(value.Normal.Y, value.Normal.Y)),
Scalar.Multiply(value.Normal.Z, value.Normal.Z));
if (!Scalar.GreaterThanOrEqual(Scalar.Abs(Scalar.Subtract(f, Scalar <T> .One)), Scalar.As <float, T>(NormalizeEpsilon)))
{
return(value); // It already normalized, so we don't need to further process.
}
T fInv = Scalar.Reciprocal(Scalar.Sqrt(f));
return(new(
Scalar.Multiply(value.Normal.X, fInv),
Scalar.Multiply(value.Normal.Y, fInv),
Scalar.Multiply(value.Normal.Z, fInv),
Scalar.Multiply(value.Distance, fInv)));
}
}
/// <summary>Transforms the given matrix by applying the given Quaternion rotation.</summary>
/// <param name="value">The source matrix to transform.</param>
/// <param name="rotation">The rotation to apply.</param>
/// <returns>The transformed matrix.</returns>
public static Matrix2X3 <T> Transform <T>(Matrix2X3 <T> value, Quaternion <T> rotation)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
// Compute rotation matrix.
T x2 = Scalar.Add(rotation.X, rotation.X);
T y2 = Scalar.Add(rotation.Y, rotation.Y);
T z2 = Scalar.Add(rotation.Z, rotation.Z);
T wx2 = Scalar.Multiply(rotation.W, x2);
T wy2 = Scalar.Multiply(rotation.W, y2);
T wz2 = Scalar.Multiply(rotation.W, z2);
T xx2 = Scalar.Multiply(rotation.X, x2);
T xy2 = Scalar.Multiply(rotation.X, y2);
T xz2 = Scalar.Multiply(rotation.X, z2);
T yy2 = Scalar.Multiply(rotation.Y, y2);
T yz2 = Scalar.Multiply(rotation.Y, z2);
T zz2 = Scalar.Multiply(rotation.Z, z2);
T q11 = Scalar.Subtract(Scalar.Subtract(Scalar <T> .One, yy2), zz2);
T q21 = Scalar.Subtract(xy2, wz2);
T q31 = Scalar.Add(xz2, wy2);
T q12 = Scalar.Add(xy2, wz2);
T q22 = Scalar.Subtract(Scalar.Subtract(Scalar <T> .One, xx2), zz2);
T q32 = Scalar.Subtract(yz2, wx2);
T q13 = Scalar.Subtract(xz2, wy2);
T q23 = Scalar.Add(yz2, wx2);
T q33 = Scalar.Subtract(Scalar.Subtract(Scalar <T> .One, xx2), yy2);
var q1 = new Vector3D <T>(q11, q12, q13);
var q2 = new Vector3D <T>(q21, q22, q23);
var q3 = new Vector3D <T>(q31, q32, q33);
return(new(value.M11 * q1 + value.M12 * q2 + value.M13 * q3, value.M21 *q1 + value.M22 * q2 + value.M23 * q3));
}
public static Plane <T> CreateFromVertices <T>(Vector3D <T> point1, Vector3D <T> point2, Vector3D <T> point3)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
var a = point1;
var b = point2;
var c = point3;
var ab = b - a;
var ac = c - a;
var cross = Vector3D.Cross(ab, ac);
Plane <T> p;
p.Normal = cross;
p.Distance = Scalar.Negate(Scalar.Add(
Scalar.Add(Scalar.Multiply(p.Normal.X, a.X), Scalar.Multiply(p.Normal.Y, a.Y)),
Scalar.Multiply(p.Normal.Z, a.Z)));
return(p);
/*if (Vector.IsHardwareAccelerated)
* {
* Vector3D<T> a = point2 - point1;
* Vector3D<T> b = point3 - point1;
*
* // N = Cross(a, b)
* Vector3D<T> n = Vector3D.Cross(a, b);
* Vector3D<T> normal = Vector3D.Normalize(n);
*
* // D = - Dot(N, point1)
* T d = Scalar.Negate(Vector3D.Dot(normal, point1));
*
* return new Plane<T>(normal, d);
* }
* else
* {
* T ax = Scalar.Subtract(point2.X, point1.X);
* T ay = Scalar.Subtract(point2.Y, point1.Y);
* T az = Scalar.Subtract(point2.Z, point1.Z);
*
* T bx = Scalar.Subtract(point3.X, point1.X);
* T by = Scalar.Subtract(point3.Y, point1.Y);
* T bz = Scalar.Subtract(point3.Z, point1.Z);
*
* // N=Cross(a,b)
* T nx = Scalar.Subtract(Scalar.Multiply(ay, bz), Scalar.Multiply(az, by));
* T ny = Scalar.Subtract(Scalar.Multiply(az, bx), Scalar.Multiply(ax, bz));
* T nz = Scalar.Subtract(Scalar.Multiply(ax, by), Scalar.Multiply(ay, bx));
*
* // Normalize(N)
* T ls = Scalar.Add(Scalar.Add(Scalar.Multiply(nx, nx), Scalar.Multiply(ny, ny)), Scalar.Multiply(nz, nz));
* T invNorm = Scalar.Inverse(Scalar.Sqrt(ls));
*
* Vector3D<T> normal = new Vector3D<T>(
* Scalar.Multiply(nx, invNorm),
* Scalar.Multiply(ny, invNorm),
* Scalar.Multiply(nz, invNorm));
*
* return new(normal,
* Scalar.Negate(Scalar.Add(
* Scalar.Add(Scalar.Multiply(normal.X, point1.X),
* Scalar.Multiply(normal.Y, point1.Y)), Scalar.Multiply(normal.Z, point1.Z))));
* }*/
}
public static T DotCoordinate <T>(Plane <T> plane, Vector3D <T> value)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
=> Scalar.Add(Vector3D.Dot(plane.Normal, value), plane.Distance);
/// <summary>Creates a rotation matrix using the given rotation in radians and a center point.</summary>
/// <param name="radians">The amount of rotation, in radians.</param>
/// <param name="centerPoint">The center point.</param>
/// <returns>A rotation matrix.</returns>
public static Matrix3X2 <T> CreateRotation <T>(T radians, Vector2D <T> centerPoint)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
radians = Scalar.IEEERemainder(radians, Scalar <T> .Tau);
T c, s;
if (Scalar.GreaterThan(radians, Scalar.As <float, T>(-RotationEpsilon)) && !Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>(RotationEpsilon)))
{
// Exact case for zero rotation.
c = Scalar <T> .One;
s = Scalar <T> .Zero;
}
else if (Scalar.GreaterThan(radians, Scalar.As <float, T>(
#if MATHF
MathF.PI
#else
((float)Math.PI)
#endif
/ 2 - RotationEpsilon)) && !Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>(
#if MATHF
MathF.PI
#else
((float)Math.PI)
#endif
/ 2 + RotationEpsilon)))
{
// Exact case for 90 degree rotation.
c = Scalar <T> .Zero;
s = Scalar <T> .One;
}
else if (!Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>(-
#if MATHF
MathF.PI
#else
((float)Math.PI)
#endif
+ RotationEpsilon)) || Scalar.GreaterThan(radians, Scalar.As <float, T>(
#if MATHF
MathF.PI
#else
((float)Math.PI)
#endif
- RotationEpsilon)))
{
// Exact case for 180 degree rotation.
c = Scalar <T> .MinusOne;
s = Scalar <T> .Zero;
}
else if (Scalar.GreaterThan(radians, Scalar.As <float, T>(-
#if MATHF
MathF.PI
#else
((float)Math.PI)
#endif
/ 2 - RotationEpsilon)) && !Scalar.GreaterThanOrEqual(radians, Scalar.As <float, T>(-
#if MATHF
MathF.PI
#else
((float)Math.PI)
#endif
/ 2 + RotationEpsilon)))
{
// Exact case for 270 degree rotation.
c = Scalar <T> .Zero;
s = Scalar <T> .MinusOne;
}
else
{
// Arbitrary rotation.
c = Scalar.Cos(radians);
s = Scalar.Sin(radians);
}
T x = Scalar.Add(Scalar.Multiply(centerPoint.X, Scalar.Subtract(Scalar <T> .One, c)), Scalar.Multiply(centerPoint.Y, s));
T y = Scalar.Subtract(Scalar.Multiply(centerPoint.Y, Scalar.Subtract(Scalar <T> .One, c)), Scalar.Multiply(centerPoint.X, s));
// [ c s ]
// [ -s c ]
// [ x y ]
return(new(
new(c, s),
new(Scalar.Negate(s), c),
new(x, y)));
}