/// <summary>Creates a rotation matrix using the given rotation in radians.</summary>
/// <param name="radians">The amount of rotation, in radians.</param>
/// <returns>A rotation matrix.</returns>
public static Matrix3X2 <T> CreateRotation <T>(T radians)
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);
}
// [ c s ]
// [ -s c ]
// [ 0 0 ]
Matrix3X2 <T> result = Matrix3X2 <T> .Identity;
result.M11 = c;
result.M12 = s;
result.M21 = Scalar.Negate(s);
result.M22 = c;
return(result);
}
/// <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)));
}
