/// <summary>Attempts to invert the given matrix. If the operation succeeds, the inverted matrix is stored in the result parameter.</summary>
/// <param name="matrix">The source matrix.</param>
/// <param name="result">The output matrix.</param>
/// <returns>True if the operation succeeded, False otherwise.</returns>
public static bool Invert <T>(Matrix3X2 <T> matrix, out Matrix3X2 <T> result)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
T det = Scalar.Subtract(Scalar.Multiply(matrix.M11, matrix.M22), Scalar.Multiply(matrix.M21, matrix.M12));
if (!Scalar.GreaterThanOrEqual(Scalar.Abs(det), Scalar <T> .Epsilon))
{
result = new(Scalar <T> .NaN, Scalar <T> .NaN, Scalar <T> .NaN, Scalar <T> .NaN, Scalar <T> .NaN, Scalar <T> .NaN);
return(false);
}
T invDet = Scalar.Reciprocal(det);
result = default;
result.M11 = Scalar.Multiply(matrix.M22, invDet);
result.M12 = Scalar.Negate(Scalar.Multiply(matrix.M12, invDet));
result.M21 = Scalar.Negate(Scalar.Multiply(matrix.M21, invDet));
result.M22 = Scalar.Multiply(matrix.M11, invDet);
result.M31 = Scalar.Multiply(Scalar.Subtract(Scalar.Multiply(matrix.M21, matrix.M32), Scalar.Multiply(matrix.M31, matrix.M22)), invDet);
result.M32 = Scalar.Multiply(Scalar.Subtract(Scalar.Multiply(matrix.M31, matrix.M12), Scalar.Multiply(matrix.M11, matrix.M32)), invDet);
return(true);
}
/// <summary>Linearly interpolates from matrix1 to matrix2, based on the third parameter.</summary>
/// <param name="matrix1">The first source matrix.</param>
/// <param name="matrix2">The second source matrix.</param>
/// <param name="amount">The relative weighting of matrix2.</param>
/// <returns>The interpolated matrix.</returns>
public static Matrix3X2 <T> Lerp <T>(Matrix3X2 <T> matrix1, Matrix3X2 <T> matrix2, T amount)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
return(new(Vector2D.Lerp(matrix1.Row1, matrix2.Row1, amount),
Vector2D.Lerp(matrix1.Row2, matrix2.Row2, amount),
Vector2D.Lerp(matrix1.Row3, matrix2.Row3, amount)));
}
/// <summary>Creates a translation matrix from the given vector.</summary>
/// <param name="position">The translation position.</param> `
/// <returns>A translation matrix.</returns>
public static Matrix3X2 <T> CreateTranslation <T>(Vector2D <T> position)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
Matrix3X2 <T> result = Matrix3X2 <T> .Identity;
result.M31 = position.X;
result.M32 = position.Y;
return(result);
}
/// <summary>Creates a translation matrix from the given X and Y components.</summary>
/// <param name="xPosition">The X position.</param>
/// <param name="yPosition">The Y position.</param>
/// <returns>A translation matrix.</returns>
public static Matrix3X2 <T> CreateTranslation <T>(T xPosition, T yPosition)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
Matrix3X2 <T> result = Matrix3X2 <T> .Identity;
result.M31 = xPosition;
result.M32 = yPosition;
return(result);
}
/// <summary>Creates a scale matrix that scales uniformly with the given scale.</summary>
/// <param name="scale">The uniform scale to use.</param>
/// <returns>A scaling matrix.</returns>
public static Matrix3X2 <T> CreateScale <T>(T scale)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
Matrix3X2 <T> result = Matrix3X2 <T> .Identity;
result.M11 = scale;
result.M22 = scale;
return(result);
}
/// <summary>Creates a skew matrix from the given angles in radians.</summary>
/// <param name="radiansX">The X angle, in radians.</param>
/// <param name="radiansY">The Y angle, in radians.</param>
/// <returns>A skew matrix.</returns>
public static Matrix3X2 <T> CreateSkew <T>(T radiansX, T radiansY)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
Matrix3X2 <T> result = Matrix3X2 <T> .Identity;
T xTan = Scalar.Tan(radiansX);
T yTan = Scalar.Tan(radiansY);
result.M12 = yTan;
result.M21 = xTan;
return(result);
}
/// <summary>Creates a scale matrix that scales uniformly with the given scale with an offset from the given center.</summary>
/// <param name="scale">The uniform scale to use.</param>
/// <param name="centerPoint">The center offset.</param>
/// <returns>A scaling matrix.</returns>
public static Matrix3X2 <T> CreateScale <T>(T scale, Vector2D <T> centerPoint)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
Matrix3X2 <T> result = Matrix3X2 <T> .Identity;
T tx = Scalar.Multiply(centerPoint.X, Scalar.Subtract(Scalar <T> .One, scale));
T ty = Scalar.Multiply(centerPoint.Y, Scalar.Subtract(Scalar <T> .One, scale));
result.M11 = scale;
result.M22 = scale;
result.M31 = tx;
result.M32 = ty;
return(result);
}
/// <summary>Creates a skew matrix from the given angles in radians and a center point.</summary>
/// <param name="radiansX">The X angle, in radians.</param>
/// <param name="radiansY">The Y angle, in radians.</param>
/// <param name="centerPoint">The center point.</param>
/// <returns>A skew matrix.</returns>
public static Matrix3X2 <T> CreateSkew <T>(T radiansX, T radiansY, Vector2D <T> centerPoint)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
{
Matrix3X2 <T> result = Matrix3X2 <T> .Identity;
T xTan = Scalar.Tan(radiansX);
T yTan = Scalar.Tan(radiansY);
T tx = Scalar.Negate(Scalar.Multiply(centerPoint.Y, xTan));
T ty = Scalar.Negate(Scalar.Multiply(centerPoint.X, yTan));
result.M12 = yTan;
result.M21 = xTan;
result.M31 = tx;
result.M32 = ty;
return(result);
}
public static Matrix3X2 <T> Subtract <T>(Matrix3X2 <T> value1, Matrix3X2 <T> value2)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
=> value1 - value2;
public static Matrix3X2 <T> Negate <T>(Matrix3X2 <T> value)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
=> - value;
public static Matrix3X2 <T> Multiply <T>(Matrix3X2 <T> value1, T value2)
where T : unmanaged, IFormattable, IEquatable <T>, IComparable <T>
=> value1 * value2;
/// <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);
}