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// Copyright (c) Microsoft. All rights reserved.
// Licensed under the MIT license. See LICENSE file in the project root for full license information.
using System.Globalization;
namespace System.Numerics
{
/// <summary>
/// A structure encapsulating a 3x2 matrix.
/// </summary>
public struct Matrix3x2 : IEquatable<Matrix3x2>
{
#region Public Fields
/// <summary>
/// The first element of the first row
/// </summary>
public float M11;
/// <summary>
/// The second element of the first row
/// </summary>
public float M12;
/// <summary>
/// The first element of the second row
/// </summary>
public float M21;
/// <summary>
/// The second element of the second row
/// </summary>
public float M22;
/// <summary>
/// The first element of the third row
/// </summary>
public float M31;
/// <summary>
/// The second element of the third row
/// </summary>
public float M32;
#endregion Public Fields
private static readonly Matrix3x2 _identity = new Matrix3x2
(
1f, 0f,
0f, 1f,
0f, 0f
);
/// <summary>
/// Returns the multiplicative identity matrix.
/// </summary>
public static Matrix3x2 Identity
{
get { return _identity; }
}
/// <summary>
/// Returns whether the matrix is the identity matrix.
/// </summary>
public bool IsIdentity
{
get
{
return M11 == 1f && M22 == 1f && // Check diagonal element first for early out.
M12 == 0f &&
M21 == 0f &&
M31 == 0f && M32 == 0f;
}
}
/// <summary>
/// Gets or sets the translation component of this matrix.
/// </summary>
public Vector2 Translation
{
get
{
return new Vector2(M31, M32);
}
set
{
M31 = value.X;
M32 = value.Y;
}
}
/// <summary>
/// Constructs a Matrix3x2 from the given components.
/// </summary>
public Matrix3x2(float m11, float m12,
float m21, float m22,
float m31, float m32)
{
this.M11 = m11;
this.M12 = m12;
this.M21 = m21;
this.M22 = m22;
this.M31 = m31;
this.M32 = m32;
}
/// <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 CreateTranslation(Vector2 position)
{
Matrix3x2 result;
result.M11 = 1.0f;
result.M12 = 0.0f;
result.M21 = 0.0f;
result.M22 = 1.0f;
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 CreateTranslation(float xPosition, float yPosition)
{
Matrix3x2 result;
result.M11 = 1.0f;
result.M12 = 0.0f;
result.M21 = 0.0f;
result.M22 = 1.0f;
result.M31 = xPosition;
result.M32 = yPosition;
return result;
}
/// <summary>
/// Creates a scale matrix from the given X and Y components.
/// </summary>
/// <param name="xScale">Value to scale by on the X-axis.</param>
/// <param name="yScale">Value to scale by on the Y-axis.</param>
/// <returns>A scaling matrix.</returns>
public static Matrix3x2 CreateScale(float xScale, float yScale)
{
Matrix3x2 result;
result.M11 = xScale;
result.M12 = 0.0f;
result.M21 = 0.0f;
result.M22 = yScale;
result.M31 = 0.0f;
result.M32 = 0.0f;
return result;
}
/// <summary>
/// Creates a scale matrix that is offset by a given center point.
/// </summary>
/// <param name="xScale">Value to scale by on the X-axis.</param>
/// <param name="yScale">Value to scale by on the Y-axis.</param>
/// <param name="centerPoint">The center point.</param>
/// <returns>A scaling matrix.</returns>
public static Matrix3x2 CreateScale(float xScale, float yScale, Vector2 centerPoint)
{
Matrix3x2 result;
float tx = centerPoint.X * (1 - xScale);
float ty = centerPoint.Y * (1 - yScale);
result.M11 = xScale;
result.M12 = 0.0f;
result.M21 = 0.0f;
result.M22 = yScale;
result.M31 = tx;
result.M32 = ty;
return result;
}
/// <summary>
/// Creates a scale matrix from the given vector scale.
/// </summary>
/// <param name="scales">The scale to use.</param>
/// <returns>A scaling matrix.</returns>
public static Matrix3x2 CreateScale(Vector2 scales)
{
Matrix3x2 result;
result.M11 = scales.X;
result.M12 = 0.0f;
result.M21 = 0.0f;
result.M22 = scales.Y;
result.M31 = 0.0f;
result.M32 = 0.0f;
return result;
}
/// <summary>
/// Creates a scale matrix from the given vector scale with an offset from the given center point.
/// </summary>
/// <param name="scales">The scale to use.</param>
/// <param name="centerPoint">The center offset.</param>
/// <returns>A scaling matrix.</returns>
public static Matrix3x2 CreateScale(Vector2 scales, Vector2 centerPoint)
{
Matrix3x2 result;
float tx = centerPoint.X * (1 - scales.X);
float ty = centerPoint.Y * (1 - scales.Y);
result.M11 = scales.X;
result.M12 = 0.0f;
result.M21 = 0.0f;
result.M22 = scales.Y;
result.M31 = tx;
result.M32 = ty;
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 CreateScale(float scale)
{
Matrix3x2 result;
result.M11 = scale;
result.M12 = 0.0f;
result.M21 = 0.0f;
result.M22 = scale;
result.M31 = 0.0f;
result.M32 = 0.0f;
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 CreateScale(float scale, Vector2 centerPoint)
{
Matrix3x2 result;
float tx = centerPoint.X * (1 - scale);
float ty = centerPoint.Y * (1 - scale);
result.M11 = scale;
result.M12 = 0.0f;
result.M21 = 0.0f;
result.M22 = scale;
result.M31 = tx;
result.M32 = ty;
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 CreateSkew(float radiansX, float radiansY)
{
Matrix3x2 result;
float xTan = (float)Math.Tan(radiansX);
float yTan = (float)Math.Tan(radiansY);
result.M11 = 1.0f;
result.M12 = yTan;
result.M21 = xTan;
result.M22 = 1.0f;
result.M31 = 0.0f;
result.M32 = 0.0f;
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 CreateSkew(float radiansX, float radiansY, Vector2 centerPoint)
{
Matrix3x2 result;
float xTan = (float)Math.Tan(radiansX);
float yTan = (float)Math.Tan(radiansY);
float tx = -centerPoint.Y * xTan;
float ty = -centerPoint.X * yTan;
result.M11 = 1.0f;
result.M12 = yTan;
result.M21 = xTan;
result.M22 = 1.0f;
result.M31 = tx;
result.M32 = ty;
return result;
}
/// <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 CreateRotation(float radians)
{
Matrix3x2 result;
radians = (float)Math.IEEERemainder(radians, Math.PI * 2);
float c, s;
const float epsilon = 0.001f * (float)Math.PI / 180f; // 0.1% of a degree
if (radians > -epsilon && radians < epsilon)
{
// Exact case for zero rotation.
c = 1;
s = 0;
}
else if (radians > Math.PI / 2 - epsilon && radians < Math.PI / 2 + epsilon)
{
// Exact case for 90 degree rotation.
c = 0;
s = 1;
}
else if (radians < -Math.PI + epsilon || radians > Math.PI - epsilon)
{
// Exact case for 180 degree rotation.
c = -1;
s = 0;
}
else if (radians > -Math.PI / 2 - epsilon && radians < -Math.PI / 2 + epsilon)
{
// Exact case for 270 degree rotation.
c = 0;
s = -1;
}
else
{
// Arbitrary rotation.
c = (float)Math.Cos(radians);
s = (float)Math.Sin(radians);
}
// [ c s ]
// [ -s c ]
// [ 0 0 ]
result.M11 = c;
result.M12 = s;
result.M21 = -s;
result.M22 = c;
result.M31 = 0.0f;
result.M32 = 0.0f;
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 CreateRotation(float radians, Vector2 centerPoint)
{
Matrix3x2 result;
radians = (float)Math.IEEERemainder(radians, Math.PI * 2);
float c, s;
const float epsilon = 0.001f * (float)Math.PI / 180f; // 0.1% of a degree
if (radians > -epsilon && radians < epsilon)
{
// Exact case for zero rotation.
c = 1;
s = 0;
}
else if (radians > Math.PI / 2 - epsilon && radians < Math.PI / 2 + epsilon)
{
// Exact case for 90 degree rotation.
c = 0;
s = 1;
}
else if (radians < -Math.PI + epsilon || radians > Math.PI - epsilon)
{
// Exact case for 180 degree rotation.
c = -1;
s = 0;
}
else if (radians > -Math.PI / 2 - epsilon && radians < -Math.PI / 2 + epsilon)
{
// Exact case for 270 degree rotation.
c = 0;
s = -1;
}
else
{
// Arbitrary rotation.
c = (float)Math.Cos(radians);
s = (float)Math.Sin(radians);
}
float x = centerPoint.X * (1 - c) + centerPoint.Y * s;
float y = centerPoint.Y * (1 - c) - centerPoint.X * s;
// [ c s ]
// [ -s c ]
// [ x y ]
result.M11 = c;
result.M12 = s;
result.M21 = -s;
result.M22 = c;
result.M31 = x;
result.M32 = y;
return result;
}
/// <summary>
/// Calculates the determinant for this matrix.
/// The determinant is calculated by expanding the matrix with a third column whose values are (0,0,1).
/// </summary>
/// <returns>The determinant.</returns>
public float GetDeterminant()
{
// There isn't actually any such thing as a determinant for a non-square matrix,
// but this 3x2 type is really just an optimization of a 3x3 where we happen to
// know the rightmost column is always (0, 0, 1). So we expand to 3x3 format:
//
// [ M11, M12, 0 ]
// [ M21, M22, 0 ]
// [ M31, M32, 1 ]
//
// Sum the diagonal products:
// (M11 * M22 * 1) + (M12 * 0 * M31) + (0 * M21 * M32)
//
// Subtract the opposite diagonal products:
// (M31 * M22 * 0) + (M32 * 0 * M11) + (1 * M21 * M12)
//
// Collapse out the constants and oh look, this is just a 2x2 determinant!
return (M11 * M22) - (M21 * M12);
}
/// <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(Matrix3x2 matrix, out Matrix3x2 result)
{
float det = (matrix.M11 * matrix.M22) - (matrix.M21 * matrix.M12);
if (Math.Abs(det) < float.Epsilon)
{
result = new Matrix3x2(float.NaN, float.NaN, float.NaN, float.NaN, float.NaN, float.NaN);
return false;
}
float invDet = 1.0f / det;
result.M11 = matrix.M22 * invDet;
result.M12 = -matrix.M12 * invDet;
result.M21 = -matrix.M21 * invDet;
result.M22 = matrix.M11 * invDet;
result.M31 = (matrix.M21 * matrix.M32 - matrix.M31 * matrix.M22) * invDet;
result.M32 = (matrix.M31 * matrix.M12 - 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 Lerp(Matrix3x2 matrix1, Matrix3x2 matrix2, float amount)
{
Matrix3x2 result;
// First row
result.M11 = matrix1.M11 + (matrix2.M11 - matrix1.M11) * amount;
result.M12 = matrix1.M12 + (matrix2.M12 - matrix1.M12) * amount;
// Second row
result.M21 = matrix1.M21 + (matrix2.M21 - matrix1.M21) * amount;
result.M22 = matrix1.M22 + (matrix2.M22 - matrix1.M22) * amount;
// Third row
result.M31 = matrix1.M31 + (matrix2.M31 - matrix1.M31) * amount;
result.M32 = matrix1.M32 + (matrix2.M32 - matrix1.M32) * amount;
return result;
}
/// <summary>
/// Negates the given matrix by multiplying all values by -1.
/// </summary>
/// <param name="value">The source matrix.</param>
/// <returns>The negated matrix.</returns>
public static Matrix3x2 Negate(Matrix3x2 value)
{
Matrix3x2 result;
result.M11 = -value.M11;
result.M12 = -value.M12;
result.M21 = -value.M21;
result.M22 = -value.M22;
result.M31 = -value.M31;
result.M32 = -value.M32;
return result;
}
/// <summary>
/// Adds each matrix element in value1 with its corresponding element in value2.
/// </summary>
/// <param name="value1">The first source matrix.</param>
/// <param name="value2">The second source matrix.</param>
/// <returns>The matrix containing the summed values.</returns>
public static Matrix3x2 Add(Matrix3x2 value1, Matrix3x2 value2)
{
Matrix3x2 result;
result.M11 = value1.M11 + value2.M11;
result.M12 = value1.M12 + value2.M12;
result.M21 = value1.M21 + value2.M21;
result.M22 = value1.M22 + value2.M22;
result.M31 = value1.M31 + value2.M31;
result.M32 = value1.M32 + value2.M32;
return result;
}
/// <summary>
/// Subtracts each matrix element in value2 from its corresponding element in value1.
/// </summary>
/// <param name="value1">The first source matrix.</param>
/// <param name="value2">The second source matrix.</param>
/// <returns>The matrix containing the resulting values.</returns>
public static Matrix3x2 Subtract(Matrix3x2 value1, Matrix3x2 value2)
{
Matrix3x2 result;
result.M11 = value1.M11 - value2.M11;
result.M12 = value1.M12 - value2.M12;
result.M21 = value1.M21 - value2.M21;
result.M22 = value1.M22 - value2.M22;
result.M31 = value1.M31 - value2.M31;
result.M32 = value1.M32 - value2.M32;
return result;
}
/// <summary>
/// Multiplies two matrices together and returns the resulting matrix.
/// </summary>
/// <param name="value1">The first source matrix.</param>
/// <param name="value2">The second source matrix.</param>
/// <returns>The product matrix.</returns>
public static Matrix3x2 Multiply(Matrix3x2 value1, Matrix3x2 value2)
{
Matrix3x2 result;
// First row
result.M11 = value1.M11 * value2.M11 + value1.M12 * value2.M21;
result.M12 = value1.M11 * value2.M12 + value1.M12 * value2.M22;
// Second row
result.M21 = value1.M21 * value2.M11 + value1.M22 * value2.M21;
result.M22 = value1.M21 * value2.M12 + value1.M22 * value2.M22;
// Third row
result.M31 = value1.M31 * value2.M11 + value1.M32 * value2.M21 + value2.M31;
result.M32 = value1.M31 * value2.M12 + value1.M32 * value2.M22 + value2.M32;
return result;
}
/// <summary>
/// Scales all elements in a matrix by the given scalar factor.
/// </summary>
/// <param name="value1">The source matrix.</param>
/// <param name="value2">The scaling value to use.</param>
/// <returns>The resulting matrix.</returns>
public static Matrix3x2 Multiply(Matrix3x2 value1, float value2)
{
Matrix3x2 result;
result.M11 = value1.M11 * value2;
result.M12 = value1.M12 * value2;
result.M21 = value1.M21 * value2;
result.M22 = value1.M22 * value2;
result.M31 = value1.M31 * value2;
result.M32 = value1.M32 * value2;
return result;
}
/// <summary>
/// Negates the given matrix by multiplying all values by -1.
/// </summary>
/// <param name="value">The source matrix.</param>
/// <returns>The negated matrix.</returns>
public static Matrix3x2 operator -(Matrix3x2 value)
{
Matrix3x2 m;
m.M11 = -value.M11;
m.M12 = -value.M12;
m.M21 = -value.M21;
m.M22 = -value.M22;
m.M31 = -value.M31;
m.M32 = -value.M32;
return m;
}
/// <summary>
/// Adds each matrix element in value1 with its corresponding element in value2.
/// </summary>
/// <param name="value1">The first source matrix.</param>
/// <param name="value2">The second source matrix.</param>
/// <returns>The matrix containing the summed values.</returns>
public static Matrix3x2 operator +(Matrix3x2 value1, Matrix3x2 value2)
{
Matrix3x2 m;
m.M11 = value1.M11 + value2.M11;
m.M12 = value1.M12 + value2.M12;
m.M21 = value1.M21 + value2.M21;
m.M22 = value1.M22 + value2.M22;
m.M31 = value1.M31 + value2.M31;
m.M32 = value1.M32 + value2.M32;
return m;
}
/// <summary>
/// Subtracts each matrix element in value2 from its corresponding element in value1.
/// </summary>
/// <param name="value1">The first source matrix.</param>
/// <param name="value2">The second source matrix.</param>
/// <returns>The matrix containing the resulting values.</returns>
public static Matrix3x2 operator -(Matrix3x2 value1, Matrix3x2 value2)
{
Matrix3x2 m;
m.M11 = value1.M11 - value2.M11;
m.M12 = value1.M12 - value2.M12;
m.M21 = value1.M21 - value2.M21;
m.M22 = value1.M22 - value2.M22;
m.M31 = value1.M31 - value2.M31;
m.M32 = value1.M32 - value2.M32;
return m;
}
/// <summary>
/// Multiplies two matrices together and returns the resulting matrix.
/// </summary>
/// <param name="value1">The first source matrix.</param>
/// <param name="value2">The second source matrix.</param>
/// <returns>The product matrix.</returns>
public static Matrix3x2 operator *(Matrix3x2 value1, Matrix3x2 value2)
{
Matrix3x2 m;
// First row
m.M11 = value1.M11 * value2.M11 + value1.M12 * value2.M21;
m.M12 = value1.M11 * value2.M12 + value1.M12 * value2.M22;
// Second row
m.M21 = value1.M21 * value2.M11 + value1.M22 * value2.M21;
m.M22 = value1.M21 * value2.M12 + value1.M22 * value2.M22;
// Third row
m.M31 = value1.M31 * value2.M11 + value1.M32 * value2.M21 + value2.M31;
m.M32 = value1.M31 * value2.M12 + value1.M32 * value2.M22 + value2.M32;
return m;
}
/// <summary>
/// Scales all elements in a matrix by the given scalar factor.
/// </summary>
/// <param name="value1">The source matrix.</param>
/// <param name="value2">The scaling value to use.</param>
/// <returns>The resulting matrix.</returns>
public static Matrix3x2 operator *(Matrix3x2 value1, float value2)
{
Matrix3x2 m;
m.M11 = value1.M11 * value2;
m.M12 = value1.M12 * value2;
m.M21 = value1.M21 * value2;
m.M22 = value1.M22 * value2;
m.M31 = value1.M31 * value2;
m.M32 = value1.M32 * value2;
return m;
}
/// <summary>
/// Returns a boolean indicating whether the given matrices are equal.
/// </summary>
/// <param name="value1">The first source matrix.</param>
/// <param name="value2">The second source matrix.</param>
/// <returns>True if the matrices are equal; False otherwise.</returns>
public static bool operator ==(Matrix3x2 value1, Matrix3x2 value2)
{
return (value1.M11 == value2.M11 && value1.M22 == value2.M22 && // Check diagonal element first for early out.
value1.M12 == value2.M12 &&
value1.M21 == value2.M21 &&
value1.M31 == value2.M31 && value1.M32 == value2.M32);
}
/// <summary>
/// Returns a boolean indicating whether the given matrices are not equal.
/// </summary>
/// <param name="value1">The first source matrix.</param>
/// <param name="value2">The second source matrix.</param>
/// <returns>True if the matrices are not equal; False if they are equal.</returns>
public static bool operator !=(Matrix3x2 value1, Matrix3x2 value2)
{
return (value1.M11 != value2.M11 || value1.M12 != value2.M12 ||
value1.M21 != value2.M21 || value1.M22 != value2.M22 ||
value1.M31 != value2.M31 || value1.M32 != value2.M32);
}
/// <summary>
/// Returns a boolean indicating whether the matrix is equal to the other given matrix.
/// </summary>
/// <param name="other">The other matrix to test equality against.</param>
/// <returns>True if this matrix is equal to other; False otherwise.</returns>
public bool Equals(Matrix3x2 other)
{
return (M11 == other.M11 && M22 == other.M22 && // Check diagonal element first for early out.
M12 == other.M12 &&
M21 == other.M21 &&
M31 == other.M31 && M32 == other.M32);
}
/// <summary>
/// Returns a boolean indicating whether the given Object is equal to this matrix instance.
/// </summary>
/// <param name="obj">The Object to compare against.</param>
/// <returns>True if the Object is equal to this matrix; False otherwise.</returns>
public override bool Equals(object obj)
{
if (obj is Matrix3x2)
{
return Equals((Matrix3x2)obj);
}
return false;
}
/// <summary>
/// Returns a String representing this matrix instance.
/// </summary>
/// <returns>The string representation.</returns>
public override string ToString()
{
CultureInfo ci = CultureInfo.CurrentCulture;
return String.Format(ci, "{{ {{M11:{0} M12:{1}}} {{M21:{2} M22:{3}}} {{M31:{4} M32:{5}}} }}",
M11.ToString(ci), M12.ToString(ci),
M21.ToString(ci), M22.ToString(ci),
M31.ToString(ci), M32.ToString(ci));
}
/// <summary>
/// Returns the hash code for this instance.
/// </summary>
/// <returns>The hash code.</returns>
public override int GetHashCode()
{
return M11.GetHashCode() + M12.GetHashCode() +
M21.GetHashCode() + M22.GetHashCode() +
M31.GetHashCode() + M32.GetHashCode();
}
}
}
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