struct ThreeDViewer.Mathematics.Matrix4

Overview

Represents a matrix of size 4x4. More…

struct Matrix4: IEquatable< Matrix4 >
{
    // fields

    static const int Size = 4;
    static readonly Matrix4 Identity = new(1, 0, 0, 0,             0, 1, 0, 0,             0, 0, 1, 0,             0, 0, 0, 1);
    static readonly Matrix4 ProjectionOrthoX = new(0, 0, 0, 0,             0, 1, 0, 0,             0, 0, 1, 0,             0, 0, 0, 1);
    static readonly Matrix4 ProjectionOrthoY = new(1, 0, 0, 0,             0, 0, 0, 0,             0, 0, 1, 0,             0, 0, 0, 1);
    static readonly Matrix4 ProjectionOrthoZ = new(1, 0, 0, 0,             0, 1, 0, 0,             0, 0, 0, 0,             0, 0, 0, 1);
    static readonly Matrix4 Zero = new(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);

    // properties

    double[,] Values;
    double V00;
    double V01;
    double V02;
    double V03;
    double V10;
    double V11;
    double V12;
    double V13;
    double V20;
    double V21;
    double V22;
    double V23;
    double V30;
    double V31;
    double V32;
    double V33;
    double Determinant;
    Matrix4 Normalized;
    double Trace;
    double this[int rowIndex, int columnIndex];

    // methods

    Matrix4(double values[,]);

    Matrix4(
        double value00,
        double value01,
        double value02,
        double value03,
        double value10,
        double value11,
        double value12,
        double value13,
        double value20,
        double value21,
        double value22,
        double value23,
        double value30,
        double value31,
        double value32,
        double value33
        );

    Matrix4(Matrix4 matrix);
    Matrix4(Vector4[] values, bool isColums = true);
    Matrix4 Transpose();
    override bool Equals(object other);
    bool Equals(Matrix4 other);
    bool Equals(object other, double tolerance);
    bool Equals(Matrix4 other, double tolerance);
    override int GetHashCode();
    Matrix4 Invert();
    override string ToString();
    static Matrix4 operator + (Matrix4 mat, double scalar);
    static Matrix4 operator + (double scalar, Matrix4 mat);
    static Matrix4 operator - (Matrix4 mat, double scalar);
    static Matrix4 operator - (double scalar, Matrix4 mat);
    static Matrix4 operator * (Matrix4 mat, double scalar);
    static Matrix4 operator * (double scalar, Matrix4 mat);
    static Matrix4 operator/ (Matrix4 mat, double scalar);
    static Matrix4 operator - (Matrix4 mat);
    static Matrix4 operator + (Matrix4 left, Matrix4 right);
    static Matrix4 operator - (Matrix4 left, Matrix4 right);
    static Matrix4 operator * (Matrix4 left, Matrix4 right);
    static bool operator == (Matrix4 left, Matrix4 right);
    static bool operator != (Matrix4 left, Matrix4 right);
    static Matrix4 CreateRotationX(double angle);
    static Matrix4 CreateRotationY(double angle);
    static Matrix4 CreateRotationZ(double angle);
    static Matrix4 CreateRotation(Vector3 rotation);
    static Matrix4 CreateRotationAbitraryAxis(Axis rotationAxis, double angle);
    static Matrix4 CreateScale(double scaleFactor);

    static Matrix4 CreatePerspectiveOffCenter(
        double left,
        double right,
        double bottom,
        double top,
        double depthNear,
        double depthFar
        );

    static Matrix4 CreatePerspectiveFieldOfView(
        double fovy,
        double aspect,
        double depthNear,
        double depthFar
        );

    static Matrix4 CreateTranslation(double x, double y, double z);
    static Matrix4 CreateTranslation(Vector3 vector);
    static Matrix4 LookAt(Vector3 eye, Vector3 target, Vector3 up);
    static Matrix4 Transpose(Matrix4 mat);
    static Matrix4 Normalize(Matrix4 mat);
};

Detailed Documentation

Represents a matrix of size 4x4.

Every coordinates are in [y, x] format (or [row, column]).

Fields

static const int Size = 4

Size of the matrix.

static readonly Matrix4 Identity = new(1, 0, 0, 0,             0, 1, 0, 0,             0, 0, 1, 0,             0, 0, 0, 1)

The identity matrix.

static readonly Matrix4 ProjectionOrthoX = new(0, 0, 0, 0,             0, 1, 0, 0,             0, 0, 1, 0,             0, 0, 0, 1)

Matrix for projection onto the x = 0 plane.

static readonly Matrix4 ProjectionOrthoY = new(1, 0, 0, 0,             0, 0, 0, 0,             0, 0, 1, 0,             0, 0, 0, 1)

Matrix for projection onto the y = 0 plane.

static readonly Matrix4 ProjectionOrthoZ = new(1, 0, 0, 0,             0, 1, 0, 0,             0, 0, 0, 0,             0, 0, 0, 1)

Matrix for projection onto the z = 0 plane.

static readonly Matrix4 Zero = new(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)

The zero matrix.

Properties

double[,] Values

Gets the values of the matrix.

double V00

Gets the value at 0, 0 on the matrix.

double V01

Gets the value at 0, 1 on the matrix.

double V02

Gets the value at 0, 2 on the matrix.

double V03

Gets the value at 0, 3 on the matrix.

double V10

Gets the value at 1, 0 on the matrix.

double V11

Gets the value at 1, 1 on the matrix.

double V12

Gets the value at 1, 2 on the matrix.

double V13

Gets the value at 1, 3 on the matrix.

double V20

Gets the value at 2, 0 on the matrix.

double V21

Gets the value at 2, 1 on the matrix.

double V22

Gets the value at 2, 2 on the matrix.

double V23

Gets the value at 2, 3 on the matrix.

double V30

Gets the value at 3, 0 on the matrix.

double V31

Gets the value at 3, 1 on the matrix.

double V32

Gets the value at 3, 2 on the matrix.

double V33

Gets the value at 3, 3 on the matrix.

double Determinant

Gets the determinant of the matrix.

Matrix4 Normalized

Gets the normalized matrix.

double Trace

Gets the trace of the matrix, the sum of the values along the diagonal axis.

double this[int rowIndex, int columnIndex]

Gets the value at the specified row and column.

Parameters:

rowIndex	The index of the row.
columnIndex	The index of the column.

Returns:

The element at the given row and column index.

Methods

Matrix4(double values[,])

Initializes a new instance of the Matrix4 struct.

Parameters:

values

Values of the matrix. Should be 4x4.

Matrix4(
    double value00,
    double value01,
    double value02,
    double value03,
    double value10,
    double value11,
    double value12,
    double value13,
    double value20,
    double value21,
    double value22,
    double value23,
    double value30,
    double value31,
    double value32,
    double value33
    )

Initializes a new instance of the Matrix4 struct.

Parameters:

value00	Value of the matrix in the 0, 0 position.
value01	Value of the matrix in the 0, 1 position.
value02	Value of the matrix in the 0, 2 position.
value03	Value of the matrix in the 0, 3 position.
value10	Value of the matrix in the 1, 0 position.
value11	Value of the matrix in the 1, 1 position.
value12	Value of the matrix in the 1, 2 position.
value13	Value of the matrix in the 1, 3 position.
value20	Value of the matrix in the 2, 0 position.
value21	Value of the matrix in the 2, 1 position.
value22	Value of the matrix in the 2, 2 position.
value23	Value of the matrix in the 2, 3 position.
value30	Value of the matrix in the 3, 0 position.
value31	Value of the matrix in the 3, 1 position.
value32	Value of the matrix in the 3, 2 position.
value33	Value of the matrix in the 3, 3 position.

Matrix4(Matrix4 matrix)

Initializes a new instance of the Matrix4 struct.

Parameters:

matrix

Matrix struct to take the values from.

Matrix4(Vector4[] values, bool isColums = true)

Initializes a new instance of the Matrix4 struct.

///

Parameters:

values	Values of the Matrix.
isColums	Tells if the vector is a column vector or a row vector.

Matrix4 Transpose()

Computes the transpose of this matrix.

Returns:

The transpose of this matrix.

bool Equals(object other, double tolerance)

Comparator within a tolerance.

Parameters:

other	Matrix to compare with.
tolerance	Tolerance to apply in the comparison.

Returns:

True if two matrices are equal withing a tolerance.

bool Equals(Matrix4 other, double tolerance)

Comparator within a tolerance.

Parameters:

other	Matrix to compare with.
tolerance	Tolerance to apply in the comparison.

Returns:

True if two matrices are equal withing a tolerance.

Matrix4 Invert()

Inverts this instance.

Taken from here : https://github.com/opentk/opentk/blob/master/src/OpenTK.Mathematics/Matrix/Matrix4d.cs#L1582.

Parameters:

InvalidOperationException

Thrown when the matrix is singular and cannot be inverted.

Returns:

The inverted matrix.

static Matrix4 operator + (Matrix4 mat, double scalar)

Adds a matrix and a scalar.

Parameters:

mat	Matrix to add to.
scalar	Scalar to add to the matrix.

Returns:

The added matrix.

static Matrix4 operator + (double scalar, Matrix4 mat)

Adds a matrix and a scalar.

Parameters:

mat	Matrix to add to.
scalar	Scalar to add to the matrix.

Returns:

The added matrix.

static Matrix4 operator - (Matrix4 mat, double scalar)

Substracts a matrix and a scalar.

Parameters:

mat	Matrix to substract to.
scalar	Scalar to substract to the matrix.

Returns:

The substracted matrix.

static Matrix4 operator - (double scalar, Matrix4 mat)

Substracts a matrix and a scalar.

Parameters:

mat	Matrix to substract to.
scalar	Scalar to substract to the matrix.

Returns:

The substracted matrix.

static Matrix4 operator * (Matrix4 mat, double scalar)

Multiplies a matrix and a scalar.

Parameters:

mat	Matrix to multiply.
scalar	Scalar to multiply with the matrix.

Returns:

The multiplied matrix.

static Matrix4 operator * (double scalar, Matrix4 mat)

Multiplies a matrix and a scalar.

Parameters:

mat	Matrix to multiply.
scalar	Scalar to multiply with the matrix.

Returns:

The multiplied matrix.

static Matrix4 operator/ (Matrix4 mat, double scalar)

Divides a matrix by a scalar.

Parameters:

mat	Matrix to divide.
scalar	Scalar to divide the matrix with.

Returns:

The divided matrix.

static Matrix4 operator - (Matrix4 mat)

Inverses the sign of a matrix.

Parameters:

mat	Matrix to inverse the sign of.

Returns:

The sign inverted matrix.

static Matrix4 operator + (Matrix4 left, Matrix4 right)

Adds two matrices.

Parameters:

left	The matrix on the left.
right	The matrix on the right.

Returns:

The added matrix.

static Matrix4 operator - (Matrix4 left, Matrix4 right)

Substracts two matrices.

Parameters:

left	The matrix on the left.
right	The matrix on the right.

Returns:

The substracted matrix.

static Matrix4 operator * (Matrix4 left, Matrix4 right)

Multiplies two matrices.

Parameters:

left	The left matrix.
right	The right matrix.

Returns:

The dot product of the matrices.

static bool operator == (Matrix4 left, Matrix4 right)

Check if two matrices are equal.

Parameters:

left	The left matrix.
right	The right matrix.

Returns:

True if the matrices are equal.

static bool operator != (Matrix4 left, Matrix4 right)

Check if two matrices are not equal.

Parameters:

left	The left matrix.
right	The right matrix.

Returns:

True if the matrices are not equal.

static Matrix4 CreateRotationX(double angle)

Builds a rotation matrix for a rotation around x-axis.

Parameters:

angle

The counter clockwise angle in radians.

Returns:

The rotation matrix.

static Matrix4 CreateRotationY(double angle)

Builds a rotation matrix for a rotation around y-axis.

Parameters:

angle

The counter clockwise angle in radians.

Returns:

The rotation matrix.

static Matrix4 CreateRotationZ(double angle)

Builds a rotation matrix for a rotation around z-axis.

Parameters:

angle

The counter clockwise angle in radians.

Returns:

The rotation matrix.

static Matrix4 CreateRotation(Vector3 rotation)

Builds a combined rotation matrix around the X, Y and Z axes. Angles in radians.

Parameters:

rotation

Rotation that will be applied in the matrix.

Returns:

The rotation matrix.

static Matrix4 CreateRotationAbitraryAxis(Axis rotationAxis, double angle)

Builds a rotation matrix around an arbitrary axis.

Parameters:

rotationAxis	The arbitrary axis to rotate about.
angle	The angle of the rotation.

Returns:

The constructed rotation matrix.

static Matrix4 CreateScale(double scaleFactor)

Builds a scale matrix.

Parameters:

scaleFactor

The scaling factor for this matrix.

Returns:

The scale matrix.

static Matrix4 CreatePerspectiveOffCenter(
    double left,
    double right,
    double bottom,
    double top,
    double depthNear,
    double depthFar
    )

Creates an perspective projection matrix.

Taken from here : https://github.com/opentk/opentk/blob/082c8d228d0def042b11424ac002776432f44f47/src/OpenTK.Mathematics/Matrix/Matrix4d.cs#L1024.

Parameters:

left	Left edge of the view frustum.
right	Right edge of the view frustum.
bottom	Bottom edge of the view frustum.
top	Top edge of the view frustum.
depthNear	Distance to the near clip plane.
depthFar	Distance to the far clip plane.
System.ArgumentOutOfRangeException	Thrown under the following conditions: depthNear is negative or zero depthFar is negative or zero depthNear is larger than depthFar

Returns:

A perspective projection matrix.

static Matrix4 CreatePerspectiveFieldOfView(
    double fovy,
    double aspect,
    double depthNear,
    double depthFar
    )

Creates a perspective projection matrix.

Parameters:

fovy	Angle of the field of view in the y direction (in radians).
aspect	Aspect ratio of the view (width / height).
depthNear	Distance to the near clip plane.
depthFar	Distance to the far clip plane.
System.ArgumentOutOfRangeException	Thrown under the following conditions: fovy is zero, less than zero or larger than Math.PI aspect is negative or zero depthNear is negative or zero depthFar is negative or zero depthNear is larger than depthFar

Returns:

A perspective projection matrix.

static Matrix4 CreateTranslation(double x, double y, double z)

Build a translation matrix.

Parameters:

x	X translation.
y	Y translation.
z	Z translation.

Returns:

The resulting Matrix4 instance.

static Matrix4 CreateTranslation(Vector3 vector)

Builds a translation matrix from a vector.

Parameters:

vector

The translation vector.

Returns:

The resulting Matrix4 instance.

static Matrix4 LookAt(Vector3 eye, Vector3 target, Vector3 up)

Builds a world space to view space matrix.

Parameters:

eye	Eye (camera) position in world space.
target	Target position in world space.
up	Up vector in world space (should not be parallel to the camera direction, that is target - eye).

Returns:

A Matrix that transforms world space to camera (view) space.

static Matrix4 Transpose(Matrix4 mat)

Computes the transpose of the given matrix.

Parameters:

mat	Matrix to compute the transpose of.

Returns:

The transpose of the given matrix.

static Matrix4 Normalize(Matrix4 mat)

Divides each element in the Matrix by the Determinant.

Parameters:

mat	Matrix to normalize.

Returns:

The normalized matrix.