NodeWorld
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Matrix4x4

La référence est en anglais : elle est générée à partir des commentaires du code, écrits en anglais.

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public struct Matrix4x4 : IEquatable<Matrix4x4>, IFormattable

Namespace NodeWorld.Flux.

A 4x4 matrix, mRC = row R, column C, stored column after column (as Unity's). Points are column vectors: M * p.

Fields

m00

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public float m00

The value at row 0, column 0.

m10

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public float m10

The value at row 1, column 0.

m20

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public float m20

The value at row 2, column 0.

m30

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public float m30

The value at row 3, column 0.

m01

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public float m01

The value at row 0, column 1.

m11

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public float m11

The value at row 1, column 1.

m21

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public float m21

The value at row 2, column 1.

m31

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public float m31

The value at row 3, column 1.

m02

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public float m02

The value at row 0, column 2.

m12

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public float m12

The value at row 1, column 2.

m22

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public float m22

The value at row 2, column 2.

m32

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public float m32

The value at row 3, column 2.

m03

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public float m03

The value at row 0, column 3.

m13

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public float m13

The value at row 1, column 3.

m23

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public float m23

The value at row 2, column 3.

m33

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public float m33

The value at row 3, column 3.

Constructors

Matrix4x4

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public Matrix4x4(Vector4 column0, Vector4 column1, Vector4 column2, Vector4 column3)

The matrix of these four columns.

Properties

this[]

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public float this[int row, int column] { get; set; }

The value at row and column (0 to 3).

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public float this[int index] { get; set; }

The value at index 0 to 15, column after column (index = row + column * 4).

zero

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public static Matrix4x4 zero { get; }

Every value 0.

identity

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public static Matrix4x4 identity { get; }

The identity matrix: 1 on the diagonal.

isIdentity

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public bool isIdentity { get; }

The matrix is the identity.

transpose

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public Matrix4x4 transpose { get; }

The matrix with rows and columns swapped.

determinant

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public float determinant { get; }

The determinant.

inverse

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public Matrix4x4 inverse { get; }

The inverse (cofactors / determinant); the zero matrix if the matrix is singular.

rotation

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public Quaternion rotation { get; }

The rotation part (the upper 3x3 without its scale).

lossyScale

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public Vector3 lossyScale { get; }

The scale of the upper 3x3 (length of its columns, negative if the matrix mirrors).

Methods

GetColumn

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public Vector4 GetColumn(int index)

The column index (0 to 3).

GetRow

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public Vector4 GetRow(int index)

The row index (0 to 3).

SetColumn

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public void SetColumn(int index, Vector4 column)

Sets the column index (0 to 3).

SetRow

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public void SetRow(int index, Vector4 row)

Sets the row index (0 to 3).

GetPosition

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public Vector3 GetPosition()

The translation part: m03, m13, m23.

MultiplyPoint

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public Vector3 MultiplyPoint(Vector3 point)

Transforms a point, with the projective divide.

MultiplyPoint3x4

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public Vector3 MultiplyPoint3x4(Vector3 point)

Transforms a point by an affine matrix (no projective divide).

MultiplyVector

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public Vector3 MultiplyVector(Vector3 vector)

Transforms a direction (rotation and scale only).

Transpose

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public static Matrix4x4 Transpose(Matrix4x4 m)

m with rows and columns swapped.

Determinant

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public static float Determinant(Matrix4x4 m)

The determinant of m.

Inverse

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public static Matrix4x4 Inverse(Matrix4x4 m)

The inverse of m; the zero matrix if m is singular.

TRS

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public static Matrix4x4 TRS(Vector3 pos, Quaternion q, Vector3 s)

Translation, rotation and scale: T * R * S.

SetTRS

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public void SetTRS(Vector3 pos, Quaternion q, Vector3 s)

Makes it TRS(pos, q, s).

Translate

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public static Matrix4x4 Translate(Vector3 vector)

A translation matrix.

Rotate

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public static Matrix4x4 Rotate(Quaternion q)

A rotation matrix.

Scale

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public static Matrix4x4 Scale(Vector3 vector)

A scale matrix.

Perspective

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public static Matrix4x4 Perspective(float fov, float aspect, float zNear, float zFar)

Perspective projection (clip space z from -1 to 1, as OpenGL and Unity's matrices).

Ortho

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public static Matrix4x4 Ortho(float left, float right, float bottom, float top, float zNear, float zFar)

Orthographic projection (clip space z from -1 to 1, as Perspective).

LookAt

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public static Matrix4x4 LookAt(Vector3 from, Vector3 to, Vector3 up)

A matrix placing an object at "from", its forward (z) towards "to".

Equals

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public bool Equals(Matrix4x4 other)

The sixteen values are exactly equal.

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public override bool Equals(object other)

other is a matrix with exactly the same values.

GetHashCode

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public override int GetHashCode()

A hash of the values.

ToString

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public override string ToString()

The four rows, values separated by tabs, with 5 decimals.

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public string ToString(string format)

The same text with the numbers in format.

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public string ToString(string format, IFormatProvider formatProvider)

The same text with the numbers in format (F5 when empty) and formatProvider (the invariant culture when null).

Operators

operator *

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public static Matrix4x4 operator *(Matrix4x4 lhs, Matrix4x4 rhs)

The product lhs * rhs: rhs applies first.

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public static Vector4 operator *(Matrix4x4 lhs, Vector4 v)

The matrix times the column vector v.

operator ==

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public static bool operator ==(Matrix4x4 lhs, Matrix4x4 rhs)

Every column equal (as Vector4's ==).

operator !=

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public static bool operator !=(Matrix4x4 lhs, Matrix4x4 rhs)

The matrices differ (see ==).