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Matrix3

A class representing a 3x3 matrix.

Code Example​

const m = new Matrix3();

A Note on Row-Major and Column-Major Ordering​

The constructor and set() method take arguments in row-major order, while internally they are stored in the .elements array in column-major order.

This means that calling

m.set( 11, 12, 13, 21, 22, 23, 31, 32, 33 );

will result in the .elements array containing:

m.elements = [ 11, 21, 31, 12, 22, 32, 13, 23, 33 ];

and internally all calculations are performed using column-major ordering. However, as the actual ordering makes no difference mathematically and most people are used to thinking about matrices in row-major order, the three.js documentation shows matrices in row-major order. Just bear in mind that if you are reading the source code, you'll have to take the transpose of any matrices outlined here to make sense of the calculations.

Constructor​

Matrix3​

function Matrix3( n11: Number, n12: Number, n13: Number, n21: Number, n22:
Number, n22: Number, n31: Number, n32: Number, n33: Number ): void;

Creates a 3x3 matrix with the given arguments in row-major order. If no arguments are provided, the constructor initializes the Matrix3 to the 3x3 identity matrix.

Properties​

elements​

elements: Array;

A column- major list of matrix values.

Methods​

clone​

function clone( ): Matrix3;

Creates a new Matrix3 and with identical elements to this one.

copy​

function copy( m: Matrix3 ): this;

Copies the elements of matrix m into this matrix.

determinant​

function determinant( ): Float;

Computes and returns the determinant of this matrix.

equals​

function equals( m: Matrix3 ): Boolean;

Return true if this matrix and m are equal.

extractBasis​

function extractBasis( xAxis: Vector3, yAxis: Vector3, zAxis: Vector3 ): this;

Extracts the basis of this matrix into the three axis vectors provided. If this matrix is:

a, b, c, d, e, f, g, h, i

then the xAxis, yAxis, zAxis will be set to:

xAxis = (a, d, g) yAxis = (b, e, h) zAxis = (c, f, i)

fromArray​

function fromArray( array: Array, offset: Integer ): this;

array - the array to read the elements from.
offset - (optional) index of first element in the array. Default is 0.

Sets the elements of this matrix based on an array in column-major format.

invert​

function invert( ): this;

Inverts this matrix, using the analytic method. You can not invert with a determinant of zero. If you attempt this, the method produces a zero matrix instead.

getNormalMatrix​

function getNormalMatrix( m: Matrix4 ): this;

m - Matrix4

Sets this matrix as the upper left 3x3 of the normal matrix of the passed matrix4. The normal matrix is the inverse transpose of the matrix m.

identity​

function identity( ): this;

Resets this matrix to the 3x3 identity matrix:

1, 0, 0 0, 1, 0 0, 0, 1

makeRotation​

function makeRotation( theta: Float ): this;

theta — Rotation angle in radians. Positive values rotate counterclockwise.

Sets this matrix as a 2D rotational transformation by theta radians. The resulting matrix will be:

cos(θ) -sin(θ) 0 sin(θ) cos(θ) 0 0 0 1

makeScale​

function makeScale( x: Float, y: Float ): this;

x - the amount to scale in the X axis.
y - the amount to scale in the Y axis.
Sets this matrix as a 2D scale transform:

x, 0, 0, 0, y, 0, 0, 0, 1

makeTranslation​

function makeTranslation( v: Vector2 ): this;

makeTranslation​

function makeTranslation( x: Float, y: Float ): this;

v a translation transform from vector.
or
x - the amount to translate in the X axis.
y - the amount to translate in the Y axis.
Sets this matrix as a 2D translation transform:

1, 0, x, 0, 1, y, 0, 0, 1

multiply​

function multiply( m: Matrix3 ): this;

Post-multiplies this matrix by m.

multiplyMatrices​

function multiplyMatrices( a: Matrix3, b: Matrix3 ): this;

Sets this matrix to a x b.

multiplyScalar​

function multiplyScalar( s: Float ): this;

Multiplies every component of the matrix by the scalar value s.

rotate​

function rotate( theta: Float ): this;

Rotates this matrix by the given angle (in radians).

scale​

function scale( sx: Float, sy: Float ): this;

Scales this matrix with the given scalar values.

set​

function set( n11: Float, n12: Float, n13: Float, n21: Float, n22: Float, n23:
Float, n31: Float, n32: Float, n33: Float ): this;

n11 - value to put in row 1, col 1.
n12 - value to put in row 1, col 2.
...
...
n32 - value to put in row 3, col 2.
n33 - value to put in row 3, col 3.

Sets the 3x3 matrix values to the given row-major sequence of values.

premultiply​

function premultiply( m: Matrix3 ): this;

Pre-multiplies this matrix by m.

setFromMatrix4​

function setFromMatrix4( m: Matrix4 ): this;

Set this matrix to the upper 3x3 matrix of the Matrix4 m.

setUvTransform​

function setUvTransform( tx: Float, ty: Float, sx: Float, sy: Float, rotation:
Float, cx: Float, cy: Float ): this;

tx - offset x
ty - offset y
sx - repeat x
sy - repeat y
rotation - rotation, in radians. Positive values rotate counterclockwise
cx - center x of rotation
cy - center y of rotation

Sets the UV transform matrix from offset, repeat, rotation, and center.

toArray​

function toArray( array: Array, offset: Integer ): Array;

array - (optional) array to store the resulting vector in. If not given a new array will be created.
offset - (optional) offset in the array at which to put the result.

Writes the elements of this matrix to an array in column-major format.

translate​

function translate( tx: Float, ty: Float ): this;

Translates this matrix by the given scalar values.

transpose​

function transpose( ): this;

Transposes this matrix in place.

transposeIntoArray​

function transposeIntoArray( array: Array ): this;

array - array to store the resulting vector in.

Transposes this matrix into the supplied array, and returns itself unchanged.

Source​

src/math/Matrix3.js