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							<!DOCTYPE html>
<html lang="en">
	<head>
		<meta charset="utf-8" />
		<base href="../../../" />
		<script src="page.js"></script>
		<link type="text/css" rel="stylesheet" href="page.css" />
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	<body>
		<h1>[name]</h1>

		<p class="desc">
			A class representing a 3x3
			[link:https://en.wikipedia.org/wiki/Matrix_(mathematics) matrix].
		</p>

		<h2>Code Example</h2>
		<code>
const m = new Matrix3(); 
		</code>

		<h2>A Note on Row-Major and Column-Major Ordering</h2>
		<p>
			The constructor and [page:set]() method take arguments in
			[link:https://en.wikipedia.org/wiki/Row-_and_column-major_order#Column-major_order row-major] 
			order, while internally they are stored in the [page:.elements elements] 
			array in column-major order.<br /><br />

			This means that calling
			<code>
m.set( 11, 12, 13,
       21, 22, 23,
       31, 32, 33 );
		</code>
			will result in the [page:.elements elements] array containing:
			<code> 
m.elements = [ 11, 21, 31,
			   12, 22, 32, 
			   13, 23, 33 ];
			</code>
			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
			[link:https://en.wikipedia.org/wiki/Transpose transpose] of any matrices
			outlined here to make sense of the calculations.
		</p>

		<h2>Constructor</h2>

		<h3>[name]( [param:Number n11], [param:Number n12], [param:Number n13],
			[param:Number n21], [param:Number n22], [param:Number n23],
			[param:Number n31], [param:Number n32], [param:Number n33] )</h3>
		<p>
			Creates a 3x3 matrix with the given arguments in row-major order. If no arguments are provided, the constructor initializes
			the [name] to the 3x3 [link:https://en.wikipedia.org/wiki/Identity_matrix identity matrix].
		</p>

		<h2>Properties</h2>

		<h3>[property:Array elements]</h3>
		<p>
			A [link:https://en.wikipedia.org/wiki/Row-_and_column-major_order column-major] list of matrix values.
		</p>

		<h2>Methods</h2>

		<h3>[method:Matrix3 clone]()</h3>
		<p>Creates a new Matrix3 and with identical elements to this one.</p>

		<h3>[method:this copy]( [param:Matrix3 m] )</h3>
		<p>Copies the elements of matrix [page:Matrix3 m] into this matrix.</p>

		<h3>[method:Float determinant]()</h3>
		<p>
			Computes and returns the [link:https://en.wikipedia.org/wiki/Determinant determinant] of this matrix.
		</p>

		<h3>[method:Boolean equals]( [param:Matrix3 m] )</h3>
		<p>Return true if this matrix and [page:Matrix3 m] are equal.</p>

		<h3>
			[method:this extractBasis]( [param:Vector3 xAxis], [param:Vector3 yAxis], [param:Vector3 zAxis] )
		</h3>
		<p>
			Extracts the [link:https://en.wikipedia.org/wiki/Basis_(linear_algebra) basis] 
			of this matrix into the three axis vectors provided. If this matrix
			is:
		</p>

		<math display="block">
			<mrow>
				<mo>[</mo>
				<mtable>
					<mtr>
						<mtd><mi>a</mi></mtd>
						<mtd><mi>b</mi></mtd>
						<mtd><mi>c</mi></mtd>
					</mtr>
					<mtr>
						<mtd><mi>d</mi></mtd>
						<mtd><mi>e</mi></mtd>
						<mtd><mi>f</mi></mtd>
					</mtr>
					<mtr>
						<mtd><mi>g</mi></mtd>
						<mtd><mi>h</mi></mtd>
						<mtd><mi>i</mi></mtd>
					</mtr>
				</mtable>
				<mo>]</mo>
			</mrow>
		</math>

		<p>
			then the [page:Vector3 xAxis], [page:Vector3 yAxis], [page:Vector3 zAxis]
			will be set to:
		</p>

		<p style="text-align: center">
			<math>
				<mrow>
					<mi>xAxis</mi>
					<mo>=</mo>
					<mo>[</mo>
					<mtable>
						<mtr><mtd style="height: 1rem"><mi>a</mi></mtd></mtr>
						<mtr><mtd style="height: 1rem"><mi>d</mi></mtd></mtr>
						<mtr><mtd style="height: 1rem"><mi>g</mi></mtd></mtr>
					</mtable>
					<mo>]</mo>
				</mrow>
			</math>,

			<math>
				<mrow>
					<mi>yAxis</mi>
					<mo>=</mo>
					<mo>[</mo>
					<mtable>
						<mtr><mtd style="height: 1rem"><mi>b</mi></mtd></mtr>
						<mtr><mtd style="height: 1rem"><mi>e</mi></mtd></mtr>
						<mtr><mtd style="height: 1rem"><mi>h</mi></mtd></mtr>
					</mtable>
					<mo>]</mo>
				</mrow>
			</math>, and

			<math>
				<mrow>
					<mi>zAxis</mi>
					<mo>=</mo>
					<mo>[</mo>
					<mtable>
						<mtr><mtd style="height: 1rem"><mi>c</mi></mtd></mtr>
						<mtr><mtd style="height: 1rem"><mi>f</mi></mtd></mtr>
						<mtr><mtd style="height: 1rem"><mi>i</mi></mtd></mtr>
					</mtable>
					<mo>]</mo>
				</mrow>
			</math>
		</p>

		<h3>
			[method:this fromArray]( [param:Array array], [param:Integer offset] )
		</h3>
		<p>
			[page:Array array] - the array to read the elements from.<br />
			[page:Integer offset] - (optional) index of first element in the array.
			Default is `0`.<br /><br />

			Sets the elements of this matrix based on an array in
			[link:https://en.wikipedia.org/wiki/Row-_and_column-major_order#Column-major_order column-major] format.
		</p>

		<h3>[method:this invert]()</h3>
		<p>
			Inverts this matrix, using the
			[link:https://en.wikipedia.org/wiki/Invertible_matrix#Analytic_solution analytic method]. 
			You can not invert with a determinant of zero. If you
			attempt this, the method produces a zero matrix instead.
		</p>

		<h3>[method:this getNormalMatrix]( [param:Matrix4 m] )</h3>
		<p>
			[page:Matrix4 m] - [page:Matrix4]<br /><br />

			Sets this matrix as the upper left 3x3 of the
			[link:https://en.wikipedia.org/wiki/Normal_matrix normal matrix] of the
			passed [page:Matrix4 matrix4]. 
			The normal matrix is the
			[link:https://en.wikipedia.org/wiki/Invertible_matrix inverse]
			[link:https://en.wikipedia.org/wiki/Transpose transpose] of the matrix
			[page:Matrix4 m].
		</p>

		<h3>[method:this identity]()</h3>
		<p>
			Resets this matrix to the 3x3 identity matrix:
		</p>

		<math display="block">
			<mrow>
				<mo>[</mo>
				<mtable>
					<mtr>
						<mtd><mn>1</mn></mtd>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>0</mn></mtd>
					</mtr>
					<mtr>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>1</mn></mtd>
						<mtd><mn>0</mn></mtd>
					</mtr>
					<mtr>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>1</mn></mtd>
					</mtr>
				</mtable>
				<mo>]</mo>
			</mrow>
		</math>

		<h3>[method:this makeRotation]( [param:Float theta] )</h3>
		<p>
			[page:Float theta] — Rotation angle in radians. Positive values rotate
			counterclockwise.<br /><br />

			Sets this matrix as a 2D rotational transformation by [page:Float theta]
			radians. The resulting matrix will be:
		</p>

		<math display="block">
			<mrow>
				<mo>[</mo>
				<mtable>
					<mtr>
						<mtd>
							<mi>cos</mi>
							<mi>&theta;</mi>
						</mtd>
						<mtd>
							<mi>-sin</mi>
							<mi>&theta;</mi>
						</mtd>
						<mtd>
							<mn>0</mn>
						</mtd>
					</mtr>
					<mtr>
						<mtd>
							<mi>sin</mi>
							<mi>&theta;</mi>
						</mtd>
						<mtd>
							<mi>cos</mi>
							<mi>&theta;</mi>
						</mtd>
						<mtd>
							<mn>0</mn>
						</mtd>
					</mtr>
					<mtr>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>1</mn></mtd>
					</mtr>
				</mtable>
				<mo>]</mo>
			</mrow>
		</math>

		<h3>[method:this makeScale]( [param:Float x], [param:Float y] )</h3>
		<p>
			[page:Float x] - the amount to scale in the X axis.<br />
			[page:Float y] - the amount to scale in the Y axis.<br />

			Sets this matrix as a 2D scale transform:
		</p>

		<math display="block">
			<mrow>
				<mo>[</mo>
				<mtable>
					<mtr>
						<mtd><mi>x</mi></mtd>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>0</mn></mtd>
					</mtr>
					<mtr>
						<mtd><mn>0</mn></mtd>
						<mtd><mi>y</mi></mtd>
						<mtd><mn>0</mn></mtd>
					</mtr>
					<mtr>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>1</mn></mtd>
					</mtr>
				</mtable>
				<mo>]</mo>
			</mrow>
		</math>

		<h3>[method:this makeTranslation]( [param:Vector2 v] )</h3>
		<h3>[method:this makeTranslation]( [param:Float x], [param:Float y] )</h3>
		<p>
			[page:Vector2 v] a translation transform from vector.<br />
			or<br />
			[page:Float x] - the amount to translate in the X axis.<br />
			[page:Float y] - the amount to translate in the Y axis.<br />

			Sets this matrix as a 2D translation transform:
		</p>

		<math display="block">
			<mrow>
				<mo>[</mo>
				<mtable>
					<mtr>
						<mtd><mn>1</mn></mtd>
						<mtd><mn>0</mn></mtd>
						<mtd><mi>x</mi></mtd>
					</mtr>
					<mtr>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>1</mn></mtd>
						<mtd><mi>y</mi></mtd>
					</mtr>
					<mtr>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>0</mn></mtd>
						<mtd><mn>1</mn></mtd>
					</mtr>
				</mtable>
				<mo>]</mo>
			</mrow>
		</math>

		<h3>[method:this multiply]( [param:Matrix3 m] )</h3>
		<p>Post-multiplies this matrix by [page:Matrix3 m].</p>

		<h3>
			[method:this multiplyMatrices]( [param:Matrix3 a], [param:Matrix3 b] )
		</h3>
		<p>Sets this matrix to [page:Matrix3 a] x [page:Matrix3 b].</p>

		<h3>[method:this multiplyScalar]( [param:Float s] )</h3>
		<p>Multiplies every component of the matrix by the scalar value *s*.</p>

		<h3>[method:this rotate]( [param:Float theta] )</h3>
		<p>Rotates this matrix by the given angle (in radians).</p>

		<h3>[method:this scale]( [param:Float sx], [param:Float sy] )</h3>
		<p>Scales this matrix with the given scalar values.</p>

		<h3>
			[method:this set]( [param:Float n11], [param:Float n12], [param:Float n13], [param:Float n21], [param:Float n22], [param:Float n23], [param:Float n31], [param:Float n32], [param:Float n33] )
		</h3>
		<p>
			Sets the 3x3 matrix values to the given
			[link:https://en.wikipedia.org/wiki/Row-_and_column-major_order row-major]
			sequence of values:
		</p>

		<math display="block">
			<mrow>
				<mo>[</mo>
				<mtable>
					<mtr>
						<mtd><mi>n11</mi></mtd>
						<mtd><mi>n12</mi></mtd>
						<mtd><mi>n13</mi></mtd>
					</mtr>
					<mtr>
						<mtd><mi>n21</mi></mtd>
						<mtd><mi>n22</mi></mtd>
						<mtd><mi>n23</mi></mtd>
					</mtr>
					<mtr>
						<mtd><mi>n31</mi></mtd>
						<mtd><mi>n32</mi></mtd>
						<mtd><mi>n33</mi></mtd>
					</mtr>
				</mtable>
				<mo>]</mo>
			</mrow>
		</math>

		<h3>[method:this premultiply]( [param:Matrix3 m] )</h3>
		<p>Pre-multiplies this matrix by [page:Matrix3 m].</p>

		<h3>[method:this setFromMatrix4]( [param:Matrix4 m] )</h3>
		<p>
			Set this matrix to the upper 3x3 matrix of the Matrix4 [page:Matrix4 m].
		</p>

		<h3>
			[method:this setUvTransform]( [param:Float tx], [param:Float ty], [param:Float sx], [param:Float sy], [param:Float rotation], [param:Float cx], [param:Float cy] )
		</h3>
		<p>
			[page:Float tx] - offset x<br />
			[page:Float ty] - offset y<br />
			[page:Float sx] - repeat x<br />
			[page:Float sy] - repeat y<br />
			[page:Float rotation] - rotation, in radians. Positive values rotate
			counterclockwise<br />
			[page:Float cx] - center x of rotation<br />
			[page:Float cy] - center y of rotation<br /><br />

			Sets the UV transform matrix from offset, repeat, rotation, and center.
		</p>

		<h3>
			[method:Array toArray]( [param:Array array], [param:Integer offset] )
		</h3>
		<p>
			[page:Array array] - (optional) array to store the resulting vector in. If
			not given a new array will be created.<br />
			[page:Integer offset] - (optional) offset in the array at which to put the
			result.<br /><br />

			Writes the elements of this matrix to an array in
			[link:https://en.wikipedia.org/wiki/Row-_and_column-major_order#Column-major_order column-major] format.
		</p>

		<h3>[method:this translate]( [param:Float tx], [param:Float ty] )</h3>
		<p>Translates this matrix by the given scalar values.</p>

		<h3>[method:this transpose]()</h3>
		<p>
			[link:https://en.wikipedia.org/wiki/Transpose Transposes] this matrix in
			place.
		</p>

		<h3>[method:this transposeIntoArray]( [param:Array array] )</h3>
		<p>
			[page:Array array] - array to store the resulting vector in.<br /><br />

			[link:https://en.wikipedia.org/wiki/Transpose Transposes] this matrix into
			the supplied array, and returns itself unchanged.
		</p>

		<h2>Source</h2>

		<p>
			[link:https://github.com/mrdoob/three.js/blob/master/src/[path].js src/[path].js]
		</p>
	</body>
</html>