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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" />
- </head>
- <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>θ</mi>
- </mtd>
- <mtd>
- <mi>-sin</mi>
- <mi>θ</mi>
- </mtd>
- <mtd>
- <mn>0</mn>
- </mtd>
- </mtr>
- <mtr>
- <mtd>
- <mi>sin</mi>
- <mi>θ</mi>
- </mtd>
- <mtd>
- <mi>cos</mi>
- <mi>θ</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>
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