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<!DOCTYPE html>
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<html lang="zh">
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<head>
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<meta charset="utf-8" />
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<base href="../../../" />
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<script src="page.js"></script>
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<link type="text/css" rel="stylesheet" href="page.css" />
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</head>
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<body>
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<h1>三维矩阵（[name]）</h1>
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<p class="desc">
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一个表示3X3矩阵[link:https://en.wikipedia.org/wiki/Matrix_(mathematics) matrix].的类。
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</p>
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<h2>代码示例</h2>
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<code>
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const m = new Matrix3();
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</code>
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<h2>注意行优先列优先的顺序。</h2>
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<p>
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[page:set]()方法参数采用行优先[link:https://en.wikipedia.org/wiki/Row-_and_column-major_order#Column-major_order row-major]，
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而它们在内部是用列优先[link:https://en.wikipedia.org/wiki/Row-_and_column-major_order column-major]顺序存储在数组当中。<br /><br />
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这意味着
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<code>
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m.set( 11, 12, 13,
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21, 22, 23,
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31, 32, 33 );
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</code>
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元素数组[page:.elements elements]将存储为:
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<code>
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m.elements = [ 11, 21, 31,
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12, 22, 32,
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13, 23, 33 ];
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</code>
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在内部，所有的计算都是使用列优先顺序进行的。然而，由于实际的排序在数学上没有什么不同，
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而且大多数人习惯于以行优先顺序考虑矩阵，所以three.js文档以行为主的顺序显示矩阵。
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请记住，如果您正在阅读源代码，您必须对这里列出的任何矩阵进行转置[link:https://en.wikipedia.org/wiki/Transpose transpose]，以理解计算。
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</p>
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<h2>Constructor</h2>
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<h3>[name]( [param:Number n11], [param:Number n12], [param:Number n13],
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[param:Number n21], [param:Number n22], [param:Number n23],
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[param:Number n31], [param:Number n32], [param:Number n33] )</h3>
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<p>
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Creates a 3x3 matrix with the given arguments in row-major order. If no arguments are provided, the constructor initializes
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the [name] to the 3x3 [link:https://en.wikipedia.org/wiki/Identity_matrix identity matrix].
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</p>
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<h2>属性（Properties）</h2>
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<h3>[property:Array elements]</h3>
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<p>
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矩阵列优先[link:https://en.wikipedia.org/wiki/Row-_and_column-major_order column-major]列表。
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</p>
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<h2>方法（Methods）</h2>
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<h3>[method:Matrix3 clone]()</h3>
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<p>创建一个新的矩阵，元素 [page:.elements elements] 与该矩阵相同。</p>
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<h3>[method:this copy]( [param:Matrix3 m] )</h3>
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<p>将矩阵[page:Matrix3 m]的元素复制到当前矩阵中。</p>
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<h3>[method:Float determinant]()</h3>
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<p>
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计算并返回矩阵的行列式[link:https://en.wikipedia.org/wiki/Determinant determinant] 。
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</p>
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<h3>[method:Boolean equals]( [param:Matrix3 m] )</h3>
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<p>如果矩阵[page:Matrix3 m] 与当前矩阵所有对应元素相同则返回true。</p>
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<h3>[method:this extractBasis]( [param:Vector3 xAxis], [param:Vector3 yAxis], [param:Vector3 zAxis] )</h3>
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<p>
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将该矩阵的基向量 [link:https://en.wikipedia.org/wiki/Basis_(linear_algebra) basis] 提取到提供的三个轴向中。如果该矩阵如下：
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</p>
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<math display="block">
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<mrow>
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<mo>[</mo>
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<mtable>
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<mtr>
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<mtd><mi>a</mi></mtd>
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<mtd><mi>b</mi></mtd>
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<mtd><mi>c</mi></mtd>
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</mtr>
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<mtr>
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<mtd><mi>d</mi></mtd>
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<mtd><mi>e</mi></mtd>
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<mtd><mi>f</mi></mtd>
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</mtr>
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<mtr>
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<mtd><mi>g</mi></mtd>
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<mtd><mi>h</mi></mtd>
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<mtd><mi>i</mi></mtd>
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</mtr>
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</mtable>
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<mo>]</mo>
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</mrow>
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</math>
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<p>
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那么 [page:Vector3 xAxis], [page:Vector3 yAxis], [page:Vector3 zAxis] 将会被设置为：
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</p>
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<div style="text-align: center">
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<math>
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<mrow>
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<mi>xAxis</mi>
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<mo>=</mo>
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<mo>[</mo>
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<mtable>
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<mtr><mtd style="height: 1rem"><mi>a</mi></mtd></mtr>
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<mtr><mtd style="height: 1rem"><mi>d</mi></mtd></mtr>
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<mtr><mtd style="height: 1rem"><mi>g</mi></mtd></mtr>
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</mtable>
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<mo>]</mo>
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</mrow>
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</math>,
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<math>
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<mrow>
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<mi>yAxis</mi>
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<mo>=</mo>
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<mo>[</mo>
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<mtable>
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<mtr><mtd style="height: 1rem"><mi>b</mi></mtd></mtr>
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<mtr><mtd style="height: 1rem"><mi>e</mi></mtd></mtr>
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<mtr><mtd style="height: 1rem"><mi>h</mi></mtd></mtr>
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</mtable>
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<mo>]</mo>
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</mrow>
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</math>, and
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<math>
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<mrow>
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<mi>zAxis</mi>
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<mo>=</mo>
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<mo>[</mo>
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<mtable>
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<mtr><mtd style="height: 1rem"><mi>c</mi></mtd></mtr>
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<mtr><mtd style="height: 1rem"><mi>f</mi></mtd></mtr>
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<mtr><mtd style="height: 1rem"><mi>i</mi></mtd></mtr>
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</mtable>
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<mo>]</mo>
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</mrow>
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</math>
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</div>
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<h3>[method:this fromArray]( [param:Array array], [param:Integer offset] )</h3>
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<p>
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[page:Array array] - 用来存储设置元素数据的数组<br />
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[page:Integer offset] - (可选参数) 数组的偏移量，默认值为 0。<br /><br />
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使用基于列优先格式[link:https://en.wikipedia.org/wiki/Row-_and_column-major_order#Column-major_order column-major]的数组来设置该矩阵。
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</p>
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<h3>[method:this invert]()</h3>
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<p>
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将当前矩阵翻转为它的逆矩阵，使用 [link:https://en.wikipedia.org/wiki/Invertible_matrix#Analytic_solution analytic method] 解析方式。你不能对行或列为 0 的矩阵进行翻转，如果你尝试这样做，该方法将生成一个零矩阵。
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</p>
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<h3>[method:this getNormalMatrix]( [param:Matrix4 m] )</h3>
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<p>
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[page:Matrix4 m] - [page:Matrix4]<br /><br />
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将这个矩阵设置为给定矩阵的正规矩阵[link:https://en.wikipedia.org/wiki/Normal_matrix normal matrix]（左上角的3x3）。
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正规矩阵是矩阵[page:Matrix4 m]的逆矩阵[link:https://en.wikipedia.org/wiki/Invertible_matrix inverse] 的转置[link:https://en.wikipedia.org/wiki/Transpose transpose]。
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</p>
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<h3>[method:this identity]()</h3>
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<p>
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将此矩阵重置为3x3单位矩阵:
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</p>
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<math display="block">
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<mrow>
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<mo>[</mo>
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<mtable>
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<mtr>
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<mtd><mn>1</mn></mtd>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>0</mn></mtd>
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</mtr>
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<mtr>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>1</mn></mtd>
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<mtd><mn>0</mn></mtd>
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</mtr>
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<mtr>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>1</mn></mtd>
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</mtr>
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</mtable>
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<mo>]</mo>
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</mrow>
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</math>
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<h3>[method:this makeRotation]( [param:Float theta] )</h3>
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<p>
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[page:Float theta] — Rotation angle in radians. Positive values rotate counterclockwise.<br /><br />
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Sets this matrix as a 2D rotational transformation by [page:Float theta] radians.
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The resulting matrix will be:
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</p>
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<math display="block">
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<mrow>
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<mo>[</mo>
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<mtable>
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<mtr>
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<mtd>
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<mi>cos</mi>
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<mi>θ</mi>
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</mtd>
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<mtd>
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<mi>-sin</mi>
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<mi>θ</mi>
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</mtd>
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<mtd>
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<mn>0</mn>
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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mi>sin</mi>
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<mi>θ</mi>
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</mtd>
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<mtd>
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<mi>cos</mi>
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<mi>θ</mi>
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</mtd>
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<mtd>
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<mn>0</mn>
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</mtd>
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</mtr>
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<mtr>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>1</mn></mtd>
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</mtr>
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</mtable>
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<mo>]</mo>
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</mrow>
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</math>
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<h3>[method:this makeScale]( [param:Float x], [param:Float y] )</h3>
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<p>
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[page:Float x] - the amount to scale in the X axis.<br />
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[page:Float y] - the amount to scale in the Y axis.<br />
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Sets this matrix as a 2D scale transform:<br /><br />
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<math>
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<mrow>
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<mo>[</mo>
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<mtable>
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<mtr>
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<mtd><mi>x</mi></mtd>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>0</mn></mtd>
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</mtr>
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<mtr>
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<mtd><mn>0</mn></mtd>
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<mtd><mi>y</mi></mtd>
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<mtd><mn>0</mn></mtd>
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</mtr>
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<mtr>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>1</mn></mtd>
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</mtr>
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</mtable>
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<mo>]</mo>
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</mrow>
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</math>
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</p>
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<h3>[method:this makeTranslation]( [param:Vector2 v] )</h3>
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<h3>[method:this makeTranslation]( [param:Float x], [param:Float y] )</h3>
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<p>
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[page:Vector2 v] a translation transform from vector.<br />
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or<br />
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[page:Float x] - the amount to translate in the X axis.<br />
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[page:Float y] - the amount to translate in the Y axis.<br />
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Sets this matrix as a 2D translation transform:
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</p>
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<math display="block">
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<mrow>
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<mo>[</mo>
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<mtable>
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<mtr>
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<mtd><mn>1</mn></mtd>
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<mtd><mn>0</mn></mtd>
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<mtd><mi>x</mi></mtd>
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</mtr>
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<mtr>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>1</mn></mtd>
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<mtd><mi>y</mi></mtd>
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</mtr>
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<mtr>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>0</mn></mtd>
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<mtd><mn>1</mn></mtd>
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</mtr>
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</mtable>
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<mo>]</mo>
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</mrow>
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</math>
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<h3>[method:this multiply]( [param:Matrix3 m] )</h3>
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<p>将当前矩阵乘以矩阵[page:Matrix3 m]。</p>
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<h3>[method:this multiplyMatrices]( [param:Matrix3 a], [param:Matrix3 b] )</h3>
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<p>设置当前矩阵为矩阵[page:Matrix3 a] x 矩阵[page:Matrix3 b]。</p>
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<h3>[method:this multiplyScalar]( [param:Float s] )</h3>
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<p>当前矩阵所有的元素乘以该缩放值*s*</p>
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<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>
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<p>
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使用行优先 [link:https://en.wikipedia.org/wiki/Row-_and_column-major_order row-major] 的格式来设置该矩阵:
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</p>
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<math display="block">
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<mrow>
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<mo>[</mo>
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<mtable>
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<mtr>
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<mtd><mi>n11</mi></mtd>
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<mtd><mi>n12</mi></mtd>
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<mtd><mi>n13</mi></mtd>
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</mtr>
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<mtr>
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<mtd><mi>n21</mi></mtd>
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<mtd><mi>n22</mi></mtd>
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<mtd><mi>n23</mi></mtd>
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</mtr>
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<mtr>
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<mtd><mi>n31</mi></mtd>
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<mtd><mi>n32</mi></mtd>
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<mtd><mi>n33</mi></mtd>
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</mtr>
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</mtable>
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<mo>]</mo>
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</mrow>
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</math>
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<h3>[method:this premultiply]( [param:Matrix3 m] )</h3>
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<p>将矩阵[page:Matrix3 m]乘以当前矩阵。</p>
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<h3>[method:this setFromMatrix4]( [param:Matrix4 m] )</h3>
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<p>根据参数 [page:Matrix4 m] 左上 3x3 的矩阵值，设置当前矩阵的值。</p>
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<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>
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<p>
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[page:Float tx] - x偏移量<br />
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[page:Float ty] - y偏移量<br />
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[page:Float sx] - x方向的重复比例<br />
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[page:Float sy] - y方向的重复比例<br />
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[page:Float rotation] - 旋转, 弧度。Positive values rotate counterclockwise<br />
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[page:Float cx] - 旋转中心x<br />
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[page:Float cy] - 旋转中心y<br /><br />
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使用偏移，重复，旋转和中心点位置设置UV变换矩阵。
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</p>
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<h3>[method:Array toArray]( [param:Array array], [param:Integer offset] )</h3>
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<p>
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[page:Array array] - (可选参数) 存储矩阵元素的数组，如果未指定会创建一个新的数组。<br />
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[page:Integer offset] - (可选参数) 存放矩阵元素数组的偏移量。<br /><br />
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使用列优先[link:https://en.wikipedia.org/wiki/Row-_and_column-major_order#Column-major_order column-major]格式将此矩阵的元素写入数组中。
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</p>
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<h3>[method:this transpose]()</h3>
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<p>将该矩阵转置[link:https://en.wikipedia.org/wiki/Transpose Transposes]。</p>
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<h3>[method:this transposeIntoArray]( [param:Array array] )</h3>
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<p>
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[page:Array array] - 用于存储当前矩阵转置结果的数组。<br /><br />
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将当前矩阵的转置[link:https://en.wikipedia.org/wiki/Transpose Transposes]存入给定的数组 array 中，但不改变当前矩阵，
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并返回当前矩阵。
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</p>
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<h2>源码（Source）</h2>
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<p>
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[link:https://github.com/mrdoob/three.js/blob/master/src/[path].js src/[path].js]
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</p>
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</body>
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</html>
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