395 lines
15 KiB
HTML
395 lines
15 KiB
HTML
<!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>四维矩阵（[name]）</h1>
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<p class="desc">
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表示为一个 4x4 [link:https://en.wikipedia.org/wiki/Matrix_(mathematics) matrix].<br /><br />
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在3D计算机图形学中，4x4矩阵最常用的用法是作为一个变换矩阵[link:https://en.wikipedia.org/wiki/Transformation_matrix Transformation Matrix]。
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有关WebGL中使用的变换矩阵的介绍，请参阅本教程[link:http://www.opengl-tutorial.org/beginners-tutorials/tutorial-3-matrices this tutorial]。<br /><br />
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这使得表示三维空间中的一个点的向量[page:Vector3]通过乘以矩阵来进行转换，如平移、旋转、剪切、缩放、反射、正交或透视投影等。这就是把矩阵<em>应用</em>到向量上。<br /><br />
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任何3D物体[page:Object3D]都有三个关联的矩阵：
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<ul>
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<li>
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[page:Object3D.matrix]: 存储物体的本地变换。 这是对象相对于其父对象的变换。
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</li>
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<li>
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[page:Object3D.matrixWorld]: 对象的全局或世界变换。如果对象没有父对象，那么这与存储在矩阵[page:Object3D.matrix matrix]中的本地变换相同。
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</li>
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<li>
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[page:Object3D.modelViewMatrix]: 表示对象相坐标相对于摄像机空间坐标转换，
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一个对象的 modelViewMatrix 是物体世界变换矩阵乘以摄像机相对于世界空间变换矩阵的逆矩阵。
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</li>
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</ul>
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摄像机[page:Camera Cameras] 有两个额外的四维矩阵:
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<ul>
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<li>
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[page:Camera.matrixWorldInverse]: 视矩阵 - 摄像机世界坐标变换的逆矩阵。
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</li>
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<li>
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[page:Camera.projectionMatrix]: 表示将场景中的信息投影到裁剪空间。
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</li>
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</ul>
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注意：物体的正规矩阵 [page:Object3D.normalMatrix] 并不是一个4维矩阵，而是一个三维矩阵[page:Matrix3]。
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</p>
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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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设置[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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const m = new THREE.Matrix4();
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m.set( 11, 12, 13, 14,
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21, 22, 23, 24,
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31, 32, 33, 34,
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41, 42, 43, 44 );
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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, 41,
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12, 22, 32, 42,
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13, 23, 33, 43,
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14, 24, 34, 44 ];
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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>Extracting position, rotation and scale</h2>
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<p>
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There are several options available for extracting position, rotation and scale from a Matrix4.
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<ul>
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<li>
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[page:Vector3.setFromMatrixPosition]: can be used to extract the translation component.
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</li>
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<li>
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[page:Vector3.setFromMatrixScale]: can be used to extract the scale component.
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</li>
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<li>
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[page:Quaternion.setFromRotationMatrix], [page:Euler.setFromRotationMatrix] or [page:.extractRotation extractRotation] can be used to extract the rotation component.
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</li>
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<li>
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[page:.decompose decompose] can be used to extract position, rotation and scale all at once.
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</li>
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</ul>
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</p>
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<h2>构造器（Constructor）</h2>
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<h3>[name]()</h3>
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<p>
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创建并初始化一个4X4的单位矩阵[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:Matrix4 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 compose]( [param:Vector3 position], [param:Quaternion quaternion], [param:Vector3 scale] )</h3>
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<p>
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设置将该对象位置 [page:Vector3 position]，四元数[page:Quaternion quaternion] 和 缩放[page:Vector3 scale] 组合变换的矩阵。
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</p>
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<h3>[method:this copy]( [param:Matrix4 m] )</h3>
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<p>将矩阵[page:Matrix3 m]的元素[page:.elements elements]复制到当前矩阵中。</p>
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<h3>[method:this copyPosition]( [param:Matrix4 m] )</h3>
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<p>
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将给定矩阵[param:Matrix4 m] 的平移分量拷贝到当前矩阵中。
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</p>
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<h3>[method:null decompose]( [param:Vector3 position], [param:Quaternion quaternion], [param:Vector3 scale] )</h3>
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<p>
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将矩阵分解到给定的平移[page:Vector3 position] ,旋转 [page:Quaternion quaternion]，缩放[page:Vector3 scale]分量中。<br/><br/>
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Note: Not all matrices are decomposable in this way. For example, if an object has a non-uniformly scaled parent, then the object's world matrix may not be decomposable, and this method may not be appropriate.
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</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] 。<br /><br />
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基于这个的方法概述[link:http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm here]。
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</p>
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<h3>[method:Boolean equals]( [param:Matrix4 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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将矩阵的基向量[link:https://en.wikipedia.org/wiki/Basis_(linear_algebra) basis]提取到指定的3个轴向量中。
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如果矩阵如下：
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<code>
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a, b, c, d,
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e, f, g, h,
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i, j, k, l,
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m, n, o, p
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</code>
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然后x轴y轴z轴被设为：
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<code>
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xAxis = (a, e, i)
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yAxis = (b, f, j)
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zAxis = (c, g, k)
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</code>
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</p>
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<h3>[method:this extractRotation]( [param:Matrix4 m] )</h3>
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<p>
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将给定矩阵[page:Matrix4 m]的旋转分量提取到该矩阵的旋转分量中。
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</p>
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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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Inverts this matrix, using the [link:https://en.wikipedia.org/wiki/Invertible_matrix#Analytic_solution analytic method].
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You can not invert with a determinant of zero. If you attempt this, the method produces a zero matrix instead.
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</p>
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<h3>[method:Float getMaxScaleOnAxis]()</h3>
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<p>获取3个轴方向的最大缩放值。</p>
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<h3>[method:this identity]()</h3>
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<p>将当前矩阵重置为单位矩阵[link:https://en.wikipedia.org/wiki/Identity_matrix identity matrix]。</p>
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<h3>[method:this lookAt]( [param:Vector3 eye], [param:Vector3 center], [param:Vector3 up], )</h3>
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<p>
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构造一个旋转矩阵，从[page:Vector3 eye] 指向 [page:Vector3 center]，由向量 [param:Vector3 up] 定向。
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<!-- Constructs a rotation matrix, looking from [page:Vector3 eye] towards [page:Vector3 center]
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oriented by the [page:Vector3 up] vector.-->
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</p>
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<h3>[method:this makeRotationAxis]( [param:Vector3 axis], [param:Float theta] )</h3>
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<p>
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[page:Vector3 axis] — 旋转轴，需要被归一化。<br />
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[page:Float theta] — 旋转量（弧度）。<br /><br />
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设置当前矩阵为围绕轴 [page:Vector3 axis] 旋转量为 [page:Float theta]弧度。<br />
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这是一种有点争议但在数学上可以替代通过四元数[page:Quaternions]旋转的办法。 请参阅此处[link:https://www.gamedev.net/articles/programming/math-and-physics/do-we-really-need-quaternions-r1199 here]的讨论。
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</p>
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<h3>[method:this makeBasis]( [param:Vector3 xAxis], [param:Vector3 yAxis], [param:Vector3 zAxis] )</h3>
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<p>
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通过给定的三个向量设置该矩阵为基矩阵[link:https://en.wikipedia.org/wiki/Basis_(linear_algebra) basis]：
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<code>
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xAxis.x, yAxis.x, zAxis.x, 0,
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xAxis.y, yAxis.y, zAxis.y, 0,
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xAxis.z, yAxis.z, zAxis.z, 0,
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0, 0, 0, 1
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</code>
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</p>
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<h3>[method:this makePerspective]( [param:Float left], [param:Float right], [param:Float top], [param:Float bottom], [param:Float near], [param:Float far] )</h3>
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<p>
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创建一个透视投影矩阵[link:https://en.wikipedia.org/wiki/3D_projection#Perspective_projection perspective projection]。
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在引擎内部由[page:PerspectiveCamera.updateProjectionMatrix]()使用。
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</p>
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<h3>[method:this makeOrthographic]( [param:Float left], [param:Float right], [param:Float top], [param:Float bottom], [param:Float near], [param:Float far] )</h3>
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<p>
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创建一个正交投影矩阵[link:https://en.wikipedia.org/wiki/Orthographic_projection orthographic projection]。
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在引擎内部由[page:OrthographicCamera.updateProjectionMatrix]()使用。
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</p>
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<h3>[method:this makeRotationFromEuler]( [param:Euler euler] )</h3>
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<p>
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将传入的欧拉角转换为该矩阵的旋转分量(左上角的3x3矩阵)。
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矩阵的其余部分被设为单位矩阵。根据欧拉角[page:Euler euler]的旋转顺序[page:Euler.order order]，总共有六种可能的结果。
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详细信息，请参阅本页[link:https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix this page]。
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</p>
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<h3>[method:this makeRotationFromQuaternion]( [param:Quaternion q] )</h3>
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<p>
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将这个矩阵的旋转分量设置为四元数[page:Quaternion q]指定的旋转，如下链接所诉[link:https://en.wikipedia.org/wiki/Rotation_matrix#Quaternion here]。
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矩阵的其余部分被设为单位矩阵。因此，给定四元数[page:Quaternion q] = w + xi + yj + zk，得到的矩阵为:
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<code>
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1-2y²-2z² 2xy-2zw 2xz+2yw 0
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2xy+2zw 1-2x²-2z² 2yz-2xw 0
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2xz-2yw 2yz+2xw 1-2x²-2y² 0
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0 0 0 1
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</code>
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</p>
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<h3>[method:this makeRotationX]( [param:Float theta] )</h3>
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<p>
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[page:Float theta] — Rotation angle in radians.<br /><br />
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把该矩阵设置为绕x轴旋转弧度[page:Float theta] (θ)大小的矩阵。
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结果如下：
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<code>
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1 0 0 0
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0 cos(θ) -sin(θ) 0
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0 sin(θ) cos(θ) 0
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0 0 0 1
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</code>
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</p>
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<h3>[method:this makeRotationY]( [param:Float theta] )</h3>
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<p>
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[page:Float theta] — Rotation angle in radians.<br /><br />
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把该矩阵设置为绕Y轴旋转弧度[page:Float theta] (θ)大小的矩阵。
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结果如下：
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<code>
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cos(θ) 0 sin(θ) 0
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0 1 0 0
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-sin(θ) 0 cos(θ) 0
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0 0 0 1
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</code>
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</p>
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<h3>[method:this makeRotationZ]( [param:Float theta] )</h3>
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<p>
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[page:Float theta] — Rotation angle in radians.<br /><br />
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把该矩阵设置为绕z轴旋转弧度[page:Float theta] (θ)大小的矩阵。
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结果如下：
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<code>
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cos(θ) -sin(θ) 0 0
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sin(θ) cos(θ) 0 0
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0 0 1 0
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0 0 0 1
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</code>
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</p>
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<h3>[method:this makeScale]( [param:Float x], [param:Float y], [param:Float z] )</h3>
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<p>
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[page:Float x] - 在X轴方向的缩放比。<br />
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[page:Float y] - 在Y轴方向的缩放比。<br />
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[page:Float z] - 在Z轴方向的缩放比。<br /><br />
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将这个矩阵设置为缩放变换:
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<code>
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x, 0, 0, 0,
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0, y, 0, 0,
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0, 0, z, 0,
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0, 0, 0, 1
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</code>
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</p>
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<h3>[method:this makeShear]( [param:Float x], [param:Float y], [param:Float z] )</h3>
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<p>
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[page:Float x] - 在X轴上剪切的量。<br />
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[page:Float y] - 在Y轴上剪切的量。<br />
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[page:Float z] - 在Z轴上剪切的量。<br /><br />
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将此矩阵设置为剪切变换:
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<code>
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1, y, z, 0,
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x, 1, z, 0,
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x, y, 1, 0,
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0, 0, 0, 1
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</code>
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</p>
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<h3>[method:this makeTranslation]( [param:Float x], [param:Float y], [param:Float z] )</h3>
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<p>
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[page:Float x] - 在X轴上的平移量。<br />
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[page:Float y] - 在Y轴上的平移量。<br />
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[page:Float z] - 在Z轴上的平移量。<br /><br />
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设置该矩阵为平移变换：
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<code>
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1, 0, 0, x,
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0, 1, 0, y,
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0, 0, 1, z,
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0, 0, 0, 1
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</code>
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</p>
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<h3>[method:this multiply]( [param:Matrix4 m] )</h3>
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<p>将当前矩阵乘以矩阵[page:Matrix4 m]。</p>
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<h3>[method:this multiplyMatrices]( [param:Matrix4 a], [param:Matrix4 b] )</h3>
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<p>设置当前矩阵为矩阵[page:Matrix4 a] x 矩阵[page:Matrix4 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 premultiply]( [param:Matrix4 m] )</h3>
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<p>将矩阵[page:Matrix4 m]乘以当前矩阵。</p>
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<h3>[method:this scale]( [param:Vector3 v] )</h3>
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<p>将该矩阵的列向量乘以对应向量[page:Vector3 v]的分量。</p>
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<h3>[method:this set]( [param:Float n11], [param:Float n12], [param:Float n13], [param:Float n14], [param:Float n21], [param:Float n22], [param:Float n23], [param:Float n24], [param:Float n31], [param:Float n32], [param:Float n33], [param:Float n34], [param:Float n41], [param:Float n42], [param:Float n43], [param:Float n44] )</h3>
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<p>
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以行优先的格式将传入的数值设置给该矩阵中的元素[page:.elements elements]。
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</p>
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<h3>[method:this setFromMatrix3]( [param:Matrix3 m] )</h3>
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<p>Set the upper 3x3 elements of this matrix to the values of the Matrix3 [page:Matrix3 m].</p>
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<h3>[method:this setPosition]( [param:Vector3 v] )</h3>
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<h3>[method:this setPosition]( [param:Float x], [param:Float y], [param:Float z] ) // optional API</h3>
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<p>
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取传入参数[param:Vector3 v]中值设置该矩阵的位置分量，不影响该矩阵的其余部分——即，如果该矩阵当前为:
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<code>
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a, b, c, d,
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e, f, g, h,
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i, j, k, l,
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m, n, o, p
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</code>
|
||
变成:
|
||
<code>
|
||
a, b, c, v.x,
|
||
e, f, g, v.y,
|
||
i, j, k, v.z,
|
||
m, n, o, p
|
||
</code>
|
||
</p>
|
||
|
||
<h3>[method:Array toArray]( [param:Array array], [param:Integer offset] )</h3>
|
||
<p>
|
||
[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 />
|
||
[page:Integer offset] - (可选参数) 存放矩阵元素数组的偏移量。<br /><br />
|
||
|
||
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。
|
||
</p>
|
||
|
||
<h3>[method:this transpose]()</h3>
|
||
<p>将该矩阵转置[link:https://en.wikipedia.org/wiki/Transpose Transposes]。</p>
|
||
|
||
<h2>源码（Source）</h2>
|
||
|
||
<p>
|
||
[link:https://github.com/mrdoob/three.js/blob/master/src/[path].js src/[path].js]
|
||
</p>
|
||
</body>
|
||
</html>
|