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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 4x4
- [link:https://en.wikipedia.org/wiki/Matrix_(mathematics) matrix].<br /><br />
- The most common use of a 4x4 matrix in 3D computer graphics is as a
- [link:https://en.wikipedia.org/wiki/Transformation_matrix Transformation Matrix].
- For an introduction to transformation matrices as used in WebGL,
- check out
- [link:http://www.opengl-tutorial.org/beginners-tutorials/tutorial-3-matrices this tutorial].<br /><br />
- This allows a [page:Vector3] representing a point in 3D space to undergo
- transformations such as translation, rotation, shear, scale, reflection,
- orthogonal or perspective projection and so on, by being multiplied by the
- matrix. This is known as `applying` the matrix to the vector.<br /><br />
- Every [page:Object3D] has three associated Matrix4s:
- </p>
- <ul>
- <li>
- [page:Object3D.matrix]: This stores the local transform of the object.
- This is the object's transformation relative to its parent.
- </li>
- <li>
- [page:Object3D.matrixWorld]: The global or world transform of the
- object. If the object has no parent, then this is identical to the local
- transform stored in [page:Object3D.matrix matrix].
- </li>
- <li>
- [page:Object3D.modelViewMatrix]: This represents the object's
- transformation relative to the camera's coordinate system. An object's
- modelViewMatrix is the object's matrixWorld pre-multiplied by the
- camera's matrixWorldInverse.
- </li>
- </ul>
- [page:Camera Cameras] have three additional Matrix4s:
- <ul>
- <li>
- [page:Camera.matrixWorldInverse]: The view matrix - the inverse of the
- Camera's [page:Object3D.matrixWorld matrixWorld].
- </li>
- <li>
- [page:Camera.projectionMatrix]: Represents the information how to
- project the scene to clip space.
- </li>
- <li>
- [page:Camera.projectionMatrixInverse]: The inverse of projectionMatrix.
- </li>
- </ul>
- Note: [page:Object3D.normalMatrix] is not a Matrix4, but a [page:Matrix3].
- <h2>A Note on Row-Major and Column-Major Ordering</h2>
- <p>
- The constructor and [page:.set 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>
- const m = new THREE.Matrix4();
- m.set( 11, 12, 13, 14,
- 21, 22, 23, 24,
- 31, 32, 33, 34,
- 41, 42, 43, 44 );
- </code>
- will result in the [page:.elements elements] array containing:
- <code>
- m.elements = [ 11, 21, 31, 41,
- 12, 22, 32, 42,
- 13, 23, 33, 43,
- 14, 24, 34, 44 ];
- </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>Extracting position, rotation and scale</h2>
- <p>
- There are several options available for extracting position, rotation and
- scale from a Matrix4.
- </p>
- <ul>
- <li>
- [page:Vector3.setFromMatrixPosition]: can be used to extract the
- translation component.
- </li>
- <li>
- [page:Vector3.setFromMatrixScale]: can be used to extract the scale
- component.
- </li>
- <li>
- [page:Quaternion.setFromRotationMatrix],
- [page:Euler.setFromRotationMatrix] or [page:.extractRotation extractRotation]
- can be used to extract the rotation component from a pure (unscaled) matrix.
- </li>
- <li>
- [page:.decompose decompose] can be used to extract position, rotation
- and scale all at once.
- </li>
- </ul>
- <h2>Constructor</h2>
- <h3>[name]( [param:Number n11], [param:Number n12], [param:Number n13], [param:Number n14],
- [param:Number n21], [param:Number n22], [param:Number n23], [param:Number n24],
- [param:Number n31], [param:Number n32], [param:Number n33], [param:Number n34],
- [param:Number n41], [param:Number n42], [param:Number n43], [param:Number n44] )</h3>
- <p>
- Creates a 4x4 matrix with the given arguments in row-major order. If no arguments are provided, the constructor initializes
- the [name] to the 4x4 [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_order column-major] list of matrix values.
- </p>
- <h2>Methods</h2>
- <h3>[method:Matrix4 clone]()</h3>
- <p>
- Creates a new Matrix4 with identical [page:.elements elements] to this
- one.
- </p>
- <h3>
- [method:this compose]( [param:Vector3 position], [param:Quaternion quaternion], [param:Vector3 scale] )
- </h3>
- <p>
- Sets this matrix to the transformation composed of [page:Vector3 position],
- [page:Quaternion quaternion] and [page:Vector3 scale].
- </p>
- <h3>[method:this copy]( [param:Matrix4 m] )</h3>
- <p>
- Copies the [page:.elements elements] of matrix [page:Matrix4 m] into this
- matrix.
- </p>
- <h3>[method:this copyPosition]( [param:Matrix4 m] )</h3>
- <p>
- Copies the translation component of the supplied matrix [page:Matrix4 m]
- into this matrix's translation component.
- </p>
- <h3>
- [method:this decompose]( [param:Vector3 position], [param:Quaternion quaternion], [param:Vector3 scale] )
- </h3>
- <p>
- Decomposes this matrix into its [page:Vector3 position], [page:Quaternion quaternion]
- and [page:Vector3 scale] components.<br /><br />
- 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.
- </p>
- <h3>[method:Float determinant]()</h3>
- <p>
- Computes and returns the [link:https://en.wikipedia.org/wiki/Determinant determinant] of this matrix.<br /><br />
- Based on the method outlined
- [link:http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.html here].
- </p>
- <h3>[method:Boolean equals]( [param:Matrix4 m] )</h3>
- <p>Return true if this matrix and [page:Matrix4 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>
- <mtd><mi>d</mi></mtd>
- </mtr>
- <mtr>
- <mtd><mi>e</mi></mtd>
- <mtd><mi>f</mi></mtd>
- <mtd><mi>g</mi></mtd>
- <mtd><mi>h</mi></mtd>
- </mtr>
- <mtr>
- <mtd><mi>i</mi></mtd>
- <mtd><mi>j</mi></mtd>
- <mtd><mi>k</mi></mtd>
- <mtd><mi>l</mi></mtd>
- </mtr>
- <mtr>
- <mtd><mi>m</mi></mtd>
- <mtd><mi>n</mi></mtd>
- <mtd><mi>o</mi></mtd>
- <mtd><mi>p</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>
- <div 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>e</mi></mtd></mtr>
- <mtr><mtd style="height: 1rem"><mi>i</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>f</mi></mtd></mtr>
- <mtr><mtd style="height: 1rem"><mi>j</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>g</mi></mtd></mtr>
- <mtr><mtd style="height: 1rem"><mi>k</mi></mtd></mtr>
- </mtable>
- <mo>]</mo>
- </mrow>
- </math>
- </div>
- <h3>[method:this extractRotation]( [param:Matrix4 m] )</h3>
- <p>
- Extracts the rotation component of the supplied matrix [page:Matrix4 m]
- into this matrix's rotation component.
- </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 ) offset into the array. Default is
- 0.<br /><br />
- Sets the elements of this matrix based on an [page:Array 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:Float getMaxScaleOnAxis]()</h3>
- <p>Gets the maximum scale value of the 3 axes.</p>
- <h3>[method:this identity]()</h3>
- <p>
- Resets this matrix to the
- [link:https://en.wikipedia.org/wiki/Identity_matrix identity matrix].
- </p>
- <h3>
- [method:this lookAt]( [param:Vector3 eye], [param:Vector3 target], [param:Vector3 up] )
- </h3>
- <p>
- Constructs a rotation matrix, looking from [page:Vector3 eye] towards
- [page:Vector3 target] oriented by the [page:Vector3 up] vector.
- </p>
- <h3>
- [method:this makeRotationAxis]( [param:Vector3 axis], [param:Float theta] )
- </h3>
- <p>
- [page:Vector3 axis] — Rotation axis, should be normalized.<br />
- [page:Float theta] — Rotation angle in radians.<br /><br />
- Sets this matrix as rotation transform around [page:Vector3 axis] by
- [page:Float theta] radians.<br />
- This is a somewhat controversial but mathematically sound alternative to
- rotating via [page:Quaternion Quaternions]. See the discussion
- [link:https://www.gamedev.net/articles/programming/math-and-physics/do-we-really-need-quaternions-r1199 here].
- </p>
- <h3>
- [method:this makeBasis]( [param:Vector3 xAxis], [param:Vector3 yAxis], [param:Vector3 zAxis] )
- </h3>
- <p>
- Set this to the [link:https://en.wikipedia.org/wiki/Basis_(linear_algebra) basis]
- matrix consisting of the three provided basis vectors:
- </p>
- <math display="block">
- <mrow>
- <mo>[</mo>
- <mtable>
- <mtr>
- <mtd><mi>xAxis.x</mi></mtd>
- <mtd><mi>yAxis.x</mi></mtd>
- <mtd><mi>zAxis.x</mi></mtd>
- <mtd><mn>0</mn></mtd>
- </mtr>
- <mtr>
- <mtd><mi>xAxis.y</mi></mtd>
- <mtd><mi>yAxis.y</mi></mtd>
- <mtd><mi>zAxis.y</mi></mtd>
- <mtd><mn>0</mn></mtd>
- </mtr>
- <mtr>
- <mtd><mi>xAxis.z</mi></mtd>
- <mtd><mi>yAxis.z</mi></mtd>
- <mtd><mi>zAxis.z</mi></mtd>
- <mtd><mn>0</mn></mtd>
- </mtr>
- <mtr>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>1</mn></mtd>
- </mtr>
- </mtable>
- <mo>]</mo>
- </mrow>
- </math>
- <h3>
- [method:this makePerspective]( [param:Float left], [param:Float right], [param:Float top], [param:Float bottom], [param:Float near], [param:Float far] )
- </h3>
- <p>
- Creates a
- [link:https://en.wikipedia.org/wiki/3D_projection#Perspective_projection perspective projection]
- matrix. This is used internally by
- [page:PerspectiveCamera.updateProjectionMatrix]()
- </p>
- <h3>
- [method:this makeOrthographic]( [param:Float left], [param:Float right], [param:Float top], [param:Float bottom], [param:Float near], [param:Float far] )
- </h3>
- <p>
- Creates an [link:https://en.wikipedia.org/wiki/Orthographic_projection orthographic projection]
- matrix. This is used internally by
- [page:OrthographicCamera.updateProjectionMatrix]().
- </p>
- <h3>[method:this makeRotationFromEuler]( [param:Euler euler] )</h3>
- <p>
- Sets the rotation component (the upper left 3x3 matrix) of this matrix to
- the rotation specified by the given [page:Euler Euler Angle]. The rest of
- the matrix is set to the identity. Depending on the [page:Euler.order order]
- of the [page:Euler euler], there are six possible outcomes. See
- [link:https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix this page] for a complete list.
- </p>
- <h3>[method:this makeRotationFromQuaternion]( [param:Quaternion q] )</h3>
- <p>
- Sets the rotation component of this matrix to the rotation specified by
- [page:Quaternion q], as outlined
- [link:https://en.wikipedia.org/wiki/Rotation_matrix#Quaternion here]. The
- rest of the matrix is set to the identity. So, given [page:Quaternion q] =
- w + xi + yj + zk, the resulting matrix will be:
- </p>
- <math display="block">
- <mrow>
- <mo>[</mo>
- <mtable>
- <mtr>
- <mtd>
- <mn>1</mn>
- <mo>-</mo>
- <mn>2</mn>
- <msup>
- <mi>y</mi>
- <mn>2</mn>
- </msup>
- <mo>-</mo>
- <mn>2</mn>
- <msup>
- <mi>z</mi>
- <mn>2</mn>
- </msup>
- </mtd>
- <mtd>
- <mn>2</mn>
- <mi>x</mi>
- <mi>y</mi>
- <mo>-</mo>
- <mn>2</mn>
- <mi>z</mi>
- <mi>w</mi>
- </mtd>
- <mtd>
- <mn>2</mn>
- <mi>x</mi>
- <mi>z</mi>
- <mo>+</mo>
- <mn>2</mn>
- <mi>y</mi>
- <mi>w</mi>
- </mtd>
- <mtd>
- <mn>0</mn>
- </mtd>
- </mtr>
- <mtr>
- <mtd>
- <mn>2</mn>
- <mi>x</mi>
- <mi>y</mi>
- <mo>+</mo>
- <mn>2</mn>
- <mi>z</mi>
- <mi>w</mi>
- </mtd>
- <mtd>
- <mn>1</mn>
- <mo>-</mo>
- <mn>2</mn>
- <msup>
- <mi>x</mi>
- <mn>2</mn>
- </msup>
- <mo>-</mo>
- <mn>2</mn>
- <msup>
- <mi>z</mi>
- <mn>2</mn>
- </msup>
- </mtd>
- <mtd>
- <mn>2</mn>
- <mi>y</mi>
- <mi>z</mi>
- <mo>-</mo>
- <mn>2</mn>
- <mi>x</mi>
- <mi>w</mi>
- </mtd>
- <mtd>
- <mn>0</mn>
- </mtd>
- </mtr>
- <mtr>
- <mtd>
- <mn>2</mn>
- <mi>x</mi>
- <mi>z</mi>
- <mo>-</mo>
- <mn>2</mn>
- <mi>y</mi>
- <mi>w</mi>
- </mtd>
- <mtd>
- <mn>2</mn>
- <mi>y</mi>
- <mi>z</mi>
- <mo>+</mo>
- <mn>2</mn>
- <mi>x</mi>
- <mi>w</mi>
- </mtd>
- <mtd>
- <mn>1</mn>
- <mo>-</mo>
- <mn>2</mn>
- <msup>
- <mi>x</mi>
- <mn>2</mn>
- </msup>
- <mo>-</mo>
- <mn>2</mn>
- <msup>
- <mi>y</mi>
- <mn>2</mn>
- </msup>
- </mtd>
- <mtd>
- <mn>0</mn>
- </mtd>
- </mtr>
- <mtr>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>1</mn></mtd>
- </mtr>
- </mtable>
- <mo>]</mo>
- </mrow>
- </math>
- <h3>[method:this makeRotationX]( [param:Float theta] )</h3>
- <p>
- [page:Float theta] — Rotation angle in radians.<br /><br />
- Sets this matrix as a rotational transformation around the X axis by
- [page:Float theta] (θ) radians. The resulting matrix will be:
- </p>
- <math display="block">
- <mrow>
- <mo>[</mo>
- <mtable>
- <mtr>
- <mtd><mn>1</mn></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- </mtr>
- <mtr>
- <mtd>
- <mn>0</mn>
- </mtd>
- <mtd>
- <mi>cos</mi>
- <mi>θ</mi>
- </mtd>
- <mtd>
- <mo>-</mo>
- <mi>sin</mi>
- <mi>θ</mi>
- </mtd>
- <mtd>
- <mn>0</mn>
- </mtd>
- </mtr>
- <mtr>
- <mtd>
- <mn>0</mn>
- </mtd>
- <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>0</mn></mtd>
- <mtd><mn>1</mn></mtd>
- </mtr>
- </mtable>
- <mo>]</mo>
- </mrow>
- </math>
- <h3>[method:this makeRotationY]( [param:Float theta] )</h3>
- <p>
- [page:Float theta] — Rotation angle in radians.<br /><br />
- Sets this matrix as a rotational transformation around the Y axis by
- [page:Float theta] (θ) radians. The resulting matrix will be:
- </p>
- <math display="block">
- <mrow>
- <mo>[</mo>
- <mtable>
- <mtr>
- <mtd>
- <mi>cos</mi>
- <mi>θ</mi>
- </mtd>
- <mtd>
- <mn>0</mn>
- </mtd>
- <mtd>
- <mi>sin</mi>
- <mi>θ</mi>
- </mtd>
- <mtd>
- <mn>0</mn>
- </mtd>
- </mtr>
- <mtr>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>1</mn></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- </mtr>
- <mtr>
- <mtd>
- <mo>-</mo>
- <mi>sin</mi>
- <mi>θ</mi>
- </mtd>
- <mtd>
- <mn>0</mn>
- </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>0</mn></mtd>
- <mtd><mn>1</mn></mtd>
- </mtr>
- </mtable>
- <mo>]</mo>
- </mrow>
- </math>
- <h3>[method:this makeRotationZ]( [param:Float theta] )</h3>
- <p>
- [page:Float theta] — Rotation angle in radians.<br /><br />
- Sets this matrix as a rotational transformation around the Z axis by
- [page:Float theta] (θ) radians. The resulting matrix will be:
- </p>
-
- <math display="block">
- <mrow>
- <mo>[</mo>
- <mtable>
- <mtr>
- <mtd>
- <mi>cos</mi>
- <mi>θ</mi>
- </mtd>
- <mtd>
- <mo>-</mo>
- <mi>sin</mi>
- <mi>θ</mi>
- </mtd>
- <mtd>
- <mn>0</mn>
- </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>
- <mtd>
- <mn>0</mn>
- </mtd>
- </mtr>
- <mtr>
- <mtd><mn>0</mn></mtd>
- <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>0</mn></mtd>
- <mtd><mn>1</mn></mtd>
- </mtr>
- </mtable>
- <mo>]</mo>
- </mrow>
- </math>
- <h3>
- [method:this makeScale]( [param:Float x], [param:Float y], [param:Float z] )
- </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 />
- [page:Float z] - the amount to scale in the Z axis.<br /><br />
- Sets this matrix as 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>
- <mtd><mn>0</mn></mtd>
- </mtr>
- <mtr>
- <mtd><mn>0</mn></mtd>
- <mtd><mi>y</mi></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- </mtr>
- <mtr>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mi>z</mi></mtd>
- <mtd><mn>0</mn></mtd>
- </mtr>
- <mtr>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>1</mn></mtd>
- </mtr>
- </mtable>
- <mo>]</mo>
- </mrow>
- </math>
- <h3>
- [method:this makeShear]( [param:Float xy], [param:Float xz], [param:Float yx],
- [param:Float yz], [param:Float zx], [param:Float zy] )
- </h3>
- <p>
- [page:Float xy] - the amount to shear X by Y.<br />
- [page:Float xz] - the amount to shear X by Z.<br />
- [page:Float yx] - the amount to shear Y by X.<br />
- [page:Float yz] - the amount to shear Y by Z.<br />
- [page:Float zx] - the amount to shear Z by X.<br />
- [page:Float zy] - the amount to shear Z by Y.<br /><br />
- Sets this matrix as a shear transform:
- </p>
- <math display="block">
- <mrow>
- <mo>[</mo>
- <mtable>
- <mtr>
- <mtd><mn>1</mn></mtd>
- <mtd><mi>y</mi><mi>x</mi></mtd>
- <mtd><mi>z</mi><mi>x</mi></mtd>
- <mtd><mn>0</mn></mtd>
- </mtr>
- <mtr>
- <mtd><mi>x</mi><mi>y</mi></mtd>
- <mtd><mn>1</mn></mtd>
- <mtd><mi>z</mi><mi>y</mi></mtd>
- <mtd><mn>0</mn></mtd>
- </mtr>
- <mtr>
- <mtd><mi>x</mi><mi>z</mi></mtd>
- <mtd><mi>y</mi><mi>z</mi></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>0</mn></mtd>
- <mtd><mn>1</mn></mtd>
- </mtr>
- </mtable>
- <mo>]</mo>
- </mrow>
- </math>
- <h3>[method:this makeTranslation]( [param:Vector3 v] )</h3>
- <h3>
- [method:this makeTranslation]( [param:Float x], [param:Float y], [param:Float z] ) // optional API
- </h3>
- <p>
- Sets this matrix as a translation transform from vector [page:Vector3 v], or numbers [page:Float x], [page:Float y] and [page:Float z]:
- </p>
- <math display="block">
- <mrow>
- <mo>[</mo>
- <mtable>
- <mtr>
- <mtd><mn>1</mn></mtd>
- <mtd><mn>0</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><mn>0</mn></mtd>
- <mtd><mi>y</mi></mtd>
- </mtr>
- <mtr>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>0</mn></mtd>
- <mtd><mn>1</mn></mtd>
- <mtd><mi>z</mi></mtd>
- </mtr>
- <mtr>
- <mtd><mn>0</mn></mtd>
- <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:Matrix4 m] )</h3>
- <p>Post-multiplies this matrix by [page:Matrix4 m].</p>
- <h3>
- [method:this multiplyMatrices]( [param:Matrix4 a], [param:Matrix4 b] )
- </h3>
- <p>Sets this matrix to [page:Matrix4 a] x [page:Matrix4 b].</p>
- <h3>[method:this multiplyScalar]( [param:Float s] )</h3>
- <p>
- Multiplies every component of the matrix by a scalar value [page:Float s].
- </p>
- <h3>[method:this premultiply]( [param:Matrix4 m] )</h3>
- <p>Pre-multiplies this matrix by [page:Matrix4 m].</p>
- <h3>[method:this scale]( [param:Vector3 v] )</h3>
- <p>Multiplies the columns of this matrix by vector [page:Vector3 v].</p>
- <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>
- <p>
- Set the [page:.elements elements] of this matrix to the supplied row-major
- values [page:Float n11], [page:Float n12], ... [page:Float n44].
- </p>
- <h3>[method:this setFromMatrix3]( [param:Matrix3 m] )</h3>
- <p>
- Set the upper 3x3 elements of this matrix to the values of the Matrix3
- [page:Matrix3 m].
- </p>
- <h3>[method:this setPosition]( [param:Vector3 v] )</h3>
- <h3>
- [method:this setPosition]( [param:Float x], [param:Float y], [param:Float z] ) // optional API
- </h3>
- <p>
- Sets the position component for this matrix from vector [page:Vector3 v],
- without affecting the rest of the matrix - i.e. if the matrix is
- currently:
- </p>
- <math display="block">
- <mrow>
- <mo>[</mo>
- <mtable>
- <mtr>
- <mtd><mi>a</mi></mtd>
- <mtd><mi>b</mi></mtd>
- <mtd><mi>c</mi></mtd>
- <mtd><mi>d</mi></mtd>
- </mtr>
- <mtr>
- <mtd><mi>e</mi></mtd>
- <mtd><mi>f</mi></mtd>
- <mtd><mi>g</mi></mtd>
- <mtd><mi>h</mi></mtd>
- </mtr>
- <mtr>
- <mtd><mi>i</mi></mtd>
- <mtd><mi>j</mi></mtd>
- <mtd><mi>k</mi></mtd>
- <mtd><mi>l</mi></mtd>
- </mtr>
- <mtr>
- <mtd><mi>m</mi></mtd>
- <mtd><mi>n</mi></mtd>
- <mtd><mi>o</mi></mtd>
- <mtd><mi>p</mi></mtd>
- </mtr>
- </mtable>
- <mo>]</mo>
- </mrow>
- </math>
- <p>This becomes:</p>
- <math display="block">
- <mrow>
- <mo>[</mo>
- <mtable>
- <mtr>
- <mtd><mi>a</mi></mtd>
- <mtd><mi>b</mi></mtd>
- <mtd><mi>c</mi></mtd>
- <mtd><mi>v.x</mi></mtd>
- </mtr>
- <mtr>
- <mtd><mi>e</mi></mtd>
- <mtd><mi>f</mi></mtd>
- <mtd><mi>g</mi></mtd>
- <mtd><mi>v.y</mi></mtd>
- </mtr>
- <mtr>
- <mtd><mi>i</mi></mtd>
- <mtd><mi>j</mi></mtd>
- <mtd><mi>k</mi></mtd>
- <mtd><mi>v.z</mi></mtd>
- </mtr>
- <mtr>
- <mtd><mi>m</mi></mtd>
- <mtd><mi>n</mi></mtd>
- <mtd><mi>o</mi></mtd>
- <mtd><mi>p</mi></mtd>
- </mtr>
- </mtable>
- <mo>]</mo>
- </mrow>
- </math>
- <h3>
- [method:Array toArray]( [param:Array array], [param:Integer offset] )
- </h3>
- <p>
- [page:Array array] - (optional) array to store the resulting vector in.<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 transpose]()</h3>
- <p>
- [link:https://en.wikipedia.org/wiki/Transpose Transposes] this matrix.
- </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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