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@@ -15,25 +15,33 @@
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<h2>Example</h2>
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- <code>// Simple rig for rotating around 3 axes
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-
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- var m = new THREE.Matrix4();
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-
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- var m1 = new THREE.Matrix4();
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- var m2 = new THREE.Matrix4();
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- var m3 = new THREE.Matrix4();
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+ <code>
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+var m = new Matrix4();
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+ </code>
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- var alpha = 0;
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- var beta = Math.PI;
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- var gamma = Math.PI/2;
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+ <h2>A Note on Row-Major and Column-Major Ordering</h2>
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+ <div>
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+ The [page:set]() method takes arguments in [link:https://en.wikipedia.org/wiki/Row-_and_column-major_order#Column-major_order row-major]
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+ order, while internally they are stored in the [page:elements] array in column-major order.<br /><br />
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- m1.makeRotationX( alpha );
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- m2.makeRotationY( beta );
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- m3.makeRotationZ( gamma );
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+ This means that calling
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+ <code>
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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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- m.multiplyMatrices( m1, m2 );
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- m.multiply( m3 );
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</code>
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+ will result in the elements array containing:
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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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+ </code>
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+ and internally all calculations are performed using column-major ordering. However, as the actual ordering
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+ makes no difference mathematically and most people are used to thinking about matrices in row-major order,
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+ the rest of this document show matrices in row-major order. Just bear in mind that if you are reading the source
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+ code, you'll have to take the transpose of the matrices outlined here to make sense of the calculations.
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+ </div>
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<h2>Constructor</h2>
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@@ -64,14 +72,12 @@
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-
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-
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<h2>Methods</h2>
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<h3>[method:Array applyToBuffer]( [page:ArrayBuffer buffer], [page:Number offset], [page:Number length] )</h3>
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<div>
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[page:Array buffer] - An [link:https://developer.mozilla.org/en/docs/Web/JavaScript/Reference/Global_Objects/ArrayBuffer ArrayBuffer]
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- of floats in the form [vector1x, vector1y, vector1z, vector2x, vector2y, vector2z, ...], that represent 3D vectors.<br />>
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+ of floats in the form [vector1x, vector1y, vector1z, vector2x, vector2y, vector2z, ...], that represent 3D vectors.<br />
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[page:Number offset] - (optional) index in the array of the first vector's x component. Default is 0.<br />
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[page:Number length] - (optional) index in the array of the last vector's z component.
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Default is the last element in the array.<br /><br />
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@@ -83,7 +89,7 @@
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<h3>[method:Array applyToVector3Array]( [page:Array array], [page:Number offset], [page:Number length] )</h3>
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<div>
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[page:Array array] - An array of floats in the form [vector1x, vector1y, vector1z, vector2x, vector2y, vector2z, ...],
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- that represent 3D vectors.<br />>
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+ that represent 3D vectors.<br />
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[page:Number offset] - (optional) index in the array of the first vector's x component. Default is 0.<br />
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[page:Number length] - (optional) index in the array of the last vector's z component.
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Default is the last element in the array.<br /><br />
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@@ -94,9 +100,13 @@
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<h3>[method:Matrix4 clone]()</h3>
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<div>Creates a new Matrix4 and with identical elements to this one.</div>
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- <h3>[method:Matrix4 compose]( [page:Vector3 translation], [page:Quaternion quaternion], [page:Vector3 scale] )</h3>
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+ <h3>[method:Matrix4 compose]( [page:Vector3 position], [page:Quaternion quaternion], [page:Vector3 scale] )</h3>
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<div>
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- Sets this matrix to the transformation composed of [page:Vector3 translation], [page:Quaternion quaternion] and [page:Vector3 scale].
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+ Sets this matrix to the transformation composed of [page:Vector3 position],
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+ [page:Quaternion quaternion] and [page:Vector3 scale]. Internally this calls
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+ [page:.makeRotationFromQuaternion makeRotationFromQuaternion]( [page:Quaternion quaternion] )
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+ followed by [page:.scale scale]( [page:Vector3 scale] ), then finally
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+ [page:.setPosition setPosition]( [page:Vector3 position] ).
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</div>
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<h3>[method:Matrix4 copy]( [page:Matrix4 m] )</h3>
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@@ -104,200 +114,270 @@
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<h3>[method:Matrix4 copyPosition]( [page:Matrix4 m] )</h3>
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<div>
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- Copies the translation component of the supplied matrix *m* into this matrix's translation component.
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+ Copies the translation component of the supplied matrix [page:Matrix4 m] into this
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+ matrix's translation component.
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</div>
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- <h3>[method:null decompose]( [page:Vector3 translation], [page:Quaternion quaternion], [page:Vector3 scale] )</h3>
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+ <h3>[method:null decompose]( [page:Vector3 position], [page:Quaternion quaternion], [page:Vector3 scale] )</h3>
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<div>
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- Decomposes this matrix into the *translation*, *quaternion* and *scale* components.
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+ Decomposes this matrix into it's [page:Vector3 position], [page:Quaternion quaternion] and
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+ [page:Vector3 scale] components.
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</div>
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+ <h3>[method:Float determinant]()</h3>
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<h3>[method:Float determinant]()</h3>
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<div>
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- Computes and returns the determinant of this matrix.<br />
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+ Computes and returns the
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+ [link:https://en.wikipedia.org/wiki/Determinant determinant] of this matrix.<br /><br />
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+
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Based on [link:http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm]
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</div>
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<h3>[method:Boolean equals]( [page:Matrix4 m] )</h3>
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- <div>Return true if this and [page:Matrix4 m] are equals.</div>
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+ <div>Return true if this and [page:Matrix4 m] are equal.</div>
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<h3>[method:Matrix4 extractBasis]( [page:Vector3 xAxis], [page:Vector3 yAxis], [page:Vector3 zAxis] )</h3>
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<div>
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- Extracts basis of into the three axis vectors provided. Returns the current matrix.
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+ Extracts the [link:https://en.wikipedia.org/wiki/Basis_(linear_algebra) basis] of this
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+ matrix into the three axis vectors provided.
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</div>
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<h3>[method:Matrix4 extractRotation]( [page:Matrix4 m] )</h3>
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<div>
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- Extracts the rotation of the supplied matrix *m* into this matrix rotation component.
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+ Extracts the rotation component of the supplied matrix [page:Matrix4 m] into this matrix's
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+ rotation component.
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</div>
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<h3>[method:Matrix4 fromArray]( [page:Array array], [page:Integer offset] )</h3>
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<div>
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- array -- [page:Array] The array to read the elements from.<br />
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- offset -- [page:Integer] optional offset into the array. Default is 0.
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- </div>
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- <div>
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- Sets the elements of this matrix based on an array in column-major format.
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+ [page:Array array] - the array to read the elements from.<br />
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+ [page:Integer offset] - ( optional ) offset into the array. Default is 0.<br /><br />
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+
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+ Sets the elements of this matrix based on an [page:Array array] in
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+ [link:https://en.wikipedia.org/wiki/Row-_and_column-major_order#Column-major_order column-major] format.
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</div>
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- <h3>[method:Matrix4 getInverse]( [page:Matrix4 m] )</h3>
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+ <h3>[method:Matrix4 getInverse]( [page:Matrix4 m], [page:Boolean throwOnDegenerate] )</h3>
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<div>
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- Sets this matrix to the inverse of matrix *m*.<br />
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- Based on [link:http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm].
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+ [page:Matrix4 m] - the matrix to take the inverse of.<br />
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+ [page:Boolean throwOnDegenerate] - (optional) If true, throw an error if the matrix is degenerate (not invertible).<br /><br />
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+
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+ Set this matrix to the [link:https://en.wikipedia.org/wiki/Invertible_matrix inverse] of the passed matrix [page:Matrix4 m],
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+ using the method outlined [link:http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm here].
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+
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+ If [page:Boolean throwOnDegenerate] is not set and the matrix is invertible, set this to the 4x4 identity matrix.
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</div>
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+
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<h3>[method:Float getMaxScaleOnAxis]()</h3>
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- <div>
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- Gets the maximum scale value of the 3 axes.
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- </div>
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+ <div>Gets the maximum scale value of the 3 axes.</div>
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<h3>[method:Matrix4 identity]()</h3>
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- <div>
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- Resets this matrix to identity.
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- </div>
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+ <div>Resets this matrix to [link:https://en.wikipedia.org/wiki/Identity_matrix identity matrix].</div>
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<h3>[method:Matrix4 lookAt]( [page:Vector3 eye], [page:Vector3 center], [page:Vector3 up], )</h3>
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<div>
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- Constructs a rotation matrix, looking from *eye* towards *center* with defined *up* vector.
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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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</div>
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<h3>[method:Matrix4 makeRotationAxis]( [page:Vector3 axis], [page:Float theta] )</h3>
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<div>
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- axis — Rotation axis, should be normalized.
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- theta — Rotation angle in radians.
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- </div>
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- <div>
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- Sets this matrix as rotation transform around *axis* by *angle* radians.<br />
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- Based on [link:http://www.gamedev.net/reference/articles/article1199.asp].
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+ [page:Vector3 axis] — Rotation axis, should be normalized.<br />
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+ [page:Float theta] — Rotation angle in radians.<br /><br />
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+
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+ Sets this matrix as rotation transform around [page:Vector3 axis] by [page:Float theta] radians.<br />
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+
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+ This is a somewhat controversial but mathematically sound alternative to rotating via [page:Quaternions].
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+ [link:http://www.gamedev.net/reference/articles/article1199.asp].
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</div>
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<h3>[method:Matrix4 makeBasis]( [page:Vector3 xAxis], [page:Vector3 yAxis], [page:Vector3 zAxis] )</h3>
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<div>
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- Creates the basis matrix consisting of the three provided axis vectors. Returns the current matrix.
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+ Creates the [link:https://en.wikipedia.org/wiki/Basis_(linear_algebra) basis] matrix consisting
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+ of the three provided basis vectors.
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</div>
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<h3>[method:Matrix4 makeFrustum]( [page:Float left], [page:Float right], [page:Float bottom], [page:Float top], [page:Float near], [page:Float far] )</h3>
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<div>
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- Creates a [page:Frustum frustum] matrix.
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+ Creates a matrix representing a [link:https://en.wikipedia.org/wiki/Frustum frustum].
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+ This is used internally by [page:PerspectiveCamera.updateProjectionMatrix]()
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</div>
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<h3>[method:Matrix4 makeOrthographic]( [page:Float left], [page:Float right], [page:Float top], [page:Float bottom], [page:Float near], [page:Float far] )</h3>
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<div>
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- Creates an orthographic projection matrix.
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+ Creates an [link:https://en.wikipedia.org/wiki/Orthographic_projection orthographic projection] matrix.
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+ This is used internally by [page:OrthographicCamera.updateProjectionMatrix]().
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</div>
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<h3>[method:Matrix4 makePerspective]( [page:Float fov], [page:Float aspect], [page:Float near], [page:Float far] )</h3>
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<div>
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- Creates a perspective projection matrix.
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+ Creates a [link:https://en.wikipedia.org/wiki/3D_projection#Perspective_projection perspective projection] matrix.
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+
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</div>
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<h3>[method:Matrix4 makeRotationFromEuler]( [page:Euler euler] )</h3>
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<div>
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- euler — Rotation vector followed by order of rotations, e.g., "XYZ".
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- </div>
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- <div>
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- Sets the rotation submatrix of this matrix to the rotation specified by Euler angles, the rest of the matrix is identity.<br />
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- Default order is *"XYZ"*.
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+ Sets the rotation component of this matrix to the rotation specified by the given [page:Euler Euler Angle].
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+ The rest of the matrix is set to the identity.
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</div>
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<h3>[method:Matrix4 makeRotationFromQuaternion]( [page:Quaternion q] )</h3>
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<div>
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- Sets the rotation submatrix of this matrix to the rotation specified by *q*. The rest of the matrix is identity.
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+ Sets the rotation component of this matrix to the rotation specified by [page:Quaternion q].
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+ The rest of the matrix is set to the identity.
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</div>
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<h3>[method:Matrix4 makeRotationX]( [page:Float theta] )</h3>
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<div>
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- theta — Rotation angle in radians.
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- </div>
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- <div>
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- Sets this matrix as rotation transform around x axis by *theta* radians.
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+ [page:Float theta] — Rotation angle in radians.<br /><br />
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+
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+ Sets this matrix as a rotational transformation around the X axis by [page:Float theta] (θ) radians.
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+ The resulting matrix will be:
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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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</div>
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<h3>[method:Matrix4 makeRotationY]( [page:Float theta] )</h3>
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<div>
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- theta — Rotation angle in radians.
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- </div>
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- <div>
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- Sets this matrix as rotation transform around y axis by *theta* radians.
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+ [page:Float theta] — Rotation angle in radians.<br /><br />
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+
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+ Sets this matrix as a rotational transformation around the Y axis by [page:Float theta] (θ) radians.
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+ The resulting matrix will be:
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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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</div>
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<h3>[method:Matrix4 makeRotationZ]( [page:Float theta] )</h3>
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<div>
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- theta — Rotation angle in radians.
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- </div>
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- <div>
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- Sets this matrix as rotation transform around z axis by *theta* radians.
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+ [page:Float theta] — Rotation angle in radians.<br /><br />
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+
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+ Sets this matrix as a rotational transformation around the Z axis by [page:Float theta] (θ) radians.
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+ The resulting matrix will be:
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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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</div>
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<h3>[method:Matrix4 makeScale]( [page:Float x], [page:Float y], [page:Float z] )</h3>
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<div>
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- Sets this matrix as scale transform.
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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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+ [page:Float z] - the amount to scale in the Z axis.<br /><br />
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+
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+ Sets this matrix as scale transform:
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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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</div>
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<h3>[method:Matrix4 makeShear]( [page:Float x], [page:Float y], [page:Float z] )</h3>
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<div>
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- Sets this matrix as shear transform.
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+ [page:Float x] - the amount to shear in the X axis.<br />
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+ [page:Float y] - the amount to shear in the Y axis.<br />
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+ [page:Float z] - the amount to shear in the Z axis.<br /><br />
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+
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+ Sets this matrix as a shear transform:
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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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</div>
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<h3>[method:Matrix4 makeTranslation]( [page:Float x], [page:Float y], [page:Float z] )</h3>
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<div>
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- Sets this matrix as translation transform.
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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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+ [page:Float z] - the amount to translate in the Z axis.<br /><br />
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+
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+ Sets this matrix as a translation transform:
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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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</div>
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<h3>[method:Matrix4 multiply]( [page:Matrix4 m] )</h3>
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- <div>
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- Post-multiplies this matrix by *m*.
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- </div>
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+ <div>Post-multiplies this matrix by [page:Matrix4 m].</div>
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<h3>[method:Matrix4 multiplyMatrices]( [page:Matrix4 a], [page:Matrix4 b] )</h3>
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- <div>
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- Sets this matrix to *a x b*.
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- </div>
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+ <div>Sets this matrix to [page:Matrix4 a] x [page:Matrix4 b].</div>
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<h3>[method:Matrix4 multiplyScalar]( [page:Float s] )</h3>
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- <div>
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- Multiplies every component of the matrix by a scalar value *s*.
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- </div>
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+ <div>Multiplies every component of the matrix by a scalar value [page:Float s].</div>
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<h3>[method:Matrix4 multiplyToArray]( [page:Matrix4 a], [page:Matrix4 b], [page:Array r] )</h3>
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<div>
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- Sets this matrix to *a x b* and stores the result into the flat array *r*.<br />
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- *r* can be either a regular Array or a TypedArray.
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+ Sets this matrix to [page:Matrix4 a] x [page:Matrix4 b] and stores the result into the flat array [page:Array r],
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+ in [link:https://en.wikipedia.org/wiki/Row-_and_column-major_order#Column-major_order column-major] order.
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+
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+ [page:Array r] can be either a regular Array or a [link:https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays TypedArray].
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</div>
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<h3>[method:Matrix4 premultiply]( [page:Matrix4 m] )</h3>
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- <div>
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- Pre-multiplies this matrix by *m*.
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- </div>
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+ <div>Pre-multiplies this matrix by [page:Matrix4 m].</div>
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<h3>[method:Matrix4 scale]( [page:Vector3 v] )</h3>
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- <div>
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- Multiplies the columns of this matrix by vector *v*.
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- </div>
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+ <div>Multiplies the columns of this matrix by vector [page:Vector3 v].</div>
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- <h3>[method:Matrix4 set]( [page:Float n11], [page:Float n12], [page:Float n13], [page:Float n14], [page:Float n21], [page:Float n22], [page:Float n23], [page:Float n24], [page:Float n31], [page:Float n32], [page:Float n33], [page:Float n34], [page:Float n41], [page:Float n42], [page:Float n43], [page:Float n44] )</h3>
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+ <h3>[method:Matrix4 set](
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+ [page:Float n11], [page:Float n12], [page:Float n13], [page:Float n14],
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+ [page:Float n21], [page:Float n22], [page:Float n23], [page:Float n24],
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+ [page:Float n31], [page:Float n32], [page:Float n33], [page:Float n34],
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+ [page:Float n41], [page:Float n42], [page:Float n43], [page:Float n44] )</h3>
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<div>
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- Sets all fields of this matrix to the supplied row-major values n11..n44.
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+ Set the [page:.elements elements] of this matrix to the supplied row-major values [page:Float n11],
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+ [page:Float n12], ... [page:Float n44].
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</div>
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<h3>[method:Matrix4 setPosition]( [page:Vector3 v] )</h3>
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<div>
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- Sets the position component for this matrix from vector *v*.
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+ Sets the position component for this matrix from vector [page:Vector3 v], without affecting the
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+ rest of the matrix - i.e. if the matrix is currently:
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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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+This becomes:
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+<code>
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+a, b, c, v.x,
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+e, f, g, v.y,
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|
+i, j, k, v.z,
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+m, n, o, p
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|
+</code>
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|
</div>
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<h3>[method:Array toArray]( [page:Array array], [page:Integer offset] )</h3>
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|
<div>
|
|
|
- array -- [page:Array] optional array to store the vector <br />
|
|
|
- offset -- [page:Integer] optional offset into the array
|
|
|
- </div>
|
|
|
- <div>
|
|
|
- Writes the elements of this matrix to an array in column-major format.
|
|
|
+ [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 />
|
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|
+
|
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|
+ 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.
|
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|
</div>
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<h3>[method:Matrix4 transpose]()</h3>
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|
|
- <div>
|
|
|
- Transposes this matrix.
|
|
|
- </div>
|
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|
+ <div>[link:https://en.wikipedia.org/wiki/Transpose Transposes] this matrix.</div>
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<h2>Source</h2>
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