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265 lines
10 KiB
265 lines
10 KiB
2 years ago
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<!DOCTYPE html>
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<html lang="en">
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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>[name]</h1>
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<p class="desc">
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Implementation of a [link:http://en.wikipedia.org/wiki/Quaternion quaternion].<br/>
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Quaternions are used in three.js to represent [link:https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation rotations].
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</p>
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<p>
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Iterating through a [name] instance will yield its components (x, y, z, w) in the corresponding order.
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</p>
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<h2>Code Example</h2>
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<code>
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const quaternion = new THREE.Quaternion();
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quaternion.setFromAxisAngle( new THREE.Vector3( 0, 1, 0 ), Math.PI / 2 );
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const vector = new THREE.Vector3( 1, 0, 0 );
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vector.applyQuaternion( quaternion );
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</code>
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<h2>Constructor</h2>
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<h3>[name]( [param:Float x], [param:Float y], [param:Float z], [param:Float w] )</h3>
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<p>
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[page:Float x] - x coordinate<br />
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[page:Float y] - y coordinate<br />
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[page:Float z] - z coordinate<br />
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[page:Float w] - w coordinate
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</p>
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<h2>Properties</h2>
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<h3>[property:Boolean isQuaternion]</h3>
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<p>
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Read-only flag to check if a given object is of type [name].
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</p>
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<h3>[property:Float x]</h3>
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<h3>[property:Float y]</h3>
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<h3>[property:Float z]</h3>
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<h3>[property:Float w]</h3>
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<h2>Methods</h2>
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<h3>[method:Float angleTo]( [param:Quaternion q] )</h3>
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<p>
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Returns the angle between this quaternion and quaternion [page:Quaternion q] in radians.
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</p>
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<h3>[method:Quaternion clone]()</h3>
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<p>
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Creates a new Quaternion with identical [page:.x x], [page:.y y],
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[page:.z z] and [page:.w w] properties to this one.
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</p>
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<h3>[method:this conjugate]()</h3>
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<p>
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Returns the rotational conjugate of this quaternion. The conjugate of a quaternion
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represents the same rotation in the opposite direction about the rotational axis.
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</p>
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<h3>[method:this copy]( [param:Quaternion q] )</h3>
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<p>
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Copies the [page:.x x], [page:.y y], [page:.z z] and [page:.w w] properties
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of [page:Quaternion q] into this quaternion.
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</p>
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<h3>[method:Boolean equals]( [param:Quaternion v] )</h3>
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<p>
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[page:Quaternion v] - Quaternion that this quaternion will be compared to.<br /><br />
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Compares the [page:.x x], [page:.y y], [page:.z z] and [page:.w w] properties of
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[page:Quaternion v] to the equivalent properties of this quaternion to determine if they
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represent the same rotation.
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</p>
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<h3>[method:Float dot]( [param:Quaternion v] )</h3>
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<p>
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Calculates the [link:https://en.wikipedia.org/wiki/Dot_product dot product] of
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quaternions [page:Quaternion v] and this one.
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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] - array of format (x, y, z, w) used to construct the quaternion.<br />
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[page:Integer offset] - (optional) an offset into the array.<br /><br />
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Sets this quaternion's [page:.x x], [page:.y y], [page:.z z] and [page:.w w] properties
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from an array.
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</p>
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<h3>[method:this identity]()</h3>
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<p>
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Sets this quaternion to the identity quaternion; that is, to the quaternion that represents "no rotation".
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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 quaternion - calculates the [page:.conjugate conjugate]. The quaternion is assumed to have unit length.
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</p>
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<h3>[method:Float length]()</h3>
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<p>Computes the [link:https://en.wikipedia.org/wiki/Euclidean_distance Euclidean length]
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(straight-line length) of this quaternion, considered as a 4 dimensional vector.</p>
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<h3>[method:Float lengthSq]()</h3>
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<p>
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Computes the squared [link:https://en.wikipedia.org/wiki/Euclidean_distance Euclidean length]
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(straight-line length) of this quaternion, considered as a 4 dimensional
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vector. This can be useful if you are comparing the lengths of two quaternions,
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as this is a slightly more efficient calculation than [page:.length length]().
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</p>
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<h3>[method:this normalize]()</h3>
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<p>
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[link:https://en.wikipedia.org/wiki/Normalized_vector Normalizes] this quaternion - that is,
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calculated the quaternion that performs the same rotation as this one, but has [page:.length length]
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equal to `1`.
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</p>
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<h3>[method:this multiply]( [param:Quaternion q] )</h3>
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<p>Multiplies this quaternion by [page:Quaternion q].</p>
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<h3>[method:this multiplyQuaternions]( [param:Quaternion a], [param:Quaternion b] )</h3>
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<p>
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Sets this quaternion to [page:Quaternion a] x [page:Quaternion b].<br />
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Adapted from the method outlined [link:http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm here].
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</p>
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<h3>[method:this premultiply]( [param:Quaternion q] )</h3>
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<p>Pre-multiplies this quaternion by [page:Quaternion q].</p>
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<h3>[method:this random]()</h3>
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<p>
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Sets this quaternion to a uniformly random, normalized quaternion.
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</p>
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<h3>[method:this rotateTowards]( [param:Quaternion q], [param:Float step] )</h3>
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<p>
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[page:Quaternion q] - The target quaternion.<br />
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[page:Float step] - The angular step in radians.<br /><br />
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Rotates this quaternion by a given angular step to the defined quaternion *q*.
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The method ensures that the final quaternion will not overshoot *q*.
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</p>
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<h3>[method:this slerp]( [param:Quaternion qb], [param:Float t] )</h3>
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<p>
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[page:Quaternion qb] - The other quaternion rotation<br />
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[page:Float t] - interpolation factor in the closed interval `[0, 1]`.<br /><br />
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Handles the spherical linear interpolation between quaternions. [page:Float t] represents the
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amount of rotation between this quaternion (where [page:Float t] is 0) and [page:Quaternion qb] (where
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[page:Float t] is 1). This quaternion is set to the result. Also see the static version of the
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`slerp` below.
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<code>
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// rotate a mesh towards a target quaternion
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mesh.quaternion.slerp( endQuaternion, 0.01 );
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</code>
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</p>
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<h3>[method:this slerpQuaternions]( [param:Quaternion qa], [param:Quaternion qb], [param:Float t] )</h3>
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<p>Performs a spherical linear interpolation between the given quaternions and stores the result in this quaternion.</p>
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<h3>[method:this set]( [param:Float x], [param:Float y], [param:Float z], [param:Float w] )</h3>
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<p>Sets [page:.x x], [page:.y y], [page:.z z], [page:.w w] properties of this quaternion.</p>
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<h3>[method:this setFromAxisAngle]( [param:Vector3 axis], [param:Float angle] )</h3>
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<p>
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Sets this quaternion from rotation specified by [page:Vector3 axis] and [page:Float angle].<br />
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Adapted from the method [link:http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm here].<br />
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`Axis` is assumed to be normalized, `angle` is in radians.
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</p>
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<h3>[method:this setFromEuler]( [param:Euler euler] )</h3>
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<p>Sets this quaternion from the rotation specified by [page:Euler] angle.</p>
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<h3>[method:this setFromRotationMatrix]( [param:Matrix4 m] )</h3>
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<p>
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[page:Matrix4 m] - a [page:Matrix4] of which the upper 3x3 of matrix is a pure
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[link:https://en.wikipedia.org/wiki/Rotation_matrix rotation matrix] (i.e. unscaled).<br />
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Sets this quaternion from rotation component of [page:Matrix4 m].<br />
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Adapted from the method [link:http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm here].
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</p>
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<h3>[method:this setFromUnitVectors]( [param:Vector3 vFrom], [param:Vector3 vTo] )</h3>
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<p>
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Sets this quaternion to the rotation required to rotate direction vector [page:Vector3 vFrom] to
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direction vector [page:Vector3 vTo].<br />
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Adapted from the method [link:http://lolengine.net/blog/2013/09/18/beautiful-maths-quaternion-from-vectors here].<br />
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[page:Vector3 vFrom] and [page:Vector3 vTo] are assumed to be normalized.
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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] - An optional array to store the quaternion. If not specified, a new array will be created.<br/>
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[page:Integer offset] - (optional) if specified, the result will be copied
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into this [page:Array].<br /><br />
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Returns the numerical elements of this quaternion in an array of format [x, y, z, w].
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</p>
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<h3>[method:this fromBufferAttribute]( [param:BufferAttribute attribute], [param:Integer index] )</h3>
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<p>
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[page:BufferAttribute attribute] - the source attribute.<br />
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[page:Integer index] - index in the attribute.<br /><br />
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Sets [page:.x x], [page:.y y], [page:.z z], [page:.w w] properties of this quaternion from the [page:BufferAttribute attribute].
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</p>
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<h2>Static Methods</h2>
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<h3>[method:undefined slerpFlat]( [param:Array dst], [param:Integer dstOffset], [param:Array src0], [param:Integer srcOffset0], [param:Array src1], [param:Integer srcOffset1], [param:Float t] )</h3>
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<p>
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[page:Array dst] - The output array.<br />
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[page:Integer dstOffset] - An offset into the output array.<br />
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[page:Array src0] - The source array of the starting quaternion.<br />
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[page:Integer srcOffset0] - An offset into the array `src0`.<br />
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[page:Array src1] - The source array of the target quaternion.<br />
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[page:Integer srcOffset1] - An offset into the array `src1`.<br />
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[page:Float t] - Normalized interpolation factor (between 0 and 1).<br /><br />
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This SLERP implementation assumes the quaternion data are managed in flat arrays.
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</p>
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<h3>[method:Array multiplyQuaternionsFlat]( [param:Array dst], [param:Integer dstOffset], [param:Array src0], [param:Integer srcOffset0], [param:Array src1], [param:Integer srcOffset1] )</h3>
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<p>
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[page:Array dst] - The output array.<br />
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[page:Integer dstOffset] - An offset into the output array.<br />
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[page:Array src0] - The source array of the starting quaternion.<br />
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[page:Integer srcOffset0] - An offset into the array `src0`.<br />
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[page:Array src1] - The source array of the target quaternion.<br />
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[page:Integer srcOffset1] - An offset into the array `src1`.<br /><br />
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This multiplication implementation assumes the quaternion data are managed in flat arrays.
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</p>
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<!-- Note: Do not add non-static methods to the bottom of this page. Put them above the <h2>Static Methods</h2> -->
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<h2>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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