Quaternion.html 7.5 KB

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  1. <!DOCTYPE html>
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  10. <body>
  11. <h1>[name]</h1>
  12. <div class="desc">Implementation of a <a href="http://en.wikipedia.org/wiki/Quaternion">quaternion</a>. This is used for rotating things without encountering the dreaded <a href="http://en.wikipedia.org/wiki/Gimbal_lock">gimbal lock</a> issue, amongst other advantages.</div>
  13. <h2>Example</h2>
  14. <code>var quaternion = new THREE.Quaternion();
  15. quaternion.setFromAxisAngle( new THREE.Vector3( 0, 1, 0 ), Math.PI / 2 );
  16. var vector = new THREE.Vector3( 1, 0, 0 );
  17. vector.applyQuaternion( quaternion );
  18. </code>
  19. <h2>Constructor</h2>
  20. <h3>[name]( [page:Float x], [page:Float y], [page:Float z], [page:Float w] )</h3>
  21. <div>
  22. x - x coordinate<br />
  23. y - y coordinate<br />
  24. z - z coordinate<br />
  25. w - w coordinate
  26. </div>
  27. <h2>Properties</h2>
  28. <h3>[property:Float x]</h3>
  29. <h3>[property:Float y]</h3>
  30. <h3>[property:Float z]</h3>
  31. <h3>[property:Float w]</h3>
  32. <h2>Methods</h2>
  33. <h3>[method:Quaternion set]( [page:Float x], [page:Float y], [page:Float z], [page:Float w] ) [page:Quaternion this]</h3>
  34. <div>
  35. Sets values of this quaternion.
  36. </div>
  37. <h3>[method:Quaternion copy]( [page:Quaternion q] ) [page:Quaternion this]</h3>
  38. <div>
  39. Copies values of *q* to this quaternion.
  40. </div>
  41. <h3>[method:Quaternion fromArray]( [page:Array array], [page:Integer offset] ) [page:Quaternion this]</h3>
  42. <div>
  43. array -- Array of format (x, y, z, w) used to construct the quaternion.<br />
  44. offset -- An optional offset into the array.
  45. </div>
  46. <div>
  47. Sets this quaternion's component values from an array.
  48. </div>
  49. <h3>[method:Quaternion setFromEuler]( [page:Euler euler] ) [page:Quaternion this]</h3>
  50. <div>
  51. Sets this quaternion from rotation specified by Euler angle.
  52. </div>
  53. <h3>[method:Quaternion setFromAxisAngle]( [page:Vector3 axis], [page:Float angle] ) [page:Quaternion this]</h3>
  54. <div>
  55. Sets this quaternion from rotation specified by axis and angle.<br />
  56. Adapted from [link:http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm].<br />
  57. *Axis* is asumed to be normalized, *angle* is in radians.
  58. </div>
  59. <h3>[method:Quaternion setFromRotationMatrix]( [page:Matrix4 m] ) [page:Quaternion this]</h3>
  60. <div>
  61. Sets this quaternion from rotation component of *m*.<br />
  62. Adapted from [link:http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm].
  63. </div>
  64. <h3>[method:Quaternion setFromUnitVectors]( [page:Vector3 vFrom], [page:Vector3 vTo] ) [page:Quaternion this]</h3>
  65. <div>
  66. Sets this quaternion to the rotation required to rotate direction vector *vFrom* to direction vector *vTo*.<br />
  67. Adapted from [link:http://lolengine.net/blog/2013/09/18/beautiful-maths-quaternion-from-vectors].<br />
  68. *vFrom* and *vTo* are assumed to be normalized.
  69. </div>
  70. <h3>[method:Quaternion inverse]() [page:Quaternion this]</h3>
  71. <div>
  72. Inverts this quaternion.
  73. </div>
  74. <h3>[method:Float length]() [page:Quaternion this]</h3>
  75. <div>
  76. Computes length of this quaternion.
  77. </div>
  78. <h3>[method:Quaternion normalize]() [page:Quaternion this]</h3>
  79. <div>
  80. Normalizes this quaternion.
  81. </div>
  82. <h3>[method:Quaternion multiply]( [page:Quaternion b] ) [page:Quaternion this]</h3>
  83. <div>
  84. Multiplies this quaternion by *b*.
  85. </div>
  86. <h3>[method:Quaternion multiplyQuaternions]( [page:Quaternion a], [page:Quaternion b] ) [page:Quaternion this]</h3>
  87. <div>
  88. Sets this quaternion to *a x b*<br />
  89. Adapted from [link:http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm].
  90. </div>
  91. <h3>[method:Quaternion multiplyVector3]( [page:Vector3 vector], [page:Vector3 dest] ) [page:Quaternion this]</h3>
  92. <div>
  93. Rotates *vector* by this quaternion into *dest*.<br />
  94. If *dest* is not specified, result goes to *vec*.
  95. </div>
  96. <h3>[method:Float lengthSq]() [page:Quaternion this]</h3>
  97. <div>
  98. Calculates the squared length of the quaternion.
  99. </div>
  100. <h3>[method:Quaternion conjugate]() [page:Quaternion this]</h3>
  101. <div>
  102. Returns the rotational conjugate of this quaternion. The conjugate of a quaternion
  103. represents the same rotation in the opposite direction about the rotational axis.
  104. </div>
  105. <h3>[method:Quaternion slerp]( [page:Quaternion quaternionB], [page:float t] ) [page:Quaternion this]</h3>
  106. <div>
  107. quaternionB -- The other quaternion rotation<br />
  108. t -- Normalized 0 to 1 interpolation factor
  109. </div>
  110. <div>
  111. Handles the spherical linear interpolation between quaternions. *t* represents the amount of rotation
  112. between this quaternion (where *t* is 0) and quaternionB (where *t* is 1). This quaternion is set to
  113. the result. Also see the static version of the *slerp* below.
  114. </div>
  115. <code>
  116. // rotate a mesh towards a target quaternion
  117. mesh.quaternion.slerp( endQuaternion, 0.01 );
  118. </code>
  119. <h3>[method:Boolean equals]( [page:Quaternion v] ) [page:Quaternion this]</h3>
  120. <div>
  121. v -- Quaternion that this quaternion will be compared to.
  122. </div>
  123. <div>
  124. Compares each component of *v* to each component of this quaternion to determine if they
  125. represent the same rotation.
  126. </div>
  127. <h3>[method:Quaternion clone]() [page:Quaternion this]</h3>
  128. <div>
  129. Clones this quaternion.
  130. </div>
  131. <h3>[method:Array toArray]( [page:Array array], [page:Integer offset] ) [page:Quaternion this]</h3>
  132. <div>
  133. array -- An optional array to store the quaternion.<br/>
  134. offset -- An optional offset into the output array.
  135. </div>
  136. <div>
  137. Returns the numerical elements of this quaternion in an array of format (x, y, z, w).
  138. </div>
  139. <h2>Static Methods</h2>
  140. <h3>[method:Quaternion slerp]( [page:Quaternion qStart], [page:Quaternion qEnd], [page:Quaternion qTarget], [page:Float t] )</h3>
  141. <div>
  142. qStart -- The starting quaternion (where *t* is 0)<br />
  143. qEnd -- The ending quaternion (where *t* is 1)<br />
  144. qTarget -- The target quaternion that gets set with the result<br />
  145. t -- Normalized 0 to 1 interpolation factor
  146. </div>
  147. <div>
  148. Unlike the normal method, the static version of slerp sets a target quaternion to the result of the slerp operation.
  149. </div>
  150. <code>
  151. // Code setup
  152. var startQuaternion = new THREE.Quaternion().set( 0, 0, 0, 1 ).normalize();
  153. var endQuaternion = new THREE.Quaternion().set( 1, 1, 1, 1 ).normalize();
  154. var t = 0;
  155. </code>
  156. <code>
  157. // Update a mesh's rotation in the loop
  158. t = ( t + 0.01 ) % 1; // constant angular momentum
  159. THREE.Quaternion.slerp( startQuaternion, endQuaternion, mesh.quaternion, t );
  160. </code>
  161. <h3>[method:Quaternion slerpFlat]( [page:Array dst], [page:Integer dstOffset], [page:Array src0], [page:Integer srcOffset0], [page:Array src1], [page:Integer srcOffset1], [page:Float t] )</h3>
  162. <div>
  163. dst -- The output array.<br />
  164. dstOffset -- An offset into the output array.<br />
  165. src0 -- The source array of the starting quaternion.<br />
  166. srcOffset0 -- An offset into the array *src0*.<br />
  167. src1 -- The source array of the target quatnerion.<br />
  168. srcOffset1 -- An offset into the array *src1*.<br />
  169. t -- Interpolation factor 0 at start, 1 at end.
  170. </div>
  171. <div>
  172. Like the static *slerp* method above, but operates directly on flat arrays of numbers.
  173. </div>
  174. <!-- Note: Do not add non-static methods to the bottom of this page. Put them above the <h2>Static Methods</h2> -->
  175. <h2>Source</h2>
  176. [link:https://github.com/mrdoob/three.js/blob/master/src/[path].js src/[path].js]
  177. </body>
  178. </html>