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diff --git a/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/geometry/euclidean/threed/Rotation.html b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/geometry/euclidean/threed/Rotation.html new file mode 100644 index 0000000..251fd9f --- /dev/null +++ b/commons-math3-3.6.1/docs/apidocs/org/apache/commons/math3/geometry/euclidean/threed/Rotation.html @@ -0,0 +1,1103 @@ +<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> +<!-- NewPage --> +<html lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> +<title>Rotation (Apache Commons Math 3.6.1 API)</title> +<link rel="stylesheet" type="text/css" href="../../../../../../../stylesheet.css" title="Style"> +</head> +<body> +<script type="text/javascript"><!-- + if (location.href.indexOf('is-external=true') == -1) { + parent.document.title="Rotation (Apache Commons Math 3.6.1 API)"; + } +//--> +</script> +<noscript> +<div>JavaScript is disabled on your browser.</div> +</noscript> +<!-- ========= START OF TOP NAVBAR ======= --> +<div class="topNav"><a name="navbar_top"> +<!-- --> +</a><a href="#skip-navbar_top" title="Skip navigation links"></a><a name="navbar_top_firstrow"> +<!-- --> +</a> +<ul class="navList" title="Navigation"> +<li><a href="../../../../../../../overview-summary.html">Overview</a></li> +<li><a href="package-summary.html">Package</a></li> +<li class="navBarCell1Rev">Class</li> +<li><a href="class-use/Rotation.html">Use</a></li> +<li><a href="package-tree.html">Tree</a></li> +<li><a href="../../../../../../../deprecated-list.html">Deprecated</a></li> +<li><a href="../../../../../../../index-all.html">Index</a></li> +<li><a href="../../../../../../../help-doc.html">Help</a></li> +</ul> +<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div> +</div> +<div class="subNav"> +<ul class="navList"> +<li><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/PolyhedronsSet.html" title="class in org.apache.commons.math3.geometry.euclidean.threed"><span class="strong">Prev Class</span></a></li> +<li><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed"><span class="strong">Next Class</span></a></li> +</ul> +<ul class="navList"> +<li><a href="../../../../../../../index.html?org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" target="_top">Frames</a></li> +<li><a href="Rotation.html" target="_top">No Frames</a></li> +</ul> +<ul class="navList" id="allclasses_navbar_top"> +<li><a href="../../../../../../../allclasses-noframe.html">All Classes</a></li> +</ul> +<div> +<script type="text/javascript"><!-- + allClassesLink = document.getElementById("allclasses_navbar_top"); + if(window==top) { + allClassesLink.style.display = "block"; + } + else { + allClassesLink.style.display = "none"; + } + //--> +</script> +</div> +<div> +<ul class="subNavList"> +<li>Summary: </li> +<li>Nested | </li> +<li><a href="#field_summary">Field</a> | </li> +<li><a href="#constructor_summary">Constr</a> | </li> +<li><a href="#method_summary">Method</a></li> +</ul> +<ul class="subNavList"> +<li>Detail: </li> +<li><a href="#field_detail">Field</a> | </li> +<li><a href="#constructor_detail">Constr</a> | </li> +<li><a href="#method_detail">Method</a></li> +</ul> +</div> +<a name="skip-navbar_top"> +<!-- --> +</a></div> +<!-- ========= END OF TOP NAVBAR ========= --> +<!-- ======== START OF CLASS DATA ======== --> +<div class="header"> +<div class="subTitle">org.apache.commons.math3.geometry.euclidean.threed</div> +<h2 title="Class Rotation" class="title">Class Rotation</h2> +</div> +<div class="contentContainer"> +<ul class="inheritance"> +<li><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li> +<li> +<ul class="inheritance"> +<li>org.apache.commons.math3.geometry.euclidean.threed.Rotation</li> +</ul> +</li> +</ul> +<div class="description"> +<ul class="blockList"> +<li class="blockList"> +<dl> +<dt>All Implemented Interfaces:</dt> +<dd><a href="http://docs.oracle.com/javase/7/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</a></dd> +</dl> +<hr> +<br> +<pre>public class <span class="strong">Rotation</span> +extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a> +implements <a href="http://docs.oracle.com/javase/7/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</a></pre> +<div class="block">This class implements rotations in a three-dimensional space. + + <p>Rotations can be represented by several different mathematical + entities (matrices, axe and angle, Cardan or Euler angles, + quaternions). This class presents an higher level abstraction, more + user-oriented and hiding this implementation details. Well, for the + curious, we use quaternions for the internal representation. The + user can build a rotation from any of these representations, and + any of these representations can be retrieved from a + <code>Rotation</code> instance (see the various constructors and + getters). In addition, a rotation can also be built implicitly + from a set of vectors and their image.</p> + <p>This implies that this class can be used to convert from one + representation to another one. For example, converting a rotation + matrix into a set of Cardan angles from can be done using the + following single line of code:</p> + <pre> + double[] angles = new Rotation(matrix, 1.0e-10).getAngles(RotationOrder.XYZ); + </pre> + <p>Focus is oriented on what a rotation <em>do</em> rather than on its + underlying representation. Once it has been built, and regardless of its + internal representation, a rotation is an <em>operator</em> which basically + transforms three dimensional <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed"><code>vectors</code></a> into other three + dimensional <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed"><code>vectors</code></a>. Depending on the application, the + meaning of these vectors may vary and the semantics of the rotation also.</p> + <p>For example in an spacecraft attitude simulation tool, users will often + consider the vectors are fixed (say the Earth direction for example) and the + frames change. The rotation transforms the coordinates of the vector in inertial + frame into the coordinates of the same vector in satellite frame. In this + case, the rotation implicitly defines the relation between the two frames.</p> + <p>Another example could be a telescope control application, where the rotation + would transform the sighting direction at rest into the desired observing + direction when the telescope is pointed towards an object of interest. In this + case the rotation transforms the direction at rest in a topocentric frame + into the sighting direction in the same topocentric frame. This implies in this + case the frame is fixed and the vector moves.</p> + <p>In many case, both approaches will be combined. In our telescope example, + we will probably also need to transform the observing direction in the topocentric + frame into the observing direction in inertial frame taking into account the observatory + location and the Earth rotation, which would essentially be an application of the + first approach.</p> + + <p>These examples show that a rotation is what the user wants it to be. This + class does not push the user towards one specific definition and hence does not + provide methods like <code>projectVectorIntoDestinationFrame</code> or + <code>computeTransformedDirection</code>. It provides simpler and more generic + methods: <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#applyTo(org.apache.commons.math3.geometry.euclidean.threed.Vector3D)"><code>applyTo(Vector3D)</code></a> and <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#applyInverseTo(org.apache.commons.math3.geometry.euclidean.threed.Vector3D)"><code>applyInverseTo(Vector3D)</code></a>.</p> + + <p>Since a rotation is basically a vectorial operator, several rotations can be + composed together and the composite operation <code>r = r<sub>1</sub> o + r<sub>2</sub></code> (which means that for each vector <code>u</code>, + <code>r(u) = r<sub>1</sub>(r<sub>2</sub>(u))</code>) is also a rotation. Hence + we can consider that in addition to vectors, a rotation can be applied to other + rotations as well (or to itself). With our previous notations, we would say we + can apply <code>r<sub>1</sub></code> to <code>r<sub>2</sub></code> and the result + we get is <code>r = r<sub>1</sub> o r<sub>2</sub></code>. For this purpose, the + class provides the methods: <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#applyTo(org.apache.commons.math3.geometry.euclidean.threed.Rotation)"><code>applyTo(Rotation)</code></a> and + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#applyInverseTo(org.apache.commons.math3.geometry.euclidean.threed.Rotation)"><code>applyInverseTo(Rotation)</code></a>.</p> + + <p>Rotations are guaranteed to be immutable objects.</p></div> +<dl><dt><span class="strong">Since:</span></dt> + <dd>1.2</dd> +<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed"><code>Vector3D</code></a>, +<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.html" title="class in org.apache.commons.math3.geometry.euclidean.threed"><code>RotationOrder</code></a>, +<a href="../../../../../../../serialized-form.html#org.apache.commons.math3.geometry.euclidean.threed.Rotation">Serialized Form</a></dd></dl> +</li> +</ul> +</div> +<div class="summary"> +<ul class="blockList"> +<li class="blockList"> +<!-- =========== FIELD SUMMARY =========== --> +<ul class="blockList"> +<li class="blockList"><a name="field_summary"> +<!-- --> +</a> +<h3>Field Summary</h3> +<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Field Summary table, listing fields, and an explanation"> +<caption><span>Fields</span><span class="tabEnd"> </span></caption> +<tr> +<th class="colFirst" scope="col">Modifier and Type</th> +<th class="colLast" scope="col">Field and Description</th> +</tr> +<tr class="altColor"> +<td class="colFirst"><code>static <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#IDENTITY">IDENTITY</a></strong></code> +<div class="block">Identity rotation.</div> +</td> +</tr> +</table> +</li> +</ul> +<!-- ======== CONSTRUCTOR SUMMARY ======== --> +<ul class="blockList"> +<li class="blockList"><a name="constructor_summary"> +<!-- --> +</a> +<h3>Constructor Summary</h3> +<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Constructor Summary table, listing constructors, and an explanation"> +<caption><span>Constructors</span><span class="tabEnd"> </span></caption> +<tr> +<th class="colOne" scope="col">Constructor and Description</th> +</tr> +<tr class="altColor"> +<td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(double[][],%20double)">Rotation</a></strong>(double[][] m, + double threshold)</code> +<div class="block">Build a rotation from a 3X3 matrix.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(double,%20double,%20double,%20double,%20boolean)">Rotation</a></strong>(double q0, + double q1, + double q2, + double q3, + boolean needsNormalization)</code> +<div class="block">Build a rotation from the quaternion coordinates.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder,%20double,%20double,%20double)">Rotation</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">RotationOrder</a> order, + double alpha1, + double alpha2, + double alpha3)</code> +<div class="block"><strong>Deprecated.</strong> +<div class="block"><i>as of 3.6, replaced with <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention,%20double,%20double,%20double)"><code>Rotation(RotationOrder, RotationConvention, double, double, double)</code></a></i></div> +</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention,%20double,%20double,%20double)">Rotation</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">RotationOrder</a> order, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention, + double alpha1, + double alpha2, + double alpha3)</code> +<div class="block">Build a rotation from three Cardan or Euler elementary rotations.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20double)">Rotation</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> axis, + double angle)</code> +<div class="block"><strong>Deprecated.</strong> +<div class="block"><i>as of 3.6, replaced with <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20double,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>Rotation(Vector3D, double, RotationConvention)</code></a></i></div> +</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20double,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)">Rotation</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> axis, + double angle, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention)</code> +<div class="block">Build a rotation from an axis and an angle.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20org.apache.commons.math3.geometry.euclidean.threed.Vector3D)">Rotation</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> u, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> v)</code> +<div class="block">Build one of the rotations that transform one vector into another one.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20org.apache.commons.math3.geometry.euclidean.threed.Vector3D)">Rotation</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> u1, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> u2, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> v1, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> v2)</code> +<div class="block">Build the rotation that transforms a pair of vectors into another pair.</div> +</td> +</tr> +</table> +</li> +</ul> +<!-- ========== METHOD SUMMARY =========== --> +<ul class="blockList"> +<li class="blockList"><a name="method_summary"> +<!-- --> +</a> +<h3>Method Summary</h3> +<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation"> +<caption><span>Methods</span><span class="tabEnd"> </span></caption> +<tr> +<th class="colFirst" scope="col">Modifier and Type</th> +<th class="colLast" scope="col">Method and Description</th> +</tr> +<tr class="altColor"> +<td class="colFirst"><code>void</code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#applyInverseTo(double[],%20double[])">applyInverseTo</a></strong>(double[] in, + double[] out)</code> +<div class="block">Apply the inverse of the rotation to a vector stored in an array.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#applyInverseTo(org.apache.commons.math3.geometry.euclidean.threed.Rotation)">applyInverseTo</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r)</code> +<div class="block">Apply the inverse of the instance to another rotation.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#applyInverseTo(org.apache.commons.math3.geometry.euclidean.threed.Vector3D)">applyInverseTo</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> u)</code> +<div class="block">Apply the inverse of the rotation to a vector.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code>void</code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#applyTo(double[],%20double[])">applyTo</a></strong>(double[] in, + double[] out)</code> +<div class="block">Apply the rotation to a vector stored in an array.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#applyTo(org.apache.commons.math3.geometry.euclidean.threed.Rotation)">applyTo</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r)</code> +<div class="block">Apply the instance to another rotation.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#applyTo(org.apache.commons.math3.geometry.euclidean.threed.Vector3D)">applyTo</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> u)</code> +<div class="block">Apply the rotation to a vector.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#compose(org.apache.commons.math3.geometry.euclidean.threed.Rotation,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)">compose</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention)</code> +<div class="block">Compose the instance with another rotation.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#composeInverse(org.apache.commons.math3.geometry.euclidean.threed.Rotation,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)">composeInverse</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention)</code> +<div class="block">Compose the inverse of the instance with another rotation.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code>static double</code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#distance(org.apache.commons.math3.geometry.euclidean.threed.Rotation,%20org.apache.commons.math3.geometry.euclidean.threed.Rotation)">distance</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r1, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r2)</code> +<div class="block">Compute the <i>distance</i> between two rotations.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code>double</code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAngle()">getAngle</a></strong>()</code> +<div class="block">Get the angle of the rotation.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code>double[]</code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAngles(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder)">getAngles</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">RotationOrder</a> order)</code> +<div class="block"><strong>Deprecated.</strong> +<div class="block"><i>as of 3.6, replaced with <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAngles(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>getAngles(RotationOrder, RotationConvention)</code></a></i></div> +</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code>double[]</code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAngles(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)">getAngles</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">RotationOrder</a> order, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention)</code> +<div class="block">Get the Cardan or Euler angles corresponding to the instance.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAxis()">getAxis</a></strong>()</code> +<div class="block"><strong>Deprecated.</strong> +<div class="block"><i>as of 3.6, replaced with <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAxis(org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>getAxis(RotationConvention)</code></a></i></div> +</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAxis(org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)">getAxis</a></strong>(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention)</code> +<div class="block">Get the normalized axis of the rotation.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code>double[][]</code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getMatrix()">getMatrix</a></strong>()</code> +<div class="block">Get the 3X3 matrix corresponding to the instance</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code>double</code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getQ0()">getQ0</a></strong>()</code> +<div class="block">Get the scalar coordinate of the quaternion.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code>double</code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getQ1()">getQ1</a></strong>()</code> +<div class="block">Get the first coordinate of the vectorial part of the quaternion.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code>double</code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getQ2()">getQ2</a></strong>()</code> +<div class="block">Get the second coordinate of the vectorial part of the quaternion.</div> +</td> +</tr> +<tr class="altColor"> +<td class="colFirst"><code>double</code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getQ3()">getQ3</a></strong>()</code> +<div class="block">Get the third coordinate of the vectorial part of the quaternion.</div> +</td> +</tr> +<tr class="rowColor"> +<td class="colFirst"><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a></code></td> +<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#revert()">revert</a></strong>()</code> +<div class="block">Revert a rotation.</div> +</td> +</tr> +</table> +<ul class="blockList"> +<li class="blockList"><a name="methods_inherited_from_class_java.lang.Object"> +<!-- --> +</a> +<h3>Methods inherited from class java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3> +<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li> +</ul> +</li> +</ul> +</li> +</ul> +</div> +<div class="details"> +<ul class="blockList"> +<li class="blockList"> +<!-- ============ FIELD DETAIL =========== --> +<ul class="blockList"> +<li class="blockList"><a name="field_detail"> +<!-- --> +</a> +<h3>Field Detail</h3> +<a name="IDENTITY"> +<!-- --> +</a> +<ul class="blockListLast"> +<li class="blockList"> +<h4>IDENTITY</h4> +<pre>public static final <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> IDENTITY</pre> +<div class="block">Identity rotation.</div> +</li> +</ul> +</li> +</ul> +<!-- ========= CONSTRUCTOR DETAIL ======== --> +<ul class="blockList"> +<li class="blockList"><a name="constructor_detail"> +<!-- --> +</a> +<h3>Constructor Detail</h3> +<a name="Rotation(double, double, double, double, boolean)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>Rotation</h4> +<pre>public Rotation(double q0, + double q1, + double q2, + double q3, + boolean needsNormalization)</pre> +<div class="block">Build a rotation from the quaternion coordinates. + <p>A rotation can be built from a <em>normalized</em> quaternion, + i.e. a quaternion for which q<sub>0</sub><sup>2</sup> + + q<sub>1</sub><sup>2</sup> + q<sub>2</sub><sup>2</sup> + + q<sub>3</sub><sup>2</sup> = 1. If the quaternion is not normalized, + the constructor can normalize it in a preprocessing step.</p> + <p>Note that some conventions put the scalar part of the quaternion + as the 4<sup>th</sup> component and the vector part as the first three + components. This is <em>not</em> our convention. We put the scalar part + as the first component.</p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>q0</code> - scalar part of the quaternion</dd><dd><code>q1</code> - first coordinate of the vectorial part of the quaternion</dd><dd><code>q2</code> - second coordinate of the vectorial part of the quaternion</dd><dd><code>q3</code> - third coordinate of the vectorial part of the quaternion</dd><dd><code>needsNormalization</code> - if true, the coordinates are considered + not to be normalized, a normalization preprocessing step is performed + before using them</dd></dl> +</li> +</ul> +<a name="Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D, double)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>Rotation</h4> +<pre><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a> +public Rotation(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> axis, + double angle) + throws <a href="../../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></pre> +<div class="block"><span class="strong">Deprecated.</span> <i>as of 3.6, replaced with <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20double,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>Rotation(Vector3D, double, RotationConvention)</code></a></i></div> +<div class="block">Build a rotation from an axis and an angle. + <p> + Calling this constructor is equivalent to call + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20double,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>new Rotation(axis, angle, RotationConvention.VECTOR_OPERATOR)</code></a> + </p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>axis</code> - axis around which to rotate</dd><dd><code>angle</code> - rotation angle.</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the axis norm is zero</dd></dl> +</li> +</ul> +<a name="Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D, double, org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>Rotation</h4> +<pre>public Rotation(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> axis, + double angle, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention) + throws <a href="../../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></pre> +<div class="block">Build a rotation from an axis and an angle.</div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>axis</code> - axis around which to rotate</dd><dd><code>angle</code> - rotation angle</dd><dd><code>convention</code> - convention to use for the semantics of the angle</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../../../org/apache/commons/math3/exception/MathIllegalArgumentException.html" title="class in org.apache.commons.math3.exception">MathIllegalArgumentException</a></code> - if the axis norm is zero</dd><dt><span class="strong">Since:</span></dt> + <dd>3.6</dd></dl> +</li> +</ul> +<a name="Rotation(double[][], double)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>Rotation</h4> +<pre>public Rotation(double[][] m, + double threshold) + throws <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/NotARotationMatrixException.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">NotARotationMatrixException</a></pre> +<div class="block">Build a rotation from a 3X3 matrix. + + <p>Rotation matrices are orthogonal matrices, i.e. unit matrices + (which are matrices for which m.m<sup>T</sup> = I) with real + coefficients. The module of the determinant of unit matrices is + 1, among the orthogonal 3X3 matrices, only the ones having a + positive determinant (+1) are rotation matrices.</p> + + <p>When a rotation is defined by a matrix with truncated values + (typically when it is extracted from a technical sheet where only + four to five significant digits are available), the matrix is not + orthogonal anymore. This constructor handles this case + transparently by using a copy of the given matrix and applying a + correction to the copy in order to perfect its orthogonality. If + the Frobenius norm of the correction needed is above the given + threshold, then the matrix is considered to be too far from a + true rotation matrix and an exception is thrown.<p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>m</code> - rotation matrix</dd><dd><code>threshold</code> - convergence threshold for the iterative + orthogonality correction (convergence is reached when the + difference between two steps of the Frobenius norm of the + correction is below this threshold)</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/NotARotationMatrixException.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">NotARotationMatrixException</a></code> - if the matrix is not a 3X3 + matrix, or if it cannot be transformed into an orthogonal matrix + with the given threshold, or if the determinant of the resulting + orthogonal matrix is negative</dd></dl> +</li> +</ul> +<a name="Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D, org.apache.commons.math3.geometry.euclidean.threed.Vector3D, org.apache.commons.math3.geometry.euclidean.threed.Vector3D, org.apache.commons.math3.geometry.euclidean.threed.Vector3D)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>Rotation</h4> +<pre>public Rotation(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> u1, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> u2, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> v1, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> v2) + throws <a href="../../../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre> +<div class="block">Build the rotation that transforms a pair of vectors into another pair. + + <p>Except for possible scale factors, if the instance were applied to + the pair (u<sub>1</sub>, u<sub>2</sub>) it will produce the pair + (v<sub>1</sub>, v<sub>2</sub>).</p> + + <p>If the angular separation between u<sub>1</sub> and u<sub>2</sub> is + not the same as the angular separation between v<sub>1</sub> and + v<sub>2</sub>, then a corrected v'<sub>2</sub> will be used rather than + v<sub>2</sub>, the corrected vector will be in the (±v<sub>1</sub>, + +v<sub>2</sub>) half-plane.</p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u1</code> - first vector of the origin pair</dd><dd><code>u2</code> - second vector of the origin pair</dd><dd><code>v1</code> - desired image of u1 by the rotation</dd><dd><code>v2</code> - desired image of u2 by the rotation</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if the norm of one of the vectors is zero, + or if one of the pair is degenerated (i.e. the vectors of the pair are collinear)</dd></dl> +</li> +</ul> +<a name="Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D, org.apache.commons.math3.geometry.euclidean.threed.Vector3D)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>Rotation</h4> +<pre>public Rotation(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> u, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> v) + throws <a href="../../../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></pre> +<div class="block">Build one of the rotations that transform one vector into another one. + + <p>Except for a possible scale factor, if the instance were + applied to the vector u it will produce the vector v. There is an + infinite number of such rotations, this constructor choose the + one with the smallest associated angle (i.e. the one whose axis + is orthogonal to the (u, v) plane). If u and v are collinear, an + arbitrary rotation axis is chosen.</p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u</code> - origin vector</dd><dd><code>v</code> - desired image of u by the rotation</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../../../org/apache/commons/math3/exception/MathArithmeticException.html" title="class in org.apache.commons.math3.exception">MathArithmeticException</a></code> - if the norm of one of the vectors is zero</dd></dl> +</li> +</ul> +<a name="Rotation(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder, double, double, double)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>Rotation</h4> +<pre><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a> +public Rotation(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">RotationOrder</a> order, + double alpha1, + double alpha2, + double alpha3)</pre> +<div class="block"><span class="strong">Deprecated.</span> <i>as of 3.6, replaced with <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention,%20double,%20double,%20double)"><code>Rotation(RotationOrder, RotationConvention, double, double, double)</code></a></i></div> +<div class="block">Build a rotation from three Cardan or Euler elementary rotations. + + <p> + Calling this constructor is equivalent to call + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention,%20double,%20double,%20double)"><code>new Rotation(order, RotationConvention.VECTOR_OPERATOR, alpha1, alpha2, alpha3)</code></a> + </p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>order</code> - order of rotations to use</dd><dd><code>alpha1</code> - angle of the first elementary rotation</dd><dd><code>alpha2</code> - angle of the second elementary rotation</dd><dd><code>alpha3</code> - angle of the third elementary rotation</dd></dl> +</li> +</ul> +<a name="Rotation(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder, org.apache.commons.math3.geometry.euclidean.threed.RotationConvention, double, double, double)"> +<!-- --> +</a> +<ul class="blockListLast"> +<li class="blockList"> +<h4>Rotation</h4> +<pre>public Rotation(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">RotationOrder</a> order, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention, + double alpha1, + double alpha2, + double alpha3)</pre> +<div class="block">Build a rotation from three Cardan or Euler elementary rotations. + + <p>Cardan rotations are three successive rotations around the + canonical axes X, Y and Z, each axis being used once. There are + 6 such sets of rotations (XYZ, XZY, YXZ, YZX, ZXY and ZYX). Euler + rotations are three successive rotations around the canonical + axes X, Y and Z, the first and last rotations being around the + same axis. There are 6 such sets of rotations (XYX, XZX, YXY, + YZY, ZXZ and ZYZ), the most popular one being ZXZ.</p> + <p>Beware that many people routinely use the term Euler angles even + for what really are Cardan angles (this confusion is especially + widespread in the aerospace business where Roll, Pitch and Yaw angles + are often wrongly tagged as Euler angles).</p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>order</code> - order of rotations to compose, from left to right + (i.e. we will use <code>r1.compose(r2.compose(r3, convention), convention)</code>)</dd><dd><code>convention</code> - convention to use for the semantics of the angle</dd><dd><code>alpha1</code> - angle of the first elementary rotation</dd><dd><code>alpha2</code> - angle of the second elementary rotation</dd><dd><code>alpha3</code> - angle of the third elementary rotation</dd><dt><span class="strong">Since:</span></dt> + <dd>3.6</dd></dl> +</li> +</ul> +</li> +</ul> +<!-- ============ METHOD DETAIL ========== --> +<ul class="blockList"> +<li class="blockList"><a name="method_detail"> +<!-- --> +</a> +<h3>Method Detail</h3> +<a name="revert()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>revert</h4> +<pre>public <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> revert()</pre> +<div class="block">Revert a rotation. + Build a rotation which reverse the effect of another + rotation. This means that if r(u) = v, then r.revert(v) = u. The + instance is not changed.</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>a new rotation whose effect is the reverse of the effect + of the instance</dd></dl> +</li> +</ul> +<a name="getQ0()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getQ0</h4> +<pre>public double getQ0()</pre> +<div class="block">Get the scalar coordinate of the quaternion.</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>scalar coordinate of the quaternion</dd></dl> +</li> +</ul> +<a name="getQ1()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getQ1</h4> +<pre>public double getQ1()</pre> +<div class="block">Get the first coordinate of the vectorial part of the quaternion.</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>first coordinate of the vectorial part of the quaternion</dd></dl> +</li> +</ul> +<a name="getQ2()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getQ2</h4> +<pre>public double getQ2()</pre> +<div class="block">Get the second coordinate of the vectorial part of the quaternion.</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>second coordinate of the vectorial part of the quaternion</dd></dl> +</li> +</ul> +<a name="getQ3()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getQ3</h4> +<pre>public double getQ3()</pre> +<div class="block">Get the third coordinate of the vectorial part of the quaternion.</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>third coordinate of the vectorial part of the quaternion</dd></dl> +</li> +</ul> +<a name="getAxis()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getAxis</h4> +<pre><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a> +public <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> getAxis()</pre> +<div class="block"><span class="strong">Deprecated.</span> <i>as of 3.6, replaced with <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAxis(org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>getAxis(RotationConvention)</code></a></i></div> +<div class="block">Get the normalized axis of the rotation. + <p> + Calling this method is equivalent to call + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAxis(org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>getAxis(RotationConvention.VECTOR_OPERATOR)</code></a> + </p></div> +<dl><dt><span class="strong">Returns:</span></dt><dd>normalized axis of the rotation</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20double,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>Rotation(Vector3D, double, RotationConvention)</code></a></dd></dl> +</li> +</ul> +<a name="getAxis(org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getAxis</h4> +<pre>public <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> getAxis(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention)</pre> +<div class="block">Get the normalized axis of the rotation. + <p> + Note that as <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAngle()"><code>getAngle()</code></a> always returns an angle + between 0 and π, changing the convention changes the + direction of the axis, not the sign of the angle. + </p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>convention</code> - convention to use for the semantics of the angle</dd> +<dt><span class="strong">Returns:</span></dt><dd>normalized axis of the rotation</dd><dt><span class="strong">Since:</span></dt> + <dd>3.6</dd> +<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20double,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>Rotation(Vector3D, double, RotationConvention)</code></a></dd></dl> +</li> +</ul> +<a name="getAngle()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getAngle</h4> +<pre>public double getAngle()</pre> +<div class="block">Get the angle of the rotation.</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>angle of the rotation (between 0 and π)</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#Rotation(org.apache.commons.math3.geometry.euclidean.threed.Vector3D,%20double)"><code>Rotation(Vector3D, double)</code></a></dd></dl> +</li> +</ul> +<a name="getAngles(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getAngles</h4> +<pre><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Deprecated.html?is-external=true" title="class or interface in java.lang">@Deprecated</a> +public double[] getAngles(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">RotationOrder</a> order) + throws <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/CardanEulerSingularityException.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">CardanEulerSingularityException</a></pre> +<div class="block"><span class="strong">Deprecated.</span> <i>as of 3.6, replaced with <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAngles(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>getAngles(RotationOrder, RotationConvention)</code></a></i></div> +<div class="block">Get the Cardan or Euler angles corresponding to the instance. + + <p> + Calling this method is equivalent to call + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#getAngles(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>getAngles(order, RotationConvention.VECTOR_OPERATOR)</code></a> + </p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>order</code> - rotation order to use</dd> +<dt><span class="strong">Returns:</span></dt><dd>an array of three angles, in the order specified by the set</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/CardanEulerSingularityException.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">CardanEulerSingularityException</a></code> - if the rotation is + singular with respect to the angles set specified</dd></dl> +</li> +</ul> +<a name="getAngles(org.apache.commons.math3.geometry.euclidean.threed.RotationOrder, org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getAngles</h4> +<pre>public double[] getAngles(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">RotationOrder</a> order, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention) + throws <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/CardanEulerSingularityException.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">CardanEulerSingularityException</a></pre> +<div class="block">Get the Cardan or Euler angles corresponding to the instance. + + <p>The equations show that each rotation can be defined by two + different values of the Cardan or Euler angles set. For example + if Cardan angles are used, the rotation defined by the angles + a<sub>1</sub>, a<sub>2</sub> and a<sub>3</sub> is the same as + the rotation defined by the angles π + a<sub>1</sub>, π + - a<sub>2</sub> and π + a<sub>3</sub>. This method implements + the following arbitrary choices:</p> + <ul> + <li>for Cardan angles, the chosen set is the one for which the + second angle is between -π/2 and π/2 (i.e its cosine is + positive),</li> + <li>for Euler angles, the chosen set is the one for which the + second angle is between 0 and π (i.e its sine is positive).</li> + </ul> + + <p>Cardan and Euler angle have a very disappointing drawback: all + of them have singularities. This means that if the instance is + too close to the singularities corresponding to the given + rotation order, it will be impossible to retrieve the angles. For + Cardan angles, this is often called gimbal lock. There is + <em>nothing</em> to do to prevent this, it is an intrinsic problem + with Cardan and Euler representation (but not a problem with the + rotation itself, which is perfectly well defined). For Cardan + angles, singularities occur when the second angle is close to + -π/2 or +π/2, for Euler angle singularities occur when the + second angle is close to 0 or π, this implies that the identity + rotation is always singular for Euler angles!</p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>order</code> - rotation order to use</dd><dd><code>convention</code> - convention to use for the semantics of the angle</dd> +<dt><span class="strong">Returns:</span></dt><dd>an array of three angles, in the order specified by the set</dd> +<dt><span class="strong">Throws:</span></dt> +<dd><code><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/CardanEulerSingularityException.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">CardanEulerSingularityException</a></code> - if the rotation is + singular with respect to the angles set specified</dd><dt><span class="strong">Since:</span></dt> + <dd>3.6</dd></dl> +</li> +</ul> +<a name="getMatrix()"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>getMatrix</h4> +<pre>public double[][] getMatrix()</pre> +<div class="block">Get the 3X3 matrix corresponding to the instance</div> +<dl><dt><span class="strong">Returns:</span></dt><dd>the matrix corresponding to the instance</dd></dl> +</li> +</ul> +<a name="applyTo(org.apache.commons.math3.geometry.euclidean.threed.Vector3D)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>applyTo</h4> +<pre>public <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> applyTo(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> u)</pre> +<div class="block">Apply the rotation to a vector.</div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u</code> - vector to apply the rotation to</dd> +<dt><span class="strong">Returns:</span></dt><dd>a new vector which is the image of u by the rotation</dd></dl> +</li> +</ul> +<a name="applyTo(double[], double[])"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>applyTo</h4> +<pre>public void applyTo(double[] in, + double[] out)</pre> +<div class="block">Apply the rotation to a vector stored in an array.</div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>in</code> - an array with three items which stores vector to rotate</dd><dd><code>out</code> - an array with three items to put result to (it can be the same + array as in)</dd></dl> +</li> +</ul> +<a name="applyInverseTo(org.apache.commons.math3.geometry.euclidean.threed.Vector3D)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>applyInverseTo</h4> +<pre>public <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> applyInverseTo(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> u)</pre> +<div class="block">Apply the inverse of the rotation to a vector.</div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u</code> - vector to apply the inverse of the rotation to</dd> +<dt><span class="strong">Returns:</span></dt><dd>a new vector which such that u is its image by the rotation</dd></dl> +</li> +</ul> +<a name="applyInverseTo(double[], double[])"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>applyInverseTo</h4> +<pre>public void applyInverseTo(double[] in, + double[] out)</pre> +<div class="block">Apply the inverse of the rotation to a vector stored in an array.</div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>in</code> - an array with three items which stores vector to rotate</dd><dd><code>out</code> - an array with three items to put result to (it can be the same + array as in)</dd></dl> +</li> +</ul> +<a name="applyTo(org.apache.commons.math3.geometry.euclidean.threed.Rotation)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>applyTo</h4> +<pre>public <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> applyTo(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r)</pre> +<div class="block">Apply the instance to another rotation. + <p> + Calling this method is equivalent to call + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#compose(org.apache.commons.math3.geometry.euclidean.threed.Rotation,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>compose(r, RotationConvention.VECTOR_OPERATOR)</code></a>. + </p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>r</code> - rotation to apply the rotation to</dd> +<dt><span class="strong">Returns:</span></dt><dd>a new rotation which is the composition of r by the instance</dd></dl> +</li> +</ul> +<a name="compose(org.apache.commons.math3.geometry.euclidean.threed.Rotation, org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>compose</h4> +<pre>public <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> compose(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention)</pre> +<div class="block">Compose the instance with another rotation. + <p> + If the semantics of the rotations composition corresponds to a + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html#VECTOR_OPERATOR"><code>vector operator</code></a> convention, + applying the instance to a rotation is computing the composition + in an order compliant with the following rule : let <code>u</code> be any + vector and <code>v</code> its image by <code>r1</code> (i.e. + <code>r1.applyTo(u) = v</code>). Let <code>w</code> be the image of <code>v</code> by + rotation <code>r2</code> (i.e. <code>r2.applyTo(v) = w</code>). Then + <code>w = comp.applyTo(u)</code>, where + <code>comp = r2.compose(r1, RotationConvention.VECTOR_OPERATOR)</code>. + </p> + <p> + If the semantics of the rotations composition corresponds to a + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html#FRAME_TRANSFORM"><code>frame transform</code></a> convention, + the application order will be reversed. So keeping the exact same + meaning of all <code>r1</code>, <code>r2</code>, <code>u</code>, <code>v</code>, <code>w</code> + and <code>comp</code> as above, <code>comp</code> could also be computed as + <code>comp = r1.compose(r2, RotationConvention.FRAME_TRANSFORM)</code>. + </p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>r</code> - rotation to apply the rotation to</dd><dd><code>convention</code> - convention to use for the semantics of the angle</dd> +<dt><span class="strong">Returns:</span></dt><dd>a new rotation which is the composition of r by the instance</dd></dl> +</li> +</ul> +<a name="applyInverseTo(org.apache.commons.math3.geometry.euclidean.threed.Rotation)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>applyInverseTo</h4> +<pre>public <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> applyInverseTo(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r)</pre> +<div class="block">Apply the inverse of the instance to another rotation. + <p> + Calling this method is equivalent to call + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html#composeInverse(org.apache.commons.math3.geometry.euclidean.threed.Rotation,%20org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"><code>composeInverse(r, RotationConvention.VECTOR_OPERATOR)</code></a>. + </p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>r</code> - rotation to apply the rotation to</dd> +<dt><span class="strong">Returns:</span></dt><dd>a new rotation which is the composition of r by the inverse + of the instance</dd></dl> +</li> +</ul> +<a name="composeInverse(org.apache.commons.math3.geometry.euclidean.threed.Rotation, org.apache.commons.math3.geometry.euclidean.threed.RotationConvention)"> +<!-- --> +</a> +<ul class="blockList"> +<li class="blockList"> +<h4>composeInverse</h4> +<pre>public <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> composeInverse(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed">RotationConvention</a> convention)</pre> +<div class="block">Compose the inverse of the instance with another rotation. + <p> + If the semantics of the rotations composition corresponds to a + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html#VECTOR_OPERATOR"><code>vector operator</code></a> convention, + applying the inverse of the instance to a rotation is computing + the composition in an order compliant with the following rule : + let <code>u</code> be any vector and <code>v</code> its image by <code>r1</code> + (i.e. <code>r1.applyTo(u) = v</code>). Let <code>w</code> be the inverse image + of <code>v</code> by <code>r2</code> (i.e. <code>r2.applyInverseTo(v) = w</code>). + Then <code>w = comp.applyTo(u)</code>, where + <code>comp = r2.composeInverse(r1)</code>. + </p> + <p> + If the semantics of the rotations composition corresponds to a + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html#FRAME_TRANSFORM"><code>frame transform</code></a> convention, + the application order will be reversed, which means it is the + <em>innermost</em> rotation that will be reversed. So keeping the exact same + meaning of all <code>r1</code>, <code>r2</code>, <code>u</code>, <code>v</code>, <code>w</code> + and <code>comp</code> as above, <code>comp</code> could also be computed as + <code>comp = r1.revert().composeInverse(r2.revert(), RotationConvention.FRAME_TRANSFORM)</code>. + </p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>r</code> - rotation to apply the rotation to</dd><dd><code>convention</code> - convention to use for the semantics of the angle</dd> +<dt><span class="strong">Returns:</span></dt><dd>a new rotation which is the composition of r by the inverse + of the instance</dd></dl> +</li> +</ul> +<a name="distance(org.apache.commons.math3.geometry.euclidean.threed.Rotation, org.apache.commons.math3.geometry.euclidean.threed.Rotation)"> +<!-- --> +</a> +<ul class="blockListLast"> +<li class="blockList"> +<h4>distance</h4> +<pre>public static double distance(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r1, + <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Rotation</a> r2)</pre> +<div class="block">Compute the <i>distance</i> between two rotations. + <p>The <i>distance</i> is intended here as a way to check if two + rotations are almost similar (i.e. they transform vectors the same way) + or very different. It is mathematically defined as the angle of + the rotation r that prepended to one of the rotations gives the other + one:</p> + <pre> + r<sub>1</sub>(r) = r<sub>2</sub> + </pre> + <p>This distance is an angle between 0 and π. Its value is the smallest + possible upper bound of the angle in radians between r<sub>1</sub>(v) + and r<sub>2</sub>(v) for all possible vectors v. This upper bound is + reached for some v. The distance is equal to 0 if and only if the two + rotations are identical.</p> + <p>Comparing two rotations should always be done using this value rather + than for example comparing the components of the quaternions. It is much + more stable, and has a geometric meaning. Also comparing quaternions + components is error prone since for example quaternions (0.36, 0.48, -0.48, -0.64) + and (-0.36, -0.48, 0.48, 0.64) represent exactly the same rotation despite + their components are different (they are exact opposites).</p></div> +<dl><dt><span class="strong">Parameters:</span></dt><dd><code>r1</code> - first rotation</dd><dd><code>r2</code> - second rotation</dd> +<dt><span class="strong">Returns:</span></dt><dd><i>distance</i> between r1 and r2</dd></dl> +</li> +</ul> +</li> +</ul> +</li> +</ul> +</div> +</div> +<!-- ========= END OF CLASS DATA ========= --> +<!-- ======= START OF BOTTOM NAVBAR ====== --> +<div class="bottomNav"><a name="navbar_bottom"> +<!-- --> +</a><a href="#skip-navbar_bottom" title="Skip navigation links"></a><a name="navbar_bottom_firstrow"> +<!-- --> +</a> +<ul class="navList" title="Navigation"> +<li><a href="../../../../../../../overview-summary.html">Overview</a></li> +<li><a href="package-summary.html">Package</a></li> +<li class="navBarCell1Rev">Class</li> +<li><a href="class-use/Rotation.html">Use</a></li> +<li><a href="package-tree.html">Tree</a></li> +<li><a href="../../../../../../../deprecated-list.html">Deprecated</a></li> +<li><a href="../../../../../../../index-all.html">Index</a></li> +<li><a href="../../../../../../../help-doc.html">Help</a></li> +</ul> +<div class="aboutLanguage"><em><script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script></em></div> +</div> +<div class="subNav"> +<ul class="navList"> +<li><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/PolyhedronsSet.html" title="class in org.apache.commons.math3.geometry.euclidean.threed"><span class="strong">Prev Class</span></a></li> +<li><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/RotationConvention.html" title="enum in org.apache.commons.math3.geometry.euclidean.threed"><span class="strong">Next Class</span></a></li> +</ul> +<ul class="navList"> +<li><a href="../../../../../../../index.html?org/apache/commons/math3/geometry/euclidean/threed/Rotation.html" target="_top">Frames</a></li> +<li><a href="Rotation.html" target="_top">No Frames</a></li> +</ul> +<ul class="navList" id="allclasses_navbar_bottom"> +<li><a href="../../../../../../../allclasses-noframe.html">All Classes</a></li> +</ul> +<div> +<script type="text/javascript"><!-- + allClassesLink = document.getElementById("allclasses_navbar_bottom"); + if(window==top) { + allClassesLink.style.display = "block"; + } + else { + allClassesLink.style.display = "none"; + } + //--> +</script> +</div> +<div> +<ul class="subNavList"> +<li>Summary: </li> +<li>Nested | </li> +<li><a href="#field_summary">Field</a> | </li> +<li><a href="#constructor_summary">Constr</a> | </li> +<li><a href="#method_summary">Method</a></li> +</ul> +<ul class="subNavList"> +<li>Detail: </li> +<li><a href="#field_detail">Field</a> | </li> +<li><a href="#constructor_detail">Constr</a> | </li> +<li><a href="#method_detail">Method</a></li> +</ul> +</div> +<a name="skip-navbar_bottom"> +<!-- --> +</a></div> +<!-- ======== END OF BOTTOM NAVBAR ======= --> +<p class="legalCopy"><small>Copyright © 2003–2016 <a href="http://www.apache.org/">The Apache Software Foundation</a>. 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