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| <div class="subTitle">org.apache.commons.math3.geometry.euclidean.threed</div> |
| <h2 title="Class SphericalCoordinates" class="title">Class SphericalCoordinates</h2> |
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| <li>org.apache.commons.math3.geometry.euclidean.threed.SphericalCoordinates</li> |
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| <pre>public class <span class="strong">SphericalCoordinates</span> |
| extends <a href="http://docs.oracle.com/javase/6/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/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</a></pre> |
| <div class="block">This class provides conversions related to <a |
| href="http://mathworld.wolfram.com/SphericalCoordinates.html">spherical coordinates</a>. |
| <p> |
| The conventions used here are the mathematical ones, i.e. spherical coordinates are |
| related to Cartesian coordinates as follows: |
| </p> |
| <ul> |
| <li>x = r cos(θ) sin(Φ)</li> |
| <li>y = r sin(θ) sin(Φ)</li> |
| <li>z = r cos(Φ)</li> |
| </ul> |
| <ul> |
| <li>r = √(x<sup>2</sup>+y<sup>2</sup>+z<sup>2</sup>)</li> |
| <li>θ = atan2(y, x)</li> |
| <li>Φ = acos(z/r)</li> |
| </ul> |
| <p> |
| r is the radius, θ is the azimuthal angle in the x-y plane and Φ is the polar |
| (co-latitude) angle. These conventions are <em>different</em> from the conventions used |
| in physics (and in particular in spherical harmonics) where the meanings of θ and |
| Φ are reversed. |
| </p> |
| <p> |
| This class provides conversion of coordinates and also of gradient and Hessian |
| between spherical and Cartesian coordinates. |
| </p></div> |
| <dl><dt><span class="strong">Since:</span></dt> |
| <dd>3.2</dd> |
| <dt><span class="strong">Version:</span></dt> |
| <dd>$Id: SphericalCoordinates.java 1443364 2013-02-07 09:28:04Z luc $</dd> |
| <dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../../serialized-form.html#org.apache.commons.math3.geometry.euclidean.threed.SphericalCoordinates">Serialized Form</a></dd></dl> |
| </li> |
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| <td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#SphericalCoordinates(double, double, double)">SphericalCoordinates</a></strong>(double r, |
| double theta, |
| double phi)</code> |
| <div class="block">Build a spherical coordinates transformer from spherical coordinates.</div> |
| </td> |
| </tr> |
| <tr class="rowColor"> |
| <td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#SphericalCoordinates(org.apache.commons.math3.geometry.euclidean.threed.Vector3D)">SphericalCoordinates</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> v)</code> |
| <div class="block">Build a spherical coordinates transformer from Cartesian coordinates.</div> |
| </td> |
| </tr> |
| </table> |
| </li> |
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| <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/SphericalCoordinates.html#getCartesian()">getCartesian</a></strong>()</code> |
| <div class="block">Get the Cartesian coordinates.</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/SphericalCoordinates.html#getPhi()">getPhi</a></strong>()</code> |
| <div class="block">Get the polar (co-latitude) angle.</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/SphericalCoordinates.html#getR()">getR</a></strong>()</code> |
| <div class="block">Get the radius.</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/SphericalCoordinates.html#getTheta()">getTheta</a></strong>()</code> |
| <div class="block">Get the azimuthal angle in x-y plane.</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/SphericalCoordinates.html#toCartesianGradient(double[])">toCartesianGradient</a></strong>(double[] sGradient)</code> |
| <div class="block">Convert a gradient with respect to spherical coordinates into a gradient |
| with respect to Cartesian coordinates.</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/SphericalCoordinates.html#toCartesianHessian(double[][], double[])">toCartesianHessian</a></strong>(double[][] sHessian, |
| double[] sGradient)</code> |
| <div class="block">Convert a Hessian with respect to spherical coordinates into a Hessian |
| with respect to Cartesian coordinates.</div> |
| </td> |
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| <a name="SphericalCoordinates(org.apache.commons.math3.geometry.euclidean.threed.Vector3D)"> |
| <!-- --> |
| </a> |
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| <h4>SphericalCoordinates</h4> |
| <pre>public SphericalCoordinates(<a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/Vector3D.html" title="class in org.apache.commons.math3.geometry.euclidean.threed">Vector3D</a> v)</pre> |
| <div class="block">Build a spherical coordinates transformer from Cartesian coordinates.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>v</code> - Cartesian coordinates</dd></dl> |
| </li> |
| </ul> |
| <a name="SphericalCoordinates(double, double, double)"> |
| <!-- --> |
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| <h4>SphericalCoordinates</h4> |
| <pre>public SphericalCoordinates(double r, |
| double theta, |
| double phi)</pre> |
| <div class="block">Build a spherical coordinates transformer from spherical coordinates.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>r</code> - radius</dd><dd><code>theta</code> - azimuthal angle in x-y plane</dd><dd><code>phi</code> - polar (co-latitude) angle</dd></dl> |
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| <a name="getCartesian()"> |
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| <h4>getCartesian</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> getCartesian()</pre> |
| <div class="block">Get the Cartesian coordinates.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>Cartesian coordinates</dd></dl> |
| </li> |
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| <a name="getR()"> |
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| <h4>getR</h4> |
| <pre>public double getR()</pre> |
| <div class="block">Get the radius.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>radius r</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getTheta()"><code>getTheta()</code></a>, |
| <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getPhi()"><code>getPhi()</code></a></dd></dl> |
| </li> |
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| <a name="getTheta()"> |
| <!-- --> |
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| <h4>getTheta</h4> |
| <pre>public double getTheta()</pre> |
| <div class="block">Get the azimuthal angle in x-y plane.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>azimuthal angle in x-y plane θ</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getR()"><code>getR()</code></a>, |
| <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getPhi()"><code>getPhi()</code></a></dd></dl> |
| </li> |
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| <a name="getPhi()"> |
| <!-- --> |
| </a> |
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| <li class="blockList"> |
| <h4>getPhi</h4> |
| <pre>public double getPhi()</pre> |
| <div class="block">Get the polar (co-latitude) angle.</div> |
| <dl><dt><span class="strong">Returns:</span></dt><dd>polar (co-latitude) angle Φ</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getR()"><code>getR()</code></a>, |
| <a href="../../../../../../../org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.html#getTheta()"><code>getTheta()</code></a></dd></dl> |
| </li> |
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| <h4>toCartesianGradient</h4> |
| <pre>public double[] toCartesianGradient(double[] sGradient)</pre> |
| <div class="block">Convert a gradient with respect to spherical coordinates into a gradient |
| with respect to Cartesian coordinates.</div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>sGradient</code> - gradient with respect to spherical coordinates |
| {df/dr, df/dθ, df/dΦ}</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>gradient with respect to Cartesian coordinates |
| {df/dx, df/dy, df/dz}</dd></dl> |
| </li> |
| </ul> |
| <a name="toCartesianHessian(double[][], double[])"> |
| <!-- --> |
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| <h4>toCartesianHessian</h4> |
| <pre>public double[][] toCartesianHessian(double[][] sHessian, |
| double[] sGradient)</pre> |
| <div class="block">Convert a Hessian with respect to spherical coordinates into a Hessian |
| with respect to Cartesian coordinates. |
| <p> |
| As Hessian are always symmetric, we use only the lower left part of the provided |
| spherical Hessian, so the upper part may not be initialized. However, we still |
| do fill up the complete array we create, with guaranteed symmetry. |
| </p></div> |
| <dl><dt><span class="strong">Parameters:</span></dt><dd><code>sHessian</code> - Hessian with respect to spherical coordinates |
| {{d<sup>2</sup>f/dr<sup>2</sup>, d<sup>2</sup>f/drdθ, d<sup>2</sup>f/drdΦ}, |
| {d<sup>2</sup>f/drdθ, d<sup>2</sup>f/dθ<sup>2</sup>, d<sup>2</sup>f/dθdΦ}, |
| {d<sup>2</sup>f/drdΦ, d<sup>2</sup>f/dθdΦ, d<sup>2</sup>f/dΦ<sup>2</sup>}</dd><dd><code>sGradient</code> - gradient with respect to spherical coordinates |
| {df/dr, df/dθ, df/dΦ}</dd> |
| <dt><span class="strong">Returns:</span></dt><dd>Hessian with respect to Cartesian coordinates |
| {{d<sup>2</sup>f/dx<sup>2</sup>, d<sup>2</sup>f/dxdy, d<sup>2</sup>f/dxdz}, |
| {d<sup>2</sup>f/dxdy, d<sup>2</sup>f/dy<sup>2</sup>, d<sup>2</sup>f/dydz}, |
| {d<sup>2</sup>f/dxdz, d<sup>2</sup>f/dydz, d<sup>2</sup>f/dz<sup>2</sup>}}</dd></dl> |
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