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| <li>Summary: </li> |
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| <div class="subTitle"><span class="packageLabelInType">Package</span> <a href="package-summary.html">org.apache.sis.referencing.operation.transform</a></div> |
| <h2 title="Interface LinearTransform" class="title">Interface LinearTransform</h2> |
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| <dl> |
| <dt>All Superinterfaces:</dt> |
| <dd><code><a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true" title="class or interface in org.opengis.referencing.operation" class="externalLink">MathTransform</a></code></dd> |
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| <hr> |
| <pre>public interface <span class="typeNameLabel">LinearTransform</span> |
| extends <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true" title="class or interface in org.opengis.referencing.operation" class="externalLink">MathTransform</a></pre> |
| <div class="block">A usually affine, or otherwise a projective transform, which convert coordinates using only linear equations. |
| A projective transform is capable of mapping an arbitrary quadrilateral into another arbitrary quadrilateral, |
| while preserving the straightness of lines. In the special case where the transform is affine, the parallelism |
| of lines in the source is preserved in the output. |
| |
| <p>Such a coordinate transformation can be represented by a matrix of arbitrary size, which is given by the |
| <a href="#getMatrix()"><code>getMatrix()</code></a> method. The relationship between matrix size and transform dimensions is as below:</p> |
| |
| <ul> |
| <li>The <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/Matrix.html?is-external=true#getNumCol()" title="class or interface in org.opengis.referencing.operation" class="externalLink">number of columns</a> in the matrix is equal to |
| the number of <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#getSourceDimensions()" title="class or interface in org.opengis.referencing.operation" class="externalLink">source dimensions</a> plus 1</li> |
| <li>The <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/Matrix.html?is-external=true#getNumRow()" title="class or interface in org.opengis.referencing.operation" class="externalLink">number of rows</a> in the matrix is equal to |
| the number of <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#getTargetDimensions()" title="class or interface in org.opengis.referencing.operation" class="externalLink">target dimensions</a> plus 1.</li> |
| </ul> |
| |
| <div class="section">Affine transform</div> |
| In most cases the transform in affine. For such transforms, the last matrix row contains only zero values |
| except in the last column, which contains 1. For example a conversion from projected coordinates (metres) |
| to display coordinates (pixel) can be done as below: |
| |
| <div style="text-align:center"> |
| <img src="../matrix/doc-files/AffineTransform.png" alt="Matrix representation of an affine transform"> |
| </div> |
| |
| <div class="section">Projective transform</div> |
| If the last matrix row does not met the above constraints, then the transform is not affine. |
| A <cite>projective</cite> transform can be used as a generalization of affine transforms. |
| In such case the computation performed by SIS is similar to <code>PerspectiveTransform</code> |
| in <cite>Java Advanced Imaging</cite>. |
| For example a square matrix of size 4×4 is used for transforming three-dimensional coordinates. |
| The transformed points <code>(x',y',z')</code> are computed as below: |
| |
| <div style="text-align:center"> <div class="horizontal-flow"> |
| <div> |
| <math display="block" alttext="MathML capable browser required"> |
| <mfenced open="[" close="]"> |
| <mtable> |
| <mtr><mtd><mi>x</mi><mo>'</mo></mtd></mtr> |
| <mtr><mtd><mi>y</mi><mo>'</mo></mtd></mtr> |
| <mtr><mtd><mi>z</mi><mo>'</mo></mtd></mtr> |
| </mtable> |
| </mfenced> |
| <mo>=</mo> |
| <mfenced open="[" close="]"> |
| <mtable> |
| <mtr><mtd><mi>u</mi><mo>/</mo><mi>t</mi></mtd></mtr> |
| <mtr><mtd><mi>v</mi><mo>/</mo><mi>t</mi></mtd></mtr> |
| <mtr><mtd><mi>w</mi><mo>/</mo><mi>t</mi></mtd></mtr> |
| </mtable> |
| </mfenced> |
| </math> |
| |
| </div><div style="vertical-align: middle" > |
| <blockquote>where <var>u</var>, <var>v</var>, <var>w</var> and <var>t</var> are obtained by</blockquote> |
| </div><div> |
| |
| <math display="block" alttext="MathML capable browser required"> |
| <mfenced open="[" close="]"> |
| <mtable> |
| <mtr><mtd><mi>u</mi></mtd></mtr> |
| <mtr><mtd><mi>v</mi></mtd></mtr> |
| <mtr><mtd><mi>w</mi></mtd></mtr> |
| <mtr><mtd><mi>t</mi></mtd></mtr> |
| </mtable> |
| </mfenced> |
| <mo>=</mo> |
| <mfenced open="[" close="]"> |
| <mtable> |
| <mtr> |
| <mtd><msub><mi>m</mi><mn>00</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>01</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>02</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>03</mn></msub></mtd> |
| </mtr> |
| <mtr> |
| <mtd><msub><mi>m</mi><mn>10</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>11</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>12</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>13</mn></msub></mtd> |
| </mtr> |
| <mtr> |
| <mtd><msub><mi>m</mi><mn>20</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>21</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>22</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>23</mn></msub></mtd> |
| </mtr> |
| <mtr> |
| <mtd><msub><mi>m</mi><mn>30</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>31</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>32</mn></msub></mtd> |
| <mtd><msub><mi>m</mi><mn>33</mn></msub></mtd> |
| </mtr> |
| </mtable> |
| </mfenced> |
| <mo>×</mo> |
| <mfenced open="[" close="]"> |
| <mtable> |
| <mtr><mtd><mi>x</mi></mtd></mtr> |
| <mtr><mtd><mi>y</mi></mtd></mtr> |
| <mtr><mtd><mi>z</mi></mtd></mtr> |
| <mtr><mtd><mn>1</mn></mtd></mtr> |
| </mtable> |
| </mfenced> |
| </math> |
| </div> |
| </div> |
| |
| |
| |
| |
| </div> |
| |
| <div class="section">Instantiation</div> |
| The easiest way to instantiate a <code>LinearTransform</code> is to use the <a href="MathTransforms.html#linear(org.opengis.referencing.operation.Matrix)"><code>MathTransforms.linear(Matrix)</code></a> |
| convenience method.</div> |
| <dl> |
| <dt><span class="simpleTagLabel">Since:</span></dt> |
| <dd>0.4</dd> |
| <dt><span class="seeLabel">See Also:</span></dt> |
| <dd><a href="MathTransforms.html#linear(org.opengis.referencing.operation.Matrix)"><code>MathTransforms.linear(Matrix)</code></a>, |
| <a href="../builder/LinearTransformBuilder.html" title="class in org.apache.sis.referencing.operation.builder"><code>LinearTransformBuilder</code></a>, |
| <a href="https://docs.oracle.com/javase/8/docs/api/java/awt/geom/AffineTransform.html?is-external=true" title="class or interface in java.awt.geom" class="externalLink"><code>AffineTransform</code></a>, |
| <a href="http://mathworld.wolfram.com/AffineTransformation.html">Affine transformation on MathWorld</a></dd> |
| |
| <p><font size="-1">Defined in the <code>sis-referencing</code> module</font></p> |
| </dl> |
| </li> |
| </ul> |
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| <h3>Method Summary</h3> |
| <table class="memberSummary"> |
| <caption><span id="t0" class="activeTableTab"><span>All Methods</span><span class="tabEnd"> </span></span><span id="t2" class="tableTab"><span><a href="javascript:show(2);">Instance Methods</a></span><span class="tabEnd"> </span></span><span id="t3" class="tableTab"><span><a href="javascript:show(4);">Abstract Methods</a></span><span class="tabEnd"> </span></span></caption> |
| <tr> |
| <th class="colFirst" scope="col">Modifier and Type</th> |
| <th class="colSecond" scope="col">Method</th> |
| <th class="colLast" scope="col">Description</th> |
| </tr> |
| <tr id="i0" class="altColor"> |
| <td class="colFirst"><code>void</code></td> |
| <th class="colSecond" scope="row"><code><span class="memberNameLink"><a href="#deltaTransform(double%5B%5D,int,double%5B%5D,int,int)">deltaTransform</a></span>​(double[] srcPts, |
| int srcOff, |
| double[] dstPts, |
| int dstOff, |
| int numPts)</code></th> |
| <td class="colLast"> |
| <div class="block">Transforms an array of relative distance vectors.</div> |
| </td> |
| </tr> |
| <tr id="i1" class="rowColor"> |
| <td class="colFirst"><code><a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/Matrix.html?is-external=true" title="class or interface in org.opengis.referencing.operation" class="externalLink">Matrix</a></code></td> |
| <th class="colSecond" scope="row"><code><span class="memberNameLink"><a href="#getMatrix()">getMatrix</a></span>()</code></th> |
| <td class="colLast"> |
| <div class="block">Returns the coefficients of this linear transform as a matrix.</div> |
| </td> |
| </tr> |
| <tr id="i2" class="altColor"> |
| <td class="colFirst"><code><a href="LinearTransform.html" title="interface in org.apache.sis.referencing.operation.transform">LinearTransform</a></code></td> |
| <th class="colSecond" scope="row"><code><span class="memberNameLink"><a href="#inverse()">inverse</a></span>()</code></th> |
| <td class="colLast"> |
| <div class="block">Returns the inverse transform of this object, which shall also be linear.</div> |
| </td> |
| </tr> |
| <tr id="i3" class="rowColor"> |
| <td class="colFirst"><code>boolean</code></td> |
| <th class="colSecond" scope="row"><code><span class="memberNameLink"><a href="#isAffine()">isAffine</a></span>()</code></th> |
| <td class="colLast"> |
| <div class="block">Returns <code>true</code> if this transform is affine.</div> |
| </td> |
| </tr> |
| </table> |
| <ul class="blockList"> |
| <li class="blockList"><a id="methods.inherited.from.class.MathTransform"> |
| <!-- --> |
| </a> |
| <h3>Methods inherited from interface <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true" title="class or interface in org.opengis.referencing.operation" class="externalLink">MathTransform</a></h3> |
| <code><a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#derivative(org.opengis.geometry.DirectPosition)" title="class or interface in org.opengis.referencing.operation" class="externalLink">derivative</a>, <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#getSourceDimensions()" title="class or interface in org.opengis.referencing.operation" class="externalLink">getSourceDimensions</a>, <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#getTargetDimensions()" title="class or interface in org.opengis.referencing.operation" class="externalLink">getTargetDimensions</a>, <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#isIdentity()" title="class or interface in org.opengis.referencing.operation" class="externalLink">isIdentity</a>, <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#toWKT()" title="class or interface in org.opengis.referencing.operation" class="externalLink">toWKT</a>, <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#transform(double%5B%5D,int,double%5B%5D,int,int)" title="class or interface in org.opengis.referencing.operation" class="externalLink">transform</a>, <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#transform(double%5B%5D,int,float%5B%5D,int,int)" title="class or interface in org.opengis.referencing.operation" class="externalLink">transform</a>, <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#transform(float%5B%5D,int,double%5B%5D,int,int)" title="class or interface in org.opengis.referencing.operation" class="externalLink">transform</a>, <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#transform(float%5B%5D,int,float%5B%5D,int,int)" title="class or interface in org.opengis.referencing.operation" class="externalLink">transform</a>, <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#transform(org.opengis.geometry.DirectPosition,org.opengis.geometry.DirectPosition)" title="class or interface in org.opengis.referencing.operation" class="externalLink">transform</a></code></li> |
| </ul> |
| </li> |
| </ul> |
| </section> |
| </li> |
| </ul> |
| </div> |
| <div class="details"> |
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| <!-- ============ METHOD DETAIL ========== --> |
| <section role="region"> |
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| </a> |
| <h3>Method Detail</h3> |
| <a id="isAffine()"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>isAffine</h4> |
| <pre class="methodSignature">boolean isAffine()</pre> |
| <div class="block">Returns <code>true</code> if this transform is affine. |
| An affine transform preserves parallelism.</div> |
| <dl> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd><code>true</code> if this transform is affine.</dd> |
| <dt><span class="simpleTagLabel">Since:</span></dt> |
| <dd>0.6</dd> |
| <dt><span class="seeLabel">See Also:</span></dt> |
| <dd><a href="../matrix/MatrixSIS.html#isAffine()"><code>MatrixSIS.isAffine()</code></a></dd> |
| </dl> |
| </li> |
| </ul> |
| <a id="getMatrix()"> |
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| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>getMatrix</h4> |
| <pre class="methodSignature"><a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/Matrix.html?is-external=true" title="class or interface in org.opengis.referencing.operation" class="externalLink">Matrix</a> getMatrix()</pre> |
| <div class="block">Returns the coefficients of this linear transform as a matrix. |
| Converting a coordinate with this <code>MathTransform</code> is equivalent to multiplying the |
| returned matrix by a vector containing the coordinate values with an additional 1 in the last row. |
| See <a href="LinearTransform.html" title="interface in org.apache.sis.referencing.operation.transform"><code>LinearTransform</code></a> class Javadoc for more details.</div> |
| <dl> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>the coefficients of this linear transform as a matrix.</dd> |
| <dt><span class="seeLabel">See Also:</span></dt> |
| <dd><a href="MathTransforms.html#getMatrix(org.opengis.referencing.operation.MathTransform)"><code>MathTransforms.getMatrix(MathTransform)</code></a></dd> |
| </dl> |
| </li> |
| </ul> |
| <a id="deltaTransform(double[],int,double[],int,int)"> |
| <!-- --> |
| </a> |
| <ul class="blockList"> |
| <li class="blockList"> |
| <h4>deltaTransform</h4> |
| <pre class="methodSignature">void deltaTransform​(double[] srcPts, |
| int srcOff, |
| double[] dstPts, |
| int dstOff, |
| int numPts) |
| throws <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/TransformException.html?is-external=true" title="class or interface in org.opengis.referencing.operation" class="externalLink">TransformException</a></pre> |
| <div class="block">Transforms an array of relative distance vectors. |
| Distance vectors are transformed without applying the translation components. |
| The supplied array of distance values will contain packed values. |
| |
| <div class="note"><b>Example:</b> if the source dimension is 3, then the values will be packed in this order: |
| (<var>Δx₀</var>,<var>Δy₀</var>,<var>Δz₀</var>, |
| <var>Δx₁</var>,<var>Δy₁</var>,<var>Δz₁</var> …). |
| </div></div> |
| <dl> |
| <dt><span class="paramLabel">Parameters:</span></dt> |
| <dd><code>srcPts</code> - the array containing the source vectors.</dd> |
| <dd><code>srcOff</code> - the offset to the first vector to be transformed in the source array.</dd> |
| <dd><code>dstPts</code> - the array into which the transformed vectors are returned. Can be the same than <code>srcPts</code>.</dd> |
| <dd><code>dstOff</code> - the offset to the location of the first transformed vector that is stored in the destination array.</dd> |
| <dd><code>numPts</code> - the number of vector objects to be transformed.</dd> |
| <dt><span class="throwsLabel">Throws:</span></dt> |
| <dd><code><a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/TransformException.html?is-external=true" title="class or interface in org.opengis.referencing.operation" class="externalLink">TransformException</a></code> - if a vector can not be transformed.</dd> |
| <dt><span class="simpleTagLabel">Since:</span></dt> |
| <dd>0.7</dd> |
| <dt><span class="seeLabel">See Also:</span></dt> |
| <dd><a href="https://docs.oracle.com/javase/8/docs/api/java/awt/geom/AffineTransform.html?is-external=true#deltaTransform(double%5B%5D,int,double%5B%5D,int,int)" title="class or interface in java.awt.geom" class="externalLink"><code>AffineTransform.deltaTransform(double[], int, double[], int, int)</code></a></dd> |
| </dl> |
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| </ul> |
| <a id="inverse()"> |
| <!-- --> |
| </a> |
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| <h4>inverse</h4> |
| <pre class="methodSignature"><a href="LinearTransform.html" title="interface in org.apache.sis.referencing.operation.transform">LinearTransform</a> inverse() |
| throws <a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/NoninvertibleTransformException.html?is-external=true" title="class or interface in org.opengis.referencing.operation" class="externalLink">NoninvertibleTransformException</a></pre> |
| <div class="block">Returns the inverse transform of this object, which shall also be linear. |
| The target of the inverse transform is the source of the original. |
| The source of the inverse transform is the target of the original.</div> |
| <dl> |
| <dt><span class="overrideSpecifyLabel">Specified by:</span></dt> |
| <dd><code><a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true#inverse()" title="class or interface in org.opengis.referencing.operation" class="externalLink">inverse</a></code> in interface <code><a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/MathTransform.html?is-external=true" title="class or interface in org.opengis.referencing.operation" class="externalLink">MathTransform</a></code></dd> |
| <dt><span class="returnLabel">Returns:</span></dt> |
| <dd>the inverse transform.</dd> |
| <dt><span class="throwsLabel">Throws:</span></dt> |
| <dd><code><a href="http://www.geoapi.org/3.0/javadoc/org/opengis/referencing/operation/NoninvertibleTransformException.html?is-external=true" title="class or interface in org.opengis.referencing.operation" class="externalLink">NoninvertibleTransformException</a></code> - if the transform can not be inverted.</dd> |
| <dt><span class="simpleTagLabel">Since:</span></dt> |
| <dd>0.7</dd> |
| <dt><span class="seeLabel">See Also:</span></dt> |
| <dd><a href="https://docs.oracle.com/javase/8/docs/api/java/awt/geom/AffineTransform.html?is-external=true#createInverse()" title="class or interface in java.awt.geom" class="externalLink"><code>AffineTransform.createInverse()</code></a></dd> |
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