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Posted to commits@commons.apache.org by er...@apache.org on 2014/12/30 18:15:37 UTC
svn commit: r934426 [8/10] - in
/websites/production/commons/content/proper/commons-math/apidocs:
org/apache/commons/math3/analysis/interpolation/
org/apache/commons/math3/analysis/interpolation/class-use/
org/apache/commons/math3/fitting/ org/apache/c...
Added: websites/production/commons/content/proper/commons-math/apidocs/src-html/org/apache/commons/math3/geometry/partitioning/BSPTree.VanishingCutHandler.html
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--- websites/production/commons/content/proper/commons-math/apidocs/src-html/org/apache/commons/math3/geometry/partitioning/BSPTree.VanishingCutHandler.html (added)
+++ websites/production/commons/content/proper/commons-math/apidocs/src-html/org/apache/commons/math3/geometry/partitioning/BSPTree.VanishingCutHandler.html Tue Dec 30 17:15:36 2014
@@ -0,0 +1,889 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
+<html lang="en">
+<head>
+<title>Source code</title>
+<link rel="stylesheet" type="text/css" href="../../../../../../../stylesheet.css" title="Style">
+</head>
+<body>
+<div class="sourceContainer">
+<pre><span class="sourceLineNo">001</span>/*<a name="line.1"></a>
+<span class="sourceLineNo">002</span> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
+<span class="sourceLineNo">003</span> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a>
+<span class="sourceLineNo">004</span> * this work for additional information regarding copyright ownership.<a name="line.4"></a>
+<span class="sourceLineNo">005</span> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
+<span class="sourceLineNo">006</span> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
+<span class="sourceLineNo">007</span> * the License. You may obtain a copy of the License at<a name="line.7"></a>
+<span class="sourceLineNo">008</span> *<a name="line.8"></a>
+<span class="sourceLineNo">009</span> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
+<span class="sourceLineNo">010</span> *<a name="line.10"></a>
+<span class="sourceLineNo">011</span> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
+<span class="sourceLineNo">012</span> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
+<span class="sourceLineNo">013</span> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
+<span class="sourceLineNo">014</span> * See the License for the specific language governing permissions and<a name="line.14"></a>
+<span class="sourceLineNo">015</span> * limitations under the License.<a name="line.15"></a>
+<span class="sourceLineNo">016</span> */<a name="line.16"></a>
+<span class="sourceLineNo">017</span>package org.apache.commons.math3.geometry.partitioning;<a name="line.17"></a>
+<span class="sourceLineNo">018</span><a name="line.18"></a>
+<span class="sourceLineNo">019</span>import java.util.ArrayList;<a name="line.19"></a>
+<span class="sourceLineNo">020</span>import java.util.List;<a name="line.20"></a>
+<span class="sourceLineNo">021</span><a name="line.21"></a>
+<span class="sourceLineNo">022</span>import org.apache.commons.math3.exception.MathIllegalStateException;<a name="line.22"></a>
+<span class="sourceLineNo">023</span>import org.apache.commons.math3.exception.MathInternalError;<a name="line.23"></a>
+<span class="sourceLineNo">024</span>import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.24"></a>
+<span class="sourceLineNo">025</span>import org.apache.commons.math3.geometry.Point;<a name="line.25"></a>
+<span class="sourceLineNo">026</span>import org.apache.commons.math3.geometry.Space;<a name="line.26"></a>
+<span class="sourceLineNo">027</span>import org.apache.commons.math3.geometry.Vector;<a name="line.27"></a>
+<span class="sourceLineNo">028</span>import org.apache.commons.math3.util.FastMath;<a name="line.28"></a>
+<span class="sourceLineNo">029</span><a name="line.29"></a>
+<span class="sourceLineNo">030</span>/** This class represent a Binary Space Partition tree.<a name="line.30"></a>
+<span class="sourceLineNo">031</span><a name="line.31"></a>
+<span class="sourceLineNo">032</span> * <p>BSP trees are an efficient way to represent space partitions and<a name="line.32"></a>
+<span class="sourceLineNo">033</span> * to associate attributes with each cell. Each node in a BSP tree<a name="line.33"></a>
+<span class="sourceLineNo">034</span> * represents a convex region which is partitioned in two convex<a name="line.34"></a>
+<span class="sourceLineNo">035</span> * sub-regions at each side of a cut hyperplane. The root tree<a name="line.35"></a>
+<span class="sourceLineNo">036</span> * contains the complete space.</p><a name="line.36"></a>
+<span class="sourceLineNo">037</span><a name="line.37"></a>
+<span class="sourceLineNo">038</span> * <p>The main use of such partitions is to use a boolean attribute to<a name="line.38"></a>
+<span class="sourceLineNo">039</span> * define an inside/outside property, hence representing arbitrary<a name="line.39"></a>
+<span class="sourceLineNo">040</span> * polytopes (line segments in 1D, polygons in 2D and polyhedrons in<a name="line.40"></a>
+<span class="sourceLineNo">041</span> * 3D) and to operate on them.</p><a name="line.41"></a>
+<span class="sourceLineNo">042</span><a name="line.42"></a>
+<span class="sourceLineNo">043</span> * <p>Another example would be to represent Voronoi tesselations, the<a name="line.43"></a>
+<span class="sourceLineNo">044</span> * attribute of each cell holding the defining point of the cell.</p><a name="line.44"></a>
+<span class="sourceLineNo">045</span><a name="line.45"></a>
+<span class="sourceLineNo">046</span> * <p>The application-defined attributes are shared among copied<a name="line.46"></a>
+<span class="sourceLineNo">047</span> * instances and propagated to split parts. These attributes are not<a name="line.47"></a>
+<span class="sourceLineNo">048</span> * used by the BSP-tree algorithms themselves, so the application can<a name="line.48"></a>
+<span class="sourceLineNo">049</span> * use them for any purpose. Since the tree visiting method holds<a name="line.49"></a>
+<span class="sourceLineNo">050</span> * internal and leaf nodes differently, it is possible to use<a name="line.50"></a>
+<span class="sourceLineNo">051</span> * different classes for internal nodes attributes and leaf nodes<a name="line.51"></a>
+<span class="sourceLineNo">052</span> * attributes. This should be used with care, though, because if the<a name="line.52"></a>
+<span class="sourceLineNo">053</span> * tree is modified in any way after attributes have been set, some<a name="line.53"></a>
+<span class="sourceLineNo">054</span> * internal nodes may become leaf nodes and some leaf nodes may become<a name="line.54"></a>
+<span class="sourceLineNo">055</span> * internal nodes.</p><a name="line.55"></a>
+<span class="sourceLineNo">056</span><a name="line.56"></a>
+<span class="sourceLineNo">057</span> * <p>One of the main sources for the development of this package was<a name="line.57"></a>
+<span class="sourceLineNo">058</span> * Bruce Naylor, John Amanatides and William Thibault paper <a<a name="line.58"></a>
+<span class="sourceLineNo">059</span> * href="http://www.cs.yorku.ca/~amana/research/bsptSetOp.pdf">Merging<a name="line.59"></a>
+<span class="sourceLineNo">060</span> * BSP Trees Yields Polyhedral Set Operations</a> Proc. Siggraph '90,<a name="line.60"></a>
+<span class="sourceLineNo">061</span> * Computer Graphics 24(4), August 1990, pp 115-124, published by the<a name="line.61"></a>
+<span class="sourceLineNo">062</span> * Association for Computing Machinery (ACM).</p><a name="line.62"></a>
+<span class="sourceLineNo">063</span><a name="line.63"></a>
+<span class="sourceLineNo">064</span> * @param <S> Type of the space.<a name="line.64"></a>
+<span class="sourceLineNo">065</span><a name="line.65"></a>
+<span class="sourceLineNo">066</span> * @since 3.0<a name="line.66"></a>
+<span class="sourceLineNo">067</span> */<a name="line.67"></a>
+<span class="sourceLineNo">068</span>public class BSPTree<S extends Space> {<a name="line.68"></a>
+<span class="sourceLineNo">069</span><a name="line.69"></a>
+<span class="sourceLineNo">070</span> /** Cut sub-hyperplane. */<a name="line.70"></a>
+<span class="sourceLineNo">071</span> private SubHyperplane<S> cut;<a name="line.71"></a>
+<span class="sourceLineNo">072</span><a name="line.72"></a>
+<span class="sourceLineNo">073</span> /** Tree at the plus side of the cut hyperplane. */<a name="line.73"></a>
+<span class="sourceLineNo">074</span> private BSPTree<S> plus;<a name="line.74"></a>
+<span class="sourceLineNo">075</span><a name="line.75"></a>
+<span class="sourceLineNo">076</span> /** Tree at the minus side of the cut hyperplane. */<a name="line.76"></a>
+<span class="sourceLineNo">077</span> private BSPTree<S> minus;<a name="line.77"></a>
+<span class="sourceLineNo">078</span><a name="line.78"></a>
+<span class="sourceLineNo">079</span> /** Parent tree. */<a name="line.79"></a>
+<span class="sourceLineNo">080</span> private BSPTree<S> parent;<a name="line.80"></a>
+<span class="sourceLineNo">081</span><a name="line.81"></a>
+<span class="sourceLineNo">082</span> /** Application-defined attribute. */<a name="line.82"></a>
+<span class="sourceLineNo">083</span> private Object attribute;<a name="line.83"></a>
+<span class="sourceLineNo">084</span><a name="line.84"></a>
+<span class="sourceLineNo">085</span> /** Build a tree having only one root cell representing the whole space.<a name="line.85"></a>
+<span class="sourceLineNo">086</span> */<a name="line.86"></a>
+<span class="sourceLineNo">087</span> public BSPTree() {<a name="line.87"></a>
+<span class="sourceLineNo">088</span> cut = null;<a name="line.88"></a>
+<span class="sourceLineNo">089</span> plus = null;<a name="line.89"></a>
+<span class="sourceLineNo">090</span> minus = null;<a name="line.90"></a>
+<span class="sourceLineNo">091</span> parent = null;<a name="line.91"></a>
+<span class="sourceLineNo">092</span> attribute = null;<a name="line.92"></a>
+<span class="sourceLineNo">093</span> }<a name="line.93"></a>
+<span class="sourceLineNo">094</span><a name="line.94"></a>
+<span class="sourceLineNo">095</span> /** Build a tree having only one root cell representing the whole space.<a name="line.95"></a>
+<span class="sourceLineNo">096</span> * @param attribute attribute of the tree (may be null)<a name="line.96"></a>
+<span class="sourceLineNo">097</span> */<a name="line.97"></a>
+<span class="sourceLineNo">098</span> public BSPTree(final Object attribute) {<a name="line.98"></a>
+<span class="sourceLineNo">099</span> cut = null;<a name="line.99"></a>
+<span class="sourceLineNo">100</span> plus = null;<a name="line.100"></a>
+<span class="sourceLineNo">101</span> minus = null;<a name="line.101"></a>
+<span class="sourceLineNo">102</span> parent = null;<a name="line.102"></a>
+<span class="sourceLineNo">103</span> this.attribute = attribute;<a name="line.103"></a>
+<span class="sourceLineNo">104</span> }<a name="line.104"></a>
+<span class="sourceLineNo">105</span><a name="line.105"></a>
+<span class="sourceLineNo">106</span> /** Build a BSPTree from its underlying elements.<a name="line.106"></a>
+<span class="sourceLineNo">107</span> * <p>This method does <em>not</em> perform any verification on<a name="line.107"></a>
+<span class="sourceLineNo">108</span> * consistency of its arguments, it should therefore be used only<a name="line.108"></a>
+<span class="sourceLineNo">109</span> * when then caller knows what it is doing.</p><a name="line.109"></a>
+<span class="sourceLineNo">110</span> * <p>This method is mainly useful to build trees<a name="line.110"></a>
+<span class="sourceLineNo">111</span> * bottom-up. Building trees top-down is realized with the help of<a name="line.111"></a>
+<span class="sourceLineNo">112</span> * method {@link #insertCut insertCut}.</p><a name="line.112"></a>
+<span class="sourceLineNo">113</span> * @param cut cut sub-hyperplane for the tree<a name="line.113"></a>
+<span class="sourceLineNo">114</span> * @param plus plus side sub-tree<a name="line.114"></a>
+<span class="sourceLineNo">115</span> * @param minus minus side sub-tree<a name="line.115"></a>
+<span class="sourceLineNo">116</span> * @param attribute attribute associated with the node (may be null)<a name="line.116"></a>
+<span class="sourceLineNo">117</span> * @see #insertCut<a name="line.117"></a>
+<span class="sourceLineNo">118</span> */<a name="line.118"></a>
+<span class="sourceLineNo">119</span> public BSPTree(final SubHyperplane<S> cut, final BSPTree<S> plus, final BSPTree<S> minus,<a name="line.119"></a>
+<span class="sourceLineNo">120</span> final Object attribute) {<a name="line.120"></a>
+<span class="sourceLineNo">121</span> this.cut = cut;<a name="line.121"></a>
+<span class="sourceLineNo">122</span> this.plus = plus;<a name="line.122"></a>
+<span class="sourceLineNo">123</span> this.minus = minus;<a name="line.123"></a>
+<span class="sourceLineNo">124</span> this.parent = null;<a name="line.124"></a>
+<span class="sourceLineNo">125</span> this.attribute = attribute;<a name="line.125"></a>
+<span class="sourceLineNo">126</span> plus.parent = this;<a name="line.126"></a>
+<span class="sourceLineNo">127</span> minus.parent = this;<a name="line.127"></a>
+<span class="sourceLineNo">128</span> }<a name="line.128"></a>
+<span class="sourceLineNo">129</span><a name="line.129"></a>
+<span class="sourceLineNo">130</span> /** Insert a cut sub-hyperplane in a node.<a name="line.130"></a>
+<span class="sourceLineNo">131</span> * <p>The sub-tree starting at this node will be completely<a name="line.131"></a>
+<span class="sourceLineNo">132</span> * overwritten. The new cut sub-hyperplane will be built from the<a name="line.132"></a>
+<span class="sourceLineNo">133</span> * intersection of the provided hyperplane with the cell. If the<a name="line.133"></a>
+<span class="sourceLineNo">134</span> * hyperplane does intersect the cell, the cell will have two<a name="line.134"></a>
+<span class="sourceLineNo">135</span> * children cells with {@code null} attributes on each side of<a name="line.135"></a>
+<span class="sourceLineNo">136</span> * the inserted cut sub-hyperplane. If the hyperplane does not<a name="line.136"></a>
+<span class="sourceLineNo">137</span> * intersect the cell then <em>no</em> cut hyperplane will be<a name="line.137"></a>
+<span class="sourceLineNo">138</span> * inserted and the cell will be changed to a leaf cell. The<a name="line.138"></a>
+<span class="sourceLineNo">139</span> * attribute of the node is never changed.</p><a name="line.139"></a>
+<span class="sourceLineNo">140</span> * <p>This method is mainly useful when called on leaf nodes<a name="line.140"></a>
+<span class="sourceLineNo">141</span> * (i.e. nodes for which {@link #getCut getCut} returns<a name="line.141"></a>
+<span class="sourceLineNo">142</span> * {@code null}), in this case it provides a way to build a<a name="line.142"></a>
+<span class="sourceLineNo">143</span> * tree top-down (whereas the {@link #BSPTree(SubHyperplane,<a name="line.143"></a>
+<span class="sourceLineNo">144</span> * BSPTree, BSPTree, Object) 4 arguments constructor} is devoted to<a name="line.144"></a>
+<span class="sourceLineNo">145</span> * build trees bottom-up).</p><a name="line.145"></a>
+<span class="sourceLineNo">146</span> * @param hyperplane hyperplane to insert, it will be chopped in<a name="line.146"></a>
+<span class="sourceLineNo">147</span> * order to fit in the cell defined by the parent nodes of the<a name="line.147"></a>
+<span class="sourceLineNo">148</span> * instance<a name="line.148"></a>
+<span class="sourceLineNo">149</span> * @return true if a cut sub-hyperplane has been inserted (i.e. if<a name="line.149"></a>
+<span class="sourceLineNo">150</span> * the cell now has two leaf child nodes)<a name="line.150"></a>
+<span class="sourceLineNo">151</span> * @see #BSPTree(SubHyperplane, BSPTree, BSPTree, Object)<a name="line.151"></a>
+<span class="sourceLineNo">152</span> */<a name="line.152"></a>
+<span class="sourceLineNo">153</span> public boolean insertCut(final Hyperplane<S> hyperplane) {<a name="line.153"></a>
+<span class="sourceLineNo">154</span><a name="line.154"></a>
+<span class="sourceLineNo">155</span> if (cut != null) {<a name="line.155"></a>
+<span class="sourceLineNo">156</span> plus.parent = null;<a name="line.156"></a>
+<span class="sourceLineNo">157</span> minus.parent = null;<a name="line.157"></a>
+<span class="sourceLineNo">158</span> }<a name="line.158"></a>
+<span class="sourceLineNo">159</span><a name="line.159"></a>
+<span class="sourceLineNo">160</span> final SubHyperplane<S> chopped = fitToCell(hyperplane.wholeHyperplane());<a name="line.160"></a>
+<span class="sourceLineNo">161</span> if (chopped == null || chopped.isEmpty()) {<a name="line.161"></a>
+<span class="sourceLineNo">162</span> cut = null;<a name="line.162"></a>
+<span class="sourceLineNo">163</span> plus = null;<a name="line.163"></a>
+<span class="sourceLineNo">164</span> minus = null;<a name="line.164"></a>
+<span class="sourceLineNo">165</span> return false;<a name="line.165"></a>
+<span class="sourceLineNo">166</span> }<a name="line.166"></a>
+<span class="sourceLineNo">167</span><a name="line.167"></a>
+<span class="sourceLineNo">168</span> cut = chopped;<a name="line.168"></a>
+<span class="sourceLineNo">169</span> plus = new BSPTree<S>();<a name="line.169"></a>
+<span class="sourceLineNo">170</span> plus.parent = this;<a name="line.170"></a>
+<span class="sourceLineNo">171</span> minus = new BSPTree<S>();<a name="line.171"></a>
+<span class="sourceLineNo">172</span> minus.parent = this;<a name="line.172"></a>
+<span class="sourceLineNo">173</span> return true;<a name="line.173"></a>
+<span class="sourceLineNo">174</span><a name="line.174"></a>
+<span class="sourceLineNo">175</span> }<a name="line.175"></a>
+<span class="sourceLineNo">176</span><a name="line.176"></a>
+<span class="sourceLineNo">177</span> /** Copy the instance.<a name="line.177"></a>
+<span class="sourceLineNo">178</span> * <p>The instance created is completely independent of the original<a name="line.178"></a>
+<span class="sourceLineNo">179</span> * one. A deep copy is used, none of the underlying objects are<a name="line.179"></a>
+<span class="sourceLineNo">180</span> * shared (except for the nodes attributes and immutable<a name="line.180"></a>
+<span class="sourceLineNo">181</span> * objects).</p><a name="line.181"></a>
+<span class="sourceLineNo">182</span> * @return a new tree, copy of the instance<a name="line.182"></a>
+<span class="sourceLineNo">183</span> */<a name="line.183"></a>
+<span class="sourceLineNo">184</span> public BSPTree<S> copySelf() {<a name="line.184"></a>
+<span class="sourceLineNo">185</span><a name="line.185"></a>
+<span class="sourceLineNo">186</span> if (cut == null) {<a name="line.186"></a>
+<span class="sourceLineNo">187</span> return new BSPTree<S>(attribute);<a name="line.187"></a>
+<span class="sourceLineNo">188</span> }<a name="line.188"></a>
+<span class="sourceLineNo">189</span><a name="line.189"></a>
+<span class="sourceLineNo">190</span> return new BSPTree<S>(cut.copySelf(), plus.copySelf(), minus.copySelf(),<a name="line.190"></a>
+<span class="sourceLineNo">191</span> attribute);<a name="line.191"></a>
+<span class="sourceLineNo">192</span><a name="line.192"></a>
+<span class="sourceLineNo">193</span> }<a name="line.193"></a>
+<span class="sourceLineNo">194</span><a name="line.194"></a>
+<span class="sourceLineNo">195</span> /** Get the cut sub-hyperplane.<a name="line.195"></a>
+<span class="sourceLineNo">196</span> * @return cut sub-hyperplane, null if this is a leaf tree<a name="line.196"></a>
+<span class="sourceLineNo">197</span> */<a name="line.197"></a>
+<span class="sourceLineNo">198</span> public SubHyperplane<S> getCut() {<a name="line.198"></a>
+<span class="sourceLineNo">199</span> return cut;<a name="line.199"></a>
+<span class="sourceLineNo">200</span> }<a name="line.200"></a>
+<span class="sourceLineNo">201</span><a name="line.201"></a>
+<span class="sourceLineNo">202</span> /** Get the tree on the plus side of the cut hyperplane.<a name="line.202"></a>
+<span class="sourceLineNo">203</span> * @return tree on the plus side of the cut hyperplane, null if this<a name="line.203"></a>
+<span class="sourceLineNo">204</span> * is a leaf tree<a name="line.204"></a>
+<span class="sourceLineNo">205</span> */<a name="line.205"></a>
+<span class="sourceLineNo">206</span> public BSPTree<S> getPlus() {<a name="line.206"></a>
+<span class="sourceLineNo">207</span> return plus;<a name="line.207"></a>
+<span class="sourceLineNo">208</span> }<a name="line.208"></a>
+<span class="sourceLineNo">209</span><a name="line.209"></a>
+<span class="sourceLineNo">210</span> /** Get the tree on the minus side of the cut hyperplane.<a name="line.210"></a>
+<span class="sourceLineNo">211</span> * @return tree on the minus side of the cut hyperplane, null if this<a name="line.211"></a>
+<span class="sourceLineNo">212</span> * is a leaf tree<a name="line.212"></a>
+<span class="sourceLineNo">213</span> */<a name="line.213"></a>
+<span class="sourceLineNo">214</span> public BSPTree<S> getMinus() {<a name="line.214"></a>
+<span class="sourceLineNo">215</span> return minus;<a name="line.215"></a>
+<span class="sourceLineNo">216</span> }<a name="line.216"></a>
+<span class="sourceLineNo">217</span><a name="line.217"></a>
+<span class="sourceLineNo">218</span> /** Get the parent node.<a name="line.218"></a>
+<span class="sourceLineNo">219</span> * @return parent node, null if the node has no parents<a name="line.219"></a>
+<span class="sourceLineNo">220</span> */<a name="line.220"></a>
+<span class="sourceLineNo">221</span> public BSPTree<S> getParent() {<a name="line.221"></a>
+<span class="sourceLineNo">222</span> return parent;<a name="line.222"></a>
+<span class="sourceLineNo">223</span> }<a name="line.223"></a>
+<span class="sourceLineNo">224</span><a name="line.224"></a>
+<span class="sourceLineNo">225</span> /** Associate an attribute with the instance.<a name="line.225"></a>
+<span class="sourceLineNo">226</span> * @param attribute attribute to associate with the node<a name="line.226"></a>
+<span class="sourceLineNo">227</span> * @see #getAttribute<a name="line.227"></a>
+<span class="sourceLineNo">228</span> */<a name="line.228"></a>
+<span class="sourceLineNo">229</span> public void setAttribute(final Object attribute) {<a name="line.229"></a>
+<span class="sourceLineNo">230</span> this.attribute = attribute;<a name="line.230"></a>
+<span class="sourceLineNo">231</span> }<a name="line.231"></a>
+<span class="sourceLineNo">232</span><a name="line.232"></a>
+<span class="sourceLineNo">233</span> /** Get the attribute associated with the instance.<a name="line.233"></a>
+<span class="sourceLineNo">234</span> * @return attribute associated with the node or null if no<a name="line.234"></a>
+<span class="sourceLineNo">235</span> * attribute has been explicitly set using the {@link #setAttribute<a name="line.235"></a>
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+<span class="sourceLineNo">304</span> }<a name="line.304"></a>
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+<span class="sourceLineNo">320</span><a name="line.320"></a>
+<span class="sourceLineNo">321</span> /** Get the cell to which a point belongs.<a name="line.321"></a>
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+<span class="sourceLineNo">328</span> * @return the tree cell to which the point belongs<a name="line.328"></a>
+<span class="sourceLineNo">329</span> */<a name="line.329"></a>
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+<span class="sourceLineNo">350</span><a name="line.350"></a>
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+<span class="sourceLineNo">352</span> * @param point point to check<a name="line.352"></a>
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+<span class="sourceLineNo">354</span> * close to the point (in absolute value)<a name="line.354"></a>
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+<span class="sourceLineNo">363</span><a name="line.363"></a>
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+<span class="sourceLineNo">365</span> * @param point point to check<a name="line.365"></a>
+<span class="sourceLineNo">366</span> * @param maxOffset offset below which a cut sub-hyperplane is considered<a name="line.366"></a>
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+<span class="sourceLineNo">368</span> * @param close list to fill<a name="line.368"></a>
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+<span class="sourceLineNo">373</span><a name="line.373"></a>
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+<span class="sourceLineNo">376</span><a name="line.376"></a>
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+<span class="sourceLineNo">392</span><a name="line.392"></a>
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+<span class="sourceLineNo">395</span> * explicitly from leaves to root.</p><a name="line.395"></a>
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+<span class="sourceLineNo">403</span> plus = null;<a name="line.403"></a>
+<span class="sourceLineNo">404</span> minus = null;<a name="line.404"></a>
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+<span class="sourceLineNo">406</span> }<a name="line.406"></a>
+<span class="sourceLineNo">407</span><a name="line.407"></a>
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+<span class="sourceLineNo">410</span> * tree), it is the responsibility of the caller to ensure a copy<a name="line.410"></a>
+<span class="sourceLineNo">411</span> * has been done before if any of the former tree should be<a name="line.411"></a>
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+<span class="sourceLineNo">413</span> * <p>The algorithm used here is directly derived from the one<a name="line.413"></a>
+<span class="sourceLineNo">414</span> * described in the Naylor, Amanatides and Thibault paper (section<a name="line.414"></a>
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+<span class="sourceLineNo">429</span><a name="line.429"></a>
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+<span class="sourceLineNo">432</span> * <em>unusable</em> after the operation, as well as the<a name="line.432"></a>
+<span class="sourceLineNo">433</span> * instance itself)<a name="line.433"></a>
+<span class="sourceLineNo">434</span> * @param leafMerger object implementing the final merging phase<a name="line.434"></a>
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+<span class="sourceLineNo">437</span> * @param parentTree parent tree to connect to (may be null)<a name="line.437"></a>
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+<span class="sourceLineNo">440</span> * parentTree is null<a name="line.440"></a>
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+<span class="sourceLineNo">443</span> * since all connections have already been established<a name="line.443"></a>
+<span class="sourceLineNo">444</span> */<a name="line.444"></a>
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+<span class="sourceLineNo">448</span> // cell/tree operation<a name="line.448"></a>
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+<span class="sourceLineNo">451</span> // tree/cell operation<a name="line.451"></a>
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+<span class="sourceLineNo">454</span> // tree/tree operation<a name="line.454"></a>
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+<span class="sourceLineNo">457</span> merged.parent = parentTree;<a name="line.457"></a>
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+<span class="sourceLineNo">463</span> }<a name="line.463"></a>
+<span class="sourceLineNo">464</span><a name="line.464"></a>
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+<span class="sourceLineNo">474</span><a name="line.474"></a>
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+<span class="sourceLineNo">479</span> * leaf and another BSP tree.<a name="line.479"></a>
+<span class="sourceLineNo">480</span> * <p>As explained in Bruce Naylor, John Amanatides and William<a name="line.480"></a>
+<span class="sourceLineNo">481</span> * Thibault paper <a<a name="line.481"></a>
+<span class="sourceLineNo">482</span> * href="http://www.cs.yorku.ca/~amana/research/bsptSetOp.pdf">Merging<a name="line.482"></a>
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+<span class="sourceLineNo">485</span> * generic recursive merging operation where only the final part,<a name="line.485"></a>
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+<span class="sourceLineNo">487</span> * operation semantics. For example, a tree representing a region<a name="line.487"></a>
+<span class="sourceLineNo">488</span> * using a boolean attribute to identify inside cells and outside<a name="line.488"></a>
+<span class="sourceLineNo">489</span> * cells would use four different objects to implement the final<a name="line.489"></a>
+<span class="sourceLineNo">490</span> * merging phase of the four set operations union, intersection,<a name="line.490"></a>
+<span class="sourceLineNo">491</span> * difference and symmetric difference (exclusive or).</p><a name="line.491"></a>
+<span class="sourceLineNo">492</span> * @param <S> Type of the space.<a name="line.492"></a>
+<span class="sourceLineNo">493</span> */<a name="line.493"></a>
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+<span class="sourceLineNo">496</span> /** Merge a leaf node and a tree node.<a name="line.496"></a>
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+<span class="sourceLineNo">498</span> * resulting from a {@code tree1.merge(tree2, leafMerger)}<a name="line.498"></a>
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+<span class="sourceLineNo">506</span> * ({@code tree1}) or the argument tree<a name="line.506"></a>
+<span class="sourceLineNo">507</span> * ({@code tree2}). The third argument of the method is<a name="line.507"></a>
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+<span class="sourceLineNo">509</span> * operations.</p><a name="line.509"></a>
+<span class="sourceLineNo">510</span> * <p>The {@link BSPTree#insertInTree BSPTree.insertInTree} method<a name="line.510"></a>
+<span class="sourceLineNo">511</span> * may be useful to implement this method.</p><a name="line.511"></a>
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+<span class="sourceLineNo">529</span><a name="line.529"></a>
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+<span class="sourceLineNo">531</span> * <p><a name="line.531"></a>
+<span class="sourceLineNo">532</span> * Such cases happens for example when a cut sub-hyperplane is inserted into<a name="line.532"></a>
+<span class="sourceLineNo">533</span> * another tree (during a merge operation), and is split in several parts,<a name="line.533"></a>
+<span class="sourceLineNo">534</span> * some of which becomes smaller than the tolerance. The corresponding node<a name="line.534"></a>
+<span class="sourceLineNo">535</span> * as then no cut sub-hyperplane anymore, but does have children. This interface<a name="line.535"></a>
+<span class="sourceLineNo">536</span> * specifies how to handle this situation.<a name="line.536"></a>
+<span class="sourceLineNo">537</span> * setting<a name="line.537"></a>
+<span class="sourceLineNo">538</span> * </p><a name="line.538"></a>
+<span class="sourceLineNo">539</span> * @since 3.4<a name="line.539"></a>
+<span class="sourceLineNo">540</span> */<a name="line.540"></a>
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+<span class="sourceLineNo">543</span> /** Fix a node with both vanished cut and children.<a name="line.543"></a>
+<span class="sourceLineNo">544</span> * @param node node to fix<a name="line.544"></a>
+<span class="sourceLineNo">545</span> * @return fixed node<a name="line.545"></a>
+<span class="sourceLineNo">546</span> */<a name="line.546"></a>
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+<span class="sourceLineNo">548</span><a name="line.548"></a>
+<span class="sourceLineNo">549</span> }<a name="line.549"></a>
+<span class="sourceLineNo">550</span><a name="line.550"></a>
+<span class="sourceLineNo">551</span> /** Split a BSP tree by an external sub-hyperplane.<a name="line.551"></a>
+<span class="sourceLineNo">552</span> * <p>Split a tree in two halves, on each side of the<a name="line.552"></a>
+<span class="sourceLineNo">553</span> * sub-hyperplane. The instance is not modified.</p><a name="line.553"></a>
+<span class="sourceLineNo">554</span> * <p>The tree returned is not upward-consistent: despite all of its<a name="line.554"></a>
+<span class="sourceLineNo">555</span> * sub-trees cut sub-hyperplanes (including its own cut<a name="line.555"></a>
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+<span class="sourceLineNo">557</span> * attached to any parent tree yet. This tree is intended to be<a name="line.557"></a>
+<span class="sourceLineNo">558</span> * later inserted into an higher level tree.</p><a name="line.558"></a>
+<span class="sourceLineNo">559</span> * <p>The algorithm used here is the one given in Naylor, Amanatides<a name="line.559"></a>
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+<span class="sourceLineNo">561</span> * Tree).</p><a name="line.561"></a>
+<span class="sourceLineNo">562</span> * @param sub partitioning sub-hyperplane, must be already clipped<a name="line.562"></a>
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+<span class="sourceLineNo">565</span> * @return a tree having the specified sub-hyperplane as its cut<a name="line.565"></a>
+<span class="sourceLineNo">566</span> * sub-hyperplane, the two parts of the split instance as its two<a name="line.566"></a>
+<span class="sourceLineNo">567</span> * sub-trees and a null parent<a name="line.567"></a>
+<span class="sourceLineNo">568</span> */<a name="line.568"></a>
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+<span class="sourceLineNo">571</span> if (cut == null) {<a name="line.571"></a>
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+<span class="sourceLineNo">574</span><a name="line.574"></a>
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+<span class="sourceLineNo">589</span> split.minus.condense();<a name="line.589"></a>
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+<span class="sourceLineNo">591</span> }<a name="line.591"></a>
+<span class="sourceLineNo">592</span> return split;<a name="line.592"></a>
+<span class="sourceLineNo">593</span> }<a name="line.593"></a>
+<span class="sourceLineNo">594</span> case MINUS :<a name="line.594"></a>
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+<span class="sourceLineNo">598</span> split.plus =<a name="line.598"></a>
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+<span class="sourceLineNo">600</span> split.plus.condense();<a name="line.600"></a>
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+<span class="sourceLineNo">602</span> } else {<a name="line.602"></a>
+<span class="sourceLineNo">603</span> split.minus =<a name="line.603"></a>
+<span class="sourceLineNo">604</span> new BSPTree<S>(cut.copySelf(), plus.copySelf(), split.minus, attribute);<a name="line.604"></a>
+<span class="sourceLineNo">605</span> split.minus.condense();<a name="line.605"></a>
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+<span class="sourceLineNo">608</span> return split;<a name="line.608"></a>
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+<span class="sourceLineNo">610</span> case BOTH :<a name="line.610"></a>
+<span class="sourceLineNo">611</span> {<a name="line.611"></a>
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+<span class="sourceLineNo">616</span> null);<a name="line.616"></a>
+<span class="sourceLineNo">617</span> split.plus.cut = cutParts.getPlus();<a name="line.617"></a>
+<span class="sourceLineNo">618</span> split.minus.cut = cutParts.getMinus();<a name="line.618"></a>
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+<span class="sourceLineNo">623</span> split.minus.plus.parent = split.minus;<a name="line.623"></a>
+<span class="sourceLineNo">624</span> split.plus.condense();<a name="line.624"></a>
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+<span class="sourceLineNo">628</span> default :<a name="line.628"></a>
+<span class="sourceLineNo">629</span> return cHyperplane.sameOrientationAs(sHyperplane) ?<a name="line.629"></a>
+<span class="sourceLineNo">630</span> new BSPTree<S>(sub, plus.copySelf(), minus.copySelf(), attribute) :<a name="line.630"></a>
+<span class="sourceLineNo">631</span> new BSPTree<S>(sub, minus.copySelf(), plus.copySelf(), attribute);<a name="line.631"></a>
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+<span class="sourceLineNo">633</span><a name="line.633"></a>
+<span class="sourceLineNo">634</span> }<a name="line.634"></a>
+<span class="sourceLineNo">635</span><a name="line.635"></a>
+<span class="sourceLineNo">636</span> /** Insert the instance into another tree.<a name="line.636"></a>
+<span class="sourceLineNo">637</span> * <p>The instance itself is modified so its former parent should<a name="line.637"></a>
+<span class="sourceLineNo">638</span> * not be used anymore.</p><a name="line.638"></a>
+<span class="sourceLineNo">639</span> * @param parentTree parent tree to connect to (may be null)<a name="line.639"></a>
+<span class="sourceLineNo">640</span> * @param isPlusChild if true and if parentTree is not null, the<a name="line.640"></a>
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+<span class="sourceLineNo">642</span> * parentTree is null<a name="line.642"></a>
+<span class="sourceLineNo">643</span> * @see LeafMerger<a name="line.643"></a>
+<span class="sourceLineNo">644</span> * @deprecated as of 3.4, replaced with {@link #insertInTree(BSPTree, boolean, VanishingCutHandler)}<a name="line.644"></a>
+<span class="sourceLineNo">645</span> */<a name="line.645"></a>
+<span class="sourceLineNo">646</span> @Deprecated<a name="line.646"></a>
+<span class="sourceLineNo">647</span> public void insertInTree(final BSPTree<S> parentTree, final boolean isPlusChild) {<a name="line.647"></a>
+<span class="sourceLineNo">648</span> insertInTree(parentTree, isPlusChild, new VanishingCutHandler<S>() {<a name="line.648"></a>
+<span class="sourceLineNo">649</span> /** {@inheritDoc} */<a name="line.649"></a>
+<span class="sourceLineNo">650</span> public BSPTree<S> fixNode(BSPTree<S> node) {<a name="line.650"></a>
+<span class="sourceLineNo">651</span> // the cut should not be null<a name="line.651"></a>
+<span class="sourceLineNo">652</span> throw new MathIllegalStateException(LocalizedFormats.NULL_NOT_ALLOWED);<a name="line.652"></a>
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+<span class="sourceLineNo">654</span> });<a name="line.654"></a>
+<span class="sourceLineNo">655</span> }<a name="line.655"></a>
+<span class="sourceLineNo">656</span><a name="line.656"></a>
+<span class="sourceLineNo">657</span> /** Insert the instance into another tree.<a name="line.657"></a>
+<span class="sourceLineNo">658</span> * <p>The instance itself is modified so its former parent should<a name="line.658"></a>
+<span class="sourceLineNo">659</span> * not be used anymore.</p><a name="line.659"></a>
+<span class="sourceLineNo">660</span> * @param parentTree parent tree to connect to (may be null)<a name="line.660"></a>
+<span class="sourceLineNo">661</span> * @param isPlusChild if true and if parentTree is not null, the<a name="line.661"></a>
+<span class="sourceLineNo">662</span> * resulting tree should be the plus child of its parent, ignored if<a name="line.662"></a>
+<span class="sourceLineNo">663</span> * parentTree is null<a name="line.663"></a>
+<span class="sourceLineNo">664</span> * @param vanishingHandler handler to use for handling very rare corner<a name="line.664"></a>
+<span class="sourceLineNo">665</span> * cases of vanishing cut sub-hyperplanes in internal nodes during merging<a name="line.665"></a>
+<span class="sourceLineNo">666</span> * @see LeafMerger<a name="line.666"></a>
+<span class="sourceLineNo">667</span> * @since 3.4<a name="line.667"></a>
+<span class="sourceLineNo">668</span> */<a name="line.668"></a>
+<span class="sourceLineNo">669</span> public void insertInTree(final BSPTree<S> parentTree, final boolean isPlusChild,<a name="line.669"></a>
+<span class="sourceLineNo">670</span> final VanishingCutHandler<S> vanishingHandler) {<a name="line.670"></a>
+<span class="sourceLineNo">671</span><a name="line.671"></a>
+<span class="sourceLineNo">672</span> // set up parent/child links<a name="line.672"></a>
+<span class="sourceLineNo">673</span> parent = parentTree;<a name="line.673"></a>
+<span class="sourceLineNo">674</span> if (parentTree != null) {<a name="line.674"></a>
+<span class="sourceLineNo">675</span> if (isPlusChild) {<a name="line.675"></a>
+<span class="sourceLineNo">676</span> parentTree.plus = this;<a name="line.676"></a>
+<span class="sourceLineNo">677</span> } else {<a name="line.677"></a>
+<span class="sourceLineNo">678</span> parentTree.minus = this;<a name="line.678"></a>
+<span class="sourceLineNo">679</span> }<a name="line.679"></a>
+<span class="sourceLineNo">680</span> }<a name="line.680"></a>
+<span class="sourceLineNo">681</span><a name="line.681"></a>
+<span class="sourceLineNo">682</span> // make sure the inserted tree lies in the cell defined by its parent nodes<a name="line.682"></a>
+<span class="sourceLineNo">683</span> if (cut != null) {<a name="line.683"></a>
+<span class="sourceLineNo">684</span><a name="line.684"></a>
+<span class="sourceLineNo">685</span> // explore the parent nodes from here towards tree root<a name="line.685"></a>
+<span class="sourceLineNo">686</span> for (BSPTree<S> tree = this; tree.parent != null; tree = tree.parent) {<a name="line.686"></a>
+<span class="sourceLineNo">687</span><a name="line.687"></a>
+<span class="sourceLineNo">688</span> // this is an hyperplane of some parent node<a name="line.688"></a>
+<span class="sourceLineNo">689</span> final Hyperplane<S> hyperplane = tree.parent.cut.getHyperplane();<a name="line.689"></a>
+<span class="sourceLineNo">690</span><a name="line.690"></a>
+<span class="sourceLineNo">691</span> // chop off the parts of the inserted tree that extend<a name="line.691"></a>
+<span class="sourceLineNo">692</span> // on the wrong side of this parent hyperplane<a name="line.692"></a>
+<span class="sourceLineNo">693</span> if (tree == tree.parent.plus) {<a name="line.693"></a>
+<span class="sourceLineNo">694</span> cut = cut.split(hyperplane).getPlus();<a name="line.694"></a>
+<span class="sourceLineNo">695</span> plus.chopOffMinus(hyperplane, vanishingHandler);<a name="line.695"></a>
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+<span class="sourceLineNo">700</span> minus.chopOffPlus(hyperplane, vanishingHandler);<a name="line.700"></a>
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+<span class="sourceLineNo">702</span><a name="line.702"></a>
+<span class="sourceLineNo">703</span> if (cut == null) {<a name="line.703"></a>
+<span class="sourceLineNo">704</span> // the cut sub-hyperplane has vanished<a name="line.704"></a>
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+<span class="sourceLineNo">706</span> cut = fixed.cut;<a name="line.706"></a>
+<span class="sourceLineNo">707</span> plus = fixed.plus;<a name="line.707"></a>
+<span class="sourceLineNo">708</span> minus = fixed.minus;<a name="line.708"></a>
+<span class="sourceLineNo">709</span> attribute = fixed.attribute;<a name="line.709"></a>
+<span class="sourceLineNo">710</span> }<a name="line.710"></a>
+<span class="sourceLineNo">711</span><a name="line.711"></a>
+<span class="sourceLineNo">712</span> }<a name="line.712"></a>
+<span class="sourceLineNo">713</span><a name="line.713"></a>
+<span class="sourceLineNo">714</span> // since we may have drop some parts of the inserted tree,<a name="line.714"></a>
+<span class="sourceLineNo">715</span> // perform a condensation pass to keep the tree structure simple<a name="line.715"></a>
+<span class="sourceLineNo">716</span> condense();<a name="line.716"></a>
+<span class="sourceLineNo">717</span><a name="line.717"></a>
+<span class="sourceLineNo">718</span> }<a name="line.718"></a>
+<span class="sourceLineNo">719</span><a name="line.719"></a>
+<span class="sourceLineNo">720</span> }<a name="line.720"></a>
+<span class="sourceLineNo">721</span><a name="line.721"></a>
+<span class="sourceLineNo">722</span> /** Prune a tree around a cell.<a name="line.722"></a>
+<span class="sourceLineNo">723</span> * <p><a name="line.723"></a>
+<span class="sourceLineNo">724</span> * This method can be used to extract a convex cell from a tree.<a name="line.724"></a>
+<span class="sourceLineNo">725</span> * The original cell may either be a leaf node or an internal node.<a name="line.725"></a>
+<span class="sourceLineNo">726</span> * If it is an internal node, it's subtree will be ignored (i.e. the<a name="line.726"></a>
+<span class="sourceLineNo">727</span> * extracted cell will be a leaf node in all cases). The original<a name="line.727"></a>
+<span class="sourceLineNo">728</span> * tree to which the original cell belongs is not touched at all,<a name="line.728"></a>
+<span class="sourceLineNo">729</span> * a new independent tree will be built.<a name="line.729"></a>
+<span class="sourceLineNo">730</span> * </p><a name="line.730"></a>
+<span class="sourceLineNo">731</span> * @param cellAttribute attribute to set for the leaf node<a name="line.731"></a>
+<span class="sourceLineNo">732</span> * corresponding to the initial instance cell<a name="line.732"></a>
+<span class="sourceLineNo">733</span> * @param otherLeafsAttributes attribute to set for the other leaf<a name="line.733"></a>
+<span class="sourceLineNo">734</span> * nodes<a name="line.734"></a>
+<span class="sourceLineNo">735</span> * @param internalAttributes attribute to set for the internal nodes<a name="line.735"></a>
+<span class="sourceLineNo">736</span> * @return a new tree (the original tree is left untouched) containing<a name="line.736"></a>
+<span class="sourceLineNo">737</span> * a single branch with the cell as a leaf node, and other leaf nodes<a name="line.737"></a>
+<span class="sourceLineNo">738</span> * as the remnants of the pruned branches<a name="line.738"></a>
+<span class="sourceLineNo">739</span> * @since 3.3<a name="line.739"></a>
+<span class="sourceLineNo">740</span> */<a name="line.740"></a>
+<span class="sourceLineNo">741</span> public BSPTree<S> pruneAroundConvexCell(final Object cellAttribute,<a name="line.741"></a>
+<span class="sourceLineNo">742</span> final Object otherLeafsAttributes,<a name="line.742"></a>
+<span class="sourceLineNo">743</span> final Object internalAttributes) {<a name="line.743"></a>
+<span class="sourceLineNo">744</span><a name="line.744"></a>
+<span class="sourceLineNo">745</span> // build the current cell leaf<a name="line.745"></a>
+<span class="sourceLineNo">746</span> BSPTree<S> tree = new BSPTree<S>(cellAttribute);<a name="line.746"></a>
+<span class="sourceLineNo">747</span><a name="line.747"></a>
+<span class="sourceLineNo">748</span> // build the pruned tree bottom-up<a name="line.748"></a>
+<span class="sourceLineNo">749</span> for (BSPTree<S> current = this; current.parent != null; current = current.parent) {<a name="line.749"></a>
+<span class="sourceLineNo">750</span> final SubHyperplane<S> parentCut = current.parent.cut.copySelf();<a name="line.750"></a>
+<span class="sourceLineNo">751</span> final BSPTree<S> sibling = new BSPTree<S>(otherLeafsAttributes);<a name="line.751"></a>
+<span class="sourceLineNo">752</span> if (current == current.parent.plus) {<a name="line.752"></a>
+<span class="sourceLineNo">753</span> tree = new BSPTree<S>(parentCut, tree, sibling, internalAttributes);<a name="line.753"></a>
+<span class="sourceLineNo">754</span> } else {<a name="line.754"></a>
+<span class="sourceLineNo">755</span> tree = new BSPTree<S>(parentCut, sibling, tree, internalAttributes);<a name="line.755"></a>
+<span class="sourceLineNo">756</span> }<a name="line.756"></a>
+<span class="sourceLineNo">757</span> }<a name="line.757"></a>
+<span class="sourceLineNo">758</span><a name="line.758"></a>
+<span class="sourceLineNo">759</span> return tree;<a name="line.759"></a>
+<span class="sourceLineNo">760</span><a name="line.760"></a>
+<span class="sourceLineNo">761</span> }<a name="line.761"></a>
+<span class="sourceLineNo">762</span><a name="line.762"></a>
+<span class="sourceLineNo">763</span> /** Chop off parts of the tree.<a name="line.763"></a>
+<span class="sourceLineNo">764</span> * <p>The instance is modified in place, all the parts that are on<a name="line.764"></a>
+<span class="sourceLineNo">765</span> * the minus side of the chopping hyperplane are discarded, only the<a name="line.765"></a>
+<span class="sourceLineNo">766</span> * parts on the plus side remain.</p><a name="line.766"></a>
+<span class="sourceLineNo">767</span> * @param hyperplane chopping hyperplane<a name="line.767"></a>
+<span class="sourceLineNo">768</span> * @param vanishingHandler handler to use for handling very rare corner<a name="line.768"></a>
+<span class="sourceLineNo">769</span> * cases of vanishing cut sub-hyperplanes in internal nodes during merging<a name="line.769"></a>
+<span class="sourceLineNo">770</span> */<a name="line.770"></a>
+<span class="sourceLineNo">771</span> private void chopOffMinus(final Hyperplane<S> hyperplane, final VanishingCutHandler<S> vanishingHandler) {<a name="line.771"></a>
+<span class="sourceLineNo">772</span> if (cut != null) {<a name="line.772"></a>
+<span class="sourceLineNo">773</span><a name="line.773"></a>
+<span class="sourceLineNo">774</span> cut = cut.split(hyperplane).getPlus();<a name="line.774"></a>
+<span class="sourceLineNo">775</span> plus.chopOffMinus(hyperplane, vanishingHandler);<a name="line.775"></a>
+<span class="sourceLineNo">776</span> minus.chopOffMinus(hyperplane, vanishingHandler);<a name="line.776"></a>
+<span class="sourceLineNo">777</span><a name="line.777"></a>
+<span class="sourceLineNo">778</span> if (cut == null) {<a name="line.778"></a>
+<span class="sourceLineNo">779</span> // the cut sub-hyperplane has vanished<a name="line.779"></a>
+<span class="sourceLineNo">780</span> final BSPTree<S> fixed = vanishingHandler.fixNode(this);<a name="line.780"></a>
+<span class="sourceLineNo">781</span> cut = fixed.cut;<a name="line.781"></a>
+<span class="sourceLineNo">782</span> plus = fixed.plus;<a name="line.782"></a>
+<span class="sourceLineNo">783</span> minus = fixed.minus;<a name="line.783"></a>
+<span class="sourceLineNo">784</span> attribute = fixed.attribute;<a name="line.784"></a>
+<span class="sourceLineNo">785</span> }<a name="line.785"></a>
+<span class="sourceLineNo">786</span><a name="line.786"></a>
+<span class="sourceLineNo">787</span> }<a name="line.787"></a>
+<span class="sourceLineNo">788</span> }<a name="line.788"></a>
+<span class="sourceLineNo">789</span><a name="line.789"></a>
+<span class="sourceLineNo">790</span> /** Chop off parts of the tree.<a name="line.790"></a>
+<span class="sourceLineNo">791</span> * <p>The instance is modified in place, all the parts that are on<a name="line.791"></a>
+<span class="sourceLineNo">792</span> * the plus side of the chopping hyperplane are discarded, only the<a name="line.792"></a>
+<span class="sourceLineNo">793</span> * parts on the minus side remain.</p><a name="line.793"></a>
+<span class="sourceLineNo">794</span> * @param hyperplane chopping hyperplane<a name="line.794"></a>
+<span class="sourceLineNo">795</span> * @param vanishingHandler handler to use for handling very rare corner<a name="line.795"></a>
+<span class="sourceLineNo">796</span> * cases of vanishing cut sub-hyperplanes in internal nodes during merging<a name="line.796"></a>
+<span class="sourceLineNo">797</span> */<a name="line.797"></a>
+<span class="sourceLineNo">798</span> private void chopOffPlus(final Hyperplane<S> hyperplane, final VanishingCutHandler<S> vanishingHandler) {<a name="line.798"></a>
+<span class="sourceLineNo">799</span> if (cut != null) {<a name="line.799"></a>
+<span class="sourceLineNo">800</span><a name="line.800"></a>
+<span class="sourceLineNo">801</span> cut = cut.split(hyperplane).getMinus();<a name="line.801"></a>
+<span class="sourceLineNo">802</span> plus.chopOffPlus(hyperplane, vanishingHandler);<a name="line.802"></a>
+<span class="sourceLineNo">803</span> minus.chopOffPlus(hyperplane, vanishingHandler);<a name="line.803"></a>
+<span class="sourceLineNo">804</span><a name="line.804"></a>
+<span class="sourceLineNo">805</span> if (cut == null) {<a name="line.805"></a>
+<span class="sourceLineNo">806</span> // the cut sub-hyperplane has vanished<a name="line.806"></a>
+<span class="sourceLineNo">807</span> final BSPTree<S> fixed = vanishingHandler.fixNode(this);<a name="line.807"></a>
+<span class="sourceLineNo">808</span> cut = fixed.cut;<a name="line.808"></a>
+<span class="sourceLineNo">809</span> plus = fixed.plus;<a name="line.809"></a>
+<span class="sourceLineNo">810</span> minus = fixed.minus;<a name="line.810"></a>
+<span class="sourceLineNo">811</span> attribute = fixed.attribute;<a name="line.811"></a>
+<span class="sourceLineNo">812</span> }<a name="line.812"></a>
+<span class="sourceLineNo">813</span><a name="line.813"></a>
+<span class="sourceLineNo">814</span> }<a name="line.814"></a>
+<span class="sourceLineNo">815</span> }<a name="line.815"></a>
+<span class="sourceLineNo">816</span><a name="line.816"></a>
+<span class="sourceLineNo">817</span>}<a name="line.817"></a>
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