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<HTML> <BODY BGCOLOR="white"> <PRE> <FONT color="green">001</FONT> /*<a name="line.1"></a> <FONT color="green">002</FONT> * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a> <FONT color="green">003</FONT> * contributor license agreements. See the NOTICE file distributed with<a name="line.3"></a> <FONT color="green">004</FONT> * this work for additional information regarding copyright ownership.<a name="line.4"></a> <FONT color="green">005</FONT> * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a> <FONT color="green">006</FONT> * (the "License"); you may not use this file except in compliance with<a name="line.6"></a> <FONT color="green">007</FONT> * the License. You may obtain a copy of the License at<a name="line.7"></a> <FONT color="green">008</FONT> *<a name="line.8"></a> <FONT color="green">009</FONT> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a> <FONT color="green">010</FONT> *<a name="line.10"></a> <FONT color="green">011</FONT> * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a> <FONT color="green">012</FONT> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a> <FONT color="green">013</FONT> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a> <FONT color="green">014</FONT> * See the License for the specific language governing permissions and<a name="line.14"></a> <FONT color="green">015</FONT> * limitations under the License.<a name="line.15"></a> <FONT color="green">016</FONT> */<a name="line.16"></a> <FONT color="green">017</FONT> package org.apache.commons.math.analysis.interpolation;<a name="line.17"></a> <FONT color="green">018</FONT> <a name="line.18"></a> <FONT color="green">019</FONT> import java.util.ArrayList;<a name="line.19"></a> <FONT color="green">020</FONT> import java.util.HashMap;<a name="line.20"></a> <FONT color="green">021</FONT> import java.util.List;<a name="line.21"></a> <FONT color="green">022</FONT> import java.util.Map;<a name="line.22"></a> <FONT color="green">023</FONT> <a name="line.23"></a> <FONT color="green">024</FONT> import org.apache.commons.math.DimensionMismatchException;<a name="line.24"></a> <FONT color="green">025</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.25"></a> <FONT color="green">026</FONT> import org.apache.commons.math.analysis.MultivariateRealFunction;<a name="line.26"></a> <FONT color="green">027</FONT> import org.apache.commons.math.linear.ArrayRealVector;<a name="line.27"></a> <FONT color="green">028</FONT> import org.apache.commons.math.linear.RealVector;<a name="line.28"></a> <FONT color="green">029</FONT> import org.apache.commons.math.random.UnitSphereRandomVectorGenerator;<a name="line.29"></a> <FONT color="green">030</FONT> <a name="line.30"></a> <FONT color="green">031</FONT> /**<a name="line.31"></a> <FONT color="green">032</FONT> * Interpolating function that implements the<a name="line.32"></a> <FONT color="green">033</FONT> * <a href="http://www.dudziak.com/microsphere.php">Microsphere Projection</a>.<a name="line.33"></a> <FONT color="green">034</FONT> *<a name="line.34"></a> <FONT color="green">035</FONT> * @version $Revision: 825919 $ $Date: 2009-10-16 10:51:55 -0400 (Fri, 16 Oct 2009) $<a name="line.35"></a> <FONT color="green">036</FONT> */<a name="line.36"></a> <FONT color="green">037</FONT> public class MicrosphereInterpolatingFunction<a name="line.37"></a> <FONT color="green">038</FONT> implements MultivariateRealFunction {<a name="line.38"></a> <FONT color="green">039</FONT> /**<a name="line.39"></a> <FONT color="green">040</FONT> * Space dimension.<a name="line.40"></a> <FONT color="green">041</FONT> */<a name="line.41"></a> <FONT color="green">042</FONT> private final int dimension;<a name="line.42"></a> <FONT color="green">043</FONT> /**<a name="line.43"></a> <FONT color="green">044</FONT> * Internal accounting data for the interpolation algorithm.<a name="line.44"></a> <FONT color="green">045</FONT> * Each element of the list corresponds to one surface element of<a name="line.45"></a> <FONT color="green">046</FONT> * the microsphere.<a name="line.46"></a> <FONT color="green">047</FONT> */<a name="line.47"></a> <FONT color="green">048</FONT> private final List<MicrosphereSurfaceElement> microsphere;<a name="line.48"></a> <FONT color="green">049</FONT> /**<a name="line.49"></a> <FONT color="green">050</FONT> * Exponent used in the power law that computes the weights of the<a name="line.50"></a> <FONT color="green">051</FONT> * sample data.<a name="line.51"></a> <FONT color="green">052</FONT> */<a name="line.52"></a> <FONT color="green">053</FONT> private final double brightnessExponent;<a name="line.53"></a> <FONT color="green">054</FONT> /**<a name="line.54"></a> <FONT color="green">055</FONT> * Sample data.<a name="line.55"></a> <FONT color="green">056</FONT> */<a name="line.56"></a> <FONT color="green">057</FONT> private final Map<RealVector, Double> samples;<a name="line.57"></a> <FONT color="green">058</FONT> <a name="line.58"></a> <FONT color="green">059</FONT> /**<a name="line.59"></a> <FONT color="green">060</FONT> * Class for storing the accounting data needed to perform the<a name="line.60"></a> <FONT color="green">061</FONT> * microsphere projection.<a name="line.61"></a> <FONT color="green">062</FONT> */<a name="line.62"></a> <FONT color="green">063</FONT> private static class MicrosphereSurfaceElement {<a name="line.63"></a> <FONT color="green">064</FONT> <a name="line.64"></a> <FONT color="green">065</FONT> /** Normal vector characterizing a surface element. */<a name="line.65"></a> <FONT color="green">066</FONT> private final RealVector normal;<a name="line.66"></a> <FONT color="green">067</FONT> <a name="line.67"></a> <FONT color="green">068</FONT> /** Illumination received from the brightest sample. */<a name="line.68"></a> <FONT color="green">069</FONT> private double brightestIllumination;<a name="line.69"></a> <FONT color="green">070</FONT> <a name="line.70"></a> <FONT color="green">071</FONT> /** Brightest sample. */<a name="line.71"></a> <FONT color="green">072</FONT> private Map.Entry<RealVector, Double> brightestSample;<a name="line.72"></a> <FONT color="green">073</FONT> <a name="line.73"></a> <FONT color="green">074</FONT> /**<a name="line.74"></a> <FONT color="green">075</FONT> * @param n Normal vector characterizing a surface element<a name="line.75"></a> <FONT color="green">076</FONT> * of the microsphere.<a name="line.76"></a> <FONT color="green">077</FONT> */<a name="line.77"></a> <FONT color="green">078</FONT> MicrosphereSurfaceElement(double[] n) {<a name="line.78"></a> <FONT color="green">079</FONT> normal = new ArrayRealVector(n);<a name="line.79"></a> <FONT color="green">080</FONT> }<a name="line.80"></a> <FONT color="green">081</FONT> <a name="line.81"></a> <FONT color="green">082</FONT> /**<a name="line.82"></a> <FONT color="green">083</FONT> * Return the normal vector.<a name="line.83"></a> <FONT color="green">084</FONT> * @return the normal vector<a name="line.84"></a> <FONT color="green">085</FONT> */<a name="line.85"></a> <FONT color="green">086</FONT> RealVector normal() {<a name="line.86"></a> <FONT color="green">087</FONT> return normal;<a name="line.87"></a> <FONT color="green">088</FONT> }<a name="line.88"></a> <FONT color="green">089</FONT> <a name="line.89"></a> <FONT color="green">090</FONT> /**<a name="line.90"></a> <FONT color="green">091</FONT> * Reset "illumination" and "sampleIndex".<a name="line.91"></a> <FONT color="green">092</FONT> */<a name="line.92"></a> <FONT color="green">093</FONT> void reset() {<a name="line.93"></a> <FONT color="green">094</FONT> brightestIllumination = 0;<a name="line.94"></a> <FONT color="green">095</FONT> brightestSample = null;<a name="line.95"></a> <FONT color="green">096</FONT> }<a name="line.96"></a> <FONT color="green">097</FONT> <a name="line.97"></a> <FONT color="green">098</FONT> /**<a name="line.98"></a> <FONT color="green">099</FONT> * Store the illumination and index of the brightest sample.<a name="line.99"></a> <FONT color="green">100</FONT> * @param illuminationFromSample illumination received from sample<a name="line.100"></a> <FONT color="green">101</FONT> * @param sample current sample illuminating the element<a name="line.101"></a> <FONT color="green">102</FONT> */<a name="line.102"></a> <FONT color="green">103</FONT> void store(final double illuminationFromSample,<a name="line.103"></a> <FONT color="green">104</FONT> final Map.Entry<RealVector, Double> sample) {<a name="line.104"></a> <FONT color="green">105</FONT> if (illuminationFromSample > this.brightestIllumination) {<a name="line.105"></a> <FONT color="green">106</FONT> this.brightestIllumination = illuminationFromSample;<a name="line.106"></a> <FONT color="green">107</FONT> this.brightestSample = sample;<a name="line.107"></a> <FONT color="green">108</FONT> }<a name="line.108"></a> <FONT color="green">109</FONT> }<a name="line.109"></a> <FONT color="green">110</FONT> <a name="line.110"></a> <FONT color="green">111</FONT> /**<a name="line.111"></a> <FONT color="green">112</FONT> * Get the illumination of the element.<a name="line.112"></a> <FONT color="green">113</FONT> * @return the illumination.<a name="line.113"></a> <FONT color="green">114</FONT> */<a name="line.114"></a> <FONT color="green">115</FONT> double illumination() {<a name="line.115"></a> <FONT color="green">116</FONT> return brightestIllumination;<a name="line.116"></a> <FONT color="green">117</FONT> }<a name="line.117"></a> <FONT color="green">118</FONT> <a name="line.118"></a> <FONT color="green">119</FONT> /**<a name="line.119"></a> <FONT color="green">120</FONT> * Get the sample illuminating the element the most.<a name="line.120"></a> <FONT color="green">121</FONT> * @return the sample.<a name="line.121"></a> <FONT color="green">122</FONT> */<a name="line.122"></a> <FONT color="green">123</FONT> Map.Entry<RealVector, Double> sample() {<a name="line.123"></a> <FONT color="green">124</FONT> return brightestSample;<a name="line.124"></a> <FONT color="green">125</FONT> }<a name="line.125"></a> <FONT color="green">126</FONT> }<a name="line.126"></a> <FONT color="green">127</FONT> <a name="line.127"></a> <FONT color="green">128</FONT> /**<a name="line.128"></a> <FONT color="green">129</FONT> * @param xval the arguments for the interpolation points.<a name="line.129"></a> <FONT color="green">130</FONT> * {@code xval[i][0]} is the first component of interpolation point<a name="line.130"></a> <FONT color="green">131</FONT> * {@code i}, {@code xval[i][1]} is the second component, and so on<a name="line.131"></a> <FONT color="green">132</FONT> * until {@code xval[i][d-1]}, the last component of that interpolation<a name="line.132"></a> <FONT color="green">133</FONT> * point (where {@code dimension} is thus the dimension of the sampled<a name="line.133"></a> <FONT color="green">134</FONT> * space).<a name="line.134"></a> <FONT color="green">135</FONT> * @param yval the values for the interpolation points<a name="line.135"></a> <FONT color="green">136</FONT> * @param brightnessExponent Brightness dimming factor.<a name="line.136"></a> <FONT color="green">137</FONT> * @param microsphereElements Number of surface elements of the<a name="line.137"></a> <FONT color="green">138</FONT> * microsphere.<a name="line.138"></a> <FONT color="green">139</FONT> * @param rand Unit vector generator for creating the microsphere.<a name="line.139"></a> <FONT color="green">140</FONT> * @throws DimensionMismatchException if the lengths of {@code yval} and<a name="line.140"></a> <FONT color="green">141</FONT> * {@code xval} (equal to {@code n}, the number of interpolation points)<a name="line.141"></a> <FONT color="green">142</FONT> * do not match, or the the arrays {@code xval[0]} ... {@code xval[n]},<a name="line.142"></a> <FONT color="green">143</FONT> * have lengths different from {@code dimension}.<a name="line.143"></a> <FONT color="green">144</FONT> * @throws IllegalArgumentException if there are no data (xval null or zero length)<a name="line.144"></a> <FONT color="green">145</FONT> */<a name="line.145"></a> <FONT color="green">146</FONT> public MicrosphereInterpolatingFunction(double[][] xval,<a name="line.146"></a> <FONT color="green">147</FONT> double[] yval,<a name="line.147"></a> <FONT color="green">148</FONT> int brightnessExponent,<a name="line.148"></a> <FONT color="green">149</FONT> int microsphereElements,<a name="line.149"></a> <FONT color="green">150</FONT> UnitSphereRandomVectorGenerator rand)<a name="line.150"></a> <FONT color="green">151</FONT> throws DimensionMismatchException, IllegalArgumentException {<a name="line.151"></a> <FONT color="green">152</FONT> if (xval.length == 0 || xval[0] == null) {<a name="line.152"></a> <FONT color="green">153</FONT> throw MathRuntimeException.createIllegalArgumentException("no data");<a name="line.153"></a> <FONT color="green">154</FONT> }<a name="line.154"></a> <FONT color="green">155</FONT> <a name="line.155"></a> <FONT color="green">156</FONT> if (xval.length != yval.length) {<a name="line.156"></a> <FONT color="green">157</FONT> throw new DimensionMismatchException(xval.length, yval.length);<a name="line.157"></a> <FONT color="green">158</FONT> }<a name="line.158"></a> <FONT color="green">159</FONT> <a name="line.159"></a> <FONT color="green">160</FONT> dimension = xval[0].length;<a name="line.160"></a> <FONT color="green">161</FONT> this.brightnessExponent = brightnessExponent;<a name="line.161"></a> <FONT color="green">162</FONT> <a name="line.162"></a> <FONT color="green">163</FONT> // Copy data samples.<a name="line.163"></a> <FONT color="green">164</FONT> samples = new HashMap<RealVector, Double>(yval.length);<a name="line.164"></a> <FONT color="green">165</FONT> for (int i = 0; i < xval.length; ++i) {<a name="line.165"></a> <FONT color="green">166</FONT> final double[] xvalI = xval[i];<a name="line.166"></a> <FONT color="green">167</FONT> if ( xvalI.length != dimension) {<a name="line.167"></a> <FONT color="green">168</FONT> throw new DimensionMismatchException(xvalI.length, dimension);<a name="line.168"></a> <FONT color="green">169</FONT> }<a name="line.169"></a> <FONT color="green">170</FONT> <a name="line.170"></a> <FONT color="green">171</FONT> samples.put(new ArrayRealVector(xvalI), yval[i]);<a name="line.171"></a> <FONT color="green">172</FONT> }<a name="line.172"></a> <FONT color="green">173</FONT> <a name="line.173"></a> <FONT color="green">174</FONT> microsphere = new ArrayList<MicrosphereSurfaceElement>(microsphereElements);<a name="line.174"></a> <FONT color="green">175</FONT> // Generate the microsphere, assuming that a fairly large number of<a name="line.175"></a> <FONT color="green">176</FONT> // randomly generated normals will represent a sphere.<a name="line.176"></a> <FONT color="green">177</FONT> for (int i = 0; i < microsphereElements; i++) {<a name="line.177"></a> <FONT color="green">178</FONT> microsphere.add(new MicrosphereSurfaceElement(rand.nextVector()));<a name="line.178"></a> <FONT color="green">179</FONT> }<a name="line.179"></a> <FONT color="green">180</FONT> <a name="line.180"></a> <FONT color="green">181</FONT> }<a name="line.181"></a> <FONT color="green">182</FONT> <a name="line.182"></a> <FONT color="green">183</FONT> /**<a name="line.183"></a> <FONT color="green">184</FONT> * @param point Interpolation point.<a name="line.184"></a> <FONT color="green">185</FONT> * @return the interpolated value.<a name="line.185"></a> <FONT color="green">186</FONT> */<a name="line.186"></a> <FONT color="green">187</FONT> public double value(double[] point) {<a name="line.187"></a> <FONT color="green">188</FONT> <a name="line.188"></a> <FONT color="green">189</FONT> final RealVector p = new ArrayRealVector(point);<a name="line.189"></a> <FONT color="green">190</FONT> <a name="line.190"></a> <FONT color="green">191</FONT> // Reset.<a name="line.191"></a> <FONT color="green">192</FONT> for (MicrosphereSurfaceElement md : microsphere) {<a name="line.192"></a> <FONT color="green">193</FONT> md.reset();<a name="line.193"></a> <FONT color="green">194</FONT> }<a name="line.194"></a> <FONT color="green">195</FONT> <a name="line.195"></a> <FONT color="green">196</FONT> // Compute contribution of each sample points to the microsphere elements illumination<a name="line.196"></a> <FONT color="green">197</FONT> for (Map.Entry<RealVector, Double> sd : samples.entrySet()) {<a name="line.197"></a> <FONT color="green">198</FONT> <a name="line.198"></a> <FONT color="green">199</FONT> // Vector between interpolation point and current sample point.<a name="line.199"></a> <FONT color="green">200</FONT> final RealVector diff = sd.getKey().subtract(p);<a name="line.200"></a> <FONT color="green">201</FONT> final double diffNorm = diff.getNorm();<a name="line.201"></a> <FONT color="green">202</FONT> <a name="line.202"></a> <FONT color="green">203</FONT> if (Math.abs(diffNorm) < Math.ulp(1d)) {<a name="line.203"></a> <FONT color="green">204</FONT> // No need to interpolate, as the interpolation point is<a name="line.204"></a> <FONT color="green">205</FONT> // actually (very close to) one of the sampled points.<a name="line.205"></a> <FONT color="green">206</FONT> return sd.getValue();<a name="line.206"></a> <FONT color="green">207</FONT> }<a name="line.207"></a> <FONT color="green">208</FONT> <a name="line.208"></a> <FONT color="green">209</FONT> for (MicrosphereSurfaceElement md : microsphere) {<a name="line.209"></a> <FONT color="green">210</FONT> final double w = Math.pow(diffNorm, -brightnessExponent);<a name="line.210"></a> <FONT color="green">211</FONT> md.store(cosAngle(diff, md.normal()) * w, sd);<a name="line.211"></a> <FONT color="green">212</FONT> }<a name="line.212"></a> <FONT color="green">213</FONT> <a name="line.213"></a> <FONT color="green">214</FONT> }<a name="line.214"></a> <FONT color="green">215</FONT> <a name="line.215"></a> <FONT color="green">216</FONT> // Interpolation calculation.<a name="line.216"></a> <FONT color="green">217</FONT> double value = 0;<a name="line.217"></a> <FONT color="green">218</FONT> double totalWeight = 0;<a name="line.218"></a> <FONT color="green">219</FONT> for (MicrosphereSurfaceElement md : microsphere) {<a name="line.219"></a> <FONT color="green">220</FONT> final double iV = md.illumination();<a name="line.220"></a> <FONT color="green">221</FONT> final Map.Entry<RealVector, Double> sd = md.sample();<a name="line.221"></a> <FONT color="green">222</FONT> if (sd != null) {<a name="line.222"></a> <FONT color="green">223</FONT> value += iV * sd.getValue();<a name="line.223"></a> <FONT color="green">224</FONT> totalWeight += iV;<a name="line.224"></a> <FONT color="green">225</FONT> }<a name="line.225"></a> <FONT color="green">226</FONT> }<a name="line.226"></a> <FONT color="green">227</FONT> <a name="line.227"></a> <FONT color="green">228</FONT> return value / totalWeight;<a name="line.228"></a> <FONT color="green">229</FONT> <a name="line.229"></a> <FONT color="green">230</FONT> }<a name="line.230"></a> <FONT color="green">231</FONT> <a name="line.231"></a> <FONT color="green">232</FONT> /**<a name="line.232"></a> <FONT color="green">233</FONT> * Compute the cosine of the angle between 2 vectors.<a name="line.233"></a> <FONT color="green">234</FONT> *<a name="line.234"></a> <FONT color="green">235</FONT> * @param v Vector.<a name="line.235"></a> <FONT color="green">236</FONT> * @param w Vector.<a name="line.236"></a> <FONT color="green">237</FONT> * @return cosine of the angle<a name="line.237"></a> <FONT color="green">238</FONT> */<a name="line.238"></a> <FONT color="green">239</FONT> private double cosAngle(final RealVector v, final RealVector w) {<a name="line.239"></a> <FONT color="green">240</FONT> return v.dotProduct(w) / (v.getNorm() * w.getNorm());<a name="line.240"></a> <FONT color="green">241</FONT> }<a name="line.241"></a> <FONT color="green">242</FONT> <a name="line.242"></a> <FONT color="green">243</FONT> }<a name="line.243"></a> </PRE> </BODY> </HTML>