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| author | dwinter |
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| date | Tue, 04 Jan 2011 10:02:07 +0100 |
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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 org.apache.commons.math.util.MathUtils;<a name="line.19"></a> <FONT color="green">020</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.20"></a> <FONT color="green">021</FONT> import org.apache.commons.math.DimensionMismatchException;<a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.analysis.BivariateRealFunction;<a name="line.22"></a> <FONT color="green">023</FONT> <a name="line.23"></a> <FONT color="green">024</FONT> /**<a name="line.24"></a> <FONT color="green">025</FONT> * Function that implements the<a name="line.25"></a> <FONT color="green">026</FONT> * <a href="http://en.wikipedia.org/wiki/Bicubic_interpolation"><a name="line.26"></a> <FONT color="green">027</FONT> * bicubic spline interpolation</a>.<a name="line.27"></a> <FONT color="green">028</FONT> *<a name="line.28"></a> <FONT color="green">029</FONT> * @version $Revision$ $Date$<a name="line.29"></a> <FONT color="green">030</FONT> * @since 2.1<a name="line.30"></a> <FONT color="green">031</FONT> */<a name="line.31"></a> <FONT color="green">032</FONT> public class BicubicSplineInterpolatingFunction<a name="line.32"></a> <FONT color="green">033</FONT> implements BivariateRealFunction {<a name="line.33"></a> <FONT color="green">034</FONT> /**<a name="line.34"></a> <FONT color="green">035</FONT> * Matrix to compute the spline coefficients from the function values<a name="line.35"></a> <FONT color="green">036</FONT> * and function derivatives values<a name="line.36"></a> <FONT color="green">037</FONT> */<a name="line.37"></a> <FONT color="green">038</FONT> private static final double[][] AINV = {<a name="line.38"></a> <FONT color="green">039</FONT> { 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },<a name="line.39"></a> <FONT color="green">040</FONT> { 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 },<a name="line.40"></a> <FONT color="green">041</FONT> { -3,3,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0 },<a name="line.41"></a> <FONT color="green">042</FONT> { 2,-2,0,0,1,1,0,0,0,0,0,0,0,0,0,0 },<a name="line.42"></a> <FONT color="green">043</FONT> { 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 },<a name="line.43"></a> <FONT color="green">044</FONT> { 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0 },<a name="line.44"></a> <FONT color="green">045</FONT> { 0,0,0,0,0,0,0,0,-3,3,0,0,-2,-1,0,0 },<a name="line.45"></a> <FONT color="green">046</FONT> { 0,0,0,0,0,0,0,0,2,-2,0,0,1,1,0,0 },<a name="line.46"></a> <FONT color="green">047</FONT> { -3,0,3,0,0,0,0,0,-2,0,-1,0,0,0,0,0 },<a name="line.47"></a> <FONT color="green">048</FONT> { 0,0,0,0,-3,0,3,0,0,0,0,0,-2,0,-1,0 },<a name="line.48"></a> <FONT color="green">049</FONT> { 9,-9,-9,9,6,3,-6,-3,6,-6,3,-3,4,2,2,1 },<a name="line.49"></a> <FONT color="green">050</FONT> { -6,6,6,-6,-3,-3,3,3,-4,4,-2,2,-2,-2,-1,-1 },<a name="line.50"></a> <FONT color="green">051</FONT> { 2,0,-2,0,0,0,0,0,1,0,1,0,0,0,0,0 },<a name="line.51"></a> <FONT color="green">052</FONT> { 0,0,0,0,2,0,-2,0,0,0,0,0,1,0,1,0 },<a name="line.52"></a> <FONT color="green">053</FONT> { -6,6,6,-6,-4,-2,4,2,-3,3,-3,3,-2,-1,-2,-1 },<a name="line.53"></a> <FONT color="green">054</FONT> { 4,-4,-4,4,2,2,-2,-2,2,-2,2,-2,1,1,1,1 }<a name="line.54"></a> <FONT color="green">055</FONT> };<a name="line.55"></a> <FONT color="green">056</FONT> <a name="line.56"></a> <FONT color="green">057</FONT> /** Samples x-coordinates */<a name="line.57"></a> <FONT color="green">058</FONT> private final double[] xval;<a name="line.58"></a> <FONT color="green">059</FONT> /** Samples y-coordinates */<a name="line.59"></a> <FONT color="green">060</FONT> private final double[] yval;<a name="line.60"></a> <FONT color="green">061</FONT> /** Set of cubic splines pacthing the whole data grid */<a name="line.61"></a> <FONT color="green">062</FONT> private final BicubicSplineFunction[][] splines;<a name="line.62"></a> <FONT color="green">063</FONT> <a name="line.63"></a> <FONT color="green">064</FONT> /**<a name="line.64"></a> <FONT color="green">065</FONT> * @param x Sample values of the x-coordinate, in increasing order<a name="line.65"></a> <FONT color="green">066</FONT> * @param y Sample values of the y-coordinate, in increasing order<a name="line.66"></a> <FONT color="green">067</FONT> * @param z Values of the function on every grid point<a name="line.67"></a> <FONT color="green">068</FONT> * @param dZdX Values of the partial derivative of function with respect<a name="line.68"></a> <FONT color="green">069</FONT> * to x on every grid point<a name="line.69"></a> <FONT color="green">070</FONT> * @param dZdY Values of the partial derivative of function with respect<a name="line.70"></a> <FONT color="green">071</FONT> * to y on every grid point<a name="line.71"></a> <FONT color="green">072</FONT> * @param dZdXdY Values of the cross partial derivative of function on<a name="line.72"></a> <FONT color="green">073</FONT> * every grid point<a name="line.73"></a> <FONT color="green">074</FONT> * @throws DimensionMismatchException if the various arrays do not contain<a name="line.74"></a> <FONT color="green">075</FONT> * the expected number of elements.<a name="line.75"></a> <FONT color="green">076</FONT> * @throws IllegalArgumentException if {@code x} or {@code y} are not strictly<a name="line.76"></a> <FONT color="green">077</FONT> * increasing.<a name="line.77"></a> <FONT color="green">078</FONT> */<a name="line.78"></a> <FONT color="green">079</FONT> public BicubicSplineInterpolatingFunction(double[] x,<a name="line.79"></a> <FONT color="green">080</FONT> double[] y,<a name="line.80"></a> <FONT color="green">081</FONT> double[][] z,<a name="line.81"></a> <FONT color="green">082</FONT> double[][] dZdX,<a name="line.82"></a> <FONT color="green">083</FONT> double[][] dZdY,<a name="line.83"></a> <FONT color="green">084</FONT> double[][] dZdXdY)<a name="line.84"></a> <FONT color="green">085</FONT> throws DimensionMismatchException {<a name="line.85"></a> <FONT color="green">086</FONT> final int xLen = x.length;<a name="line.86"></a> <FONT color="green">087</FONT> final int yLen = y.length;<a name="line.87"></a> <FONT color="green">088</FONT> <a name="line.88"></a> <FONT color="green">089</FONT> if (xLen == 0 || yLen == 0 || z.length == 0 || z[0].length == 0) {<a name="line.89"></a> <FONT color="green">090</FONT> throw MathRuntimeException.createIllegalArgumentException("no data");<a name="line.90"></a> <FONT color="green">091</FONT> }<a name="line.91"></a> <FONT color="green">092</FONT> if (xLen != z.length) {<a name="line.92"></a> <FONT color="green">093</FONT> throw new DimensionMismatchException(xLen, z.length);<a name="line.93"></a> <FONT color="green">094</FONT> }<a name="line.94"></a> <FONT color="green">095</FONT> if (xLen != dZdX.length) {<a name="line.95"></a> <FONT color="green">096</FONT> throw new DimensionMismatchException(xLen, dZdX.length);<a name="line.96"></a> <FONT color="green">097</FONT> }<a name="line.97"></a> <FONT color="green">098</FONT> if (xLen != dZdY.length) {<a name="line.98"></a> <FONT color="green">099</FONT> throw new DimensionMismatchException(xLen, dZdY.length);<a name="line.99"></a> <FONT color="green">100</FONT> }<a name="line.100"></a> <FONT color="green">101</FONT> if (xLen != dZdXdY.length) {<a name="line.101"></a> <FONT color="green">102</FONT> throw new DimensionMismatchException(xLen, dZdXdY.length);<a name="line.102"></a> <FONT color="green">103</FONT> }<a name="line.103"></a> <FONT color="green">104</FONT> <a name="line.104"></a> <FONT color="green">105</FONT> MathUtils.checkOrder(x, 1, true);<a name="line.105"></a> <FONT color="green">106</FONT> MathUtils.checkOrder(y, 1, true);<a name="line.106"></a> <FONT color="green">107</FONT> <a name="line.107"></a> <FONT color="green">108</FONT> xval = x.clone();<a name="line.108"></a> <FONT color="green">109</FONT> yval = y.clone();<a name="line.109"></a> <FONT color="green">110</FONT> <a name="line.110"></a> <FONT color="green">111</FONT> final int lastI = xLen - 1;<a name="line.111"></a> <FONT color="green">112</FONT> final int lastJ = yLen - 1;<a name="line.112"></a> <FONT color="green">113</FONT> splines = new BicubicSplineFunction[lastI][lastJ];<a name="line.113"></a> <FONT color="green">114</FONT> <a name="line.114"></a> <FONT color="green">115</FONT> for (int i = 0; i < lastI; i++) {<a name="line.115"></a> <FONT color="green">116</FONT> if (z[i].length != yLen) {<a name="line.116"></a> <FONT color="green">117</FONT> throw new DimensionMismatchException(z[i].length, yLen);<a name="line.117"></a> <FONT color="green">118</FONT> }<a name="line.118"></a> <FONT color="green">119</FONT> if (dZdX[i].length != yLen) {<a name="line.119"></a> <FONT color="green">120</FONT> throw new DimensionMismatchException(dZdX[i].length, yLen);<a name="line.120"></a> <FONT color="green">121</FONT> }<a name="line.121"></a> <FONT color="green">122</FONT> if (dZdY[i].length != yLen) {<a name="line.122"></a> <FONT color="green">123</FONT> throw new DimensionMismatchException(dZdY[i].length, yLen);<a name="line.123"></a> <FONT color="green">124</FONT> }<a name="line.124"></a> <FONT color="green">125</FONT> if (dZdXdY[i].length != yLen) {<a name="line.125"></a> <FONT color="green">126</FONT> throw new DimensionMismatchException(dZdXdY[i].length, yLen);<a name="line.126"></a> <FONT color="green">127</FONT> }<a name="line.127"></a> <FONT color="green">128</FONT> final int ip1 = i + 1;<a name="line.128"></a> <FONT color="green">129</FONT> for (int j = 0; j < lastJ; j++) {<a name="line.129"></a> <FONT color="green">130</FONT> final int jp1 = j + 1;<a name="line.130"></a> <FONT color="green">131</FONT> final double[] beta = new double[] {<a name="line.131"></a> <FONT color="green">132</FONT> z[i][j], z[ip1][j], z[i][jp1], z[ip1][jp1],<a name="line.132"></a> <FONT color="green">133</FONT> dZdX[i][j], dZdX[ip1][j], dZdX[i][jp1], dZdX[ip1][jp1],<a name="line.133"></a> <FONT color="green">134</FONT> dZdY[i][j], dZdY[ip1][j], dZdY[i][jp1], dZdY[ip1][jp1],<a name="line.134"></a> <FONT color="green">135</FONT> dZdXdY[i][j], dZdXdY[ip1][j], dZdXdY[i][jp1], dZdXdY[ip1][jp1]<a name="line.135"></a> <FONT color="green">136</FONT> };<a name="line.136"></a> <FONT color="green">137</FONT> <a name="line.137"></a> <FONT color="green">138</FONT> splines[i][j] = new BicubicSplineFunction(computeSplineCoefficients(beta));<a name="line.138"></a> <FONT color="green">139</FONT> }<a name="line.139"></a> <FONT color="green">140</FONT> }<a name="line.140"></a> <FONT color="green">141</FONT> }<a name="line.141"></a> <FONT color="green">142</FONT> <a name="line.142"></a> <FONT color="green">143</FONT> /**<a name="line.143"></a> <FONT color="green">144</FONT> * {@inheritDoc}<a name="line.144"></a> <FONT color="green">145</FONT> */<a name="line.145"></a> <FONT color="green">146</FONT> public double value(double x, double y) {<a name="line.146"></a> <FONT color="green">147</FONT> final int i = searchIndex(x, xval);<a name="line.147"></a> <FONT color="green">148</FONT> if (i == -1) {<a name="line.148"></a> <FONT color="green">149</FONT> throw MathRuntimeException.createIllegalArgumentException("{0} out of [{1}, {2}] range",<a name="line.149"></a> <FONT color="green">150</FONT> x, xval[0], xval[xval.length - 1]);<a name="line.150"></a> <FONT color="green">151</FONT> }<a name="line.151"></a> <FONT color="green">152</FONT> final int j = searchIndex(y, yval);<a name="line.152"></a> <FONT color="green">153</FONT> if (j == -1) {<a name="line.153"></a> <FONT color="green">154</FONT> throw MathRuntimeException.createIllegalArgumentException("{0} out of [{1}, {2}] range",<a name="line.154"></a> <FONT color="green">155</FONT> y, yval[0], yval[yval.length - 1]);<a name="line.155"></a> <FONT color="green">156</FONT> }<a name="line.156"></a> <FONT color="green">157</FONT> <a name="line.157"></a> <FONT color="green">158</FONT> final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);<a name="line.158"></a> <FONT color="green">159</FONT> final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);<a name="line.159"></a> <FONT color="green">160</FONT> <a name="line.160"></a> <FONT color="green">161</FONT> return splines[i][j].value(xN, yN);<a name="line.161"></a> <FONT color="green">162</FONT> }<a name="line.162"></a> <FONT color="green">163</FONT> <a name="line.163"></a> <FONT color="green">164</FONT> /**<a name="line.164"></a> <FONT color="green">165</FONT> * @param c coordinate<a name="line.165"></a> <FONT color="green">166</FONT> * @param val coordinate samples<a name="line.166"></a> <FONT color="green">167</FONT> * @return the index in {@code val} corresponding to the interval<a name="line.167"></a> <FONT color="green">168</FONT> * containing {@code c}, or {@code -1} if {@code c} is out of the<a name="line.168"></a> <FONT color="green">169</FONT> * range defined by the end values of {@code val}<a name="line.169"></a> <FONT color="green">170</FONT> */<a name="line.170"></a> <FONT color="green">171</FONT> private int searchIndex(double c, double[] val) {<a name="line.171"></a> <FONT color="green">172</FONT> if (c < val[0]) {<a name="line.172"></a> <FONT color="green">173</FONT> return -1;<a name="line.173"></a> <FONT color="green">174</FONT> }<a name="line.174"></a> <FONT color="green">175</FONT> <a name="line.175"></a> <FONT color="green">176</FONT> int max = val.length;<a name="line.176"></a> <FONT color="green">177</FONT> for (int i = 1; i < max; i++) {<a name="line.177"></a> <FONT color="green">178</FONT> if (c <= val[i]) {<a name="line.178"></a> <FONT color="green">179</FONT> return i - 1;<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> return -1;<a name="line.183"></a> <FONT color="green">184</FONT> }<a name="line.184"></a> <FONT color="green">185</FONT> <a name="line.185"></a> <FONT color="green">186</FONT> /**<a name="line.186"></a> <FONT color="green">187</FONT> * Compute the spline coefficients from the list of function values and<a name="line.187"></a> <FONT color="green">188</FONT> * function partial derivatives values at the four corners of a grid<a name="line.188"></a> <FONT color="green">189</FONT> * element. They must be specified in the following order:<a name="line.189"></a> <FONT color="green">190</FONT> * <ul><a name="line.190"></a> <FONT color="green">191</FONT> * <li>f(0,0)</li><a name="line.191"></a> <FONT color="green">192</FONT> * <li>f(1,0)</li><a name="line.192"></a> <FONT color="green">193</FONT> * <li>f(0,1)</li><a name="line.193"></a> <FONT color="green">194</FONT> * <li>f(1,1)</li><a name="line.194"></a> <FONT color="green">195</FONT> * <li>fx(0,0)</li><a name="line.195"></a> <FONT color="green">196</FONT> * <li>fx(1,0)</li><a name="line.196"></a> <FONT color="green">197</FONT> * <li>fx(0,1)</li><a name="line.197"></a> <FONT color="green">198</FONT> * <li>fx(1,1)</li><a name="line.198"></a> <FONT color="green">199</FONT> * <li>fy(0,0)</li><a name="line.199"></a> <FONT color="green">200</FONT> * <li>fy(1,0)</li><a name="line.200"></a> <FONT color="green">201</FONT> * <li>fy(0,1)</li><a name="line.201"></a> <FONT color="green">202</FONT> * <li>fy(1,1)</li><a name="line.202"></a> <FONT color="green">203</FONT> * <li>fxy(0,0)</li><a name="line.203"></a> <FONT color="green">204</FONT> * <li>fxy(1,0)</li><a name="line.204"></a> <FONT color="green">205</FONT> * <li>fxy(0,1)</li><a name="line.205"></a> <FONT color="green">206</FONT> * <li>fxy(1,1)</li><a name="line.206"></a> <FONT color="green">207</FONT> * </ul><a name="line.207"></a> <FONT color="green">208</FONT> * @param beta List of function values and function partial derivatives<a name="line.208"></a> <FONT color="green">209</FONT> * values<a name="line.209"></a> <FONT color="green">210</FONT> * @return the spline coefficients<a name="line.210"></a> <FONT color="green">211</FONT> */<a name="line.211"></a> <FONT color="green">212</FONT> private double[] computeSplineCoefficients(double[] beta) {<a name="line.212"></a> <FONT color="green">213</FONT> final double[] a = new double[16];<a name="line.213"></a> <FONT color="green">214</FONT> <a name="line.214"></a> <FONT color="green">215</FONT> for (int i = 0; i < 16; i++) {<a name="line.215"></a> <FONT color="green">216</FONT> double result = 0;<a name="line.216"></a> <FONT color="green">217</FONT> final double[] row = AINV[i];<a name="line.217"></a> <FONT color="green">218</FONT> for (int j = 0; j < 16; j++) {<a name="line.218"></a> <FONT color="green">219</FONT> result += row[j] * beta[j];<a name="line.219"></a> <FONT color="green">220</FONT> }<a name="line.220"></a> <FONT color="green">221</FONT> a[i] = result;<a name="line.221"></a> <FONT color="green">222</FONT> }<a name="line.222"></a> <FONT color="green">223</FONT> <a name="line.223"></a> <FONT color="green">224</FONT> return a;<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> * 2D-spline function.<a name="line.228"></a> <FONT color="green">229</FONT> *<a name="line.229"></a> <FONT color="green">230</FONT> * @version $Revision$ $Date$<a name="line.230"></a> <FONT color="green">231</FONT> */<a name="line.231"></a> <FONT color="green">232</FONT> class BicubicSplineFunction<a name="line.232"></a> <FONT color="green">233</FONT> implements BivariateRealFunction {<a name="line.233"></a> <FONT color="green">234</FONT> //CHECKSTYLE: stop MultipleVariableDeclarations<a name="line.234"></a> <FONT color="green">235</FONT> /** Coefficients */<a name="line.235"></a> <FONT color="green">236</FONT> private final double<a name="line.236"></a> <FONT color="green">237</FONT> a00, a01, a02, a03,<a name="line.237"></a> <FONT color="green">238</FONT> a10, a11, a12, a13,<a name="line.238"></a> <FONT color="green">239</FONT> a20, a21, a22, a23,<a name="line.239"></a> <FONT color="green">240</FONT> a30, a31, a32, a33;<a name="line.240"></a> <FONT color="green">241</FONT> //CHECKSTYLE: resume MultipleVariableDeclarations<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> <FONT color="green">244</FONT> * @param a Spline coefficients<a name="line.244"></a> <FONT color="green">245</FONT> */<a name="line.245"></a> <FONT color="green">246</FONT> public BicubicSplineFunction(double[] a) {<a name="line.246"></a> <FONT color="green">247</FONT> this.a00 = a[0];<a name="line.247"></a> <FONT color="green">248</FONT> this.a10 = a[1];<a name="line.248"></a> <FONT color="green">249</FONT> this.a20 = a[2];<a name="line.249"></a> <FONT color="green">250</FONT> this.a30 = a[3];<a name="line.250"></a> <FONT color="green">251</FONT> this.a01 = a[4];<a name="line.251"></a> <FONT color="green">252</FONT> this.a11 = a[5];<a name="line.252"></a> <FONT color="green">253</FONT> this.a21 = a[6];<a name="line.253"></a> <FONT color="green">254</FONT> this.a31 = a[7];<a name="line.254"></a> <FONT color="green">255</FONT> this.a02 = a[8];<a name="line.255"></a> <FONT color="green">256</FONT> this.a12 = a[9];<a name="line.256"></a> <FONT color="green">257</FONT> this.a22 = a[10];<a name="line.257"></a> <FONT color="green">258</FONT> this.a32 = a[11];<a name="line.258"></a> <FONT color="green">259</FONT> this.a03 = a[12];<a name="line.259"></a> <FONT color="green">260</FONT> this.a13 = a[13];<a name="line.260"></a> <FONT color="green">261</FONT> this.a23 = a[14];<a name="line.261"></a> <FONT color="green">262</FONT> this.a33 = a[15];<a name="line.262"></a> <FONT color="green">263</FONT> }<a name="line.263"></a> <FONT color="green">264</FONT> <a name="line.264"></a> <FONT color="green">265</FONT> /**<a name="line.265"></a> <FONT color="green">266</FONT> * @param x x-coordinate of the interpolation point<a name="line.266"></a> <FONT color="green">267</FONT> * @param y y-coordinate of the interpolation point<a name="line.267"></a> <FONT color="green">268</FONT> * @return the interpolated value.<a name="line.268"></a> <FONT color="green">269</FONT> */<a name="line.269"></a> <FONT color="green">270</FONT> public double value(double x, double y) {<a name="line.270"></a> <FONT color="green">271</FONT> if (x < 0 || x > 1) {<a name="line.271"></a> <FONT color="green">272</FONT> throw MathRuntimeException.createIllegalArgumentException("{0} out of [{1}, {2}] range",<a name="line.272"></a> <FONT color="green">273</FONT> x, 0, 1);<a name="line.273"></a> <FONT color="green">274</FONT> }<a name="line.274"></a> <FONT color="green">275</FONT> if (y < 0 || y > 1) {<a name="line.275"></a> <FONT color="green">276</FONT> throw MathRuntimeException.createIllegalArgumentException("{0} out of [{1}, {2}] range",<a name="line.276"></a> <FONT color="green">277</FONT> y, 0, 1);<a name="line.277"></a> <FONT color="green">278</FONT> }<a name="line.278"></a> <FONT color="green">279</FONT> <a name="line.279"></a> <FONT color="green">280</FONT> final double x2 = x * x;<a name="line.280"></a> <FONT color="green">281</FONT> final double x3 = x2 * x;<a name="line.281"></a> <FONT color="green">282</FONT> final double y2 = y * y;<a name="line.282"></a> <FONT color="green">283</FONT> final double y3 = y2 * y;<a name="line.283"></a> <FONT color="green">284</FONT> <a name="line.284"></a> <FONT color="green">285</FONT> return a00 + a01 * y + a02 * y2 + a03 * y3 +<a name="line.285"></a> <FONT color="green">286</FONT> a10 * x + a11 * x * y + a12 * x * y2 + a13 * x * y3 +<a name="line.286"></a> <FONT color="green">287</FONT> a20 * x2 + a21 * x2 * y + a22 * x2 * y2 + a23 * x2 * y3 +<a name="line.287"></a> <FONT color="green">288</FONT> a30 * x3 + a31 * x3 * y + a32 * x3 * y2 + a33 * x3 * y3;<a name="line.288"></a> <FONT color="green">289</FONT> }<a name="line.289"></a> <FONT color="green">290</FONT> }<a name="line.290"></a> </PRE> </BODY> </HTML>