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commons-math-2.1 added
| 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> <a name="line.17"></a> <FONT color="green">018</FONT> package org.apache.commons.math.geometry;<a name="line.18"></a> <FONT color="green">019</FONT> <a name="line.19"></a> <FONT color="green">020</FONT> import java.io.Serializable;<a name="line.20"></a> <FONT color="green">021</FONT> <a name="line.21"></a> <FONT color="green">022</FONT> import org.apache.commons.math.MathRuntimeException;<a name="line.22"></a> <FONT color="green">023</FONT> import org.apache.commons.math.util.MathUtils;<a name="line.23"></a> <FONT color="green">024</FONT> <a name="line.24"></a> <FONT color="green">025</FONT> /**<a name="line.25"></a> <FONT color="green">026</FONT> * This class implements vectors in a three-dimensional space.<a name="line.26"></a> <FONT color="green">027</FONT> * <p>Instance of this class are guaranteed to be immutable.</p><a name="line.27"></a> <FONT color="green">028</FONT> * @version $Revision: 922713 $ $Date: 2010-03-13 20:26:13 -0500 (Sat, 13 Mar 2010) $<a name="line.28"></a> <FONT color="green">029</FONT> * @since 1.2<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> public class Vector3D<a name="line.32"></a> <FONT color="green">033</FONT> implements Serializable {<a name="line.33"></a> <FONT color="green">034</FONT> <a name="line.34"></a> <FONT color="green">035</FONT> /** Null vector (coordinates: 0, 0, 0). */<a name="line.35"></a> <FONT color="green">036</FONT> public static final Vector3D ZERO = new Vector3D(0, 0, 0);<a name="line.36"></a> <FONT color="green">037</FONT> <a name="line.37"></a> <FONT color="green">038</FONT> /** First canonical vector (coordinates: 1, 0, 0). */<a name="line.38"></a> <FONT color="green">039</FONT> public static final Vector3D PLUS_I = new Vector3D(1, 0, 0);<a name="line.39"></a> <FONT color="green">040</FONT> <a name="line.40"></a> <FONT color="green">041</FONT> /** Opposite of the first canonical vector (coordinates: -1, 0, 0). */<a name="line.41"></a> <FONT color="green">042</FONT> public static final Vector3D MINUS_I = new Vector3D(-1, 0, 0);<a name="line.42"></a> <FONT color="green">043</FONT> <a name="line.43"></a> <FONT color="green">044</FONT> /** Second canonical vector (coordinates: 0, 1, 0). */<a name="line.44"></a> <FONT color="green">045</FONT> public static final Vector3D PLUS_J = new Vector3D(0, 1, 0);<a name="line.45"></a> <FONT color="green">046</FONT> <a name="line.46"></a> <FONT color="green">047</FONT> /** Opposite of the second canonical vector (coordinates: 0, -1, 0). */<a name="line.47"></a> <FONT color="green">048</FONT> public static final Vector3D MINUS_J = new Vector3D(0, -1, 0);<a name="line.48"></a> <FONT color="green">049</FONT> <a name="line.49"></a> <FONT color="green">050</FONT> /** Third canonical vector (coordinates: 0, 0, 1). */<a name="line.50"></a> <FONT color="green">051</FONT> public static final Vector3D PLUS_K = new Vector3D(0, 0, 1);<a name="line.51"></a> <FONT color="green">052</FONT> <a name="line.52"></a> <FONT color="green">053</FONT> /** Opposite of the third canonical vector (coordinates: 0, 0, -1). */<a name="line.53"></a> <FONT color="green">054</FONT> public static final Vector3D MINUS_K = new Vector3D(0, 0, -1);<a name="line.54"></a> <FONT color="green">055</FONT> <a name="line.55"></a> <FONT color="green">056</FONT> // CHECKSTYLE: stop ConstantName<a name="line.56"></a> <FONT color="green">057</FONT> /** A vector with all coordinates set to NaN. */<a name="line.57"></a> <FONT color="green">058</FONT> public static final Vector3D NaN = new Vector3D(Double.NaN, Double.NaN, Double.NaN);<a name="line.58"></a> <FONT color="green">059</FONT> // CHECKSTYLE: resume ConstantName<a name="line.59"></a> <FONT color="green">060</FONT> <a name="line.60"></a> <FONT color="green">061</FONT> /** A vector with all coordinates set to positive infinity. */<a name="line.61"></a> <FONT color="green">062</FONT> public static final Vector3D POSITIVE_INFINITY =<a name="line.62"></a> <FONT color="green">063</FONT> new Vector3D(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);<a name="line.63"></a> <FONT color="green">064</FONT> <a name="line.64"></a> <FONT color="green">065</FONT> /** A vector with all coordinates set to negative infinity. */<a name="line.65"></a> <FONT color="green">066</FONT> public static final Vector3D NEGATIVE_INFINITY =<a name="line.66"></a> <FONT color="green">067</FONT> new Vector3D(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY);<a name="line.67"></a> <FONT color="green">068</FONT> <a name="line.68"></a> <FONT color="green">069</FONT> /** Default format. */<a name="line.69"></a> <FONT color="green">070</FONT> private static final Vector3DFormat DEFAULT_FORMAT =<a name="line.70"></a> <FONT color="green">071</FONT> Vector3DFormat.getInstance();<a name="line.71"></a> <FONT color="green">072</FONT> <a name="line.72"></a> <FONT color="green">073</FONT> /** Serializable version identifier. */<a name="line.73"></a> <FONT color="green">074</FONT> private static final long serialVersionUID = 5133268763396045979L;<a name="line.74"></a> <FONT color="green">075</FONT> <a name="line.75"></a> <FONT color="green">076</FONT> /** Abscissa. */<a name="line.76"></a> <FONT color="green">077</FONT> private final double x;<a name="line.77"></a> <FONT color="green">078</FONT> <a name="line.78"></a> <FONT color="green">079</FONT> /** Ordinate. */<a name="line.79"></a> <FONT color="green">080</FONT> private final double y;<a name="line.80"></a> <FONT color="green">081</FONT> <a name="line.81"></a> <FONT color="green">082</FONT> /** Height. */<a name="line.82"></a> <FONT color="green">083</FONT> private final double z;<a name="line.83"></a> <FONT color="green">084</FONT> <a name="line.84"></a> <FONT color="green">085</FONT> /** Simple constructor.<a name="line.85"></a> <FONT color="green">086</FONT> * Build a vector from its coordinates<a name="line.86"></a> <FONT color="green">087</FONT> * @param x abscissa<a name="line.87"></a> <FONT color="green">088</FONT> * @param y ordinate<a name="line.88"></a> <FONT color="green">089</FONT> * @param z height<a name="line.89"></a> <FONT color="green">090</FONT> * @see #getX()<a name="line.90"></a> <FONT color="green">091</FONT> * @see #getY()<a name="line.91"></a> <FONT color="green">092</FONT> * @see #getZ()<a name="line.92"></a> <FONT color="green">093</FONT> */<a name="line.93"></a> <FONT color="green">094</FONT> public Vector3D(double x, double y, double z) {<a name="line.94"></a> <FONT color="green">095</FONT> this.x = x;<a name="line.95"></a> <FONT color="green">096</FONT> this.y = y;<a name="line.96"></a> <FONT color="green">097</FONT> this.z = z;<a name="line.97"></a> <FONT color="green">098</FONT> }<a name="line.98"></a> <FONT color="green">099</FONT> <a name="line.99"></a> <FONT color="green">100</FONT> /** Simple constructor.<a name="line.100"></a> <FONT color="green">101</FONT> * Build a vector from its azimuthal coordinates<a name="line.101"></a> <FONT color="green">102</FONT> * @param alpha azimuth (&alpha;) around Z<a name="line.102"></a> <FONT color="green">103</FONT> * (0 is +X, &pi;/2 is +Y, &pi; is -X and 3&pi;/2 is -Y)<a name="line.103"></a> <FONT color="green">104</FONT> * @param delta elevation (&delta;) above (XY) plane, from -&pi;/2 to +&pi;/2<a name="line.104"></a> <FONT color="green">105</FONT> * @see #getAlpha()<a name="line.105"></a> <FONT color="green">106</FONT> * @see #getDelta()<a name="line.106"></a> <FONT color="green">107</FONT> */<a name="line.107"></a> <FONT color="green">108</FONT> public Vector3D(double alpha, double delta) {<a name="line.108"></a> <FONT color="green">109</FONT> double cosDelta = Math.cos(delta);<a name="line.109"></a> <FONT color="green">110</FONT> this.x = Math.cos(alpha) * cosDelta;<a name="line.110"></a> <FONT color="green">111</FONT> this.y = Math.sin(alpha) * cosDelta;<a name="line.111"></a> <FONT color="green">112</FONT> this.z = Math.sin(delta);<a name="line.112"></a> <FONT color="green">113</FONT> }<a name="line.113"></a> <FONT color="green">114</FONT> <a name="line.114"></a> <FONT color="green">115</FONT> /** Multiplicative constructor<a name="line.115"></a> <FONT color="green">116</FONT> * Build a vector from another one and a scale factor.<a name="line.116"></a> <FONT color="green">117</FONT> * The vector built will be a * u<a name="line.117"></a> <FONT color="green">118</FONT> * @param a scale factor<a name="line.118"></a> <FONT color="green">119</FONT> * @param u base (unscaled) vector<a name="line.119"></a> <FONT color="green">120</FONT> */<a name="line.120"></a> <FONT color="green">121</FONT> public Vector3D(double a, Vector3D u) {<a name="line.121"></a> <FONT color="green">122</FONT> this.x = a * u.x;<a name="line.122"></a> <FONT color="green">123</FONT> this.y = a * u.y;<a name="line.123"></a> <FONT color="green">124</FONT> this.z = a * u.z;<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> /** Linear constructor<a name="line.127"></a> <FONT color="green">128</FONT> * Build a vector from two other ones and corresponding scale factors.<a name="line.128"></a> <FONT color="green">129</FONT> * The vector built will be a1 * u1 + a2 * u2<a name="line.129"></a> <FONT color="green">130</FONT> * @param a1 first scale factor<a name="line.130"></a> <FONT color="green">131</FONT> * @param u1 first base (unscaled) vector<a name="line.131"></a> <FONT color="green">132</FONT> * @param a2 second scale factor<a name="line.132"></a> <FONT color="green">133</FONT> * @param u2 second base (unscaled) vector<a name="line.133"></a> <FONT color="green">134</FONT> */<a name="line.134"></a> <FONT color="green">135</FONT> public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2) {<a name="line.135"></a> <FONT color="green">136</FONT> this.x = a1 * u1.x + a2 * u2.x;<a name="line.136"></a> <FONT color="green">137</FONT> this.y = a1 * u1.y + a2 * u2.y;<a name="line.137"></a> <FONT color="green">138</FONT> this.z = a1 * u1.z + a2 * u2.z;<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> /** Linear constructor<a name="line.141"></a> <FONT color="green">142</FONT> * Build a vector from three other ones and corresponding scale factors.<a name="line.142"></a> <FONT color="green">143</FONT> * The vector built will be a1 * u1 + a2 * u2 + a3 * u3<a name="line.143"></a> <FONT color="green">144</FONT> * @param a1 first scale factor<a name="line.144"></a> <FONT color="green">145</FONT> * @param u1 first base (unscaled) vector<a name="line.145"></a> <FONT color="green">146</FONT> * @param a2 second scale factor<a name="line.146"></a> <FONT color="green">147</FONT> * @param u2 second base (unscaled) vector<a name="line.147"></a> <FONT color="green">148</FONT> * @param a3 third scale factor<a name="line.148"></a> <FONT color="green">149</FONT> * @param u3 third base (unscaled) vector<a name="line.149"></a> <FONT color="green">150</FONT> */<a name="line.150"></a> <FONT color="green">151</FONT> public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2,<a name="line.151"></a> <FONT color="green">152</FONT> double a3, Vector3D u3) {<a name="line.152"></a> <FONT color="green">153</FONT> this.x = a1 * u1.x + a2 * u2.x + a3 * u3.x;<a name="line.153"></a> <FONT color="green">154</FONT> this.y = a1 * u1.y + a2 * u2.y + a3 * u3.y;<a name="line.154"></a> <FONT color="green">155</FONT> this.z = a1 * u1.z + a2 * u2.z + a3 * u3.z;<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> /** Linear constructor<a name="line.158"></a> <FONT color="green">159</FONT> * Build a vector from four other ones and corresponding scale factors.<a name="line.159"></a> <FONT color="green">160</FONT> * The vector built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4<a name="line.160"></a> <FONT color="green">161</FONT> * @param a1 first scale factor<a name="line.161"></a> <FONT color="green">162</FONT> * @param u1 first base (unscaled) vector<a name="line.162"></a> <FONT color="green">163</FONT> * @param a2 second scale factor<a name="line.163"></a> <FONT color="green">164</FONT> * @param u2 second base (unscaled) vector<a name="line.164"></a> <FONT color="green">165</FONT> * @param a3 third scale factor<a name="line.165"></a> <FONT color="green">166</FONT> * @param u3 third base (unscaled) vector<a name="line.166"></a> <FONT color="green">167</FONT> * @param a4 fourth scale factor<a name="line.167"></a> <FONT color="green">168</FONT> * @param u4 fourth base (unscaled) vector<a name="line.168"></a> <FONT color="green">169</FONT> */<a name="line.169"></a> <FONT color="green">170</FONT> public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2,<a name="line.170"></a> <FONT color="green">171</FONT> double a3, Vector3D u3, double a4, Vector3D u4) {<a name="line.171"></a> <FONT color="green">172</FONT> this.x = a1 * u1.x + a2 * u2.x + a3 * u3.x + a4 * u4.x;<a name="line.172"></a> <FONT color="green">173</FONT> this.y = a1 * u1.y + a2 * u2.y + a3 * u3.y + a4 * u4.y;<a name="line.173"></a> <FONT color="green">174</FONT> this.z = a1 * u1.z + a2 * u2.z + a3 * u3.z + a4 * u4.z;<a name="line.174"></a> <FONT color="green">175</FONT> }<a name="line.175"></a> <FONT color="green">176</FONT> <a name="line.176"></a> <FONT color="green">177</FONT> /** Get the abscissa of the vector.<a name="line.177"></a> <FONT color="green">178</FONT> * @return abscissa of the vector<a name="line.178"></a> <FONT color="green">179</FONT> * @see #Vector3D(double, double, double)<a name="line.179"></a> <FONT color="green">180</FONT> */<a name="line.180"></a> <FONT color="green">181</FONT> public double getX() {<a name="line.181"></a> <FONT color="green">182</FONT> return x;<a name="line.182"></a> <FONT color="green">183</FONT> }<a name="line.183"></a> <FONT color="green">184</FONT> <a name="line.184"></a> <FONT color="green">185</FONT> /** Get the ordinate of the vector.<a name="line.185"></a> <FONT color="green">186</FONT> * @return ordinate of the vector<a name="line.186"></a> <FONT color="green">187</FONT> * @see #Vector3D(double, double, double)<a name="line.187"></a> <FONT color="green">188</FONT> */<a name="line.188"></a> <FONT color="green">189</FONT> public double getY() {<a name="line.189"></a> <FONT color="green">190</FONT> return y;<a name="line.190"></a> <FONT color="green">191</FONT> }<a name="line.191"></a> <FONT color="green">192</FONT> <a name="line.192"></a> <FONT color="green">193</FONT> /** Get the height of the vector.<a name="line.193"></a> <FONT color="green">194</FONT> * @return height of the vector<a name="line.194"></a> <FONT color="green">195</FONT> * @see #Vector3D(double, double, double)<a name="line.195"></a> <FONT color="green">196</FONT> */<a name="line.196"></a> <FONT color="green">197</FONT> public double getZ() {<a name="line.197"></a> <FONT color="green">198</FONT> return z;<a name="line.198"></a> <FONT color="green">199</FONT> }<a name="line.199"></a> <FONT color="green">200</FONT> <a name="line.200"></a> <FONT color="green">201</FONT> /** Get the L<sub>1</sub> norm for the vector.<a name="line.201"></a> <FONT color="green">202</FONT> * @return L<sub>1</sub> norm for the vector<a name="line.202"></a> <FONT color="green">203</FONT> */<a name="line.203"></a> <FONT color="green">204</FONT> public double getNorm1() {<a name="line.204"></a> <FONT color="green">205</FONT> return Math.abs(x) + Math.abs(y) + Math.abs(z);<a name="line.205"></a> <FONT color="green">206</FONT> }<a name="line.206"></a> <FONT color="green">207</FONT> <a name="line.207"></a> <FONT color="green">208</FONT> /** Get the L<sub>2</sub> norm for the vector.<a name="line.208"></a> <FONT color="green">209</FONT> * @return euclidian norm for the vector<a name="line.209"></a> <FONT color="green">210</FONT> */<a name="line.210"></a> <FONT color="green">211</FONT> public double getNorm() {<a name="line.211"></a> <FONT color="green">212</FONT> return Math.sqrt (x * x + y * y + z * z);<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> /** Get the square of the norm for the vector.<a name="line.215"></a> <FONT color="green">216</FONT> * @return square of the euclidian norm for the vector<a name="line.216"></a> <FONT color="green">217</FONT> */<a name="line.217"></a> <FONT color="green">218</FONT> public double getNormSq() {<a name="line.218"></a> <FONT color="green">219</FONT> return x * x + y * y + z * z;<a name="line.219"></a> <FONT color="green">220</FONT> }<a name="line.220"></a> <FONT color="green">221</FONT> <a name="line.221"></a> <FONT color="green">222</FONT> /** Get the L<sub>&infin;</sub> norm for the vector.<a name="line.222"></a> <FONT color="green">223</FONT> * @return L<sub>&infin;</sub> norm for the vector<a name="line.223"></a> <FONT color="green">224</FONT> */<a name="line.224"></a> <FONT color="green">225</FONT> public double getNormInf() {<a name="line.225"></a> <FONT color="green">226</FONT> return Math.max(Math.max(Math.abs(x), Math.abs(y)), Math.abs(z));<a name="line.226"></a> <FONT color="green">227</FONT> }<a name="line.227"></a> <FONT color="green">228</FONT> <a name="line.228"></a> <FONT color="green">229</FONT> /** Get the azimuth of the vector.<a name="line.229"></a> <FONT color="green">230</FONT> * @return azimuth (&alpha;) of the vector, between -&pi; and +&pi;<a name="line.230"></a> <FONT color="green">231</FONT> * @see #Vector3D(double, double)<a name="line.231"></a> <FONT color="green">232</FONT> */<a name="line.232"></a> <FONT color="green">233</FONT> public double getAlpha() {<a name="line.233"></a> <FONT color="green">234</FONT> return Math.atan2(y, x);<a name="line.234"></a> <FONT color="green">235</FONT> }<a name="line.235"></a> <FONT color="green">236</FONT> <a name="line.236"></a> <FONT color="green">237</FONT> /** Get the elevation of the vector.<a name="line.237"></a> <FONT color="green">238</FONT> * @return elevation (&delta;) of the vector, between -&pi;/2 and +&pi;/2<a name="line.238"></a> <FONT color="green">239</FONT> * @see #Vector3D(double, double)<a name="line.239"></a> <FONT color="green">240</FONT> */<a name="line.240"></a> <FONT color="green">241</FONT> public double getDelta() {<a name="line.241"></a> <FONT color="green">242</FONT> return Math.asin(z / getNorm());<a name="line.242"></a> <FONT color="green">243</FONT> }<a name="line.243"></a> <FONT color="green">244</FONT> <a name="line.244"></a> <FONT color="green">245</FONT> /** Add a vector to the instance.<a name="line.245"></a> <FONT color="green">246</FONT> * @param v vector to add<a name="line.246"></a> <FONT color="green">247</FONT> * @return a new vector<a name="line.247"></a> <FONT color="green">248</FONT> */<a name="line.248"></a> <FONT color="green">249</FONT> public Vector3D add(Vector3D v) {<a name="line.249"></a> <FONT color="green">250</FONT> return new Vector3D(x + v.x, y + v.y, z + v.z);<a name="line.250"></a> <FONT color="green">251</FONT> }<a name="line.251"></a> <FONT color="green">252</FONT> <a name="line.252"></a> <FONT color="green">253</FONT> /** Add a scaled vector to the instance.<a name="line.253"></a> <FONT color="green">254</FONT> * @param factor scale factor to apply to v before adding it<a name="line.254"></a> <FONT color="green">255</FONT> * @param v vector to add<a name="line.255"></a> <FONT color="green">256</FONT> * @return a new vector<a name="line.256"></a> <FONT color="green">257</FONT> */<a name="line.257"></a> <FONT color="green">258</FONT> public Vector3D add(double factor, Vector3D v) {<a name="line.258"></a> <FONT color="green">259</FONT> return new Vector3D(x + factor * v.x, y + factor * v.y, z + factor * v.z);<a name="line.259"></a> <FONT color="green">260</FONT> }<a name="line.260"></a> <FONT color="green">261</FONT> <a name="line.261"></a> <FONT color="green">262</FONT> /** Subtract a vector from the instance.<a name="line.262"></a> <FONT color="green">263</FONT> * @param v vector to subtract<a name="line.263"></a> <FONT color="green">264</FONT> * @return a new vector<a name="line.264"></a> <FONT color="green">265</FONT> */<a name="line.265"></a> <FONT color="green">266</FONT> public Vector3D subtract(Vector3D v) {<a name="line.266"></a> <FONT color="green">267</FONT> return new Vector3D(x - v.x, y - v.y, z - v.z);<a name="line.267"></a> <FONT color="green">268</FONT> }<a name="line.268"></a> <FONT color="green">269</FONT> <a name="line.269"></a> <FONT color="green">270</FONT> /** Subtract a scaled vector from the instance.<a name="line.270"></a> <FONT color="green">271</FONT> * @param factor scale factor to apply to v before subtracting it<a name="line.271"></a> <FONT color="green">272</FONT> * @param v vector to subtract<a name="line.272"></a> <FONT color="green">273</FONT> * @return a new vector<a name="line.273"></a> <FONT color="green">274</FONT> */<a name="line.274"></a> <FONT color="green">275</FONT> public Vector3D subtract(double factor, Vector3D v) {<a name="line.275"></a> <FONT color="green">276</FONT> return new Vector3D(x - factor * v.x, y - factor * v.y, z - factor * v.z);<a name="line.276"></a> <FONT color="green">277</FONT> }<a name="line.277"></a> <FONT color="green">278</FONT> <a name="line.278"></a> <FONT color="green">279</FONT> /** Get a normalized vector aligned with the instance.<a name="line.279"></a> <FONT color="green">280</FONT> * @return a new normalized vector<a name="line.280"></a> <FONT color="green">281</FONT> * @exception ArithmeticException if the norm is zero<a name="line.281"></a> <FONT color="green">282</FONT> */<a name="line.282"></a> <FONT color="green">283</FONT> public Vector3D normalize() {<a name="line.283"></a> <FONT color="green">284</FONT> double s = getNorm();<a name="line.284"></a> <FONT color="green">285</FONT> if (s == 0) {<a name="line.285"></a> <FONT color="green">286</FONT> throw MathRuntimeException.createArithmeticException("cannot normalize a zero norm vector");<a name="line.286"></a> <FONT color="green">287</FONT> }<a name="line.287"></a> <FONT color="green">288</FONT> return scalarMultiply(1 / s);<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> <FONT color="green">291</FONT> /** Get a vector orthogonal to the instance.<a name="line.291"></a> <FONT color="green">292</FONT> * <p>There are an infinite number of normalized vectors orthogonal<a name="line.292"></a> <FONT color="green">293</FONT> * to the instance. This method picks up one of them almost<a name="line.293"></a> <FONT color="green">294</FONT> * arbitrarily. It is useful when one needs to compute a reference<a name="line.294"></a> <FONT color="green">295</FONT> * frame with one of the axes in a predefined direction. The<a name="line.295"></a> <FONT color="green">296</FONT> * following example shows how to build a frame having the k axis<a name="line.296"></a> <FONT color="green">297</FONT> * aligned with the known vector u :<a name="line.297"></a> <FONT color="green">298</FONT> * <pre><code><a name="line.298"></a> <FONT color="green">299</FONT> * Vector3D k = u.normalize();<a name="line.299"></a> <FONT color="green">300</FONT> * Vector3D i = k.orthogonal();<a name="line.300"></a> <FONT color="green">301</FONT> * Vector3D j = Vector3D.crossProduct(k, i);<a name="line.301"></a> <FONT color="green">302</FONT> * </code></pre></p><a name="line.302"></a> <FONT color="green">303</FONT> * @return a new normalized vector orthogonal to the instance<a name="line.303"></a> <FONT color="green">304</FONT> * @exception ArithmeticException if the norm of the instance is null<a name="line.304"></a> <FONT color="green">305</FONT> */<a name="line.305"></a> <FONT color="green">306</FONT> public Vector3D orthogonal() {<a name="line.306"></a> <FONT color="green">307</FONT> <a name="line.307"></a> <FONT color="green">308</FONT> double threshold = 0.6 * getNorm();<a name="line.308"></a> <FONT color="green">309</FONT> if (threshold == 0) {<a name="line.309"></a> <FONT color="green">310</FONT> throw MathRuntimeException.createArithmeticException("zero norm");<a name="line.310"></a> <FONT color="green">311</FONT> }<a name="line.311"></a> <FONT color="green">312</FONT> <a name="line.312"></a> <FONT color="green">313</FONT> if ((x >= -threshold) && (x <= threshold)) {<a name="line.313"></a> <FONT color="green">314</FONT> double inverse = 1 / Math.sqrt(y * y + z * z);<a name="line.314"></a> <FONT color="green">315</FONT> return new Vector3D(0, inverse * z, -inverse * y);<a name="line.315"></a> <FONT color="green">316</FONT> } else if ((y >= -threshold) && (y <= threshold)) {<a name="line.316"></a> <FONT color="green">317</FONT> double inverse = 1 / Math.sqrt(x * x + z * z);<a name="line.317"></a> <FONT color="green">318</FONT> return new Vector3D(-inverse * z, 0, inverse * x);<a name="line.318"></a> <FONT color="green">319</FONT> }<a name="line.319"></a> <FONT color="green">320</FONT> double inverse = 1 / Math.sqrt(x * x + y * y);<a name="line.320"></a> <FONT color="green">321</FONT> return new Vector3D(inverse * y, -inverse * x, 0);<a name="line.321"></a> <FONT color="green">322</FONT> <a name="line.322"></a> <FONT color="green">323</FONT> }<a name="line.323"></a> <FONT color="green">324</FONT> <a name="line.324"></a> <FONT color="green">325</FONT> /** Compute the angular separation between two vectors.<a name="line.325"></a> <FONT color="green">326</FONT> * <p>This method computes the angular separation between two<a name="line.326"></a> <FONT color="green">327</FONT> * vectors using the dot product for well separated vectors and the<a name="line.327"></a> <FONT color="green">328</FONT> * cross product for almost aligned vectors. This allows to have a<a name="line.328"></a> <FONT color="green">329</FONT> * good accuracy in all cases, even for vectors very close to each<a name="line.329"></a> <FONT color="green">330</FONT> * other.</p><a name="line.330"></a> <FONT color="green">331</FONT> * @param v1 first vector<a name="line.331"></a> <FONT color="green">332</FONT> * @param v2 second vector<a name="line.332"></a> <FONT color="green">333</FONT> * @return angular separation between v1 and v2<a name="line.333"></a> <FONT color="green">334</FONT> * @exception ArithmeticException if either vector has a null norm<a name="line.334"></a> <FONT color="green">335</FONT> */<a name="line.335"></a> <FONT color="green">336</FONT> public static double angle(Vector3D v1, Vector3D v2) {<a name="line.336"></a> <FONT color="green">337</FONT> <a name="line.337"></a> <FONT color="green">338</FONT> double normProduct = v1.getNorm() * v2.getNorm();<a name="line.338"></a> <FONT color="green">339</FONT> if (normProduct == 0) {<a name="line.339"></a> <FONT color="green">340</FONT> throw MathRuntimeException.createArithmeticException("zero norm");<a name="line.340"></a> <FONT color="green">341</FONT> }<a name="line.341"></a> <FONT color="green">342</FONT> <a name="line.342"></a> <FONT color="green">343</FONT> double dot = dotProduct(v1, v2);<a name="line.343"></a> <FONT color="green">344</FONT> double threshold = normProduct * 0.9999;<a name="line.344"></a> <FONT color="green">345</FONT> if ((dot < -threshold) || (dot > threshold)) {<a name="line.345"></a> <FONT color="green">346</FONT> // the vectors are almost aligned, compute using the sine<a name="line.346"></a> <FONT color="green">347</FONT> Vector3D v3 = crossProduct(v1, v2);<a name="line.347"></a> <FONT color="green">348</FONT> if (dot >= 0) {<a name="line.348"></a> <FONT color="green">349</FONT> return Math.asin(v3.getNorm() / normProduct);<a name="line.349"></a> <FONT color="green">350</FONT> }<a name="line.350"></a> <FONT color="green">351</FONT> return Math.PI - Math.asin(v3.getNorm() / normProduct);<a name="line.351"></a> <FONT color="green">352</FONT> }<a name="line.352"></a> <FONT color="green">353</FONT> <a name="line.353"></a> <FONT color="green">354</FONT> // the vectors are sufficiently separated to use the cosine<a name="line.354"></a> <FONT color="green">355</FONT> return Math.acos(dot / normProduct);<a name="line.355"></a> <FONT color="green">356</FONT> <a name="line.356"></a> <FONT color="green">357</FONT> }<a name="line.357"></a> <FONT color="green">358</FONT> <a name="line.358"></a> <FONT color="green">359</FONT> /** Get the opposite of the instance.<a name="line.359"></a> <FONT color="green">360</FONT> * @return a new vector which is opposite to the instance<a name="line.360"></a> <FONT color="green">361</FONT> */<a name="line.361"></a> <FONT color="green">362</FONT> public Vector3D negate() {<a name="line.362"></a> <FONT color="green">363</FONT> return new Vector3D(-x, -y, -z);<a name="line.363"></a> <FONT color="green">364</FONT> }<a name="line.364"></a> <FONT color="green">365</FONT> <a name="line.365"></a> <FONT color="green">366</FONT> /** Multiply the instance by a scalar<a name="line.366"></a> <FONT color="green">367</FONT> * @param a scalar<a name="line.367"></a> <FONT color="green">368</FONT> * @return a new vector<a name="line.368"></a> <FONT color="green">369</FONT> */<a name="line.369"></a> <FONT color="green">370</FONT> public Vector3D scalarMultiply(double a) {<a name="line.370"></a> <FONT color="green">371</FONT> return new Vector3D(a * x, a * y, a * z);<a name="line.371"></a> <FONT color="green">372</FONT> }<a name="line.372"></a> <FONT color="green">373</FONT> <a name="line.373"></a> <FONT color="green">374</FONT> /**<a name="line.374"></a> <FONT color="green">375</FONT> * Returns true if any coordinate of this vector is NaN; false otherwise<a name="line.375"></a> <FONT color="green">376</FONT> * @return true if any coordinate of this vector is NaN; false otherwise<a name="line.376"></a> <FONT color="green">377</FONT> */<a name="line.377"></a> <FONT color="green">378</FONT> public boolean isNaN() {<a name="line.378"></a> <FONT color="green">379</FONT> return Double.isNaN(x) || Double.isNaN(y) || Double.isNaN(z);<a name="line.379"></a> <FONT color="green">380</FONT> }<a name="line.380"></a> <FONT color="green">381</FONT> <a name="line.381"></a> <FONT color="green">382</FONT> /**<a name="line.382"></a> <FONT color="green">383</FONT> * Returns true if any coordinate of this vector is infinite and none are NaN;<a name="line.383"></a> <FONT color="green">384</FONT> * false otherwise<a name="line.384"></a> <FONT color="green">385</FONT> * @return true if any coordinate of this vector is infinite and none are NaN;<a name="line.385"></a> <FONT color="green">386</FONT> * false otherwise<a name="line.386"></a> <FONT color="green">387</FONT> */<a name="line.387"></a> <FONT color="green">388</FONT> public boolean isInfinite() {<a name="line.388"></a> <FONT color="green">389</FONT> return !isNaN() && (Double.isInfinite(x) || Double.isInfinite(y) || Double.isInfinite(z));<a name="line.389"></a> <FONT color="green">390</FONT> }<a name="line.390"></a> <FONT color="green">391</FONT> <a name="line.391"></a> <FONT color="green">392</FONT> /**<a name="line.392"></a> <FONT color="green">393</FONT> * Test for the equality of two 3D vectors.<a name="line.393"></a> <FONT color="green">394</FONT> * <p><a name="line.394"></a> <FONT color="green">395</FONT> * If all coordinates of two 3D vectors are exactly the same, and none are<a name="line.395"></a> <FONT color="green">396</FONT> * <code>Double.NaN</code>, the two 3D vectors are considered to be equal.<a name="line.396"></a> <FONT color="green">397</FONT> * </p><a name="line.397"></a> <FONT color="green">398</FONT> * <p><a name="line.398"></a> <FONT color="green">399</FONT> * <code>NaN</code> coordinates are considered to affect globally the vector<a name="line.399"></a> <FONT color="green">400</FONT> * and be equals to each other - i.e, if either (or all) coordinates of the<a name="line.400"></a> <FONT color="green">401</FONT> * 3D vector are equal to <code>Double.NaN</code>, the 3D vector is equal to<a name="line.401"></a> <FONT color="green">402</FONT> * {@link #NaN}.<a name="line.402"></a> <FONT color="green">403</FONT> * </p><a name="line.403"></a> <FONT color="green">404</FONT> *<a name="line.404"></a> <FONT color="green">405</FONT> * @param other Object to test for equality to this<a name="line.405"></a> <FONT color="green">406</FONT> * @return true if two 3D vector objects are equal, false if<a name="line.406"></a> <FONT color="green">407</FONT> * object is null, not an instance of Vector3D, or<a name="line.407"></a> <FONT color="green">408</FONT> * not equal to this Vector3D instance<a name="line.408"></a> <FONT color="green">409</FONT> *<a name="line.409"></a> <FONT color="green">410</FONT> */<a name="line.410"></a> <FONT color="green">411</FONT> @Override<a name="line.411"></a> <FONT color="green">412</FONT> public boolean equals(Object other) {<a name="line.412"></a> <FONT color="green">413</FONT> <a name="line.413"></a> <FONT color="green">414</FONT> if (this == other) {<a name="line.414"></a> <FONT color="green">415</FONT> return true;<a name="line.415"></a> <FONT color="green">416</FONT> }<a name="line.416"></a> <FONT color="green">417</FONT> <a name="line.417"></a> <FONT color="green">418</FONT> if (other instanceof Vector3D) {<a name="line.418"></a> <FONT color="green">419</FONT> final Vector3D rhs = (Vector3D)other;<a name="line.419"></a> <FONT color="green">420</FONT> if (rhs.isNaN()) {<a name="line.420"></a> <FONT color="green">421</FONT> return this.isNaN();<a name="line.421"></a> <FONT color="green">422</FONT> }<a name="line.422"></a> <FONT color="green">423</FONT> <a name="line.423"></a> <FONT color="green">424</FONT> return (x == rhs.x) && (y == rhs.y) && (z == rhs.z);<a name="line.424"></a> <FONT color="green">425</FONT> }<a name="line.425"></a> <FONT color="green">426</FONT> return false;<a name="line.426"></a> <FONT color="green">427</FONT> }<a name="line.427"></a> <FONT color="green">428</FONT> <a name="line.428"></a> <FONT color="green">429</FONT> /**<a name="line.429"></a> <FONT color="green">430</FONT> * Get a hashCode for the 3D vector.<a name="line.430"></a> <FONT color="green">431</FONT> * <p><a name="line.431"></a> <FONT color="green">432</FONT> * All NaN values have the same hash code.</p><a name="line.432"></a> <FONT color="green">433</FONT> *<a name="line.433"></a> <FONT color="green">434</FONT> * @return a hash code value for this object<a name="line.434"></a> <FONT color="green">435</FONT> */<a name="line.435"></a> <FONT color="green">436</FONT> @Override<a name="line.436"></a> <FONT color="green">437</FONT> public int hashCode() {<a name="line.437"></a> <FONT color="green">438</FONT> if (isNaN()) {<a name="line.438"></a> <FONT color="green">439</FONT> return 8;<a name="line.439"></a> <FONT color="green">440</FONT> }<a name="line.440"></a> <FONT color="green">441</FONT> return 31 * (23 * MathUtils.hash(x) + 19 * MathUtils.hash(y) + MathUtils.hash(z));<a name="line.441"></a> <FONT color="green">442</FONT> }<a name="line.442"></a> <FONT color="green">443</FONT> <a name="line.443"></a> <FONT color="green">444</FONT> /** Compute the dot-product of two vectors.<a name="line.444"></a> <FONT color="green">445</FONT> * @param v1 first vector<a name="line.445"></a> <FONT color="green">446</FONT> * @param v2 second vector<a name="line.446"></a> <FONT color="green">447</FONT> * @return the dot product v1.v2<a name="line.447"></a> <FONT color="green">448</FONT> */<a name="line.448"></a> <FONT color="green">449</FONT> public static double dotProduct(Vector3D v1, Vector3D v2) {<a name="line.449"></a> <FONT color="green">450</FONT> return v1.x * v2.x + v1.y * v2.y + v1.z * v2.z;<a name="line.450"></a> <FONT color="green">451</FONT> }<a name="line.451"></a> <FONT color="green">452</FONT> <a name="line.452"></a> <FONT color="green">453</FONT> /** Compute the cross-product of two vectors.<a name="line.453"></a> <FONT color="green">454</FONT> * @param v1 first vector<a name="line.454"></a> <FONT color="green">455</FONT> * @param v2 second vector<a name="line.455"></a> <FONT color="green">456</FONT> * @return the cross product v1 ^ v2 as a new Vector<a name="line.456"></a> <FONT color="green">457</FONT> */<a name="line.457"></a> <FONT color="green">458</FONT> public static Vector3D crossProduct(Vector3D v1, Vector3D v2) {<a name="line.458"></a> <FONT color="green">459</FONT> return new Vector3D(v1.y * v2.z - v1.z * v2.y,<a name="line.459"></a> <FONT color="green">460</FONT> v1.z * v2.x - v1.x * v2.z,<a name="line.460"></a> <FONT color="green">461</FONT> v1.x * v2.y - v1.y * v2.x);<a name="line.461"></a> <FONT color="green">462</FONT> }<a name="line.462"></a> <FONT color="green">463</FONT> <a name="line.463"></a> <FONT color="green">464</FONT> /** Compute the distance between two vectors according to the L<sub>1</sub> norm.<a name="line.464"></a> <FONT color="green">465</FONT> * <p>Calling this method is equivalent to calling:<a name="line.465"></a> <FONT color="green">466</FONT> * <code>v1.subtract(v2).getNorm1()</code> except that no intermediate<a name="line.466"></a> <FONT color="green">467</FONT> * vector is built</p><a name="line.467"></a> <FONT color="green">468</FONT> * @param v1 first vector<a name="line.468"></a> <FONT color="green">469</FONT> * @param v2 second vector<a name="line.469"></a> <FONT color="green">470</FONT> * @return the distance between v1 and v2 according to the L<sub>1</sub> norm<a name="line.470"></a> <FONT color="green">471</FONT> */<a name="line.471"></a> <FONT color="green">472</FONT> public static double distance1(Vector3D v1, Vector3D v2) {<a name="line.472"></a> <FONT color="green">473</FONT> final double dx = Math.abs(v2.x - v1.x);<a name="line.473"></a> <FONT color="green">474</FONT> final double dy = Math.abs(v2.y - v1.y);<a name="line.474"></a> <FONT color="green">475</FONT> final double dz = Math.abs(v2.z - v1.z);<a name="line.475"></a> <FONT color="green">476</FONT> return dx + dy + dz;<a name="line.476"></a> <FONT color="green">477</FONT> }<a name="line.477"></a> <FONT color="green">478</FONT> <a name="line.478"></a> <FONT color="green">479</FONT> /** Compute the distance between two vectors according to the L<sub>2</sub> norm.<a name="line.479"></a> <FONT color="green">480</FONT> * <p>Calling this method is equivalent to calling:<a name="line.480"></a> <FONT color="green">481</FONT> * <code>v1.subtract(v2).getNorm()</code> except that no intermediate<a name="line.481"></a> <FONT color="green">482</FONT> * vector is built</p><a name="line.482"></a> <FONT color="green">483</FONT> * @param v1 first vector<a name="line.483"></a> <FONT color="green">484</FONT> * @param v2 second vector<a name="line.484"></a> <FONT color="green">485</FONT> * @return the distance between v1 and v2 according to the L<sub>2</sub> norm<a name="line.485"></a> <FONT color="green">486</FONT> */<a name="line.486"></a> <FONT color="green">487</FONT> public static double distance(Vector3D v1, Vector3D v2) {<a name="line.487"></a> <FONT color="green">488</FONT> final double dx = v2.x - v1.x;<a name="line.488"></a> <FONT color="green">489</FONT> final double dy = v2.y - v1.y;<a name="line.489"></a> <FONT color="green">490</FONT> final double dz = v2.z - v1.z;<a name="line.490"></a> <FONT color="green">491</FONT> return Math.sqrt(dx * dx + dy * dy + dz * dz);<a name="line.491"></a> <FONT color="green">492</FONT> }<a name="line.492"></a> <FONT color="green">493</FONT> <a name="line.493"></a> <FONT color="green">494</FONT> /** Compute the distance between two vectors according to the L<sub>&infin;</sub> norm.<a name="line.494"></a> <FONT color="green">495</FONT> * <p>Calling this method is equivalent to calling:<a name="line.495"></a> <FONT color="green">496</FONT> * <code>v1.subtract(v2).getNormInf()</code> except that no intermediate<a name="line.496"></a> <FONT color="green">497</FONT> * vector is built</p><a name="line.497"></a> <FONT color="green">498</FONT> * @param v1 first vector<a name="line.498"></a> <FONT color="green">499</FONT> * @param v2 second vector<a name="line.499"></a> <FONT color="green">500</FONT> * @return the distance between v1 and v2 according to the L<sub>&infin;</sub> norm<a name="line.500"></a> <FONT color="green">501</FONT> */<a name="line.501"></a> <FONT color="green">502</FONT> public static double distanceInf(Vector3D v1, Vector3D v2) {<a name="line.502"></a> <FONT color="green">503</FONT> final double dx = Math.abs(v2.x - v1.x);<a name="line.503"></a> <FONT color="green">504</FONT> final double dy = Math.abs(v2.y - v1.y);<a name="line.504"></a> <FONT color="green">505</FONT> final double dz = Math.abs(v2.z - v1.z);<a name="line.505"></a> <FONT color="green">506</FONT> return Math.max(Math.max(dx, dy), dz);<a name="line.506"></a> <FONT color="green">507</FONT> }<a name="line.507"></a> <FONT color="green">508</FONT> <a name="line.508"></a> <FONT color="green">509</FONT> /** Compute the square of the distance between two vectors.<a name="line.509"></a> <FONT color="green">510</FONT> * <p>Calling this method is equivalent to calling:<a name="line.510"></a> <FONT color="green">511</FONT> * <code>v1.subtract(v2).getNormSq()</code> except that no intermediate<a name="line.511"></a> <FONT color="green">512</FONT> * vector is built</p><a name="line.512"></a> <FONT color="green">513</FONT> * @param v1 first vector<a name="line.513"></a> <FONT color="green">514</FONT> * @param v2 second vector<a name="line.514"></a> <FONT color="green">515</FONT> * @return the square of the distance between v1 and v2<a name="line.515"></a> <FONT color="green">516</FONT> */<a name="line.516"></a> <FONT color="green">517</FONT> public static double distanceSq(Vector3D v1, Vector3D v2) {<a name="line.517"></a> <FONT color="green">518</FONT> final double dx = v2.x - v1.x;<a name="line.518"></a> <FONT color="green">519</FONT> final double dy = v2.y - v1.y;<a name="line.519"></a> <FONT color="green">520</FONT> final double dz = v2.z - v1.z;<a name="line.520"></a> <FONT color="green">521</FONT> return dx * dx + dy * dy + dz * dz;<a name="line.521"></a> <FONT color="green">522</FONT> }<a name="line.522"></a> <FONT color="green">523</FONT> <a name="line.523"></a> <FONT color="green">524</FONT> /** Get a string representation of this vector.<a name="line.524"></a> <FONT color="green">525</FONT> * @return a string representation of this vector<a name="line.525"></a> <FONT color="green">526</FONT> */<a name="line.526"></a> <FONT color="green">527</FONT> @Override<a name="line.527"></a> <FONT color="green">528</FONT> public String toString() {<a name="line.528"></a> <FONT color="green">529</FONT> return DEFAULT_FORMAT.format(this);<a name="line.529"></a> <FONT color="green">530</FONT> }<a name="line.530"></a> <FONT color="green">531</FONT> <a name="line.531"></a> <FONT color="green">532</FONT> }<a name="line.532"></a> </PRE> </BODY> </HTML>