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Posted to commits@commons.apache.org by lu...@apache.org on 2013/04/07 01:42:02 UTC
svn commit: r857558 [11/39] - in
/websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3:
./ analysis/ analysis/differentiation/ analysis/interpolation/ complex/
dfp/ distribution/ distribution/fitting/ ex...
Modified: websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/geometry/euclidean/threed/Vector3DTest.html
==============================================================================
--- websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/geometry/euclidean/threed/Vector3DTest.html (original)
+++ websites/production/commons/content/proper/commons-math/testapidocs/src-html/org/apache/commons/math3/geometry/euclidean/threed/Vector3DTest.html Sat Apr 6 23:42:01 2013
@@ -20,319 +20,399 @@
<FONT color="green">017</FONT> <a name="line.17"></a>
<FONT color="green">018</FONT> package org.apache.commons.math3.geometry.euclidean.threed;<a name="line.18"></a>
<FONT color="green">019</FONT> <a name="line.19"></a>
-<FONT color="green">020</FONT> import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.20"></a>
-<FONT color="green">021</FONT> import org.apache.commons.math3.exception.MathArithmeticException;<a name="line.21"></a>
-<FONT color="green">022</FONT> import org.apache.commons.math3.random.Well1024a;<a name="line.22"></a>
-<FONT color="green">023</FONT> import org.apache.commons.math3.util.FastMath;<a name="line.23"></a>
-<FONT color="green">024</FONT> import org.junit.Assert;<a name="line.24"></a>
-<FONT color="green">025</FONT> import org.junit.Test;<a name="line.25"></a>
-<FONT color="green">026</FONT> <a name="line.26"></a>
-<FONT color="green">027</FONT> public class Vector3DTest {<a name="line.27"></a>
-<FONT color="green">028</FONT> @Test<a name="line.28"></a>
-<FONT color="green">029</FONT> public void testConstructors() throws DimensionMismatchException {<a name="line.29"></a>
-<FONT color="green">030</FONT> double r = FastMath.sqrt(2) /2;<a name="line.30"></a>
-<FONT color="green">031</FONT> checkVector(new Vector3D(2, new Vector3D(FastMath.PI / 3, -FastMath.PI / 4)),<a name="line.31"></a>
-<FONT color="green">032</FONT> r, r * FastMath.sqrt(3), -2 * r);<a name="line.32"></a>
-<FONT color="green">033</FONT> checkVector(new Vector3D(2, Vector3D.PLUS_I,<a name="line.33"></a>
-<FONT color="green">034</FONT> -3, Vector3D.MINUS_K),<a name="line.34"></a>
-<FONT color="green">035</FONT> 2, 0, 3);<a name="line.35"></a>
-<FONT color="green">036</FONT> checkVector(new Vector3D(2, Vector3D.PLUS_I,<a name="line.36"></a>
-<FONT color="green">037</FONT> 5, Vector3D.PLUS_J,<a name="line.37"></a>
-<FONT color="green">038</FONT> -3, Vector3D.MINUS_K),<a name="line.38"></a>
-<FONT color="green">039</FONT> 2, 5, 3);<a name="line.39"></a>
-<FONT color="green">040</FONT> checkVector(new Vector3D(2, Vector3D.PLUS_I,<a name="line.40"></a>
-<FONT color="green">041</FONT> 5, Vector3D.PLUS_J,<a name="line.41"></a>
-<FONT color="green">042</FONT> 5, Vector3D.MINUS_J,<a name="line.42"></a>
-<FONT color="green">043</FONT> -3, Vector3D.MINUS_K),<a name="line.43"></a>
-<FONT color="green">044</FONT> 2, 0, 3);<a name="line.44"></a>
-<FONT color="green">045</FONT> checkVector(new Vector3D(new double[] { 2, 5, -3 }),<a name="line.45"></a>
-<FONT color="green">046</FONT> 2, 5, -3);<a name="line.46"></a>
-<FONT color="green">047</FONT> }<a name="line.47"></a>
-<FONT color="green">048</FONT> <a name="line.48"></a>
-<FONT color="green">049</FONT> @Test(expected=DimensionMismatchException.class)<a name="line.49"></a>
-<FONT color="green">050</FONT> public void testWrongDimension() throws DimensionMismatchException {<a name="line.50"></a>
-<FONT color="green">051</FONT> new Vector3D(new double[] { 2, 5 });<a name="line.51"></a>
-<FONT color="green">052</FONT> }<a name="line.52"></a>
-<FONT color="green">053</FONT> <a name="line.53"></a>
-<FONT color="green">054</FONT> @Test<a name="line.54"></a>
-<FONT color="green">055</FONT> public void testCoordinates() {<a name="line.55"></a>
-<FONT color="green">056</FONT> Vector3D v = new Vector3D(1, 2, 3);<a name="line.56"></a>
-<FONT color="green">057</FONT> Assert.assertTrue(FastMath.abs(v.getX() - 1) < 1.0e-12);<a name="line.57"></a>
-<FONT color="green">058</FONT> Assert.assertTrue(FastMath.abs(v.getY() - 2) < 1.0e-12);<a name="line.58"></a>
-<FONT color="green">059</FONT> Assert.assertTrue(FastMath.abs(v.getZ() - 3) < 1.0e-12);<a name="line.59"></a>
-<FONT color="green">060</FONT> double[] coordinates = v.toArray();<a name="line.60"></a>
-<FONT color="green">061</FONT> Assert.assertTrue(FastMath.abs(coordinates[0] - 1) < 1.0e-12);<a name="line.61"></a>
-<FONT color="green">062</FONT> Assert.assertTrue(FastMath.abs(coordinates[1] - 2) < 1.0e-12);<a name="line.62"></a>
-<FONT color="green">063</FONT> Assert.assertTrue(FastMath.abs(coordinates[2] - 3) < 1.0e-12);<a name="line.63"></a>
+<FONT color="green">020</FONT> import java.text.DecimalFormat;<a name="line.20"></a>
+<FONT color="green">021</FONT> import java.text.DecimalFormatSymbols;<a name="line.21"></a>
+<FONT color="green">022</FONT> import java.text.NumberFormat;<a name="line.22"></a>
+<FONT color="green">023</FONT> import java.util.Locale;<a name="line.23"></a>
+<FONT color="green">024</FONT> <a name="line.24"></a>
+<FONT color="green">025</FONT> import org.apache.commons.math3.TestUtils;<a name="line.25"></a>
+<FONT color="green">026</FONT> import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.26"></a>
+<FONT color="green">027</FONT> import org.apache.commons.math3.exception.MathArithmeticException;<a name="line.27"></a>
+<FONT color="green">028</FONT> import org.apache.commons.math3.geometry.Space;<a name="line.28"></a>
+<FONT color="green">029</FONT> import org.apache.commons.math3.random.Well1024a;<a name="line.29"></a>
+<FONT color="green">030</FONT> import org.apache.commons.math3.util.FastMath;<a name="line.30"></a>
+<FONT color="green">031</FONT> import org.apache.commons.math3.util.Precision;<a name="line.31"></a>
+<FONT color="green">032</FONT> import org.junit.Assert;<a name="line.32"></a>
+<FONT color="green">033</FONT> import org.junit.Test;<a name="line.33"></a>
+<FONT color="green">034</FONT> <a name="line.34"></a>
+<FONT color="green">035</FONT> public class Vector3DTest {<a name="line.35"></a>
+<FONT color="green">036</FONT> @Test<a name="line.36"></a>
+<FONT color="green">037</FONT> public void testConstructors() throws DimensionMismatchException {<a name="line.37"></a>
+<FONT color="green">038</FONT> double r = FastMath.sqrt(2) /2;<a name="line.38"></a>
+<FONT color="green">039</FONT> checkVector(new Vector3D(2, new Vector3D(FastMath.PI / 3, -FastMath.PI / 4)),<a name="line.39"></a>
+<FONT color="green">040</FONT> r, r * FastMath.sqrt(3), -2 * r);<a name="line.40"></a>
+<FONT color="green">041</FONT> checkVector(new Vector3D(2, Vector3D.PLUS_I,<a name="line.41"></a>
+<FONT color="green">042</FONT> -3, Vector3D.MINUS_K),<a name="line.42"></a>
+<FONT color="green">043</FONT> 2, 0, 3);<a name="line.43"></a>
+<FONT color="green">044</FONT> checkVector(new Vector3D(2, Vector3D.PLUS_I,<a name="line.44"></a>
+<FONT color="green">045</FONT> 5, Vector3D.PLUS_J,<a name="line.45"></a>
+<FONT color="green">046</FONT> -3, Vector3D.MINUS_K),<a name="line.46"></a>
+<FONT color="green">047</FONT> 2, 5, 3);<a name="line.47"></a>
+<FONT color="green">048</FONT> checkVector(new Vector3D(2, Vector3D.PLUS_I,<a name="line.48"></a>
+<FONT color="green">049</FONT> 5, Vector3D.PLUS_J,<a name="line.49"></a>
+<FONT color="green">050</FONT> 5, Vector3D.MINUS_J,<a name="line.50"></a>
+<FONT color="green">051</FONT> -3, Vector3D.MINUS_K),<a name="line.51"></a>
+<FONT color="green">052</FONT> 2, 0, 3);<a name="line.52"></a>
+<FONT color="green">053</FONT> checkVector(new Vector3D(new double[] { 2, 5, -3 }),<a name="line.53"></a>
+<FONT color="green">054</FONT> 2, 5, -3);<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> @Test<a name="line.57"></a>
+<FONT color="green">058</FONT> public void testSpace() {<a name="line.58"></a>
+<FONT color="green">059</FONT> Space space = new Vector3D(1, 2, 2).getSpace();<a name="line.59"></a>
+<FONT color="green">060</FONT> Assert.assertEquals(3, space.getDimension());<a name="line.60"></a>
+<FONT color="green">061</FONT> Assert.assertEquals(2, space.getSubSpace().getDimension());<a name="line.61"></a>
+<FONT color="green">062</FONT> Space deserialized = (Space) TestUtils.serializeAndRecover(space);<a name="line.62"></a>
+<FONT color="green">063</FONT> Assert.assertTrue(space == deserialized);<a name="line.63"></a>
<FONT color="green">064</FONT> }<a name="line.64"></a>
<FONT color="green">065</FONT> <a name="line.65"></a>
<FONT color="green">066</FONT> @Test<a name="line.66"></a>
-<FONT color="green">067</FONT> public void testNorm1() {<a name="line.67"></a>
-<FONT color="green">068</FONT> Assert.assertEquals(0.0, Vector3D.ZERO.getNorm1(), 0);<a name="line.68"></a>
-<FONT color="green">069</FONT> Assert.assertEquals(6.0, new Vector3D(1, -2, 3).getNorm1(), 0);<a name="line.69"></a>
-<FONT color="green">070</FONT> }<a name="line.70"></a>
-<FONT color="green">071</FONT> <a name="line.71"></a>
-<FONT color="green">072</FONT> @Test<a name="line.72"></a>
-<FONT color="green">073</FONT> public void testNorm() {<a name="line.73"></a>
-<FONT color="green">074</FONT> Assert.assertEquals(0.0, Vector3D.ZERO.getNorm(), 0);<a name="line.74"></a>
-<FONT color="green">075</FONT> Assert.assertEquals(FastMath.sqrt(14), new Vector3D(1, 2, 3).getNorm(), 1.0e-12);<a name="line.75"></a>
-<FONT color="green">076</FONT> }<a name="line.76"></a>
-<FONT color="green">077</FONT> <a name="line.77"></a>
-<FONT color="green">078</FONT> @Test<a name="line.78"></a>
-<FONT color="green">079</FONT> public void testNormInf() {<a name="line.79"></a>
-<FONT color="green">080</FONT> Assert.assertEquals(0.0, Vector3D.ZERO.getNormInf(), 0);<a name="line.80"></a>
-<FONT color="green">081</FONT> Assert.assertEquals(3.0, new Vector3D(1, -2, 3).getNormInf(), 0);<a name="line.81"></a>
+<FONT color="green">067</FONT> public void testZero() {<a name="line.67"></a>
+<FONT color="green">068</FONT> Assert.assertEquals(0, new Vector3D(1, 2, 2).getZero().getNorm(), 1.0e-15);<a name="line.68"></a>
+<FONT color="green">069</FONT> }<a name="line.69"></a>
+<FONT color="green">070</FONT> <a name="line.70"></a>
+<FONT color="green">071</FONT> @Test<a name="line.71"></a>
+<FONT color="green">072</FONT> public void testEquals() {<a name="line.72"></a>
+<FONT color="green">073</FONT> Vector3D u1 = new Vector3D(1, 2, 3);<a name="line.73"></a>
+<FONT color="green">074</FONT> Vector3D u2 = new Vector3D(1, 2, 3);<a name="line.74"></a>
+<FONT color="green">075</FONT> Assert.assertTrue(u1.equals(u1));<a name="line.75"></a>
+<FONT color="green">076</FONT> Assert.assertTrue(u1.equals(u2));<a name="line.76"></a>
+<FONT color="green">077</FONT> Assert.assertFalse(u1.equals(new Rotation(1, 0, 0, 0, false)));<a name="line.77"></a>
+<FONT color="green">078</FONT> Assert.assertFalse(u1.equals(new Vector3D(1, 2, 3 + 10 * Precision.EPSILON)));<a name="line.78"></a>
+<FONT color="green">079</FONT> Assert.assertFalse(u1.equals(new Vector3D(1, 2 + 10 * Precision.EPSILON, 3)));<a name="line.79"></a>
+<FONT color="green">080</FONT> Assert.assertFalse(u1.equals(new Vector3D(1 + 10 * Precision.EPSILON, 2, 3)));<a name="line.80"></a>
+<FONT color="green">081</FONT> Assert.assertTrue(new Vector3D(0, Double.NaN, 0).equals(new Vector3D(0, 0, Double.NaN)));<a name="line.81"></a>
<FONT color="green">082</FONT> }<a name="line.82"></a>
<FONT color="green">083</FONT> <a name="line.83"></a>
<FONT color="green">084</FONT> @Test<a name="line.84"></a>
-<FONT color="green">085</FONT> public void testDistance1() {<a name="line.85"></a>
-<FONT color="green">086</FONT> Vector3D v1 = new Vector3D(1, -2, 3);<a name="line.86"></a>
-<FONT color="green">087</FONT> Vector3D v2 = new Vector3D(-4, 2, 0);<a name="line.87"></a>
-<FONT color="green">088</FONT> Assert.assertEquals(0.0, Vector3D.distance1(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);<a name="line.88"></a>
-<FONT color="green">089</FONT> Assert.assertEquals(12.0, Vector3D.distance1(v1, v2), 1.0e-12);<a name="line.89"></a>
-<FONT color="green">090</FONT> Assert.assertEquals(v1.subtract(v2).getNorm1(), Vector3D.distance1(v1, v2), 1.0e-12);<a name="line.90"></a>
-<FONT color="green">091</FONT> }<a name="line.91"></a>
-<FONT color="green">092</FONT> <a name="line.92"></a>
-<FONT color="green">093</FONT> @Test<a name="line.93"></a>
-<FONT color="green">094</FONT> public void testDistance() {<a name="line.94"></a>
-<FONT color="green">095</FONT> Vector3D v1 = new Vector3D(1, -2, 3);<a name="line.95"></a>
-<FONT color="green">096</FONT> Vector3D v2 = new Vector3D(-4, 2, 0);<a name="line.96"></a>
-<FONT color="green">097</FONT> Assert.assertEquals(0.0, Vector3D.distance(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);<a name="line.97"></a>
-<FONT color="green">098</FONT> Assert.assertEquals(FastMath.sqrt(50), Vector3D.distance(v1, v2), 1.0e-12);<a name="line.98"></a>
-<FONT color="green">099</FONT> Assert.assertEquals(v1.subtract(v2).getNorm(), Vector3D.distance(v1, v2), 1.0e-12);<a name="line.99"></a>
-<FONT color="green">100</FONT> }<a name="line.100"></a>
-<FONT color="green">101</FONT> <a name="line.101"></a>
-<FONT color="green">102</FONT> @Test<a name="line.102"></a>
-<FONT color="green">103</FONT> public void testDistanceSq() {<a name="line.103"></a>
-<FONT color="green">104</FONT> Vector3D v1 = new Vector3D(1, -2, 3);<a name="line.104"></a>
-<FONT color="green">105</FONT> Vector3D v2 = new Vector3D(-4, 2, 0);<a name="line.105"></a>
-<FONT color="green">106</FONT> Assert.assertEquals(0.0, Vector3D.distanceSq(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);<a name="line.106"></a>
-<FONT color="green">107</FONT> Assert.assertEquals(50.0, Vector3D.distanceSq(v1, v2), 1.0e-12);<a name="line.107"></a>
-<FONT color="green">108</FONT> Assert.assertEquals(Vector3D.distance(v1, v2) * Vector3D.distance(v1, v2),<a name="line.108"></a>
-<FONT color="green">109</FONT> Vector3D.distanceSq(v1, v2), 1.0e-12);<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> @Test<a name="line.112"></a>
-<FONT color="green">113</FONT> public void testDistanceInf() {<a name="line.113"></a>
-<FONT color="green">114</FONT> Vector3D v1 = new Vector3D(1, -2, 3);<a name="line.114"></a>
-<FONT color="green">115</FONT> Vector3D v2 = new Vector3D(-4, 2, 0);<a name="line.115"></a>
-<FONT color="green">116</FONT> Assert.assertEquals(0.0, Vector3D.distanceInf(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);<a name="line.116"></a>
-<FONT color="green">117</FONT> Assert.assertEquals(5.0, Vector3D.distanceInf(v1, v2), 1.0e-12);<a name="line.117"></a>
-<FONT color="green">118</FONT> Assert.assertEquals(v1.subtract(v2).getNormInf(), Vector3D.distanceInf(v1, v2), 1.0e-12);<a name="line.118"></a>
-<FONT color="green">119</FONT> }<a name="line.119"></a>
-<FONT color="green">120</FONT> <a name="line.120"></a>
-<FONT color="green">121</FONT> @Test<a name="line.121"></a>
-<FONT color="green">122</FONT> public void testSubtract() {<a name="line.122"></a>
-<FONT color="green">123</FONT> Vector3D v1 = new Vector3D(1, 2, 3);<a name="line.123"></a>
-<FONT color="green">124</FONT> Vector3D v2 = new Vector3D(-3, -2, -1);<a name="line.124"></a>
-<FONT color="green">125</FONT> v1 = v1.subtract(v2);<a name="line.125"></a>
-<FONT color="green">126</FONT> checkVector(v1, 4, 4, 4);<a name="line.126"></a>
-<FONT color="green">127</FONT> <a name="line.127"></a>
-<FONT color="green">128</FONT> checkVector(v2.subtract(v1), -7, -6, -5);<a name="line.128"></a>
-<FONT color="green">129</FONT> checkVector(v2.subtract(3, v1), -15, -14, -13);<a name="line.129"></a>
-<FONT color="green">130</FONT> }<a name="line.130"></a>
-<FONT color="green">131</FONT> <a name="line.131"></a>
-<FONT color="green">132</FONT> @Test<a name="line.132"></a>
-<FONT color="green">133</FONT> public void testAdd() {<a name="line.133"></a>
-<FONT color="green">134</FONT> Vector3D v1 = new Vector3D(1, 2, 3);<a name="line.134"></a>
-<FONT color="green">135</FONT> Vector3D v2 = new Vector3D(-3, -2, -1);<a name="line.135"></a>
-<FONT color="green">136</FONT> v1 = v1.add(v2);<a name="line.136"></a>
-<FONT color="green">137</FONT> checkVector(v1, -2, 0, 2);<a name="line.137"></a>
-<FONT color="green">138</FONT> <a name="line.138"></a>
-<FONT color="green">139</FONT> checkVector(v2.add(v1), -5, -2, 1);<a name="line.139"></a>
-<FONT color="green">140</FONT> checkVector(v2.add(3, v1), -9, -2, 5);<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> @Test<a name="line.143"></a>
-<FONT color="green">144</FONT> public void testScalarProduct() {<a name="line.144"></a>
-<FONT color="green">145</FONT> Vector3D v = new Vector3D(1, 2, 3);<a name="line.145"></a>
-<FONT color="green">146</FONT> v = v.scalarMultiply(3);<a name="line.146"></a>
-<FONT color="green">147</FONT> checkVector(v, 3, 6, 9);<a name="line.147"></a>
-<FONT color="green">148</FONT> <a name="line.148"></a>
-<FONT color="green">149</FONT> checkVector(v.scalarMultiply(0.5), 1.5, 3, 4.5);<a name="line.149"></a>
+<FONT color="green">085</FONT> public void testHash() {<a name="line.85"></a>
+<FONT color="green">086</FONT> Assert.assertEquals(new Vector3D(0, Double.NaN, 0).hashCode(), new Vector3D(0, 0, Double.NaN).hashCode());<a name="line.86"></a>
+<FONT color="green">087</FONT> Vector3D u = new Vector3D(1, 2, 3);<a name="line.87"></a>
+<FONT color="green">088</FONT> Vector3D v = new Vector3D(1, 2, 3 + 10 * Precision.EPSILON);<a name="line.88"></a>
+<FONT color="green">089</FONT> Assert.assertTrue(u.hashCode() != v.hashCode());<a name="line.89"></a>
+<FONT color="green">090</FONT> }<a name="line.90"></a>
+<FONT color="green">091</FONT> <a name="line.91"></a>
+<FONT color="green">092</FONT> @Test<a name="line.92"></a>
+<FONT color="green">093</FONT> public void testInfinite() {<a name="line.93"></a>
+<FONT color="green">094</FONT> Assert.assertTrue(new Vector3D(1, 1, Double.NEGATIVE_INFINITY).isInfinite());<a name="line.94"></a>
+<FONT color="green">095</FONT> Assert.assertTrue(new Vector3D(1, Double.NEGATIVE_INFINITY, 1).isInfinite());<a name="line.95"></a>
+<FONT color="green">096</FONT> Assert.assertTrue(new Vector3D(Double.NEGATIVE_INFINITY, 1, 1).isInfinite());<a name="line.96"></a>
+<FONT color="green">097</FONT> Assert.assertFalse(new Vector3D(1, 1, 2).isInfinite());<a name="line.97"></a>
+<FONT color="green">098</FONT> Assert.assertFalse(new Vector3D(1, Double.NaN, Double.NEGATIVE_INFINITY).isInfinite());<a name="line.98"></a>
+<FONT color="green">099</FONT> }<a name="line.99"></a>
+<FONT color="green">100</FONT> <a name="line.100"></a>
+<FONT color="green">101</FONT> @Test<a name="line.101"></a>
+<FONT color="green">102</FONT> public void testNaN() {<a name="line.102"></a>
+<FONT color="green">103</FONT> Assert.assertTrue(new Vector3D(1, 1, Double.NaN).isNaN());<a name="line.103"></a>
+<FONT color="green">104</FONT> Assert.assertTrue(new Vector3D(1, Double.NaN, 1).isNaN());<a name="line.104"></a>
+<FONT color="green">105</FONT> Assert.assertTrue(new Vector3D(Double.NaN, 1, 1).isNaN());<a name="line.105"></a>
+<FONT color="green">106</FONT> Assert.assertFalse(new Vector3D(1, 1, 2).isNaN());<a name="line.106"></a>
+<FONT color="green">107</FONT> Assert.assertFalse(new Vector3D(1, 1, Double.NEGATIVE_INFINITY).isNaN());<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> @Test<a name="line.110"></a>
+<FONT color="green">111</FONT> public void testToString() {<a name="line.111"></a>
+<FONT color="green">112</FONT> Assert.assertEquals("{3; 2; 1}", new Vector3D(3, 2, 1).toString());<a name="line.112"></a>
+<FONT color="green">113</FONT> NumberFormat format = new DecimalFormat("0.000", new DecimalFormatSymbols(Locale.US));<a name="line.113"></a>
+<FONT color="green">114</FONT> Assert.assertEquals("{3.000; 2.000; 1.000}", new Vector3D(3, 2, 1).toString(format));<a name="line.114"></a>
+<FONT color="green">115</FONT> }<a name="line.115"></a>
+<FONT color="green">116</FONT> <a name="line.116"></a>
+<FONT color="green">117</FONT> @Test(expected=DimensionMismatchException.class)<a name="line.117"></a>
+<FONT color="green">118</FONT> public void testWrongDimension() throws DimensionMismatchException {<a name="line.118"></a>
+<FONT color="green">119</FONT> new Vector3D(new double[] { 2, 5 });<a name="line.119"></a>
+<FONT color="green">120</FONT> }<a name="line.120"></a>
+<FONT color="green">121</FONT> <a name="line.121"></a>
+<FONT color="green">122</FONT> @Test<a name="line.122"></a>
+<FONT color="green">123</FONT> public void testCoordinates() {<a name="line.123"></a>
+<FONT color="green">124</FONT> Vector3D v = new Vector3D(1, 2, 3);<a name="line.124"></a>
+<FONT color="green">125</FONT> Assert.assertTrue(FastMath.abs(v.getX() - 1) < 1.0e-12);<a name="line.125"></a>
+<FONT color="green">126</FONT> Assert.assertTrue(FastMath.abs(v.getY() - 2) < 1.0e-12);<a name="line.126"></a>
+<FONT color="green">127</FONT> Assert.assertTrue(FastMath.abs(v.getZ() - 3) < 1.0e-12);<a name="line.127"></a>
+<FONT color="green">128</FONT> double[] coordinates = v.toArray();<a name="line.128"></a>
+<FONT color="green">129</FONT> Assert.assertTrue(FastMath.abs(coordinates[0] - 1) < 1.0e-12);<a name="line.129"></a>
+<FONT color="green">130</FONT> Assert.assertTrue(FastMath.abs(coordinates[1] - 2) < 1.0e-12);<a name="line.130"></a>
+<FONT color="green">131</FONT> Assert.assertTrue(FastMath.abs(coordinates[2] - 3) < 1.0e-12);<a name="line.131"></a>
+<FONT color="green">132</FONT> }<a name="line.132"></a>
+<FONT color="green">133</FONT> <a name="line.133"></a>
+<FONT color="green">134</FONT> @Test<a name="line.134"></a>
+<FONT color="green">135</FONT> public void testNorm1() {<a name="line.135"></a>
+<FONT color="green">136</FONT> Assert.assertEquals(0.0, Vector3D.ZERO.getNorm1(), 0);<a name="line.136"></a>
+<FONT color="green">137</FONT> Assert.assertEquals(6.0, new Vector3D(1, -2, 3).getNorm1(), 0);<a name="line.137"></a>
+<FONT color="green">138</FONT> }<a name="line.138"></a>
+<FONT color="green">139</FONT> <a name="line.139"></a>
+<FONT color="green">140</FONT> @Test<a name="line.140"></a>
+<FONT color="green">141</FONT> public void testNorm() {<a name="line.141"></a>
+<FONT color="green">142</FONT> Assert.assertEquals(0.0, Vector3D.ZERO.getNorm(), 0);<a name="line.142"></a>
+<FONT color="green">143</FONT> Assert.assertEquals(FastMath.sqrt(14), new Vector3D(1, 2, 3).getNorm(), 1.0e-12);<a name="line.143"></a>
+<FONT color="green">144</FONT> }<a name="line.144"></a>
+<FONT color="green">145</FONT> <a name="line.145"></a>
+<FONT color="green">146</FONT> @Test<a name="line.146"></a>
+<FONT color="green">147</FONT> public void testNormSq() {<a name="line.147"></a>
+<FONT color="green">148</FONT> Assert.assertEquals(0.0, new Vector3D(0, 0, 0).getNormSq(), 0);<a name="line.148"></a>
+<FONT color="green">149</FONT> Assert.assertEquals(14, new Vector3D(1, 2, 3).getNormSq(), 1.0e-12);<a name="line.149"></a>
<FONT color="green">150</FONT> }<a name="line.150"></a>
<FONT color="green">151</FONT> <a name="line.151"></a>
<FONT color="green">152</FONT> @Test<a name="line.152"></a>
-<FONT color="green">153</FONT> public void testVectorialProducts() {<a name="line.153"></a>
-<FONT color="green">154</FONT> Vector3D v1 = new Vector3D(2, 1, -4);<a name="line.154"></a>
-<FONT color="green">155</FONT> Vector3D v2 = new Vector3D(3, 1, -1);<a name="line.155"></a>
-<FONT color="green">156</FONT> <a name="line.156"></a>
-<FONT color="green">157</FONT> Assert.assertTrue(FastMath.abs(Vector3D.dotProduct(v1, v2) - 11) < 1.0e-12);<a name="line.157"></a>
-<FONT color="green">158</FONT> <a name="line.158"></a>
-<FONT color="green">159</FONT> Vector3D v3 = Vector3D.crossProduct(v1, v2);<a name="line.159"></a>
-<FONT color="green">160</FONT> checkVector(v3, 3, -10, -1);<a name="line.160"></a>
-<FONT color="green">161</FONT> <a name="line.161"></a>
-<FONT color="green">162</FONT> Assert.assertTrue(FastMath.abs(Vector3D.dotProduct(v1, v3)) < 1.0e-12);<a name="line.162"></a>
-<FONT color="green">163</FONT> Assert.assertTrue(FastMath.abs(Vector3D.dotProduct(v2, v3)) < 1.0e-12);<a name="line.163"></a>
-<FONT color="green">164</FONT> }<a name="line.164"></a>
-<FONT color="green">165</FONT> <a name="line.165"></a>
-<FONT color="green">166</FONT> @Test<a name="line.166"></a>
-<FONT color="green">167</FONT> public void testCrossProductCancellation() {<a name="line.167"></a>
-<FONT color="green">168</FONT> Vector3D v1 = new Vector3D(9070467121.0, 4535233560.0, 1);<a name="line.168"></a>
-<FONT color="green">169</FONT> Vector3D v2 = new Vector3D(9070467123.0, 4535233561.0, 1);<a name="line.169"></a>
-<FONT color="green">170</FONT> checkVector(Vector3D.crossProduct(v1, v2), -1, 2, 1);<a name="line.170"></a>
-<FONT color="green">171</FONT> <a name="line.171"></a>
-<FONT color="green">172</FONT> double scale = FastMath.scalb(1.0, 100);<a name="line.172"></a>
-<FONT color="green">173</FONT> Vector3D big1 = new Vector3D(scale, v1);<a name="line.173"></a>
-<FONT color="green">174</FONT> Vector3D small2 = new Vector3D(1 / scale, v2);<a name="line.174"></a>
-<FONT color="green">175</FONT> checkVector(Vector3D.crossProduct(big1, small2), -1, 2, 1);<a name="line.175"></a>
-<FONT color="green">176</FONT> <a name="line.176"></a>
-<FONT color="green">177</FONT> }<a name="line.177"></a>
-<FONT color="green">178</FONT> <a name="line.178"></a>
-<FONT color="green">179</FONT> @Test<a name="line.179"></a>
-<FONT color="green">180</FONT> public void testAngular() {<a name="line.180"></a>
-<FONT color="green">181</FONT> Assert.assertEquals(0, Vector3D.PLUS_I.getAlpha(), 1.0e-10);<a name="line.181"></a>
-<FONT color="green">182</FONT> Assert.assertEquals(0, Vector3D.PLUS_I.getDelta(), 1.0e-10);<a name="line.182"></a>
-<FONT color="green">183</FONT> Assert.assertEquals(FastMath.PI / 2, Vector3D.PLUS_J.getAlpha(), 1.0e-10);<a name="line.183"></a>
-<FONT color="green">184</FONT> Assert.assertEquals(0, Vector3D.PLUS_J.getDelta(), 1.0e-10);<a name="line.184"></a>
-<FONT color="green">185</FONT> Assert.assertEquals(0, Vector3D.PLUS_K.getAlpha(), 1.0e-10);<a name="line.185"></a>
-<FONT color="green">186</FONT> Assert.assertEquals(FastMath.PI / 2, Vector3D.PLUS_K.getDelta(), 1.0e-10);<a name="line.186"></a>
-<FONT color="green">187</FONT> <a name="line.187"></a>
-<FONT color="green">188</FONT> Vector3D u = new Vector3D(-1, 1, -1);<a name="line.188"></a>
-<FONT color="green">189</FONT> Assert.assertEquals(3 * FastMath.PI /4, u.getAlpha(), 1.0e-10);<a name="line.189"></a>
-<FONT color="green">190</FONT> Assert.assertEquals(-1.0 / FastMath.sqrt(3), FastMath.sin(u.getDelta()), 1.0e-10);<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> @Test<a name="line.193"></a>
-<FONT color="green">194</FONT> public void testAngularSeparation() throws MathArithmeticException {<a name="line.194"></a>
-<FONT color="green">195</FONT> Vector3D v1 = new Vector3D(2, -1, 4);<a name="line.195"></a>
-<FONT color="green">196</FONT> <a name="line.196"></a>
-<FONT color="green">197</FONT> Vector3D k = v1.normalize();<a name="line.197"></a>
-<FONT color="green">198</FONT> Vector3D i = k.orthogonal();<a name="line.198"></a>
-<FONT color="green">199</FONT> Vector3D v2 = k.scalarMultiply(FastMath.cos(1.2)).add(i.scalarMultiply(FastMath.sin(1.2)));<a name="line.199"></a>
-<FONT color="green">200</FONT> <a name="line.200"></a>
-<FONT color="green">201</FONT> Assert.assertTrue(FastMath.abs(Vector3D.angle(v1, v2) - 1.2) < 1.0e-12);<a name="line.201"></a>
-<FONT color="green">202</FONT> }<a name="line.202"></a>
-<FONT color="green">203</FONT> <a name="line.203"></a>
-<FONT color="green">204</FONT> @Test<a name="line.204"></a>
-<FONT color="green">205</FONT> public void testNormalize() throws MathArithmeticException {<a name="line.205"></a>
-<FONT color="green">206</FONT> Assert.assertEquals(1.0, new Vector3D(5, -4, 2).normalize().getNorm(), 1.0e-12);<a name="line.206"></a>
-<FONT color="green">207</FONT> try {<a name="line.207"></a>
-<FONT color="green">208</FONT> Vector3D.ZERO.normalize();<a name="line.208"></a>
-<FONT color="green">209</FONT> Assert.fail("an exception should have been thrown");<a name="line.209"></a>
-<FONT color="green">210</FONT> } catch (MathArithmeticException ae) {<a name="line.210"></a>
-<FONT color="green">211</FONT> // expected behavior<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> @Test<a name="line.215"></a>
-<FONT color="green">216</FONT> public void testOrthogonal() throws MathArithmeticException {<a name="line.216"></a>
-<FONT color="green">217</FONT> Vector3D v1 = new Vector3D(0.1, 2.5, 1.3);<a name="line.217"></a>
-<FONT color="green">218</FONT> Assert.assertEquals(0.0, Vector3D.dotProduct(v1, v1.orthogonal()), 1.0e-12);<a name="line.218"></a>
-<FONT color="green">219</FONT> Vector3D v2 = new Vector3D(2.3, -0.003, 7.6);<a name="line.219"></a>
-<FONT color="green">220</FONT> Assert.assertEquals(0.0, Vector3D.dotProduct(v2, v2.orthogonal()), 1.0e-12);<a name="line.220"></a>
-<FONT color="green">221</FONT> Vector3D v3 = new Vector3D(-1.7, 1.4, 0.2);<a name="line.221"></a>
-<FONT color="green">222</FONT> Assert.assertEquals(0.0, Vector3D.dotProduct(v3, v3.orthogonal()), 1.0e-12);<a name="line.222"></a>
-<FONT color="green">223</FONT> try {<a name="line.223"></a>
-<FONT color="green">224</FONT> new Vector3D(0, 0, 0).orthogonal();<a name="line.224"></a>
-<FONT color="green">225</FONT> Assert.fail("an exception should have been thrown");<a name="line.225"></a>
-<FONT color="green">226</FONT> } catch (MathArithmeticException ae) {<a name="line.226"></a>
-<FONT color="green">227</FONT> // expected behavior<a name="line.227"></a>
-<FONT color="green">228</FONT> }<a name="line.228"></a>
-<FONT color="green">229</FONT> }<a name="line.229"></a>
+<FONT color="green">153</FONT> public void testNormInf() {<a name="line.153"></a>
+<FONT color="green">154</FONT> Assert.assertEquals(0.0, Vector3D.ZERO.getNormInf(), 0);<a name="line.154"></a>
+<FONT color="green">155</FONT> Assert.assertEquals(3.0, new Vector3D(1, -2, 3).getNormInf(), 0);<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> @Test<a name="line.158"></a>
+<FONT color="green">159</FONT> public void testDistance1() {<a name="line.159"></a>
+<FONT color="green">160</FONT> Vector3D v1 = new Vector3D(1, -2, 3);<a name="line.160"></a>
+<FONT color="green">161</FONT> Vector3D v2 = new Vector3D(-4, 2, 0);<a name="line.161"></a>
+<FONT color="green">162</FONT> Assert.assertEquals(0.0, Vector3D.distance1(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);<a name="line.162"></a>
+<FONT color="green">163</FONT> Assert.assertEquals(12.0, Vector3D.distance1(v1, v2), 1.0e-12);<a name="line.163"></a>
+<FONT color="green">164</FONT> Assert.assertEquals(v1.subtract(v2).getNorm1(), Vector3D.distance1(v1, v2), 1.0e-12);<a name="line.164"></a>
+<FONT color="green">165</FONT> }<a name="line.165"></a>
+<FONT color="green">166</FONT> <a name="line.166"></a>
+<FONT color="green">167</FONT> @Test<a name="line.167"></a>
+<FONT color="green">168</FONT> public void testDistance() {<a name="line.168"></a>
+<FONT color="green">169</FONT> Vector3D v1 = new Vector3D(1, -2, 3);<a name="line.169"></a>
+<FONT color="green">170</FONT> Vector3D v2 = new Vector3D(-4, 2, 0);<a name="line.170"></a>
+<FONT color="green">171</FONT> Assert.assertEquals(0.0, Vector3D.distance(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);<a name="line.171"></a>
+<FONT color="green">172</FONT> Assert.assertEquals(FastMath.sqrt(50), Vector3D.distance(v1, v2), 1.0e-12);<a name="line.172"></a>
+<FONT color="green">173</FONT> Assert.assertEquals(v1.subtract(v2).getNorm(), Vector3D.distance(v1, v2), 1.0e-12);<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> @Test<a name="line.176"></a>
+<FONT color="green">177</FONT> public void testDistanceSq() {<a name="line.177"></a>
+<FONT color="green">178</FONT> Vector3D v1 = new Vector3D(1, -2, 3);<a name="line.178"></a>
+<FONT color="green">179</FONT> Vector3D v2 = new Vector3D(-4, 2, 0);<a name="line.179"></a>
+<FONT color="green">180</FONT> Assert.assertEquals(0.0, Vector3D.distanceSq(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);<a name="line.180"></a>
+<FONT color="green">181</FONT> Assert.assertEquals(50.0, Vector3D.distanceSq(v1, v2), 1.0e-12);<a name="line.181"></a>
+<FONT color="green">182</FONT> Assert.assertEquals(Vector3D.distance(v1, v2) * Vector3D.distance(v1, v2),<a name="line.182"></a>
+<FONT color="green">183</FONT> Vector3D.distanceSq(v1, v2), 1.0e-12);<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> @Test<a name="line.186"></a>
+<FONT color="green">187</FONT> public void testDistanceInf() {<a name="line.187"></a>
+<FONT color="green">188</FONT> Vector3D v1 = new Vector3D(1, -2, 3);<a name="line.188"></a>
+<FONT color="green">189</FONT> Vector3D v2 = new Vector3D(-4, 2, 0);<a name="line.189"></a>
+<FONT color="green">190</FONT> Assert.assertEquals(0.0, Vector3D.distanceInf(Vector3D.MINUS_I, Vector3D.MINUS_I), 0);<a name="line.190"></a>
+<FONT color="green">191</FONT> Assert.assertEquals(5.0, Vector3D.distanceInf(v1, v2), 1.0e-12);<a name="line.191"></a>
+<FONT color="green">192</FONT> Assert.assertEquals(v1.subtract(v2).getNormInf(), Vector3D.distanceInf(v1, v2), 1.0e-12);<a name="line.192"></a>
+<FONT color="green">193</FONT> }<a name="line.193"></a>
+<FONT color="green">194</FONT> <a name="line.194"></a>
+<FONT color="green">195</FONT> @Test<a name="line.195"></a>
+<FONT color="green">196</FONT> public void testSubtract() {<a name="line.196"></a>
+<FONT color="green">197</FONT> Vector3D v1 = new Vector3D(1, 2, 3);<a name="line.197"></a>
+<FONT color="green">198</FONT> Vector3D v2 = new Vector3D(-3, -2, -1);<a name="line.198"></a>
+<FONT color="green">199</FONT> v1 = v1.subtract(v2);<a name="line.199"></a>
+<FONT color="green">200</FONT> checkVector(v1, 4, 4, 4);<a name="line.200"></a>
+<FONT color="green">201</FONT> <a name="line.201"></a>
+<FONT color="green">202</FONT> checkVector(v2.subtract(v1), -7, -6, -5);<a name="line.202"></a>
+<FONT color="green">203</FONT> checkVector(v2.subtract(3, v1), -15, -14, -13);<a name="line.203"></a>
+<FONT color="green">204</FONT> }<a name="line.204"></a>
+<FONT color="green">205</FONT> <a name="line.205"></a>
+<FONT color="green">206</FONT> @Test<a name="line.206"></a>
+<FONT color="green">207</FONT> public void testAdd() {<a name="line.207"></a>
+<FONT color="green">208</FONT> Vector3D v1 = new Vector3D(1, 2, 3);<a name="line.208"></a>
+<FONT color="green">209</FONT> Vector3D v2 = new Vector3D(-3, -2, -1);<a name="line.209"></a>
+<FONT color="green">210</FONT> v1 = v1.add(v2);<a name="line.210"></a>
+<FONT color="green">211</FONT> checkVector(v1, -2, 0, 2);<a name="line.211"></a>
+<FONT color="green">212</FONT> <a name="line.212"></a>
+<FONT color="green">213</FONT> checkVector(v2.add(v1), -5, -2, 1);<a name="line.213"></a>
+<FONT color="green">214</FONT> checkVector(v2.add(3, v1), -9, -2, 5);<a name="line.214"></a>
+<FONT color="green">215</FONT> }<a name="line.215"></a>
+<FONT color="green">216</FONT> <a name="line.216"></a>
+<FONT color="green">217</FONT> @Test<a name="line.217"></a>
+<FONT color="green">218</FONT> public void testScalarProduct() {<a name="line.218"></a>
+<FONT color="green">219</FONT> Vector3D v = new Vector3D(1, 2, 3);<a name="line.219"></a>
+<FONT color="green">220</FONT> v = v.scalarMultiply(3);<a name="line.220"></a>
+<FONT color="green">221</FONT> checkVector(v, 3, 6, 9);<a name="line.221"></a>
+<FONT color="green">222</FONT> <a name="line.222"></a>
+<FONT color="green">223</FONT> checkVector(v.scalarMultiply(0.5), 1.5, 3, 4.5);<a name="line.223"></a>
+<FONT color="green">224</FONT> }<a name="line.224"></a>
+<FONT color="green">225</FONT> <a name="line.225"></a>
+<FONT color="green">226</FONT> @Test<a name="line.226"></a>
+<FONT color="green">227</FONT> public void testVectorialProducts() {<a name="line.227"></a>
+<FONT color="green">228</FONT> Vector3D v1 = new Vector3D(2, 1, -4);<a name="line.228"></a>
+<FONT color="green">229</FONT> Vector3D v2 = new Vector3D(3, 1, -1);<a name="line.229"></a>
<FONT color="green">230</FONT> <a name="line.230"></a>
-<FONT color="green">231</FONT> @Test<a name="line.231"></a>
-<FONT color="green">232</FONT> public void testAngle() throws MathArithmeticException {<a name="line.232"></a>
-<FONT color="green">233</FONT> Assert.assertEquals(0.22572612855273393616,<a name="line.233"></a>
-<FONT color="green">234</FONT> Vector3D.angle(new Vector3D(1, 2, 3), new Vector3D(4, 5, 6)),<a name="line.234"></a>
-<FONT color="green">235</FONT> 1.0e-12);<a name="line.235"></a>
-<FONT color="green">236</FONT> Assert.assertEquals(7.98595620686106654517199e-8,<a name="line.236"></a>
-<FONT color="green">237</FONT> Vector3D.angle(new Vector3D(1, 2, 3), new Vector3D(2, 4, 6.000001)),<a name="line.237"></a>
-<FONT color="green">238</FONT> 1.0e-12);<a name="line.238"></a>
-<FONT color="green">239</FONT> Assert.assertEquals(3.14159257373023116985197793156,<a name="line.239"></a>
-<FONT color="green">240</FONT> Vector3D.angle(new Vector3D(1, 2, 3), new Vector3D(-2, -4, -6.000001)),<a name="line.240"></a>
-<FONT color="green">241</FONT> 1.0e-12);<a name="line.241"></a>
-<FONT color="green">242</FONT> try {<a name="line.242"></a>
-<FONT color="green">243</FONT> Vector3D.angle(Vector3D.ZERO, Vector3D.PLUS_I);<a name="line.243"></a>
-<FONT color="green">244</FONT> Assert.fail("an exception should have been thrown");<a name="line.244"></a>
-<FONT color="green">245</FONT> } catch (MathArithmeticException ae) {<a name="line.245"></a>
-<FONT color="green">246</FONT> // expected behavior<a name="line.246"></a>
-<FONT color="green">247</FONT> }<a name="line.247"></a>
-<FONT color="green">248</FONT> }<a name="line.248"></a>
-<FONT color="green">249</FONT> <a name="line.249"></a>
-<FONT color="green">250</FONT> @Test<a name="line.250"></a>
-<FONT color="green">251</FONT> public void testAccurateDotProduct() {<a name="line.251"></a>
-<FONT color="green">252</FONT> // the following two vectors are nearly but not exactly orthogonal<a name="line.252"></a>
-<FONT color="green">253</FONT> // naive dot product (i.e. computing u1.x * u2.x + u1.y * u2.y + u1.z * u2.z<a name="line.253"></a>
-<FONT color="green">254</FONT> // leads to a result of 0.0, instead of the correct -1.855129...<a name="line.254"></a>
-<FONT color="green">255</FONT> Vector3D u1 = new Vector3D(-1321008684645961.0 / 268435456.0,<a name="line.255"></a>
-<FONT color="green">256</FONT> -5774608829631843.0 / 268435456.0,<a name="line.256"></a>
-<FONT color="green">257</FONT> -7645843051051357.0 / 8589934592.0);<a name="line.257"></a>
-<FONT color="green">258</FONT> Vector3D u2 = new Vector3D(-5712344449280879.0 / 2097152.0,<a name="line.258"></a>
-<FONT color="green">259</FONT> -4550117129121957.0 / 2097152.0,<a name="line.259"></a>
-<FONT color="green">260</FONT> 8846951984510141.0 / 131072.0);<a name="line.260"></a>
-<FONT color="green">261</FONT> double sNaive = u1.getX() * u2.getX() + u1.getY() * u2.getY() + u1.getZ() * u2.getZ();<a name="line.261"></a>
-<FONT color="green">262</FONT> double sAccurate = u1.dotProduct(u2);<a name="line.262"></a>
-<FONT color="green">263</FONT> Assert.assertEquals(0.0, sNaive, 1.0e-30);<a name="line.263"></a>
-<FONT color="green">264</FONT> Assert.assertEquals(-2088690039198397.0 / 1125899906842624.0, sAccurate, 1.0e-16);<a name="line.264"></a>
+<FONT color="green">231</FONT> Assert.assertTrue(FastMath.abs(Vector3D.dotProduct(v1, v2) - 11) < 1.0e-12);<a name="line.231"></a>
+<FONT color="green">232</FONT> <a name="line.232"></a>
+<FONT color="green">233</FONT> Vector3D v3 = Vector3D.crossProduct(v1, v2);<a name="line.233"></a>
+<FONT color="green">234</FONT> checkVector(v3, 3, -10, -1);<a name="line.234"></a>
+<FONT color="green">235</FONT> <a name="line.235"></a>
+<FONT color="green">236</FONT> Assert.assertTrue(FastMath.abs(Vector3D.dotProduct(v1, v3)) < 1.0e-12);<a name="line.236"></a>
+<FONT color="green">237</FONT> Assert.assertTrue(FastMath.abs(Vector3D.dotProduct(v2, v3)) < 1.0e-12);<a name="line.237"></a>
+<FONT color="green">238</FONT> }<a name="line.238"></a>
+<FONT color="green">239</FONT> <a name="line.239"></a>
+<FONT color="green">240</FONT> @Test<a name="line.240"></a>
+<FONT color="green">241</FONT> public void testCrossProductCancellation() {<a name="line.241"></a>
+<FONT color="green">242</FONT> Vector3D v1 = new Vector3D(9070467121.0, 4535233560.0, 1);<a name="line.242"></a>
+<FONT color="green">243</FONT> Vector3D v2 = new Vector3D(9070467123.0, 4535233561.0, 1);<a name="line.243"></a>
+<FONT color="green">244</FONT> checkVector(Vector3D.crossProduct(v1, v2), -1, 2, 1);<a name="line.244"></a>
+<FONT color="green">245</FONT> <a name="line.245"></a>
+<FONT color="green">246</FONT> double scale = FastMath.scalb(1.0, 100);<a name="line.246"></a>
+<FONT color="green">247</FONT> Vector3D big1 = new Vector3D(scale, v1);<a name="line.247"></a>
+<FONT color="green">248</FONT> Vector3D small2 = new Vector3D(1 / scale, v2);<a name="line.248"></a>
+<FONT color="green">249</FONT> checkVector(Vector3D.crossProduct(big1, small2), -1, 2, 1);<a name="line.249"></a>
+<FONT color="green">250</FONT> <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> @Test<a name="line.253"></a>
+<FONT color="green">254</FONT> public void testAngular() {<a name="line.254"></a>
+<FONT color="green">255</FONT> Assert.assertEquals(0, Vector3D.PLUS_I.getAlpha(), 1.0e-10);<a name="line.255"></a>
+<FONT color="green">256</FONT> Assert.assertEquals(0, Vector3D.PLUS_I.getDelta(), 1.0e-10);<a name="line.256"></a>
+<FONT color="green">257</FONT> Assert.assertEquals(FastMath.PI / 2, Vector3D.PLUS_J.getAlpha(), 1.0e-10);<a name="line.257"></a>
+<FONT color="green">258</FONT> Assert.assertEquals(0, Vector3D.PLUS_J.getDelta(), 1.0e-10);<a name="line.258"></a>
+<FONT color="green">259</FONT> Assert.assertEquals(0, Vector3D.PLUS_K.getAlpha(), 1.0e-10);<a name="line.259"></a>
+<FONT color="green">260</FONT> Assert.assertEquals(FastMath.PI / 2, Vector3D.PLUS_K.getDelta(), 1.0e-10);<a name="line.260"></a>
+<FONT color="green">261</FONT> <a name="line.261"></a>
+<FONT color="green">262</FONT> Vector3D u = new Vector3D(-1, 1, -1);<a name="line.262"></a>
+<FONT color="green">263</FONT> Assert.assertEquals(3 * FastMath.PI /4, u.getAlpha(), 1.0e-10);<a name="line.263"></a>
+<FONT color="green">264</FONT> Assert.assertEquals(-1.0 / FastMath.sqrt(3), FastMath.sin(u.getDelta()), 1.0e-10);<a name="line.264"></a>
<FONT color="green">265</FONT> }<a name="line.265"></a>
<FONT color="green">266</FONT> <a name="line.266"></a>
<FONT color="green">267</FONT> @Test<a name="line.267"></a>
-<FONT color="green">268</FONT> public void testDotProduct() {<a name="line.268"></a>
-<FONT color="green">269</FONT> // we compare accurate versus naive dot product implementations<a name="line.269"></a>
-<FONT color="green">270</FONT> // on regular vectors (i.e. not extreme cases like in the previous test)<a name="line.270"></a>
-<FONT color="green">271</FONT> Well1024a random = new Well1024a(553267312521321234l);<a name="line.271"></a>
-<FONT color="green">272</FONT> for (int i = 0; i < 10000; ++i) {<a name="line.272"></a>
-<FONT color="green">273</FONT> double ux = 10000 * random.nextDouble();<a name="line.273"></a>
-<FONT color="green">274</FONT> double uy = 10000 * random.nextDouble();<a name="line.274"></a>
-<FONT color="green">275</FONT> double uz = 10000 * random.nextDouble();<a name="line.275"></a>
-<FONT color="green">276</FONT> double vx = 10000 * random.nextDouble();<a name="line.276"></a>
-<FONT color="green">277</FONT> double vy = 10000 * random.nextDouble();<a name="line.277"></a>
-<FONT color="green">278</FONT> double vz = 10000 * random.nextDouble();<a name="line.278"></a>
-<FONT color="green">279</FONT> double sNaive = ux * vx + uy * vy + uz * vz;<a name="line.279"></a>
-<FONT color="green">280</FONT> double sAccurate = new Vector3D(ux, uy, uz).dotProduct(new Vector3D(vx, vy, vz));<a name="line.280"></a>
-<FONT color="green">281</FONT> Assert.assertEquals(sNaive, sAccurate, 2.5e-16 * sAccurate);<a name="line.281"></a>
-<FONT color="green">282</FONT> }<a name="line.282"></a>
-<FONT color="green">283</FONT> }<a name="line.283"></a>
-<FONT color="green">284</FONT> <a name="line.284"></a>
-<FONT color="green">285</FONT> @Test<a name="line.285"></a>
-<FONT color="green">286</FONT> public void testAccurateCrossProduct() {<a name="line.286"></a>
-<FONT color="green">287</FONT> // the vectors u1 and u2 are nearly but not exactly anti-parallel<a name="line.287"></a>
-<FONT color="green">288</FONT> // (7.31e-16 degrees from 180 degrees) naive cross product (i.e.<a name="line.288"></a>
-<FONT color="green">289</FONT> // computing u1.x * u2.x + u1.y * u2.y + u1.z * u2.z<a name="line.289"></a>
-<FONT color="green">290</FONT> // leads to a result of [0.0009765, -0.0001220, -0.0039062],<a name="line.290"></a>
-<FONT color="green">291</FONT> // instead of the correct [0.0006913, -0.0001254, -0.0007909]<a name="line.291"></a>
-<FONT color="green">292</FONT> final Vector3D u1 = new Vector3D(-1321008684645961.0 / 268435456.0,<a name="line.292"></a>
-<FONT color="green">293</FONT> -5774608829631843.0 / 268435456.0,<a name="line.293"></a>
-<FONT color="green">294</FONT> -7645843051051357.0 / 8589934592.0);<a name="line.294"></a>
-<FONT color="green">295</FONT> final Vector3D u2 = new Vector3D( 1796571811118507.0 / 2147483648.0,<a name="line.295"></a>
-<FONT color="green">296</FONT> 7853468008299307.0 / 2147483648.0,<a name="line.296"></a>
-<FONT color="green">297</FONT> 2599586637357461.0 / 17179869184.0);<a name="line.297"></a>
-<FONT color="green">298</FONT> final Vector3D u3 = new Vector3D(12753243807587107.0 / 18446744073709551616.0, <a name="line.298"></a>
-<FONT color="green">299</FONT> -2313766922703915.0 / 18446744073709551616.0, <a name="line.299"></a>
-<FONT color="green">300</FONT> -227970081415313.0 / 288230376151711744.0);<a name="line.300"></a>
-<FONT color="green">301</FONT> Vector3D cNaive = new Vector3D(u1.getY() * u2.getZ() - u1.getZ() * u2.getY(),<a name="line.301"></a>
-<FONT color="green">302</FONT> u1.getZ() * u2.getX() - u1.getX() * u2.getZ(),<a name="line.302"></a>
-<FONT color="green">303</FONT> u1.getX() * u2.getY() - u1.getY() * u2.getX());<a name="line.303"></a>
-<FONT color="green">304</FONT> Vector3D cAccurate = u1.crossProduct(u2);<a name="line.304"></a>
-<FONT color="green">305</FONT> Assert.assertTrue(u3.distance(cNaive) > 2.9 * u3.getNorm());<a name="line.305"></a>
-<FONT color="green">306</FONT> Assert.assertEquals(0.0, u3.distance(cAccurate), 1.0e-30 * cAccurate.getNorm());<a name="line.306"></a>
-<FONT color="green">307</FONT> }<a name="line.307"></a>
-<FONT color="green">308</FONT> <a name="line.308"></a>
-<FONT color="green">309</FONT> @Test<a name="line.309"></a>
-<FONT color="green">310</FONT> public void testCrossProduct() {<a name="line.310"></a>
-<FONT color="green">311</FONT> // we compare accurate versus naive cross product implementations<a name="line.311"></a>
-<FONT color="green">312</FONT> // on regular vectors (i.e. not extreme cases like in the previous test)<a name="line.312"></a>
-<FONT color="green">313</FONT> Well1024a random = new Well1024a(885362227452043214l);<a name="line.313"></a>
-<FONT color="green">314</FONT> for (int i = 0; i < 10000; ++i) {<a name="line.314"></a>
-<FONT color="green">315</FONT> double ux = 10000 * random.nextDouble();<a name="line.315"></a>
-<FONT color="green">316</FONT> double uy = 10000 * random.nextDouble();<a name="line.316"></a>
-<FONT color="green">317</FONT> double uz = 10000 * random.nextDouble();<a name="line.317"></a>
-<FONT color="green">318</FONT> double vx = 10000 * random.nextDouble();<a name="line.318"></a>
-<FONT color="green">319</FONT> double vy = 10000 * random.nextDouble();<a name="line.319"></a>
-<FONT color="green">320</FONT> double vz = 10000 * random.nextDouble();<a name="line.320"></a>
-<FONT color="green">321</FONT> Vector3D cNaive = new Vector3D(uy * vz - uz * vy, uz * vx - ux * vz, ux * vy - uy * vx);<a name="line.321"></a>
-<FONT color="green">322</FONT> Vector3D cAccurate = new Vector3D(ux, uy, uz).crossProduct(new Vector3D(vx, vy, vz));<a name="line.322"></a>
-<FONT color="green">323</FONT> Assert.assertEquals(0.0, cAccurate.distance(cNaive), 6.0e-15 * cAccurate.getNorm());<a name="line.323"></a>
-<FONT color="green">324</FONT> }<a name="line.324"></a>
-<FONT color="green">325</FONT> }<a name="line.325"></a>
-<FONT color="green">326</FONT> <a name="line.326"></a>
-<FONT color="green">327</FONT> private void checkVector(Vector3D v, double x, double y, double z) {<a name="line.327"></a>
-<FONT color="green">328</FONT> Assert.assertEquals(x, v.getX(), 1.0e-12);<a name="line.328"></a>
-<FONT color="green">329</FONT> Assert.assertEquals(y, v.getY(), 1.0e-12);<a name="line.329"></a>
-<FONT color="green">330</FONT> Assert.assertEquals(z, v.getZ(), 1.0e-12);<a name="line.330"></a>
-<FONT color="green">331</FONT> }<a name="line.331"></a>
-<FONT color="green">332</FONT> }<a name="line.332"></a>
+<FONT color="green">268</FONT> public void testAngularSeparation() throws MathArithmeticException {<a name="line.268"></a>
+<FONT color="green">269</FONT> Vector3D v1 = new Vector3D(2, -1, 4);<a name="line.269"></a>
+<FONT color="green">270</FONT> <a name="line.270"></a>
+<FONT color="green">271</FONT> Vector3D k = v1.normalize();<a name="line.271"></a>
+<FONT color="green">272</FONT> Vector3D i = k.orthogonal();<a name="line.272"></a>
+<FONT color="green">273</FONT> Vector3D v2 = k.scalarMultiply(FastMath.cos(1.2)).add(i.scalarMultiply(FastMath.sin(1.2)));<a name="line.273"></a>
+<FONT color="green">274</FONT> <a name="line.274"></a>
+<FONT color="green">275</FONT> Assert.assertTrue(FastMath.abs(Vector3D.angle(v1, v2) - 1.2) < 1.0e-12);<a name="line.275"></a>
+<FONT color="green">276</FONT> }<a name="line.276"></a>
+<FONT color="green">277</FONT> <a name="line.277"></a>
+<FONT color="green">278</FONT> @Test<a name="line.278"></a>
+<FONT color="green">279</FONT> public void testNormalize() throws MathArithmeticException {<a name="line.279"></a>
+<FONT color="green">280</FONT> Assert.assertEquals(1.0, new Vector3D(5, -4, 2).normalize().getNorm(), 1.0e-12);<a name="line.280"></a>
+<FONT color="green">281</FONT> try {<a name="line.281"></a>
+<FONT color="green">282</FONT> Vector3D.ZERO.normalize();<a name="line.282"></a>
+<FONT color="green">283</FONT> Assert.fail("an exception should have been thrown");<a name="line.283"></a>
+<FONT color="green">284</FONT> } catch (MathArithmeticException ae) {<a name="line.284"></a>
+<FONT color="green">285</FONT> // expected behavior<a name="line.285"></a>
+<FONT color="green">286</FONT> }<a name="line.286"></a>
+<FONT color="green">287</FONT> }<a name="line.287"></a>
+<FONT color="green">288</FONT> <a name="line.288"></a>
+<FONT color="green">289</FONT> @Test<a name="line.289"></a>
+<FONT color="green">290</FONT> public void testNegate() {<a name="line.290"></a>
+<FONT color="green">291</FONT> checkVector(new Vector3D(0.1, 2.5, 1.3).negate(), -0.1, -2.5, -1.3);<a name="line.291"></a>
+<FONT color="green">292</FONT> }<a name="line.292"></a>
+<FONT color="green">293</FONT> <a name="line.293"></a>
+<FONT color="green">294</FONT> @Test<a name="line.294"></a>
+<FONT color="green">295</FONT> public void testOrthogonal() throws MathArithmeticException {<a name="line.295"></a>
+<FONT color="green">296</FONT> Vector3D v1 = new Vector3D(0.1, 2.5, 1.3);<a name="line.296"></a>
+<FONT color="green">297</FONT> Assert.assertEquals(0.0, Vector3D.dotProduct(v1, v1.orthogonal()), 1.0e-12);<a name="line.297"></a>
+<FONT color="green">298</FONT> Vector3D v2 = new Vector3D(2.3, -0.003, 7.6);<a name="line.298"></a>
+<FONT color="green">299</FONT> Assert.assertEquals(0.0, Vector3D.dotProduct(v2, v2.orthogonal()), 1.0e-12);<a name="line.299"></a>
+<FONT color="green">300</FONT> Vector3D v3 = new Vector3D(-1.7, 1.4, 0.2);<a name="line.300"></a>
+<FONT color="green">301</FONT> Assert.assertEquals(0.0, Vector3D.dotProduct(v3, v3.orthogonal()), 1.0e-12);<a name="line.301"></a>
+<FONT color="green">302</FONT> Vector3D v4 = new Vector3D(4.2, 0.1, -1.8);<a name="line.302"></a>
+<FONT color="green">303</FONT> Assert.assertEquals(0.0, Vector3D.dotProduct(v4, v4.orthogonal()), 1.0e-12);<a name="line.303"></a>
+<FONT color="green">304</FONT> try {<a name="line.304"></a>
+<FONT color="green">305</FONT> new Vector3D(0, 0, 0).orthogonal();<a name="line.305"></a>
+<FONT color="green">306</FONT> Assert.fail("an exception should have been thrown");<a name="line.306"></a>
+<FONT color="green">307</FONT> } catch (MathArithmeticException ae) {<a name="line.307"></a>
+<FONT color="green">308</FONT> // expected behavior<a name="line.308"></a>
+<FONT color="green">309</FONT> }<a name="line.309"></a>
+<FONT color="green">310</FONT> }<a name="line.310"></a>
+<FONT color="green">311</FONT> @Test<a name="line.311"></a>
+<FONT color="green">312</FONT> public void testAngle() throws MathArithmeticException {<a name="line.312"></a>
+<FONT color="green">313</FONT> Assert.assertEquals(0.22572612855273393616,<a name="line.313"></a>
+<FONT color="green">314</FONT> Vector3D.angle(new Vector3D(1, 2, 3), new Vector3D(4, 5, 6)),<a name="line.314"></a>
+<FONT color="green">315</FONT> 1.0e-12);<a name="line.315"></a>
+<FONT color="green">316</FONT> Assert.assertEquals(7.98595620686106654517199e-8,<a name="line.316"></a>
+<FONT color="green">317</FONT> Vector3D.angle(new Vector3D(1, 2, 3), new Vector3D(2, 4, 6.000001)),<a name="line.317"></a>
+<FONT color="green">318</FONT> 1.0e-12);<a name="line.318"></a>
+<FONT color="green">319</FONT> Assert.assertEquals(3.14159257373023116985197793156,<a name="line.319"></a>
+<FONT color="green">320</FONT> Vector3D.angle(new Vector3D(1, 2, 3), new Vector3D(-2, -4, -6.000001)),<a name="line.320"></a>
+<FONT color="green">321</FONT> 1.0e-12);<a name="line.321"></a>
+<FONT color="green">322</FONT> try {<a name="line.322"></a>
+<FONT color="green">323</FONT> Vector3D.angle(Vector3D.ZERO, Vector3D.PLUS_I);<a name="line.323"></a>
+<FONT color="green">324</FONT> Assert.fail("an exception should have been thrown");<a name="line.324"></a>
+<FONT color="green">325</FONT> } catch (MathArithmeticException ae) {<a name="line.325"></a>
+<FONT color="green">326</FONT> // expected behavior<a name="line.326"></a>
+<FONT color="green">327</FONT> }<a name="line.327"></a>
+<FONT color="green">328</FONT> }<a name="line.328"></a>
+<FONT color="green">329</FONT> <a name="line.329"></a>
+<FONT color="green">330</FONT> @Test<a name="line.330"></a>
+<FONT color="green">331</FONT> public void testAccurateDotProduct() {<a name="line.331"></a>
+<FONT color="green">332</FONT> // the following two vectors are nearly but not exactly orthogonal<a name="line.332"></a>
+<FONT color="green">333</FONT> // naive dot product (i.e. computing u1.x * u2.x + u1.y * u2.y + u1.z * u2.z<a name="line.333"></a>
+<FONT color="green">334</FONT> // leads to a result of 0.0, instead of the correct -1.855129...<a name="line.334"></a>
+<FONT color="green">335</FONT> Vector3D u1 = new Vector3D(-1321008684645961.0 / 268435456.0,<a name="line.335"></a>
+<FONT color="green">336</FONT> -5774608829631843.0 / 268435456.0,<a name="line.336"></a>
+<FONT color="green">337</FONT> -7645843051051357.0 / 8589934592.0);<a name="line.337"></a>
+<FONT color="green">338</FONT> Vector3D u2 = new Vector3D(-5712344449280879.0 / 2097152.0,<a name="line.338"></a>
+<FONT color="green">339</FONT> -4550117129121957.0 / 2097152.0,<a name="line.339"></a>
+<FONT color="green">340</FONT> 8846951984510141.0 / 131072.0);<a name="line.340"></a>
+<FONT color="green">341</FONT> double sNaive = u1.getX() * u2.getX() + u1.getY() * u2.getY() + u1.getZ() * u2.getZ();<a name="line.341"></a>
+<FONT color="green">342</FONT> double sAccurate = u1.dotProduct(u2);<a name="line.342"></a>
+<FONT color="green">343</FONT> Assert.assertEquals(0.0, sNaive, 1.0e-30);<a name="line.343"></a>
+<FONT color="green">344</FONT> Assert.assertEquals(-2088690039198397.0 / 1125899906842624.0, sAccurate, 1.0e-16);<a name="line.344"></a>
+<FONT color="green">345</FONT> }<a name="line.345"></a>
+<FONT color="green">346</FONT> <a name="line.346"></a>
+<FONT color="green">347</FONT> @Test<a name="line.347"></a>
+<FONT color="green">348</FONT> public void testDotProduct() {<a name="line.348"></a>
+<FONT color="green">349</FONT> // we compare accurate versus naive dot product implementations<a name="line.349"></a>
+<FONT color="green">350</FONT> // on regular vectors (i.e. not extreme cases like in the previous test)<a name="line.350"></a>
+<FONT color="green">351</FONT> Well1024a random = new Well1024a(553267312521321234l);<a name="line.351"></a>
+<FONT color="green">352</FONT> for (int i = 0; i < 10000; ++i) {<a name="line.352"></a>
+<FONT color="green">353</FONT> double ux = 10000 * random.nextDouble();<a name="line.353"></a>
+<FONT color="green">354</FONT> double uy = 10000 * random.nextDouble();<a name="line.354"></a>
+<FONT color="green">355</FONT> double uz = 10000 * random.nextDouble();<a name="line.355"></a>
+<FONT color="green">356</FONT> double vx = 10000 * random.nextDouble();<a name="line.356"></a>
+<FONT color="green">357</FONT> double vy = 10000 * random.nextDouble();<a name="line.357"></a>
+<FONT color="green">358</FONT> double vz = 10000 * random.nextDouble();<a name="line.358"></a>
+<FONT color="green">359</FONT> double sNaive = ux * vx + uy * vy + uz * vz;<a name="line.359"></a>
+<FONT color="green">360</FONT> double sAccurate = new Vector3D(ux, uy, uz).dotProduct(new Vector3D(vx, vy, vz));<a name="line.360"></a>
+<FONT color="green">361</FONT> Assert.assertEquals(sNaive, sAccurate, 2.5e-16 * sAccurate);<a name="line.361"></a>
+<FONT color="green">362</FONT> }<a name="line.362"></a>
+<FONT color="green">363</FONT> }<a name="line.363"></a>
+<FONT color="green">364</FONT> <a name="line.364"></a>
+<FONT color="green">365</FONT> @Test<a name="line.365"></a>
+<FONT color="green">366</FONT> public void testAccurateCrossProduct() {<a name="line.366"></a>
+<FONT color="green">367</FONT> // the vectors u1 and u2 are nearly but not exactly anti-parallel<a name="line.367"></a>
+<FONT color="green">368</FONT> // (7.31e-16 degrees from 180 degrees) naive cross product (i.e.<a name="line.368"></a>
+<FONT color="green">369</FONT> // computing u1.x * u2.x + u1.y * u2.y + u1.z * u2.z<a name="line.369"></a>
+<FONT color="green">370</FONT> // leads to a result of [0.0009765, -0.0001220, -0.0039062],<a name="line.370"></a>
+<FONT color="green">371</FONT> // instead of the correct [0.0006913, -0.0001254, -0.0007909]<a name="line.371"></a>
+<FONT color="green">372</FONT> final Vector3D u1 = new Vector3D(-1321008684645961.0 / 268435456.0,<a name="line.372"></a>
+<FONT color="green">373</FONT> -5774608829631843.0 / 268435456.0,<a name="line.373"></a>
+<FONT color="green">374</FONT> -7645843051051357.0 / 8589934592.0);<a name="line.374"></a>
+<FONT color="green">375</FONT> final Vector3D u2 = new Vector3D( 1796571811118507.0 / 2147483648.0,<a name="line.375"></a>
+<FONT color="green">376</FONT> 7853468008299307.0 / 2147483648.0,<a name="line.376"></a>
+<FONT color="green">377</FONT> 2599586637357461.0 / 17179869184.0);<a name="line.377"></a>
+<FONT color="green">378</FONT> final Vector3D u3 = new Vector3D(12753243807587107.0 / 18446744073709551616.0, <a name="line.378"></a>
+<FONT color="green">379</FONT> -2313766922703915.0 / 18446744073709551616.0, <a name="line.379"></a>
+<FONT color="green">380</FONT> -227970081415313.0 / 288230376151711744.0);<a name="line.380"></a>
+<FONT color="green">381</FONT> Vector3D cNaive = new Vector3D(u1.getY() * u2.getZ() - u1.getZ() * u2.getY(),<a name="line.381"></a>
+<FONT color="green">382</FONT> u1.getZ() * u2.getX() - u1.getX() * u2.getZ(),<a name="line.382"></a>
+<FONT color="green">383</FONT> u1.getX() * u2.getY() - u1.getY() * u2.getX());<a name="line.383"></a>
+<FONT color="green">384</FONT> Vector3D cAccurate = u1.crossProduct(u2);<a name="line.384"></a>
+<FONT color="green">385</FONT> Assert.assertTrue(u3.distance(cNaive) > 2.9 * u3.getNorm());<a name="line.385"></a>
+<FONT color="green">386</FONT> Assert.assertEquals(0.0, u3.distance(cAccurate), 1.0e-30 * cAccurate.getNorm());<a name="line.386"></a>
+<FONT color="green">387</FONT> }<a name="line.387"></a>
+<FONT color="green">388</FONT> <a name="line.388"></a>
+<FONT color="green">389</FONT> @Test<a name="line.389"></a>
+<FONT color="green">390</FONT> public void testCrossProduct() {<a name="line.390"></a>
+<FONT color="green">391</FONT> // we compare accurate versus naive cross product implementations<a name="line.391"></a>
+<FONT color="green">392</FONT> // on regular vectors (i.e. not extreme cases like in the previous test)<a name="line.392"></a>
+<FONT color="green">393</FONT> Well1024a random = new Well1024a(885362227452043214l);<a name="line.393"></a>
+<FONT color="green">394</FONT> for (int i = 0; i < 10000; ++i) {<a name="line.394"></a>
+<FONT color="green">395</FONT> double ux = 10000 * random.nextDouble();<a name="line.395"></a>
+<FONT color="green">396</FONT> double uy = 10000 * random.nextDouble();<a name="line.396"></a>
+<FONT color="green">397</FONT> double uz = 10000 * random.nextDouble();<a name="line.397"></a>
+<FONT color="green">398</FONT> double vx = 10000 * random.nextDouble();<a name="line.398"></a>
+<FONT color="green">399</FONT> double vy = 10000 * random.nextDouble();<a name="line.399"></a>
+<FONT color="green">400</FONT> double vz = 10000 * random.nextDouble();<a name="line.400"></a>
+<FONT color="green">401</FONT> Vector3D cNaive = new Vector3D(uy * vz - uz * vy, uz * vx - ux * vz, ux * vy - uy * vx);<a name="line.401"></a>
+<FONT color="green">402</FONT> Vector3D cAccurate = new Vector3D(ux, uy, uz).crossProduct(new Vector3D(vx, vy, vz));<a name="line.402"></a>
+<FONT color="green">403</FONT> Assert.assertEquals(0.0, cAccurate.distance(cNaive), 6.0e-15 * cAccurate.getNorm());<a name="line.403"></a>
+<FONT color="green">404</FONT> }<a name="line.404"></a>
+<FONT color="green">405</FONT> }<a name="line.405"></a>
+<FONT color="green">406</FONT> <a name="line.406"></a>
+<FONT color="green">407</FONT> private void checkVector(Vector3D v, double x, double y, double z) {<a name="line.407"></a>
+<FONT color="green">408</FONT> Assert.assertEquals(x, v.getX(), 1.0e-12);<a name="line.408"></a>
+<FONT color="green">409</FONT> Assert.assertEquals(y, v.getY(), 1.0e-12);<a name="line.409"></a>
+<FONT color="green">410</FONT> Assert.assertEquals(z, v.getZ(), 1.0e-12);<a name="line.410"></a>
+<FONT color="green">411</FONT> }<a name="line.411"></a>
+<FONT color="green">412</FONT> }<a name="line.412"></a>