[MATH-749] Added crossProduct method to Vector2D as a replacement for getLocation, using MathArrays.linearCombination to improve accuracy.

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1563684 13f79535-47bb-0310-9956-ffa450edef68

src/main/java/org/apache/commons/math3/geometry/euclidean/twod/Vector2D.java

@@ -329,6 +329,34 @@ public class Vector2D implements Vector<Euclidean2D> {
         return MathArrays.linearCombination(x, v2.x, y, v2.y);
     }
 
+    /**
+     * Compute the cross-product of the instance and the given points.
+     * <p>
+     * The cross product can be used to determine the location of a point
+     * with regard to the line formed by (p1, p2) and is calculated as:
+     * \[
+     *    P = (x_2 - x_1)(y_3 - y_1) - (y_2 - y_1)(x_3 - x_1)
+     * \]
+     * with \(p3 = (x_3, y_3)\) being this instance.
+     * <p>
+     * If the result is 0, the points are collinear, i.e. lie on a single straight line L;
+     * if it is positive, this point lies to the left, otherwise to the right of the line
+     * formed by (p1, p2).
+     *
+     * @param p1 first point of the line
+     * @param p2 second point of the line
+     * @return the cross-product
+     *
+     * @see <a href="http://en.wikipedia.org/wiki/Cross_product">Cross product (Wikipedia)</a>
+     */
+    public double crossProduct(final Vector2D p1, final Vector2D p2) {
+        final double x1 = p2.getX() - p1.getX();
+        final double y1 = getY() - p1.getY();
+        final double x2 = getX() - p1.getX();
+        final double y2 = p2.getY() - p1.getY();
+        return MathArrays.linearCombination(x1, y1, -x2, y2);
+    }
+
     /** Compute the distance between two vectors according to the L<sub>2</sub> norm.
      * <p>Calling this method is equivalent to calling:
      * <code>p1.subtract(p2).getNorm()</code> except that no intermediate

src/test/java/org/apache/commons/math3/geometry/euclidean/twod/Vector2DTest.java

@@ -0,0 +1,40 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math3.geometry.euclidean.twod;
+
+import org.junit.Assert;
+import org.junit.Test;
+
+public class Vector2DTest {
+
+    @Test
+    public void testCrossProduct() {
+        final double epsilon = 1e-10;
+
+        Vector2D p1 = new Vector2D(1, 1);
+        Vector2D p2 = new Vector2D(2, 2);
+        
+        Vector2D p3 = new Vector2D(3, 3);
+        Assert.assertEquals(0.0, p3.crossProduct(p1, p2), epsilon);
+        
+        Vector2D p4 = new Vector2D(1, 2);
+        Assert.assertEquals(1.0, p4.crossProduct(p1, p2), epsilon);
+        
+        Vector2D p5 = new Vector2D(2, 1);
+        Assert.assertEquals(-1.0, p5.crossProduct(p1, p2), epsilon);
+    }
+}