Fun with geometry.

git-svn-id: svn+ssh://src.earth.threerings.net/narya/trunk@1535 542714f4-19e9-0310-aa3c-eee0fc999fb1

src/java/com/threerings/geom/GeomUtil.java

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+//
+// $Id: GeomUtil.java,v 1.1 2002/06/25 00:22:44 mdb Exp $
+
+package com.threerings.geom;
+
+import java.awt.Point;
+
+/**
+ * General geometry utilites.
+ */
+public class GeomUtil
+{
+    /**
+     * Computes and returns the dot product of the two vectors.
+     *
+     * @param v1s the starting point of the first vector.
+     * @param v1e the ending point of the first vector.
+     * @param v2s the starting point of the second vector.
+     * @param v2e the ending point of the second vector.
+     */
+    public static int dot (Point v1s, Point v1e, Point v2s, Point v2e)
+    {
+        return ((v1e.x - v1s.x) * (v2e.x - v2s.x) +
+                (v1e.y - v1s.y) * (v2e.y - v2s.y));
+    }
+
+    /**
+     * Computes the point nearest to the specified point <code>p3</code>
+     * on the line defined by the two points <code>p1</code> and
+     * <code>p2</code>. The computed point is stored into <code>n</code>.
+     * <em>Note:</em> <code>p1</code> and <code>p2</code> must not be
+     * coincident.
+     *
+     * @param p1 one point on the line.
+     * @param p2 another point on the line (not equal to <code>p1</code>).
+     * @param p3 the point to which we wish to be most near.
+     * @param n the point on the line defined by <code>p1</code> and
+     * <code>p2</code> that is nearest to <code>p</code>.
+     *
+     * @return the point object supplied via <code>n</code>.
+     */
+    public static Point nearestToLine (Point p1, Point p2, Point p3, Point n)
+    {
+        // see http://astronomy.swin.edu.au/~pbourke/geometry/pointline/
+        // for a (not very good) explanation of the math
+        int Ax = p2.x - p1.x, Ay = p2.y - p1.y;
+        float u = (p3.x - p1.x) * Ax + (p3.y - p1.y) * Ay;
+        u /= (Ax * Ax + Ay * Ay);
+        n.x = p1.x + Math.round(Ax * u);
+        n.y = p1.y + Math.round(Ay * u);
+        return n;
+    }
+}

tests/src/java/com/threerings/geom/NearestViz.java

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+//
+// $Id: NearestViz.java,v 1.1 2002/06/25 00:22:44 mdb Exp $
+
+package com.threerings.geom;
+
+import java.awt.BorderLayout;
+import java.awt.Color;
+import java.awt.Graphics;
+import java.awt.Point;
+
+import java.awt.event.MouseEvent;
+import java.awt.event.MouseMotionListener;
+
+import javax.swing.JFrame;
+import javax.swing.JPanel;
+
+/**
+ * Renders the nearest point on a line just for kicks.
+ */
+public class NearestViz extends JPanel
+    implements MouseMotionListener
+{
+    public NearestViz ()
+    {
+        addMouseMotionListener(this);
+    }
+
+    public void doLayout ()
+    {
+        super.doLayout();
+        _center = new Point(getWidth() / 2, getHeight() / 2);
+    }
+
+    public void paintComponent (Graphics g)
+    {
+        super.paintComponent(g);
+
+        int dx = (int)Math.round(Math.cos(_theta) * 200);
+        int dy = (int)Math.round(Math.sin(_theta) * 200);
+
+        g.setColor(Color.blue);
+        g.drawLine(_center.x, _center.y, _center.x + dx, _center.y - dy);
+        g.drawLine(_center.x, _center.y, _center.x - dx, _center.y + dy);
+
+        // locate the point nearest the spot
+        Point p2 = new Point(_center.x + dx, _center.y - dy);
+        Point n = new Point();
+        GeomUtil.nearestToLine(_center, p2, _spot, n);
+
+        g.setColor(Color.red);
+        g.drawOval(n.x - 4, n.y - 4, 8, 8);
+
+        // kick theta along for the next tick because it's fun
+        _theta += (float)(Math.PI/100);
+    }
+
+    public void mouseDragged (MouseEvent event)
+    {
+    }
+
+    public void mouseMoved (MouseEvent event)
+    {
+        _spot.x = event.getX();
+        _spot.y = event.getY();
+        repaint();
+    }
+
+    public static void main (String[] args)
+    {
+        JFrame frame = new JFrame();
+        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
+        frame.getContentPane().add(new NearestViz(), BorderLayout.CENTER);
+        frame.setSize(300, 300);
+        frame.show();
+    }
+
+    protected float _theta = (float)(3 * Math.PI / 5);
+    protected Point _center;
+    protected Point _spot = new Point();
+}