From 6a58fcca7e517714fd53543f194944d920867e2e Mon Sep 17 00:00:00 2001
From: Frank v/d Haterd <f.h.a.v.d.haterd@student.tue.nl>
Date: Wed, 18 Dec 2013 15:39:06 +0100
Subject: getTangent 2.1 finished

---
 src/RaceTrack.java | 33 +++++++++++++++++++++++++++------
 1 file changed, 27 insertions(+), 6 deletions(-)

diff --git a/src/RaceTrack.java b/src/RaceTrack.java
index 26119ab..c973fb5 100644
--- a/src/RaceTrack.java
+++ b/src/RaceTrack.java
@@ -6,6 +6,8 @@ import static java.lang.Math.*;
  * Implementation of a race track that is made from Bezier segments.
  */
 class RaceTrack {
+    protected static final int ellipse_a = 10;
+    protected static final int ellipse_b = 14;
 
     /**
      * Array with control points for the O-track.
@@ -32,6 +34,8 @@ class RaceTrack {
      */
     public RaceTrack() {
         // code goes here ...
+        
+                           
     }
 
     /**
@@ -57,8 +61,8 @@ class RaceTrack {
      * Returns the position of the curve at 0 <= {@code t} <= 1.
      */
     public Vector getPoint(double t) {
-        return new Vector(10 * cos(2 * PI * t),
-                          14 * sin(2 * PI * t),
+        return new Vector(ellipse_a * cos(2 * PI * t),
+                          ellipse_b * sin(2 * PI * t),
                           1);
     }
 
@@ -66,9 +70,26 @@ class RaceTrack {
      * Returns the tangent of the curve at 0 <= {@code t} <= 1.
      */
     public Vector getTangent(double t) {
-        // robot looks forward
-        return new Vector(0,
-                          1,
-                          1);
+        /* 
+         * Given a vector (-Y/B^2, X/A^2, 0) where X and Y are the coordinates 
+         * of the point p on the ellipse. A is the HALFWIDTH of the ellipse and 
+         * B is the HALFHEIGHT of the ellipse. 
+         * 
+         * Vector (X/A^2, Y/B^2, 0) is the normal vector through point p
+         * and the center of the ellipse. Because the X and Y coordinates
+         * are divided by the width and height of the ellipse, everything is
+         * "normalized" to a circle. Hence a line through the origin and a point
+         * p describes a normal vector for a point p on the ellipse. 
+         * 
+         * Since the dot product of the latter vector and the first (tangent) 
+         * vector results in zero, we can say the normal vector is perpendicular
+         * to the tangent vector. And because of that, the first vector 
+         * describes the tangent vector of point p. 
+         */
+        Vector p = getPoint(t);
+        
+        return new Vector(-p.y()/(ellipse_a * ellipse_a),
+                          p.x()/(ellipse_b * ellipse_b),
+                          0).normalized();
     }
 }
-- 
cgit v1.2.1