Fix broken tangent calculation of ellipse

1 files changed, 4 insertions, 18 deletions

diff --git a/src/RaceTrack.java b/src/RaceTrack.java
index 5c5b842..81fdc99 100644
--- a/src/RaceTrack.java
+++ b/src/RaceTrack.java
@@ -181,25 +181,11 @@ class RaceTrack extends BetterBase {
             return getCubicBezierTng(u, selectedControlPoints, bezier_start_i);
         }
 
-        /* 
-         * 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),
+        // tangent is derivative of ellipse:
+        // d / dt (A cos(t)) / (B sin(t)) = (-A sin(t)) / (B cos(t))
+        return new Vector(-ELLIPSE_A * sin(2 * PI * t),
+                          ELLIPSE_B * cos(2 * PI * t),
                           0).normalized();
     }