Move Object allong an ellipsoid path

Questions & Answers
1

Hi,

I'm new to Unity and whats even worse for this case of situation, not that good in mathematics :).

So my problem is, I want to move an Object with the cursor keys (left, right) or with a gamepad allong an ellipsoid path on the screen.

The screen center is also the center of the ellipse. The object should always look to the center of the ellipse (ok, I already know how to do that).

So can anybody with mathematical magic fingers tell me how the calculation for the position of the object that should move along the ellipse is?

An example script would be welcome. I'm planning to use c#, but a js script would just be as fine.

Thx alot, K

2

The mathematics is pretty simple, have a look at wikipedia.

You need to define your ellipse with a few parameters:

x, y: center of the ellipse
a, b: semimajor and semiminor axes

If you want to move on the elipses this means that you change the angle between the major axes and your position on the ellipse. Lets call this angle alpha.

Your position (X,Y) is:

X = x + (a * Math.cos(alpha));
Y = y + (b * Math.sin(alpha));

In order to move left or right you need to increase/decrease alpha and then recalculate your position.