Change in direction when a line hits an ellipse?

Asked Oct 23 '14 at 01:42

Active Jul 21 '15 at 13:01

Viewed 171 times

I'm trying to simulate reflecting light off an elliptical mirror. I currently store the ellipse in the form {center,{radii},rotationAngle} and the ray of light is specified by a direction and a starting point: {direction, pt}. See below:

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Now I can quite easily find the intersection point using RegionIntersection, but what I'm having a hard time doing is finding the new direction for the line after it hits the ellipse. I can do some (ugly) calculations using the parametric form of the ellipse to find the normal line, and then use ArcTan, etc. But I'm wondering if there's an elegant and easy way to determine the new direction for the line post-reflection.

edited Jul 21 '15 at 13:01

dionys

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asked Oct 23 '14 at 01:42

Steve D

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@belisarius: I'm afraid I don't understand. – Steve D Oct 23 '14 at 01:53
Read the second paragraph here carefully – Dr. belisarius Oct 23 '14 at 02:31
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Related: http://mathematica.stackexchange.com/questions/77148/reflecting-lines-in-ellipses-speed-up-the-code – Michael E2 Jul 21 '15 at 13:05
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Related: http://mathematica.stackexchange.com/q/38927/5478 – Kuba Jul 21 '15 at 13:09
Projection[] will be very useful here. – J. M.'s missing motivation Jul 21 '15 at 13:29

Change in direction when a line hits an ellipse?

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