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September 19th, 2014, 10:54 PM   #1
Joined: Sep 2014
From: bhubaneswar

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get angle after n reflection inside a square

Is there a general formula that tell what angle a line will make on the side of a square after it makes n reflection on the sides of the square. Provided the first angle it make on one side of the square at a certain point.

It is sure after n reflection, the line is going to make a certain angle at a certain point at a certain side of the square.

What I know, how a computer find the above, is by calculating each reflection and arriving at the n reflection.

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September 20th, 2014, 03:11 PM   #2
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At each collision the angle of incldence equals the angle of reflection. If the next collision is with a perpendicular wall, the angle is the complement. If the next collision is with the parallel wall, the angle is the same.

The computer problem is then determining which wall is hit after n collisions. This is a somewhat messy, but straightforward geometry calculation.
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