comparing two angles

Posted by Elazar Leibovich on Stack Overflow See other posts from Stack Overflow or by Elazar Leibovich
Published on 2010-05-23T14:04:37Z Indexed on 2010/05/23 14:11 UTC
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math

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vector

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geometry

Given four points in the plane, A,B,X,Y, I wish to determine which of the following two angles is smaller ?ABX or ?ABY.

I'd rather not use cos or sqrt, in order to preserve accuracy.

In the case where A=(-1,0),B=(0,0), I can compare the two angles ?ABX and ?ABY, by calculating the dot product of the vectors X,Y, and watch it's sign.

What I can do in this case is:

Determine whether or not ABX turns right or left
If ABX turns left check whether or not Y and A are on the same side of the line on segment BX. If they are - ?ABX is a smaller than ABY.
If ABX turns right, then Y and A on the same side of BX means that ?ABX is larger than ?ABY.

But this seems too complicated to me.

Any simpler approach?

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