calculating the potential effect of inaccurate triangle vertex positions on the triangle edge lenght

Posted by stingrey on Stack Overflow See other posts from Stack Overflow or by stingrey
Published on 2010-04-10T07:01:46Z Indexed on 2010/04/10 7:13 UTC
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trigonometry

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algorithm

i'm not sure how to solve the following problem:

i have a triangle with each of the three known vertex positions A,B,C being inaccurate, meaning they can each deviate up to certain known radii rA, rB, rC into arbitrary directions.

given such a triangle, i want to calculate how much the difference of two specific edge lengths (for instance the difference between lengths of edge a and edge b) of the triangle may change in the worst case. is there any elegant mathematical solution to this problem?

the naive way i thought of is calculating all 360^3 angle combinations and measuring the edge differences for each case, which is a rather high overhead.

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