# Concave Edge Detection

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How do I efficiently determine if two planes form a convex/concave edge? Thank you, L. Spiro

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That's not a meaningful question. Two non-parallel planes intersect at a line.. if you take a half-plane from each, bordered by the intersection line, then the question of whether the edge is convex or concave comes down to which half-planes you pick.

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I had a similar problem with triangles a few weeks ago. I wanted to determined if the edge between two adjacent triangles was concave or convex. What I did, was to project the non-shared vertex of one triangle into the normal of the other triangle. This way I was able to determine if the other triangle was below or above the plane on which the other triangle lies. So what you could do is pick a point "x" on the edge and a point "p" on the first plane (on the side of the edge you want to evaluate). Then, get the normal "n" of the other plane. After that, all you have to do is:

dotp(p-x, n)

If the result is positive then it's concave and if the result is negative it's convex. I'm not sure if it's exactly what you wanted, but I hope it helped.

Frounk

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Frounk, that makes sense. I am working with polygons rather than triangles, but they are always guaranteed not to be coplanar (or else they would have been merged into one larger polygon) and to share an edge (or else I would not be checking them against each other).
So I can apply the same technique.

Thank you.

L. Spiro

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