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Jacobsen style cloth's collisions

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Hi, I have some questions about implementing Jacobsen style cloth simulation. I have implemented collisions between cloth's vertices and mesh triangles. It works quite nice, but it doesn't cover all the cases - on the edges of the mesh part of the cloth's triangle can be inside the mesh even then all it's vertices are outside. Now I'm wondering how to implement collision but between cloth triangles and mesh vertices. I'm especially interested in finding way for calculation of intersection point between moving triangle and static point. Finding valid constraint function part looks easier.

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