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cross section of a tetrahedron mesh.

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I want to find the cross section of tetrahedral mesh. I have developed the partial algorithm.

Follwing are the steps(partial)

Define a plane say ax + by + cz +d =o (n.x = d)
for each tetrahedron in the mesh
for each triangle in the tetrahedron,
Find the point of intersection between the plane and the triangle.
Store intersection points

After this, I have no idea how to proceed.

Can anyone suggest?

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