How to cut a 3D object using a plane and deleting the part above the plane, but creating new faces/vertices based on the points to ensure that the geometry below the cut is maintained?

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I am working with an stl file (faces, vertices, normals, etc) and have been able to establish a plane, find the coordinates of the points where the plane intersects the edges of the 3D objects, but am not able to modify the the stl file in such a way that I keep all the geometry intact below the plane cut but remove the geometry above the plane cut.
More clarification using an analogy: Imagine you had a donut in real life that you sliced using a knife to create 2 crescent shaped halves. Now I am trying to solve the same problem using matlab and an stl file. I have the donut, I have the knife (the plane), I know all the new vertices that should be formed when the knife cuts, I am just not able to cut it in such a way that the solid part of the donut is still present and the hole (well a semicircular hole after cutting) is also present.
Is there someone who has expertise in this area and could help me out please :) Thank you!

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Accepted Answer

John D'Errico
John D'Errico on 30 May 2019
Edited: John D'Errico on 30 May 2019
Pretty simple really. Just the execution that takes some effort.
  1. Identify any simplex that has all vertices above or below the cutting plane. Keep those uncut that are in the region of interest. Discard those that are all outside. The test to see if a vertex is above or below the cutting plane is as simple as a dot product, so just a matrix*vector multiply for all vertices at once.
  2. All simplexes that remain have at least one vertex above, and one below the cutting plane. Operate on these simplexes one at a time.
  3. Retain any vertices that are entirely in the region of interest, or on the plane itself. For any edges of the simplex, locate all edges that cross the cutting plane. Using simple linear interpolation, find the point of crossing.
  4. Combine the set of vertices that are below the cutting plane with those that lie in the cutting plane from this simplex.
  5. Tessellate that set, append the set of simplexes created to those that lie entirely below the cutting plane.
This operation is not that difficult. As I said, it just takes some code.

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