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I want to calculate the two points of a 3D triangle that have a specified Z coordinate. I guess the way to do this would be to somehow create a plane which is perfectly flat with my given Z coordinate and then calculate where the triangle intersects with it (or is this wrong).
If you know how to do this in any way please help. I have searched for but have not really found anything that seems to work.
Here is a method that I hope is intuitive enough, assuming z0 is the Z value of your intersection plane:
L(A.z - z0) * (B.z - z0) <= 0, it means AB intersects the plane:
u = (B.z - z0) / (B.z - A.z)B + u * (A - B) to list L(A.z - z0) * (C.z - z0) <= 0:
u = (C.z - z0) / (C.z - A.z), add point C + u * (A - C) to list L(B.z - z0) * (C.z - z0) <= 0:
u = (C.z - z0) / (C.z - B.z), add point C + u * (B - C) to list LAt the end, if L contains two points, that's your segment; otherwise, either the triangle does not intersect or it's a degenerate case. Make sure you check for possible divisions by zero.
k consists in multiplying each of its x y and z components with k. Depending on the framework you use, there might already be a function or operator which does it for you. I assumed you wanted the intersection with the z = 0 plane but I’ll update my answer so it works with an arbitrary z0 value.
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Sep 20, 2013 at 20:14
You could just du a ray / plane intersection with two rays, after deciding how the triangle intersects with the plane (To intersect at all 1 point has to be on side A and two points on side B of the plane)
This is my standard 'way-over-the-top' ressource for intersections you can look at different implementations and pick the one best suiting your need.
I little less complex is this side, explaining what to do and providing a trianlge-ray algorithm in c (and a lot more under 'algorithms')
