How to compute the boundary of the intersection of a plane with an 3d object composed of tetrahedra?

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Nina 2013-3-5

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Hallo,

I want to compute the boundary of the intersection of a 3d odject composed of tetrahedra with a plane in 3d space. The tetrahedra can lie inside another and don't have to be connected face-to-face. If the tetrahedra are only connectetd face-to-face it is easy to detect the surface (triangle faces which belongs only to one tetrahedron). All informations about the tetrahedra are the four vertices.

I can compute the intersection points with the tetrahedra and the plane. Now my problem is to find/detect only these intersection points which lying on the boundary/surface of the object.

Has somebody an idea? Or how I can detect the surface of the object? (If I can compute the surface the intersection with the plane gets easier)

Anin

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Jan 2013-3-5

You did not explain, how the objects are defined. If you have e.g. a set of voxels, or the positions of the corners.Why does it matter, if the tetrahedron lies within another? Does this change the intersection? And what would it change if the focussed object is connected face-to-face to any other object?

Please post additional explanations by editing the question, such that all required information is found in one block, not distributed over different sections. Thanks.

Nina 2013-3-5

I edit my question and I hope it is now more understandable

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Answer 1

Jan 2013-3-5

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If you have the corners of the tetrahedron, it is easy to get the equations for the edges. Then the intersection of these lines and the plane can be found. And the result will be a closed polygone.

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Nina 2013-3-5

This is right for one tetrahedron but I have more tetrahedra which form a object. If I compute the intersection with a plane I get a few intersection points in the plane. Now I want to know which of these points are one the boundary of the object

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