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Space carving of tetrahedra

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I have been reading this paper http://openaccess.thecvf.com/content_iccv_workshops_2013/W21/papers/Sugiura_3D_Surface_Extraction_2013_ICCV_paper.pdf

I have already generated a tetrahedra for my mesh and I would like to create a surface mesh. I can't understand the algorithm. From my understanding, there is a camera that generates rays towards to the points of the tetrahedral, and I get the intersections, but how would I eliminate the triangles that are inside or outside ? how would I detect inside or outside polygons ?

Would someone give a pseudo code of the algorithm ?

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