<p>This is a known research problem in Computer Graphics to find the Boolean operations on polygonal meshes. You can take a look at some related papers at:</p>

<p><a href="http://arxiv.org/pdf/1308.4434.pdf" rel="nofollow">http://arxiv.org/pdf/1308.4434.pdf</a></p>

<p><a href="http://www.tandfonline.com/doi/abs/10.3722/cadaps.2010.405-415?journalCode=tcad20" rel="nofollow">http://www.tandfonline.com/doi/abs/10.3722/cadaps.2010.405-415?journalCode=tcad20</a>.</p>

<p>(You can find older works by taking a look at the cited papers)</p>

<p>In general, polygonal meshes are not very effective at Boolean operations. Boolean operations can be easily addressed in implicit modeling in which an object is represented by a function. Later, the object can be converted to a mesh by marching cubes (for example).</p>
How to Combine Polyhedra?
<p>Suppose I have a 2 Polyhedrons, partially overlapping in space. Each is defined by a list of connected Polygons, which in turn are defined by lists of line segments, (which are defined by 2 points). Is there a simple algorithm for creating the polyhedron which is the union of the boundary of these polyhedrons, but removes all the interior pieces?</p>

<p>Likewise after this, I'll be implementing a subtract, and Intersection Method.</p>

<p>I'm contributing to this Open Source Library. Source Code:
<a href="https://bitbucket.org/Clearspan/geometry-class-library/src/34a2ab5031879d051abb855a828368e397b4f5b6/GeometryClassLibrary/Solids/Polyhedron.cs?at=master" rel="nofollow">https://bitbucket.org/Clearspan/geometry-class-library/src/34a2ab5031879d051abb855a828368e397b4f5b6/GeometryClassLibrary/Solids/Polyhedron.cs?at=master</a></p>