Current Status of the Polyhedra.jl project

[wytchblade]

Is this project still actively being developed? I would be interested in getting in touch with the main developers as I have some capacity to contribute!

[blegat]

Hi @wytchblade , I'm maintaining it but as I am also maintaining many other packages, I don't have so much time to work on new features. Help would be much welcome! What would you be interested in working on ?
At the moment, we are working on incidence information, see JuliaPolyhedra/CDDLib.jl#101

[wytchblade]

Hi @wytchblade , I'm maintaining it but as I am also maintaining many other packages, I don't have so much time to work on new features. Help would be much welcome! What would you be interested in working on ? At the moment, we are working on incidence information, see JuliaPolyhedra/CDDLib.jl#101

Hello Dr. Blegat! SO far, I've managed to get a hold of the repo and fork it so I can look at the design. The documentation on the gihub.io site is fantastic and I will be reading through that extensively. Can you recommend some reading material that would be useful for learning the topic in more detail?

I tested out a few things in julia and was able to get julia to communicate to blender over jupyter kernel, so I'm particularly interested in experimenting with how polyhedra are rendered. Thank you very much in advance for your efforts in maintaining this plugin!

[blegat]

It's all in here: https://github.com/JuliaPolyhedra/Polyhedra.jl/blob/master/ext/PolyhedraGeometryBasicsExt.jl
The idea is as follows: We need to decompose the surface of a 3D polyhedron into triangles and we then pass the triangles to GLMakie which does the rendering. For this decomposition, we do it as follows:

• The polyhedra library (CDD, QHull, ...) takes care of computing all the vertices (V-rep) and facets (H-rep)
• For each face, we take the list of incident vertices (if the library has the list (like Add incidence field, implement getincidence CDDLib.jl#101), we can directly get it, or we need to fallback to checking for each vertex if it is incident which is slower).
• Given this list of vertices in the plane, we are back to a planar convex hull problem.
• We sort the vertices of this planar polytope in clockwise (or counter clockwise, I don't remember) and that gives us a way to create these non-overlapping triangles that cover the whole facet.

All this is very specific to convex polyhedra, so this part done by Polyhedra.jl is quite different from what Blender does. Blender does the rendering of the triangles, which is what Makie does. By the way, Makie is implementing a ray tracer which will bring it closer to Blender ;)

[wytchblade]

Thank you @blegat ! Could you recommend some learning material that might clarify the decomposition in the first step ( I assume you are performing a conversion from H-rep (a set of inequalities using the Halfspace class) to V-rep?

This process seems quite different from a Delaunay triangulation, and I was wondering if you might be able to direct me towards some information that outlines the algorithm. I'm looking for more information on how a decomposed surface of the polyhedron into triangles gets rendered by Makie? Do you also have to keep track of the interior angles?

Thank you very much in advance for your clarification. I'm taking some time to read through the documentation at this point as I'm looking to make a small implementation for blender scene that tests for inclusivity using the H-Rep!