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Simple mesh cutting algorithm that works on simple 3d manifold objects with genus 0

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A proof-of-concept Unity project for a mesh cutting algorithm. This is a simple implementation of an algorithm that splits in 2 any 3d manifold objects with genus 0. The split is done using a plane defined by the line drawn by the user and a depth in the same direction as the camera facing forward (i.e. when we draw a line, we don't see the generated plane since it's perfectly aligned with the camera and the line)

For each object tagged as *sliceable*:

We create 2 new meshes : a

*positive*mesh, which is on the positive side of the slice plane, and a*negative*mesh, which is on the other side.We go through each triangle of the mesh and, if it intersects the plane, we separate it into 3 triangles : 2 on the bigger side of the cut and 1 on the other side (we assume that it can't be cut perfectly in 2 triangles). If the triangle doesn't intersect with the plane, we simply store it in its respective mesh (positive or negative). We also keep a list of the newly created vertices, which will all lie on the boundary of the meshes.

We then create new triangles to form the boundary face (the new face generated by the cut). There is currently 2 different ways of generating the boundary face (generating a center vertex, or creating triangles fans by iterating through sorted pairs of vertices), but both of them works mostly only for a convex polygon.

Finally we create new objects for the new meshes and push them apart by a small value (indicated by the

*separation*property in the MouseSlice script)

Here are a few examples of simple shapes being cut.

| Cylinder | Refractive Sphere | Toonlit Suzanne | |---|---|---| | | | |

Note
* The material used for the sphere is *GlassRefractive* from Unity's Standard Assets
* The material used for Suzanne monkey is *ToonLit* from Unity's Standard Assets
* Those materials are used in the project's scenes, but are not included in this repo. If you want to experiment with them, import the following folders from the Standard Assets:
* Effects/GlassRefraction
* Effects/ToonShading
* Prototyping/Materials
* Prototyping/Textures

Here are some of the things that could be worked on or improved:

Use a new submesh to add a sliced surface so that we can set a separate material for it.

Smooth-shading on the sliced boundary is not preserved since we compute

Handling cuts on manifold objects of genus 1 and above. This would mostly imply detecting the number of boundaries made by cutting the object and associating vertices with their respective boundaries;

Handling non-convex sliced polygons on the surface generated by the slice. The algorithm used right now works mostly for convex polygons. Using a better triangulation algorithm could help (e.g. ear-clipping triangulation);

Optimize the cutting algorithm. It could be interesting to treat triangles as part of a face, such that when we cut through a face, we could recompute triangles based on the face's shape so that we get an efficient number of triangles. This would also help generate better boundaries;

Using Unity's Job System to parallelize the cutting process (since the algorithm is relatively slow);