how to fix inconsistent triangles when slicing a box by planes

Question

My group had developed a Blender based addon - BlenderPhotonics - which can be used as a front-end for 3D tetrahedral mesh generation (by calling our Iso2Mesh toolbox in the backend). The details of this work can be found in our paper: https://doi.org/10.1117/1.JBO.27.8.083014

Our workflow involves creating complex models using Blender's built-in functions, and then, joining all mesh objects and perform intersection. The tetrahedral mesh generator is extremely sensitive and refuses to mesh any triangular surfaces that 1) are not water-tight, 2) have self-intersecting triangles, and 3) contain inconsistent triangles (such as vertices ended up in the middle of any edge or faces).

I found that Blender 2.9+ is quite good at resolving intersections with the Exact solver enabled. However, I have struggled to slice box objects with plane objects to create a multi-layered structure.

Here is an example. The scene contains a box, a plane of matching size, and a cone. My goal is to create tetrahedral mesh from this scene.

By performing 1) converting all objects to mesh, 2) join all triangular meshes to intersect, I got the attached intersected mesh. You can see, Blender did a good job for both top and bottom planes, but the intersection of the middle-plane creates inconsistent triangles - the 4 highlighted vertices are located in the middle of the edge of the triangles on the bounding box. This makes my tetrahedral mesh generator unhappy.

My question is - why Blender inserts these 4 nodes in the first place? is there an option for Blender to refine all connected triangles if it decides to insert a new node in the middle of any edge? or, even better, not to insert these nodes at all (like the top/bottom planes)?

any suggestion on how to consistently mesh such cut structure would be appreciated!

Update: just to give some idea on what is the expected "consistent triangular mesh", here is a manually edited image. What are missing are these 8 red-colored edges. With these edges, there will be no vertex located in the middle of any edge.

The .blend file before joining is attached here

Update 2: it looks like this behavior is also version dependent - the above screenshots were taken on Blender 3.0.1 (Ubuntu 22.04), but if I use Blender 2.92, the generated tessellation is valid - see below screenshot . As you can see, only two nodes were added, but both nodes were properly tessellated.

Answer 1

ok, I am going to answer my own question here.

After testing various blender versions, now I see that this invalid triangulation issue is only a brief regression introduced in Blender 3.0.x, and it does not show up in either older (2.92) or newer (3.4.1) versions.

Here is a comparison of 3 blender versions:

• Top-left: 3.0.1: showing incorrect triangulation (the 4 rogue nodes were selected)
• Top-right: 3.4.1: showing correct triangulation
• Bottom-right: 2.92.0: showing correct triangulation

Both 3.0.1 and 3.4.1 were installed on Ubuntu 22.04 Linux. 2.92 were tested on Ubuntu 18.04 and Windows.

To reproduce this, here are the steps:

1. start a new general scene with the default cube
2. add a plane object
3. select both, right-click, select "join"
4. switch to "Edit mode", select Face->Intersect (Knife)-> select self-intersecting in the option dialog
5. again in Edit mode, select Face->Triangulation