A conception for mesh triangulation

SketchUp
,
1

Hi!
For some time I’ve been thinking about a way for creating smoother meshes.
Always when you create a surface curved in 2 directions you have to apply triangulation which is the only way to represent such a surface in mesh modelling. Each quad is always divided by two triangles with one diagonal line. That fact involves “skewing”, sometimes very unpleasantly looking. I mean, the surface is alternately convex and concave when you “walk” it. When the surface casts shadows on itself, the shadow boundary is awfully jagged. So I came up with an algorithm that could be transferred into a plugin (by someone familiar with scripting, that’s not me):

  1. Take a quad.
  2. Triangulate it normally - add a diagonal edge.
  3. Add second, flipped diagonal edge.
  4. Connect midpoints of two diagonal edges.
  5. Remove triangulation edges, save only the lastly created edge.
  6. Connect midpoint of the remaining edge with quad corners.
  7. Remove the guide edge, save the four lastly created edges.

These steps are illustrated in the attached model (you have to move to scene: “how I achieve this”)

These are steps to achieve it manually, but certainly no one would do this manually, as you usually have lots of quads. That’s why I suggest: this could be a plugin.

As you can see in the “Usage” scene, the “double triangulated” grid is far less jagged. The number of edges doubles, that’s true. But if you used classic method (only 1 diagonal line per quad) and just doubled interpolation, the result wouldn’t be as smooth.

I believe it could be helpful e.g. with modelling terrain. When a ridge is formed more-less perpendicularly to quad’s diagonals in grid, it looks very bad: (see scenes: “Usage” and “Usage comparison”). The other mesh uses my method: “2 diagonals per quad”.

What do you think? Is it worth attention? I have never seen such way of face triangulation in 3d graphics so I dare to call it my own method, although possibly some people were already thinkig similar.

double 3angulation - koncepcja na forum.skp (919.1 KB)

2

Would this not also double the amount of faces generated/calculated in the mesh?

3

Yes, it would. But, to my perception, it’s still more visually profitable than just increasing precision with standard method.

4

With this aproach quads would indeed be smoother, but there would probably still be visible edges that aren’t as smooth between quads.

Maybe SUbD is what you are looking for.

5

Depends on the output really, in my case I would never want to show any triangulation in a presentation model, render or illustration. The goal as I see it for ‘visually profitable’ is smoothness in the output (and for the sake of my computer, as low triangulation as possible while providing the best result).

6

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