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):
- Take a quad.
- Triangulate it normally - add a diagonal edge.
- Add second, flipped diagonal edge.
- Connect midpoints of two diagonal edges.
- Remove triangulation edges, save only the lastly created edge.
- Connect midpoint of the remaining edge with quad corners.
- 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)