This is a computer graphics question. We need the mesh to dilate its concave parts, while keeping its convex parts unchanged. The deformed mesh will enclose the original mesh, just like a convex hull.
THANKS!
There are many ways. For example: move all vertices that are NOT part of the convex hull to an arbitrary vertex that IS part of the convex hull.
But I suppose you want the resulting mesh not to intersect itself, and that you want the result to 'look good'?
I am not aware of existing software, and the more I think about how to implement it, the tougher it gets (e.g. concave parts that have convex islands in them that ARE part of the convex hull; tori).
Good luck!
Thank you Lambert. That's why I think it's tough. But your idea is a good hint to me. Maybe I could work out some kind of mapping between the mesh and the convex hull. THANKS!
I was thinking about something like :
FOR all non-convex-hull-patches DO
{
Label the vertices that are connected to a convex hull vertex with ONE
Label the non-labeled vertices that are connected to ONE with TWO
Label the non-labeled vertices that are connected to TWO with THREE
etc...
Map the labeled vertices to the convex hull using the label as a distance criterion to the rim (easier said than done!)
}
Note that the algorithm will fail with tori.
In my first answer, I said that "concave parts that have convex islands in them that ARE part of the convex hull" complicated the matter. In fact it does NOT: you can treat them as if they are also part of a non-convex-hull patch, and in the mapping phase, you know exactly where to put them because they keep their original position.
Thanks Lambert! Your idea is clearer than last time. Let me try it out.
Maybe I should first think better before I write a reply, but here I go again :-)
FOR all non-convex-hull-patches DO
{
Calculate the average of all current-convex-hull-rim-vertices
Initialize all current non-convex-hull-patch-vertices with that average
REPEAT UNTIL vertices hardly move anymore (some epsilon)
{
Move the non-convex-hull-patch-vertices to the average of it's neighbors
}
}
Not fast but easy to implement.
You still need to map the vertices to the convex hull...do you have any ideas on that?
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