Dilating a closed mesh in xy, but not z

[pentacular]

Hello, I'm trying to dilate a closed mesh in the x and y dimensions, without affecting z.

The implicit distance function approach here looks almost right
https://github.com/CGAL/cgal/blob/master/Polyhedron/demo/Polyhedron/Plugins/Surface_mesh/Offset_meshing_plugin.cpp

But I can't figure out a reasonable way to find the nearest point on the mesh while constraining z.

Any ideas? :)

[stla]

You mean an homothety? It's an affine transformation. CGAL allows to apply an affine transformation to a mesh, one just has to enter the matrix.

[pentacular]

No, mesh dilation isn't a homothety.

In mesh dilation structures become thicker while remaining stationary.

[stla]

That does not define a dilation (which is synonym of homothety in geometry).

[pentacular]

Yes, we could convert to nef polyhedron, apply a convex decomposition, apply minkowski summing, and then fuse back together, and convert back again to Surface_mesh.

It's a bit on the convoluted and expensive side for my taste, but it's a possibility.

[stla]

Why a convex decomposition? I didn't decompose the torus for example.

Use my R package, straightforward ;-)

[pentacular]

Your R package won't be suitable for my use-case.

https://doc.cgal.org/latest/Minkowski_sum_3/group__PkgMinkowskiSum3Ref.html applies a convex decomposition to non-convex inputs, so unless you've re-implemented it, then it's happening behind the scenes.

[stla]

Ah yes, behind the scenes.

Why would there be a use-case for which my package would not be suitable? I'm curious to know more about that. My package is nothing but a wrapper of CGAL.

[pentacular]

Well, the uses cases not involving using R come to mind. :)

[pentacular]

I wonder if CGAL::Orthogonal_k_neighbor_search would be suitable for this:

https://doc.cgal.org/latest/Spatial_searching/classCGAL_1_1Orthogonal__k__neighbor__search.html

[sloriot]

Just thinking out loud: Say you want to modify the offset meshing function with a different distance function. What you could do, is given a query point, take the plane with normal (0,0,1)that contains the query point and compute the distance of that point to the intersection polygons (you can use Polygon_mesh_slicer). Then this should give something close to what you want (from what I understand).

[pentacular]

I think it would work, but wouldn't it be prohibitively expensive to generate slices for every z candidate generated to mesh the implicit function?