CGAL users discussion list

[Zohar <>]

Hi,

Related to the problem of motion planning, I was wondering how does the the
computation geometry community address the following problem. I'm looking
for a way to calculate the distance from a point on the surface of a
triangular mesh to a point inside the mesh volume.

Currently I tried using

(Lipman09) Interior Distance Using Barycentric Coordinates

in the configuration of calculating geodesic distances over the surface, and
interpolating them inside using 3D mean value coordinates (mvc).

Currently I consider ways to improve the accuracy, and two more ideas that I
had were:

1. Use a 3D fast marching method (FMM) as suggested by

(Bronstein07) Weighted Distance Maps Computation on Parametric
Three-Dimensional Manifolds

which requires to tetrahedralize the mesh, preferably with acute tets:

http://cgal-discuss.949826.n4.nabble.com/Mesh-generation-and-acute-tets-td4655393.html

2. Tetrahedralize the mesh, find the diffusion distances between the
vertices using eigen value decomposition of the 3D laplacian, convert the
diffusion distances to geodesic distances, and finally interpolate the
distances to the inside of the tets using barycentric coordinates.


What do you think?






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