Sample Shuffling for Quality Hierarchic Surface Meshing
Sample Shuffling for Quality Hierarchic Surface Meshing
Surface Meshing
Sample Decimation
Surface Reconstruction
Foot data
No decimation
• Medial axis
• Local feature size f(p)
• -sampling
• d(p)/f(p)
Local feature size and samplingAmenta-Bern-Eppstein
Reconstruction
• Functional approach• Tangent plane [HDeDDMS92]
• Natural Neighbors [BC00]
• Voronoi/Delaunay filtering
• Alpha shapes [EM94]• Crust [AB98]
• Cocone [ACDL00]
Cocones
• Compute cocones
• Filter triangles whose duals intersect cocones
• Extract manifold
Space spanned by vectors making angle /8 with horizontal
Approximating density• Need an approximation to Restricted Voronoi on S
• Need an approximation to local feature sizes
Radius and height
• radius r(p): distance from p to pº.
• height h(p): min distance to the poles
• C(p,space spanned by vectors making angles <= with horizontal.
• pº : point at max distance from p
Deletion and Insertion
• Vertex p is deleted if there is nearby sample point
p)/h(p) < '.
• Insert p° if deletion of p destroys density
r(p)/h(p) >
Shuffling
Reconstruction (Dey-Giesen)
Cocone(P,
Compute VP;
for each pP
if pB compute T of triangles with
duals intersecting C(p endif
endfor; Extract manifold;
end
B:= Boundary(P)
Main Theorem
Theorem 1: For sufficiently small an sample P of S can be shuffled to Q s.t. a surface mesh M can be computed from Q with
• M is homeomorphic to S
• |M-S| = O(f(p) for some p on S
• each triangle has aspect ratio O(
Synthetic data (Parbol)
No decimation,
8K pts
pts
pts
Synthetic data (Hyperbol)
No decimation,
8K pts
Synthetic data (Parcyl)
No decimation,
6K pts
1K pts
0.7K pts
Experimental Data
Rocker data
No decimation,
40K pts
pts
pts
Rocker data
pts
pts
Experimental data
Hip data
No decim,
265k pts
pts
pts
126K pts
pts
Conclusions
• Introduced sample shuffling
• Achieves sample decimation retaining features
• Achieves quality meshing
• What about both coarsening and refining?
• How to take care of the boundaries?
• How to take care of noise?
• Softwares:
www.cis.ohio-state.edu/~tamaldey/cocone.html