Decimating Samples for Mesh Simplification

Surface Reconstruction A sample and PL approximation

Sample Decimation Original 40K points = 0.33 12K points = 0.4

Local feature size and sampling Medial axis Local feature size f(p) -sampling   d(p)/f(p)

Voronoi structures

Cocones Space spanned by vectors making angle  /8 with horizontal Compute cocones Filter triangles whose duals intersect cocones Extract manifold

Cocones, radius and height cocones:C(p,,v) space by vectors making  /2 -  with a vector v. radius r(p): radius of cocone height h(p): min distance to the poles

Decimate

Cocone Lemma

Guarantees

Foot  0.4 2046 points Original 20021 points  0.33 2714 points

Foot  0.4 2046 points  0.33 2714 points  0.25 4116 points

Bunny  0.4 7K points  0.33 11K points Original 35K points

Bunny  0.4 7K points  0.33 11K points Original 35K points

Experimental Data

Conclusions Introduced a measure radius/height ratio for skininess of Voronoi cells We have used the radius/height ratio for sample decimation Used it for boundary detection (SOCG01) What about decimating supersize data (PVG01) Can we use it to eliminate noise? www.cis.ohio-state.edu/~tamaldey 543,652 points 143 -> 28 min 3.5 million points Unfin-> 198 min