Decimating Samples for Mesh Simplification

Surface Reconstruction

• A sample and PL approximation

Sample Decimation

Original40K points

= 0.48K points

= 0.3312K points

Local feature size and sampling

• Medial axis

• Local feature size f(p)

• -sampling

• d(p)/f(p)

Voronoi structures

Cocones

• Compute cocones

• Filter triangles whose duals intersect cocones

• Extract manifold

Space spanned by vectors making angle /8 with horizontal

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

Original20021 points

0.42046 points

0.332714 points

Foot

0.42046 points

0.332714 points

0.254116 points

Bunny

0.47K points

0.3311K points

Original35K points

Bunny

0.47K points

0.3311K points

Original35K 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 points143 -> 28 min

3.5 million pointsUnfin-> 198 min