Decimating Samples for Mesh Simplification

1. Decimating Samples for Mesh Simplification

2. Surface Reconstruction • A sample and PL approximation

3. Sample Decimation Original 40K points • = 0.33 12K points • = 0.4 8K points

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

5. Voronoi structures

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

7. 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

8. Decimate

9. Cocone Lemma

10. Guarantees

11. Foot •  0.4 2046 points Original 20021 points •  0.33 2714 points

12. Foot •  0.4 2046 points •  0.33 2714 points •  0.25 4116 points

13. Bunny •  0.4 7K points •  0.33 11K points Original 35K points

14. Bunny •  0.4 7K points •  0.33 11K points Original 35K points

15. Experimental Data

16. 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