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Decimating Samples for Mesh Simplification

This paper presents innovative methods for sample decimation in mesh simplification and surface reconstruction, focusing on Voronoi structures and cocone calculations. It discusses techniques for reducing point clouds from 40K to as low as 2K points while maintaining integral features. Key concepts include local feature size, $epsilon$-sampling, and the utilization of a radius-to-height ratio for boundary detection. Experimental data demonstrates effective applications, including noise elimination and boundary detection in large datasets. This research contributes significantly to computational geometry and geometric modeling.

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Decimating Samples for Mesh Simplification

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  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

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