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RESEARCH PAPERS

Tight Cocone: A Water-tight Surface Reconstructor

[+] Author and Article Information
Tamal K. Dey, Samrat Goswami

Department of Computer and Information Sciences, Ohio State University, Columbus, OH 43210

J. Comput. Inf. Sci. Eng 3(4), 302-307 (Dec 24, 2003) (6 pages) doi:10.1115/1.1633278 History: Received July 01, 2003; Revised October 01, 2003; Online December 24, 2003
Copyright © 2003 by ASME
Topics: Algorithms , Water
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Figures

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Performance of TIGHT COCONE with increasing noise. Reconstructed smooth surface (left). Reconstructed surface when the points are perturbed slightly (middle). No surface is reconstructed when the perturbation is increased further (left).
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A Voronoi cell Vp is elongated along the normal np. The pole vector p+−p approximates np. The cocone Cp is the region in Vp between the two cones at p (right).
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The left column shows the preliminary surface with COCONE . The second and the third columns highlight the holes in the undersampled region bordered by the dark shaded triangles.
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The umbrella of p HAS THREE TRIANGLES pqr,prs AND pqs. THIS UMBRELLA SEPARATES THE THE TETRAHEDRA INCIDENT TO p INTO TWO CLUSTERS, THE UPPER CLUSTER {absp,asqp,abpq,bqrp,brsp} AND THE LOWER CLUSTER {cqrp,csrp,cqsp}. SUPPOSE THE WALK ENTERED p WITH THE PAIR (p,bprs). THE RIGHT PICTURE SHOWS THAT THE UNEXPLORED POINT q HAS AN UMBRELLA. THEREFORE, THE PAIR (q,bprq) IS ENTERED INTO THE STACK SINCE q is a good and unexplored point.
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The four vertices marked with dark circles border a hole. The poor tetrahedron with this four vertices is marked in. The sharp tip p of the long tetrahedron is a good point which marks it out. When this tetrahedron is peeled, the triangle opposite to p fills the hole partially. The other triangle of the hole also gets into the output by a similar peeling.
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The boundary of the union of peeled tetrahedra as peeling process progresses.
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Results of TIGHT COCONE . Second column shows the holes in the preliminary surface while the third column shows how they are filled. Triangles bordering the holes are shaded darker.

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