Meshing genus-1 point clouds using discrete one-forms

Geetika Tewari; Craig Gotsman; Steven J. Gortler

doi:10.1016/j.cag.2006.08.019

Meshing genus-1 point clouds using discrete one-forms

Geetika Tewari, Craig Gotsman, Steven J. Gortler

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

We present an algorithm to mesh point clouds sampled from a closed manifold surface of genus 1. The method relies on a doubly periodic global parameterization of the point cloud to the plane, so no segmentation of the point cloud is required. Based on some recent techniques for parameterizing higher genus meshes, when some mild conditions on the sampling density are satisfied, the algorithm generates a closed toroidal manifold which interpolates the input and is geometrically similar to the sampled surface.

Original language	English (US)
Pages (from-to)	917-926
Number of pages	10
Journal	Computers and Graphics (Pergamon)
Volume	30
Issue number	6
DOIs	https://doi.org/10.1016/j.cag.2006.08.019
State	Published - Dec 2006
Externally published	Yes

All Science Journal Classification (ASJC) codes

Software
Signal Processing
General Engineering
Human-Computer Interaction
Computer Vision and Pattern Recognition
Computer Graphics and Computer-Aided Design

Keywords

Mesh generation
Parameterization
Point cloud
Reverse engineering
Surface reconstruction
Torus

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10.1016/j.cag.2006.08.019

Cite this

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title = "Meshing genus-1 point clouds using discrete one-forms",

abstract = "We present an algorithm to mesh point clouds sampled from a closed manifold surface of genus 1. The method relies on a doubly periodic global parameterization of the point cloud to the plane, so no segmentation of the point cloud is required. Based on some recent techniques for parameterizing higher genus meshes, when some mild conditions on the sampling density are satisfied, the algorithm generates a closed toroidal manifold which interpolates the input and is geometrically similar to the sampled surface.",

keywords = "Mesh generation, Parameterization, Point cloud, Reverse engineering, Surface reconstruction, Torus",

author = "Geetika Tewari and Craig Gotsman and Gortler, {Steven J.}",

note = "Funding Information: Thanks to Dimitri Michailis for providing the software to compute the MCB. C. Gotsman's work was partially supported by European FP6 IST NoE project 506766 (AIM@SHAPE).",

year = "2006",

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AU - Tewari, Geetika

AU - Gotsman, Craig

AU - Gortler, Steven J.

N1 - Funding Information: Thanks to Dimitri Michailis for providing the software to compute the MCB. C. Gotsman's work was partially supported by European FP6 IST NoE project 506766 (AIM@SHAPE).

PY - 2006/12

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N2 - We present an algorithm to mesh point clouds sampled from a closed manifold surface of genus 1. The method relies on a doubly periodic global parameterization of the point cloud to the plane, so no segmentation of the point cloud is required. Based on some recent techniques for parameterizing higher genus meshes, when some mild conditions on the sampling density are satisfied, the algorithm generates a closed toroidal manifold which interpolates the input and is geometrically similar to the sampled surface.

AB - We present an algorithm to mesh point clouds sampled from a closed manifold surface of genus 1. The method relies on a doubly periodic global parameterization of the point cloud to the plane, so no segmentation of the point cloud is required. Based on some recent techniques for parameterizing higher genus meshes, when some mild conditions on the sampling density are satisfied, the algorithm generates a closed toroidal manifold which interpolates the input and is geometrically similar to the sampled surface.

KW - Mesh generation

KW - Parameterization

KW - Point cloud

KW - Reverse engineering

KW - Surface reconstruction

KW - Torus

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JO - Computers and Graphics (Pergamon)

JF - Computers and Graphics (Pergamon)

IS - 6

ER -

Meshing genus-1 point clouds using discrete one-forms

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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