## A Simple Algorithm for Homeomorphic Surface Reconstruction (2000)

Venue: | International Journal of Computational Geometry and Applications |

Citations: | 211 - 29 self |

### BibTeX

@INPROCEEDINGS{Amenta00asimple,

author = {Nina Amenta and Sunghee Choi and Tamal K. Dey and Naveen Leekha},

title = {A Simple Algorithm for Homeomorphic Surface Reconstruction},

booktitle = {International Journal of Computational Geometry and Applications},

year = {2000},

pages = {213--222}

}

### Years of Citing Articles

### OpenURL

### Abstract

The problem of computing a piecewise linear approximation to a surface from a set of sample points is important in solid modeling, computer graphics and computer vision. A recent algorithm [1] using the Voronoi diagram of the sample points gave a guarantee on the distance of the output surface from the original sampled surface assuming the sample was `suciently dense'. We give a similar algorithm, simplifying the computation and the proof of the geometric guarantee. In addition, we guarantee that our output surface is homeomorphic to the original surface; to our knowledge this is the rst such topological guarantee for this problem. 1 Introduction A number of applications in CAD, computer graphics, computer vision and mathematical modeling involve the computation of a piecewise lin- Dept. of Computer Science, U. of Texas, Austin TX 78712. e-mail: amenta@cs.utexas.edu, supported by NSF grant CCR-9731977 y Dept. of Computer Science, U. of Texas, Austin, TX 78712. e-mail: sunghe...

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