Direct Computing of Surface Curvatures for Point-Set Surfaces

Yang, Pinghai; Qian, Xiaoping

Direct Computing of Surface Curvatures for Point-Set Surfaces

Files

029-036.pdf (484.52 KB)

Date

2007

Authors

Yang, Pinghai
Qian, Xiaoping

Publisher

The Eurographics Association

Abstract

Accurate computing of the curvatures of a surface from its discrete form is of fundamental importance for many graphics and engineering applications. The moving least-squares (MLS) surface from Levin [Lev2003] and its variants have been successfully used to define point-set surfaces in a variety of point cloud data based modeling and rendering applications. This paper presents a set of analytical equations for direct computing of surface curvatures from pointset surfaces based on the explicit definition from [AK04a, AK04b]. Besides the Gaussian parameter involved in the MLS definition, these analytical equations allow us to conduct direct and exact differential geometric analysis on the point-set surfaces without specifying any subjective parameters. Our experimental validation on both synthetic and real point cloud data demonstrates that such direct computing from analytical equations provides a viable approach for surface curvature evaluation for unorganized point cloud data.

        @inproceedings{:10.2312/SPBG/SPBG07/029-036
,
booktitle = {Eurographics Symposium on Point-Based Graphics
},
editor = {M. Botsch and R. Pajarola and B. Chen and M. Zwicker
},
title = {{Direct Computing of Surface Curvatures for Point-Set Surfaces
}},
author = {Yang, Pinghai and 
Qian, Xiaoping
},
year = {2007
},
publisher = {The Eurographics Association
},
ISSN = {1811-7813
},
ISBN = {978-3-905673-51-7
},
DOI = {/10.2312/SPBG/SPBG07/029-036
}
}