Approximating and Intersecting Surfaces from Points

Adamson, Anders; Alexa, Marc

Approximating and Intersecting Surfaces from Points

Files

230-239.pdf (1.2 MB)

Date

2003

Authors

Adamson, Anders
Alexa, Marc

Publisher

The Eurographics Association

Abstract

Point sets become an increasingly popular shape representation. Most shape processing and rendering tasks require the approximation of a continuous surface from the point data. We present a surface approximation that is motivated by an efficient iterative ray intersection computation. On each point on a ray, a local normal direction is estimated as the direction of smallest weighted co-variances of the points. The normal direction is used to build a local polynomial approximation to the surface, which is then intersected with the ray. The distance to the polynomials essentially defines a distance field, whose zero-set is computed by repeated ray intersection. Requiring the distance field to be smooth leads to an intuitive and natural sampling criterion, namely, that normals derived from the weighted co-variances are well defined in a tubular neighborhood of the surface. For certain, well-chosen weight functions we can show that well-sampled surfaces lead to smooth distance fields with non-zero gradients and, thus, the surface is a continuously differentiable manifold. We detail spatial data structures and efficient algorithms to compute ray-surface intersections for fast ray casting and ray tracing of the surface.

        @inproceedings{:10.2312/SGP/SGP03/230-239
,
booktitle = {Eurographics Symposium on Geometry Processing
},
editor = {Leif Kobbelt and Peter Schroeder and Hugues Hoppe
},
title = {{Approximating and Intersecting Surfaces from Points
}},
author = {Adamson, Anders and 
Alexa, Marc
},
year = {2003
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-06-1
},
DOI = {/10.2312/SGP/SGP03/230-239
}
}