Projecting Points onto Planar Parametric Curves by Local Biarc Approximation

Song, Hai-Chuan; Shi, Kan-Le; Yong, Jun-Hai; Zhang, Sen

Projecting Points onto Planar Parametric Curves by Local Biarc Approximation

Files

031-036.pdf (3.77 MB)

Date

2014

Authors

Song, Hai-Chuan
Shi, Kan-Le
Yong, Jun-Hai
Zhang, Sen

Publisher

The Eurographics Association

Abstract

This paper proposes a geometric iteration algorithm for computing point projection and inversion on surfaces based on local biarc approximation. The iteration begins with initial estimation of the projection of the prescribed test point. For each iteration, we construct a 3D biarc on the original surface to locally approximate the original surface starting from the current projection point. Then we compute the projection point for the next iteration, as well as the parameter corresponding to it, by projecting the test point onto this biarc. The iterative process terminates when the projection point satisfies the required precision. Examples demonstrate that our algorithm converges faster and is less dependent on the choice of the initial value compared to the traditional geometric iteration algorithms based on single-point approximation.

        @inproceedings{:10.2312/pgs.20141248
,
booktitle = {Pacific Graphics Short Papers
},
editor = {John Keyser and Young J. Kim and Peter Wonka
},
title = {{Projecting Points onto Planar Parametric Curves by Local Biarc Approximation
}},
author = {Song, Hai-Chuan and 
Shi, Kan-Le and 
Yong, Jun-Hai and 
Zhang, Sen
},
year = {2014
},
publisher = {The Eurographics Association
},
ISBN = {978-3-905674-73-6
},
DOI = {/10.2312/pgs.20141248
}
}