A second-order algorithm for curve orthogonal projection onto parametric surface

Abstract

Repeated use of point projection to find the projection of a curve on a surface is rather inefficient as the iteration procedures in point projection is typically slow. A novel curve projection scheme is proposed for computing the orthogonal projection of a progenitor curve onto a parametric surface. Under this scheme, the projection curve is parameterized using the parameter of the progenitor curve. Differential geometric characteristics of the projection curve are analysed. A marching method with error adjustment is used to calculate the projection curve. Several examples are presented and comparisons are made to demonstrate the effectiveness of the proposed scheme.

Keywords:

• curve projection
• parametric surface
• Taylor approximation
• marching
• error adjustment

2010 AMS Subject Classifications:

• 65D10
• 34K07
• 53A05
• 65Gxx
• 30K05

Acknowledgements

We would like to thank the anonymous reviewers for their valuable comments. This work is supported by National Natural Science Foundation of China (Nos. 51075167, 61070235, 50805058 and 51075039).