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

摘要

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.