Hybrid Second-Order Iterative Algorithm for Orthogonal Projection onto a Parametric Surface

Hybrid Second-Order Iterative Algorithm for Orthogonal Projection onto a Parametric Surface

To compute the minimum distance between a point and a parametric surface, three well-known first-order algorithms have been proposed by Hartmann (1999), Hoschek, et al. (1993) and Hu, et al. (2000) (hereafter, the First-Order method). In this paper, we prove the method’s first-order convergence and its independence of the initial value. We also give some numerical examples to illustrate its fas...

A second order algorithm for orthogonal projection onto curves and surfaces

In this paper we analyze an algorithm which solves the point projection and the “inversion” problems for parametric curves and surfaces. It consists of a geometric second order iteration which converges faster than existing first order methods, and whose sensitivity to the choice of initial values is small. Applications include the ICP algorithm for shape registration.

Convergence Analysis on a Second Order Algorithm for Orthogonal Projection onto Curves

Regarding the point projection and inversion problem, a classical algorithm for orthogonal projection onto curves and surfaces has been presented by Hu and Wallner (2005). The objective of this paper is to give a convergence analysis of the projection algorithm. On the point projection problem, we give a formal proof that it is second order convergent and independent of the initial value to pro...

Algorithm for orthogonal projection of parametric curves onto B-spline surfaces

This paper proposes an algorithm for calculating the orthogonal projection of parametric curves onto B-spline surfaces. It consists of a second order tracing method with which we construct a polyline to approximate the pre-image curve of the orthogonal projection curve in the parametric domain of the base surface. The final 3D approximate curve is obtained by mapping the approximate polyline on...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations