Abstract
A new orthogonal projection method for computing the minimum distance between a point and a spatial parametric curve is presented. It consists of a geometric iteration which converges faster than the existing Newton’s method, and it is insensitive to the choice of initial values. We prove that projecting a point onto a spatial parametric curve under the method is globally second-order convergence.
Highlights
In this paper, we discuss how to compute the minimum distance between a point and a spatial parametric curve and return the nearest point on the curve as well as its corresponding parameter, which is called the point projection problem of a spatial parametric curve
We have proved that projecting a point onto a spatial parametric curve is globally second-order convergence
In order to improve the efficiency of the geometric iteration, we present a second-order iterative method to compute the minimum distance between the test point p and a spatial parametric curve c(t)
Summary
We discuss how to compute the minimum distance between a point and a spatial parametric curve and return the nearest point on the curve as well as its corresponding parameter, which is called the point projection problem (the point inversion problem) of a spatial parametric curve. It is an interesting problem due to its importance in geometric modeling, computer graphics and computer vision [1] Both projection and inversion are essential for the interactively selecting curves [1,2], the curve fitting problem [1,2], and the reconstructing curves problem [3–5]. It is a key issue in the ICP (iterative closest point) algorithm for shape registration and rendering of solid models with boundary representation and projecting of a spatial curve onto a surface for curve surface design [6]. The main objective of this paper is to analyze a geometric iterative method, which solves the projection and has second-order approximation properties. It uses only the second-order information of the curve under consideration. Numerical examples show the efficiency and the robustness of the new method
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
