Next Article in Journal
Distributed Combinatorial Maps for Parallel Mesh Processing
Previous Article in Journal
Solutions to the Sub-Optimality and Stability Issues of Recursive Pole and Zero Distribution Algorithms for the Approximation of Fractional Order Models
Article Menu

Export Article

Open AccessArticle
Algorithms 2018, 11(7), 104; https://doi.org/10.3390/a11070104

The Gradient and the Hessian of the Distance between Point and Triangle in 3D

Faculty of Engineering and Applied Science, Memorial University of Newfoundland, 40 Arctic Ave, St. John’s, NL A1B 3X7, Canada
*
Author to whom correspondence should be addressed.
Received: 5 June 2018 / Revised: 2 July 2018 / Accepted: 10 July 2018 / Published: 12 July 2018
View Full-Text   |   Download PDF [662 KB, uploaded 12 July 2018]   |  

Abstract

Computation of the distance between point and triangle in 3D is a common task in numerical analysis. The input values of the algorithm are coordinates of three points of the triangle and one point from which the distance is determined. An existing algorithm is extended to compute the gradient and the Hessian of that distance with respect to coordinates of involved points. Derivation of exact expressions for gradient and Hessian is presented, and numerical accuracy is evaluated for various cases. The algorithm has O(1) time and space complexity. The included open-source code may be used in applications where derivatives of point-triangle distance are required. View Full-Text
Keywords: point-triangle distance; gradient; Hessian point-triangle distance; gradient; Hessian
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Gribanov, I.; Taylor, R.; Sarracino, R. The Gradient and the Hessian of the Distance between Point and Triangle in 3D. Algorithms 2018, 11, 104.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Algorithms EISSN 1999-4893 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top