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Open AccessArticle

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.
Algorithms 2018, 11(7), 104;
Received: 5 June 2018 / Revised: 2 July 2018 / Accepted: 10 July 2018 / Published: 12 July 2018
PDF [662 KB, uploaded 12 July 2018]


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

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

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