Curve and surface approximation of 3D point clouds

Authored by

Johannes Bureick, Hans Neuner, Corinna Harmening, Ingo Neumann

Abstract

In many geodetic applications and tasks it is necessary to describe a 3D-point cloud by continuous mathematical functions in order to utilise them for further processing steps, especially for deformation analysis. Depending on the complexity of the object, captured by the 3D-point cloud, and the desired quality of the approximation, different functions can be used. This paper describes the most important mathematical (free-form) surfaces from polynomial functions to Bezier and B-Spline functions to Non-uniform rational B-Splines (NURBS) in this context. Beside the mathematical basics of the functions, the approximation process for curves and surfaces and the crucial modification parameters, especially the model selection, are described.

Details

Organisation(s): Geodetic Institute
External Organisation(s): TU Wien (TUW)
Type: Article
Journal: AVN Allgemeine Vermessungs-Nachrichten
Volume: 123
Pages: 315-327
No. of pages: 13
ISSN: 0002-5968
Publication date: 2016
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Civil and Structural Engineering, Geography, Planning and Development, Earth and Planetary Sciences (miscellaneous)
Electronic version(s): https://gispoint.de/artikelarchiv/avn/2016/avn-ausgabe-11-122016/3983-curve-and-surface-approximation-of-3d-point-clouds-i-kurven-und-flaechen-approximation-von-3d-punktwolkeni.html (Access: Closed )
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