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Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis

Bruno, Oscar P. and Han, Youngae and Pohlman, Matthew M. (2007) Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis. Journal of Computational Physics, 227 (2). pp. 1094-1125. ISSN 0021-9991. doi:10.1016/

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We present a new method for construction of high-order parametrizations of surfaces: starting from point clouds, the method we propose can be used to produce full surface parametrizations (by sets of local charts, each one representing a large surface patch – which, typically, contains thousands of the points in the original point-cloud) for complex surfaces of scientific and engineering relevance. The proposed approach accurately renders both smooth and non-smooth portions of a surface: it yields super-algebraically convergent Fourier series approximations to a given surface up to and including all points of geometric singularity, such as corners, edges, conical points, etc. In view of their C^∞ smoothness (except at true geometric singularities) and their properties of high-order approximation, the surfaces produced by this method are suitable for use in conjunction with high-order numerical methods for boundary value problems in domains with complex boundaries, including PDE solvers, integral equation solvers, etc. Our approach is based on a very simple concept: use of Fourier analysis to continue smooth portions of a piecewise smooth function into new functions which, defined on larger domains, are both smooth and periodic. The “continuation functions” arising from a function f converge super-algebraically to f in its domain of definition as discretizations are refined. We demonstrate the capabilities of the proposed approach for a number of surfaces of engineering relevance.

Item Type:Article
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Bruno, Oscar P.0000-0001-8369-3014
Additional Information:© 2007 Elsevier. Received 11 December 2006, Revised 24 August 2007, Accepted 28 August 2007, Available online 12 September 2007. This work was supported in part by the Air Force Office of Scientific Research, the National Science Foundation and the National Aeronautics and Space Administration.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Subject Keywords:Continuation method; Surface representation; Fourier series; Edge matching; Parametrization by projection
Issue or Number:2
Record Number:CaltechAUTHORS:20181101-152903783
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Official Citation:Oscar P. Bruno, Youngae Han, Matthew M. Pohlman, Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis, Journal of Computational Physics, Volume 227, Issue 2, 2007, Pages 1094-1125, ISSN 0021-9991, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90587
Deposited By: George Porter
Deposited On:02 Nov 2018 21:08
Last Modified:16 Nov 2021 03:33

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