NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
Curved Finite Elements and Curve ApproximationThe approximation of parameterized curves by segments of parabolas that pass through the endpoints of each curve segment arises naturally in all quadratic isoparametric transformations. While not as popular as cubics in curve design problems, the use of parabolas allows the introduction of a geometric measure of the discrepancy between given and approximating curves. The free parameters of the parabola may be used to optimize the fit, and constraints that prevent overspill and curve degeneracy are introduced. This leads to a constrained optimization problem in two varibles that can be solved quickly and reliably by a simple method that takes advantage of the special structure of the problem. For applications in the field of computer-aided design, the given curves are often cubic polynomials, and the coefficient may be calculated in closed form in terms of polynomial coefficients by using a symbolic machine language so that families of curves can be approximated with no further integration. For general curves, numerical quadrature may be used, as in the implementation where the Romberg quadrature is applied. The coefficient functions C sub 1 (gamma) and C sub 2 (gamma) are expanded as polynomials in gamma, so that for given A(s) and B(s) the integrations need only be done once. The method was used to find optimal constrained parabolic approximation to a wide variety of given curves.
Document ID
19850020278
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Baart, M. L.
(National Research Inst. for Mathematical Sciences Pretoria, South Africa)
Date Acquired
August 12, 2013
Publication Date
June 1, 1985
Publication Information
Publication: NASA. Langley Research Center Computational Geometry and Computer-Aided Design
Subject Category
Numerical Analysis
Accession Number
85N28590
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
No Preview Available