Parabolic curve approximation in design and finite element applications

Abstract

The approximation of curves by parameterized parabolic segments that connect selected nodes on the given curve arises naturally in all quadratic isoparametric transformations. The use of parabolae allows the introduction of a geometric measure of the discrepancy between given and approximating curves. The free parameters that determine a particular parabola can be used to find an optimal approximation. Constraints that prevent overspill and curve degeneracy are introduced. The resulting constrained optimization problem can be solved by a simple special purpose algorithm. Experimental results indicate that the method yields satisfactory approximations to given curves. © 1986 Butterworth & Co (Publishers) Ltd.