PARABOLIC CURVE APPROXIMATION IN DESIGN AND FINITE ELEMENT APPLICATIONS.

The approximation of curves by parameterized parablic segments that connect selected nodes on the given curve arises naturally in all quadratic isoprametric 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.