Optimised biarc curves with tension (Q1195082)

An improvement of the linearized approximation to the optimized biarc curves to describe a curve [\textit{D. B. Parkinson} and \textit{D. N. Moreton}, Comput. Aided Geom. Des. 23, 411-419 (1991; Zbl 0739.65009)] defined by a finite number of knots is studied. The improvement involves the application of the minimum strain energy biarc for each panel as a separate procedure from the gradient computation. A single tension parameter is included representing tension applied to the whole of the fitted curve. A compensation for the effects of fixed gradients at the initial and final knots is enabled. In the Appendix the biarc for 4 special cases and the biarc energy function are calculated.