The determination of the optimum blarc curve through a gsven set of points with given end gradients is considered The method adopted is that of hndmg the optimum gradients at all the given points such that the integral of the square of the local curvature along the curve Is a minimum It is shown that this is equivalent to the simultaneous solution of the same problem for a set of 2-panel (3-point) curves, and such solutions are then investigated.
A hneanzed method of solution for the required gradients is proposed that results in a set of hnear equations that can be reverted directly, and that should be capable of solution on a CNC machine control unit, following the direct input of the coordinates of the given points and relevant end slopes_ Initial results are compared with those obtained from a ngorous numencal optimization procedure for the blarc curve and with a cublc-sphne function It is shown that instabilities may be avoided, and a smoother curve obtained, by the effective decouphng of segments of the whole curve by the specihcat~on of gradients at add~tlonal, intermediate, points CNC machining, sphnes, blarcs, curve fitting, ~nterpolat~on methods