Geometric modelling using rational Gaussian curves and surfaces (Q1902397)

The author describes his rational Gaussian curves and surface approximations which are modelled on \(B\)-spline techniques. For curve approximations, he uses \({\mathbf P}(u) = \Sigma {\mathbf V}_i g_i (u)\) where the \({\mathbf V}_i\) are control points and \(g_i(u) = W_i G_i(u)/ [\Sigma W_j G_j (u)]\), \(G_i(u) = \text{exp} \{-(u - u_i)^2/2 \sigma_i ^2\}\), \(W_i \geq 0\), and for surfaces the corresponding bivariate formula. For approximation of closed curves, the formula has to be slightly changed. He gives some examples of graphics approximation and also of approximation of curves displaying empirical data, where the oscillations connected with rational approximations do not appear.