Construction of flexible blending parametric surfaces via curves (Q730889)

A blending surface is an intermediate surface smoothly joining other surfaces. Firstly, the \(G^n\) continuity of parametric curves and surfaces is introduced. After that, sufficient conditions for joining two adjacent surface patches with \(G^1\), \(G^2\) and \(G^3\) continuity along their common boundary curve are given. Then, the construction of a blending surface which connects \(G^n\) continuously two surfaces along their boundaries is described. This construction is based on using isoparametric curves of surfaces which have to be connected. The suggested blending surface is a Hermite interpolation surface passing through two types of curves: Bézier and \(C\)-curves (developed by using a trigonometric algebraic basis). Examples which illustrate the applicability of the method are included in the article, too.