IJAM, Volume 27, No. 1 (2014)

Abstract. Triangulated Irregular Network (TIN) is a data structure commonly used to represent a geometric surface in computer software systems, such as geographic information systems and terrain modeling systems. Expo-rational B-splines (ERBS), a blending type spline construction in the family of generalized expo-rational B-splines (GERBS), can be used to create an approximation surface which interpolates the vertex positions of the TIN nodes. Utilizing the properties for local support of this blending spline construction, one can construct an approximation surface which is local within the second neighbourhood with respect to the infliction nodes of the underlying TIN. We present two variations of blending functions used with the construction. The first one blends the TIN edges with a smooth component, thus, the surface approximation is only C⁰ over the TIN edges. The second blending method provides a surface approximation which is smooth over the TIN edges.