In this paper we will present a geometric approach to piecewise quadric C~1-interpolants constructed algebraically by Dahmen in 1989. These piecewise quadrics interpolate the vertices of a triangular net with prescribed normals. In Dahmen's construction certain free parameters were set to arbitrarily chosen constants. Our approach provides a geometric interpretation of these constants .it renders the Powell-Sabin interpolate as special case and provides another class of quadric splines by dualization. Furthermore, we show how to avoid the global dependencies of Dahmen's and Guo's transversal system.
展开▼
