Quadric splines Original Research Article

In this paper we will present a geometric approach to piecewise quadric C1-interpolants constructed algebraically by Dahmen in 1989. These piecewise quadrics interpolate the vertices of a triangular net with prescribed normals. In Dahmenʹs construction certain free parameters were set to arbitrarily chosen constants. Our approach provides a geometric interpretation of these constants. It renders the Powell–Sabin interpolant as a special case and provides another class of quadric splines by dualization. Furthermore, we show how to avoid the global dependencies of Dahmenʹs and Guoʹs transversal system.