Computer Aided Geometric Design 19 (2002) 207–222 www.elsevier.com/locate/comaid On C 1 -continuity of Wachspress quadrilateral patches H.P. Dikshit a,∗ , A. Ojha b a Madhya Pradesh Bhoj (Open) University, Bhopal, 462 016 India b Department of Mathematics and Computer Science, Rani Durgavati University, Jabalpur 482 001, India Received March 2001; revised September 2001 Abstract Wachspress quadrilateral patches have been recently studied in (Dahmen et al., 2000) for surface generation over quadrilateral domains. In the present paper, we study the conditions under which a composite quadrilateral patch will be C 1 . Similar to the Bézier patch, these C 1 -continuity conditions have been expressed in terms of Wachspress control points of the surface. We also determine a nice formula for k-th order (k  1) directional derivative of a quadrilateral patch. We conclude by giving numerical examples of C 1 -continuous Wachspress patches.  2002 Elsevier Science B.V. All rights reserved. Keywords: Wachspress quadrilateral patches; Bilinear Bernstein polynomials; C 1 -continuity 1. Introduction Wachspress quadrilateral patches have been recently studied in (Dahmen et al., 2000) (see also (Dikshit and Ojha, 2001)) from CAGD point of view. de Casteljau type algorithm for generation of Wachspress patches has been presented in the above mentioned paper and its relation with tensor product Bernstein polynomials has also been studied, using projective geometry concepts. It has been shown that the surface enjoys convex hull property and projective invariance. Elegant degree elevation formula has also been presented in (Dahmen et al., 2000). In continuation with our studies in (Dahmen et al., 2000), we study in the present paper, k -th order directional derivative of Wachspress patch and obtain conditions on the control points under which a composite Wachspress patch will be C 1 -continuous. * Corresponding author. E-mail address: hp_math@ignou.ac.in (H.P. Dikshit). 0167-8396/02/$ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII:S0167-8396(01)00083-8