Approximation Theory, Wavelets and Applications, S. P. Singh (ed.): 325-334, 1995

Abstract: This paper presents a subdivision scheme on triangles that we call {\em Variable Subdivision Scheme}, shortly VSS. The scheme can be seen as an iterative scheme to generate interpolating surfaces that can be irregular in some case. Moreover, it seems to be suitable to preserve the convexity of the B\'ezier net defined over the triangle since it is {\em exchangeable} with the mid-point splitting.
This property is proved by means of the algorithm used to define the scheme.