This paper presents a subdivision scheme on triangles that we call variable subdivision scheme. 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 Bézier net defined over the triangle since it is exchangeable with the mid-point splitting. This property is proved by means of the algorithm used to define the scheme
Can irregular subdivisions preserve convexity?
DE MARCHI, Stefano;
1995
Abstract
This paper presents a subdivision scheme on triangles that we call variable subdivision scheme. 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 Bézier net defined over the triangle since it is exchangeable with the mid-point splitting. This property is proved by means of the algorithm used to define the scheme
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