Monotonicity Preserving Subdivision Schemes Original Research Article

In this paper we discuss a class of subdivision schemes with a finite support suitable for curve design. We analyze the case where the masks of the scheme and the associated difference process are positive. We show that these schemes generate continuous functions of bounded variation, and that the monotonicity of the data is preserved. An estimate of the Lipschitz class of the generated functions is also obtained. For curves in Rd the control polygons generated by the scheme satisfy some variation diminishing properties, in particular, the arc-length is non-increasing. We characterize a particular subclass of schemes having bell-shaped refinable functions. Known sufficient conditions for excluding self-intersections and critical points of B-spline curves and surfaces hold also for these schemes.