The study of planar and spherical geometric subdivision schemes was done in Dyn and Hormann (2012); Bellaihou and Ikemakhen (2020). In this paper we complete this study by examining the hyperbolic case. We define general interpolatory geometric subdivision schemes generating curves on the hyperbolic plane by using geodesic polygons and the hyperbolic trigonometry. We show that a hyperbolic interpolatory geometric subdivision scheme is convergent if the sequence of maximum edge lengths is summable and the limit curve is G(1)-continuous if in addition the sequence of maximum angular defects is summable. In particular, we study the case of bisector interpolatory schemes. Some examples are given to demonstrate the properties of these schemes and some fascinating images on Poincare disk are produced from these schemes. (C) 2021 Elsevier B.V. All rights reserved.
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Elsevier