Research Communication | Open Access
Volume 2021 | Communication ID 86
Volume 2021 | Communication ID 86
| Hyperbolic interpolatory geometric subdivision schemes |
Taoufik Ahanchaou
Received |
Accepted |
Published |
January 27, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: The study of planar and spherical geometric subdivision schemes was done in [2, 3]. 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 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 G1-continuous if, in addition, the sequence of maximum angular defects is summable. In particular, we study the case of ...