Abstract
Triangulation of a simple polygon is a classical problem of immense interest in computational geometry and related fields. Recently, some specialized kinds of triangulations, namely thin and bushy triangulations have received attention owing to their use in pattern recognition and in finding geodesic properties. As triangulation of a given polygon is essentially non-unique, counting the number of ways a polygon can be triangulated is an interesting problem. In this paper, we solve two such counting problems, to find δ 1( n) ( δ b( n)) the number of thin (bushy) triangulations of an n-sided convex polygon and propose many challenging ones. These numbers provide exact upper bounds for the corresponding triangulation and may be used in analyzing average case performance of different triangulation algorithms.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
