Summary: Hamiltonian Triangulations for Fast Rendering \Lambda
Esther M. Arkin (1) y Martin Held (1);(2) z
Joseph S. B. Mitchell (1) x Steven S. Skiena (3) --
(1) Department of Applied Mathematics and Statistics
State University of New York, Stony Brook, NY 11794­3600, USA
(2) Institut f¨ur Computerwissenschaften
Paris­Lodron Universit¨at Salzburg, A­5020 Salzburg, Austria
(3) Department of Computer Science
State University of New York, Stony Brook, NY 11794­4400, USA
Abstract
High­performance rendering engines in computer graphics are often pipelined, and their
speed is bounded by the rate at which triangulation data can be sent into the machine. To
reduce the data rate, it is desirable to order the triangles so that consecutive triangles share
a face, meaning that only one additional vertex need be transmitted to describe each triangle.
Such an ordering exists if and only if the dual graph of the triangulation contains a Hamiltonian
path.
In this paper, we consider several problems concerning triangulations with Hamiltonian
duals. Specifically, we
ffl Show that any set of n points in the plane has a Hamiltonian triangulation, and give two
optimal \Theta(n log n) algorithms for constructing such a triangulation. We have implemented

Source: Arkin, Estie - Department of Applied Mathematics and Statistics, SUNY at Stony Brook
Mitchell, Joseph S.B. - Department of Applied Mathematics and Statistics, SUNY at Stony Brook

Collections: Computer Technologies and Information Sciences; Mathematics