IJPAM: Volume 55, No. 1 (2009)

SURFACE FLATTENING VIA CONFORMAL MAPPING

Qingbin Li$^1$, Junxiao Xue$^2$
$^1$Department of Mathematics and Physics
Zhengzhou Institute of Aeronautical Industry Management
Zhengzhou, 450015, P.R. CHINA
e-mail: [email protected]
$^2$Software Technology School
Zhengzhou University
Zhengzhou, 450002, P.R. CHINA
e-mail: [email protected]


Abstract.In this paper, we present a surface flattening method based on conformal mapping. The method is an iterative procedure, which incrementally flattens a 3-D surface to 2-D domain by region growing. The algorithm is greedy and begins with a seed triangle which can be chosen freely. In each operation, we develop a piecewise linear mapping function that is conformal. In addition, at first step, we initialize the planar triangle which corresponds to the seed triangle. The initialization ensures that the seed triangle flattening process produce no distortion. And in other steps, we reduce the distortion by unifying the vertices in the plane. Our flattening method has low distortion. Experiments show that our method is efficient and fast enough.

Received: June 19, 2009

AMS Subject Classification: 26A33

Key Words and Phrases: surface flattening, conformal mapping, parameterization

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 55
Issue: 1