Slit Map: Conformal Parameterization for Multiply Connected Surfaces

Surface parameterization is a fundamental tool in geometric modeling and processing. Most existing methods deal with simply connected disks. This work introduces a novel method to handle multiply connected surfaces based on holomorphic one-forms. The method maps genus zero surfaces with arbitrary number of boundaries to an annulus with concentric circular slits. Any two boundaries can be chosen to map to the inner circle and the outer circle, the other boundaries to slits. Equivalently, the surfaces can be mapped to a rectangle with horizontal slits. Compared to existing linear methods that require surface partition, this method is more intrinsic and automatic. Compared to the existing holomorphic one-form method that requires double covering, it is more efficient and has better control over singularities. Compared to the existing Ricci flow method, this one is linear and simpler. The proposed method has many merits. The images of boundaries are parallel line segments. This regularity...

• Type: Conference
• Year: 2008
• Where: GMP
• Authors: Xiaotian Yin, Junfei Dai, Shing-Tung Yau, Xianfeng Gu
• Keywords: Concentric Circular Slits, GMP 2008, Holomorphic One-form, Multiply Connected Surfaces, Solid Modeling