Handles - Edgebreaker A Simple Compression for Surfaces...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Edgebreaker: A Simple Compression for Surfaces with Handles Jarek Rossignac , Hélio Lopes , Alla Safanova , Geovan Tavares , Andrzej Szymczak Georgia Institute of Technology, College of Computing and GVU Center, Atlanta, GA. USA Pontifical Catholic University (PUC-Rio), Department of Mathematics, Rio de Janeiro, RJ, Brazil Carnegie Mellon University, Computer Science Department, Pittsburgh, PA, USA {[email protected], [email protected], [email protected], [email protected], [email protected]} ABSTRACT The Edgebreaker is an efficient scheme for compressing triangulated surfaces. A surprisingly simple implementation of Edgebreaker has been proposed for surfaces homeomorphic to a sphere. It uses the Corner-Table data structure, which represents the connectivity of a triangulated surface by two tables of integers, and encodes them with less than 2 bits per triangle. We extend this simple formulation to deal with triangulated surfaces with handles and present the detailed pseudocode for the encoding and decoding algorithms (which take one page each). We justify the validity of the proposed approach using the mathematical formulation of the Handlebody theory for surfaces, which explains the topological changes that occur when two boundary edges of a portion of a surface are identified. Keywords Triangle meshes; Connectivity Graph; 3D Compression; Handlebody Theory. 1. INTRODUCTION The Edgebreaker compression and decompression algorithms [13] may be used to encode the connectivity of any simply connected manifold triangle mesh with a guaranteed worst case code of 1.80 bits per triangle [4]. In practice, the Edgebreaker encoding may often be further compressed to less than one bit per triangle through the use of Entropy codes [14]. But the true value of Edgebreaker lies in the efficiency and surprising simplicity of the algorithms [15], which fit in a couple of pages and use only a few arrays of integers as sole data structure. Because of its simplicity, Edgebreaker is viewed as the emerging standard for 3D compression [17] and may provide an alternative for the current MPEG-4 standard that is based on Rossignac's previous work with Gabriel Taubin [19]. This simple implementation of Edgebreaker, as a state machine, is publicly available through the web [3] and has been recently enhanced to support meshes with an arbitrary number of handles (also called through-holes). We provide in this paper a detailed description of this extension, imbedding it in a theoretic setting of the Handlebody theory, and including formal proofs. An important topological property of boundary representations (abbreviated B-Reps) [1] is the Euler-Poincaré formula, dated from the turn of the century [11], which states that an orientable connected triangulated surface S without boundary is uniquely identified by its Euler characteristic χ ( S ) =|V| |E|+|F|, where |V|,|E| and |F| indicate respectively the number of vertices, edges and faces of S. The Euler characteristic classifies S according to the Euler formula that is χ ( S)= 2 2
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern