Topologically Robust Mesh Modeling : Concepts , Data Structures , and Operations

Modeling 2-manifold meshes with a simple user interface is an important problem in computer graphics and computer aided-geometric design because certain widespread used modeling operations, such as the popular subdivision algorithms require specifically 2-manifold structures and because modeling non-manifold structures greatly complicates modeling algorithms. Unfortunately, most current modeling systems do not guarantee the 2-manifold structure and can introduce nonmanifold structures. In this paper, we propose a new vertexbased representation for mesh structures and give a formal proof that this representation characterizes precisely 2-manifold structures. Based on this theoretical result, we identify a group of simple validity rules, and show that the validity of 2-manifold structures can actually be tested very efficiently on most existing data structures for mesh modeling, including the adjacency list structure in computer graph algorithms, the winged-edge structure by Baumgart, the half-edge structure by Mäntylä, and the quad-edge structure by Guibas and Stolfi. A new data structure, the DLFL structure, and a new complete set of mesh modeling operations are also proposed. We show that the new proposed data structure and mesh modeling operations are more intuitive, more efficient, and more user-friendly compared with those proposed in the literature.

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