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Vertex-Based (Lath) Representations for Three-Dimensional Objects and Meshes Hanan Samet hjs@cs.umd.edu www.cs.umd.edu/˜hjs Department of Computer Science Center for Automation Research Institute for Advanced Computer Studies University of Maryland College Park, MD 20742, USA Copyright 2007 by Hanan Samet Vertex-Based (Lath) Representations for Three-Dimensional Objects and Meshes – p.1/15 Vertex-based Data Structures 1. Edge-based winged-edge family are uniform-size one record per edge 2. Want uniform-size vertex-based or face-based representations vertex is simplest topological entity while edge and face are more complex cannot have one record per vertex each edge is always associated with just two faces (assuming a two-manifold) and with just two vertices variable number of edges and faces associated with each vertex cannot have one record per face variable number of edges and vertices associated with each face 3. Object can be described by set of all possible edge-face, edge-vertex pairs, or face-vertex pairs each pair is termed a lath (Joy, Legakis, and MacCracken) one vertex is associated with each lath more than one lath can be associated with a particular vertex a single edge is associated with each lath a single face is associated with each lath Copyright 2007 by Hanan Samet Vertex-Based Lath Representations – p.2/15 Lath Data Structures for Manifold Objects 1. Encodes lath-lath relation rather than edge-edge, edge-face, etc. 2. Must be able to make transitions between instances of lath data structure    3. Given specific lath instance of relation , we need to be       able to transition to lath corresponding to the next object of type for object , and to the   lath corresponding to the next object of type for object   4. Three items of information associated vertex transitions to next ( =clockwise) or prior ( =counterclockwise) objects if edge object, then just one transition to companion Copyright 2007 by Hanan Samet Vertex-Based Lath Representations – p.3/15 Nature of Lath Data Structure 1. Implicit data structure in contrast to winged-edge 2. Identity of faces adjacent to an edge as well as one of the vertices that comprises an edge are represented implicitly 3. Only vertex associated with each lath is represented explicitly 4. Need vertex-lath, face-lath, and edge-lath tables lath analogs of vertex-edge and face-edge tables Copyright 2007 by Hanan Samet Vertex-Based Lath Representations – p.4/15 Split-Face Lath Data Structure: Edge-Face Pairs Split an edge record into two: one per adjacent face

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