Encyclopedia of Database Systems Entry: Simplicial Complex draft 1 Entry: Simplicial Complex Andrew U. Frank Department for Geoinformation and Cartography Gusshausstrasse 27-29/E127,1 A-1040 Vienna, Austria frank@geoinfo.tuwien.ac.at http://www.geoinfo.tuwien.ac.at/staff/index.php?Current_Staff:Frank%2C_Andrew_U. gz 4361 svn 832 actual: 2415 Note: Figures are not yet in final format in this document. Synonyms KW complex, polyhedron, cell complex (these are not synonyms, but terms used to describe very similar concepts – enter them as synonyms?) Definition A simplicial complex is a topological space constructed by gluing together dimensional simplices (points, line segments, triangle, tetrahedrons, etc.). A simplicial complex K is a set of simplices, which satisfies the two conditions: 1. any face of a simplex in k is also in K 2. the intersection of any two simplices in k is a face of both simplices. Historical Background Raster (field) or vector (object) are the two dominant conceptualizations of space. Applications focusing on object with 2 or 3 dimensional geometry structure the storage of geometry as points, lines, surface, and volumes and the relations between them; a classical survey paper discussed the possible approaches mostly from the perspective of Computer Aided Design (CAD) where individual physical objects are constructed [10]. The representation of geographic information, e.g., maps, introduces consistency constraints Figure 1: Cadastral parcels provide an example of a simplicial complex