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Spatial synthesis by disjunctive constraint satisfaction

Published online by Cambridge University Press:  27 February 2009

Can A. Baykan  and
Mark S. Fox
Can A. Baykan
Affiliation:
Department of Architecture, Middle East Technical University, 06531 Ankara, Turkey
Mark S. Fox
Affiliation:
Department of Industrial Engineering, University of Toronto, 4 Taddle Creek Road, Toronto, Ontario M5S 1A4
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Abstract

The spatial synthesis problem addressed in this paper is the configuration of rectangles in 2D space, where the sides of the rectangles are parallel to an orthogonal coordinate system. Variables are the locations of the edges of the rectangles and their orientations. Algebraic constraints on these variables define a layout and constitute a constraint satisfaction problem. We give a new O(n2) algorithm for incremental path-consistency, which is applied after adding each algebraic constraint. Problem requirements are formulated as spatial relations between the rectangles, for example, adjacency, minimum distance, and nonoverlap. Spatial relations are expressed by Boolean combinations of the algebraic constraints; called disjunctive constraints. Solutions are generated by backtracking search, which selects a disjunctive constraint and instantiates its disjuncts. The selected disjuncts describe an equivalence class of configurations that is a significantly different solution. This method generates the set of significantly different solutions that satisfy all the requirements. The order of instantiating disjunctive constraints is critical for search efficiency. It is determined dynamically at each search state, using functions of heuristic measures called textures. Textures implement fail-first and prune-early strategies. Extensions to the model, that is, 3D configurations, configurations of nonrectangular shapes, constraint relaxation, optimization, and adding new rectangles during search are discussed.

Keywords

Spatial LayoutGeometric ReasoningDisjunctive Constraint Satisfaction
Type
Articles
Information
AI EDAM , Volume 11 , Issue 4 , September 1997 , pp. 245 - 262
Copyright
Copyright © Cambridge University Press 1997

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