关键词: 一致性检验, 方向关系约束集, 坐标图

Abstract: In this paper，the authors address the problem of consistency checking for point objects.A coordinates graph representation is proposed to maintain the Euclidean spatial constraints among point objects.The basic idea is to project the spatial constraints on both X and Y coordinates，and the coordinates graph is constructed on each coordinates.By using the coordinates graph representation，the problem of consistency checking is then transformed to a graph cycle detection problem.The consistency checking can be achieved with O（n+e）time as well as space complexity，where n is the number of spatial objects，and e is number of direction predicates in the constraint.The proposed approach to consistency checking for point objects is faster than O（n²）when the number of predicates is much smaller than n².

Key words: consistency checking, constraint sets of direction predicates, coordinates graph