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Abstract:

We showhowtobuildacontinuous, one-dimensional index of the points on a triangulated two-dimensional manifold such as a surface map of a geographic information system. The method involves creating an adjacency-preserving ordering of the triangular regions and then indexing each region with a space lling curve oriented in a special way. We prove that a continuous path can be created through any triangulation T, and that a con-tinuous circuit can be constructed through all but a certain family of triangulations. We provide a construction algorithm requiring O(n 2) steps, when T has n faces. We characterize the family of non-circuit-indexable triangulations, and provide a simple O(n) necessary and su cient test condition for circuit-indexability. We show howcontinuous paths and circuits can be extended to hierarchical triangulations, re-quiring only local changes to existing indices. When a cell in T is itself triangulated with m triangles, the current index of T can be augmented in O(m) steps. Key words: triangulation, triangulated irregular network, hierarchical triangulation, space lling curve, geographic information systems

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