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Multiresolution Indexing of Triangulated Irregular Networks
July/August 2004 (vol. 10 no. 4)
pp. 484-495

Abstract—We show how to build a continuous, one-dimensional index of the points on a triangulated irregular network (TIN). The index is constructed by first finding an ordering of the triangles in which consecutive triangles share a vertex or an edge. Then, the space within each triangle is continuously indexed with a space-filling curve that begins at one vertex of the triangle and ends at another. The space-filling curve is oriented such that the first point in each triangle is a vertex shared with the previous triangle and the last point is a vertex shared with the next triangle. Furthermore, our index can be refined locally and, therefore, efficiently when the TIN is augmented by filling any face with another TIN (to make a hierarchical TIN). Such processes arise, for example, in the elaboration of detail on a graphical surface.

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Index Terms:
Triangulated irregular network, TIN, space-filling curve, hierarchical triangulation, multiresolution triangulation, triangle mesh, spatial index.
John J. Bartholdi, Paul Goldsman, "Multiresolution Indexing of Triangulated Irregular Networks," IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 4, pp. 484-495, July-Aug. 2004, doi:10.1109/TVCG.2004.14
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