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<p><b>Abstract</b>—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.</p>
Triangulated irregular network, TIN, space-filling curve, hierarchical triangulation, multiresolution triangulation, triangle mesh, spatial index.

J. J. Bartholdi and P. Goldsman, "Multiresolution Indexing of Triangulated Irregular Networks," in IEEE Transactions on Visualization & Computer Graphics, vol. 10, no. , pp. 484-495, 2004.
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