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Constructing Hierarchies for Triangle Meshes
April-June 1998 (vol. 4 no. 2)
pp. 145-161

Abstract—We present a method to produce a hierarchy of triangle meshes that can be used to blend different levels of detail in a smooth fashion. The algorithm produces a sequence of meshes ${\cal M}_0, {\cal M}_1, {\cal M}_2, ..., {\cal M}_n,$ where each mesh ${\cal M}_i$ can be transformed to mesh ${\cal M}_{i+1}$ through a set of triangle-collapse operations. For each triangle, a function is generated that approximates the underlying surface in the area of the triangle, and this function serves as a basis for assigning a weight to the triangle in the ordering operation and for supplying the points to which the triangles are collapsed. The algorithm produces a limited number of intermediate meshes by selecting, at each step, a number of triangles that can be collapsed simultaneously. This technique allows us to view a triangulated surface model at varying levels of detail while insuring that the simplified mesh approximates the original surface well.

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Index Terms:
Mesh simplification, triangle meshes, level-of-detail representation, shape approximation, multiresolution.
Tran S. Gieng, Bernd Hamann, Kenneth I. Joy, Gregory L. Schussman, Issac J. Trotts, "Constructing Hierarchies for Triangle Meshes," IEEE Transactions on Visualization and Computer Graphics, vol. 4, no. 2, pp. 145-161, April-June 1998, doi:10.1109/2945.694956
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