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<p><b>Abstract</b>—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 <tmath>${\cal M}_0, {\cal M}_1, {\cal M}_2, ..., {\cal M}_n,$</tmath> where each mesh <tmath>${\cal M}_i$</tmath> can be transformed to mesh <tmath>${\cal M}_{i+1}$</tmath> 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.</p>
Mesh simplification, triangle meshes, level-of-detail representation, shape approximation, multiresolution.
Gregory L. Schussman, Kenneth I. Joy, Bernd Hamann, Tran S. Gieng, Issac J. Trotts, "Constructing Hierarchies for Triangle Meshes", IEEE Transactions on Visualization & Computer Graphics, vol. 4, no. , pp. 145-161, April-June 1998, doi:10.1109/2945.694956
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