
Title  Constructing Hierarchies for Triangle Meshes
(Article) 
in  IEEE Transactions on Visualization and Computer Graphics 
Author(s) 
Tran S. Gieng, Bernd Hamann, Ken Joy, Greg Schussman, Isaac J. Trotts 
Keyword(s)  Mesh simplification, triangle meshes, levelofdetail representation, shape approximation, multiresolution. 
Year 
April 1998

Volume  4 
Number  2 
Pages  145161 
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BibTeX  
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 00, 01, 02, ..., 0n, where each mesh 0i can be transformed to mesh 0i+1 through a set of trianglecollapse 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.
