Parameterization of Triangulations and Unorganized Points

A parameterization of a surface is a one-to-one mapping from a parameter domain to the surface. This paper studies the construction of piecewise linear parameterizations of triangulations and of discrete parameterizations of sets of unorganized points. Such parameterizations are useful tools for the approximation of triangulations by smoother surfaces as well as for the construction of triangulations from unorganized points. Parameterization can also be used as the starting point for multiresolution analysis of triangulations, through remeshing by triangulations with subdivision connectivity.

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