Least Squares Conformal Maps : A New Parameterization Method for Geo-Modeling

@inproceedings{LévyRM2002,
 abstract = { In this paper, we present the Least Squares Conformal Map approach (LSCM), a new parameterization method, based on a least-squares approximation of the Cauchy-Riemann equations. The so-defined objective function minimizes angle deformations, and we prove the following properties: the minimum is unique, independent of a similarity in texture space, independent of the resolution of the mesh and avoids generating triangle flips. The function is numerically well behaved and can therefore be very efficiently minimized. Our approach is robust, and can parameterize large charts with complex borders. We also introduce segmentation methods to decompose the model into charts with natural shapes, and a new packing algorithm to gather them in parameter space. We demonstrate our approach applied to various data sets. Possible applications to geomodeling concern reservoir grid generation, where the criterion minimized by our LSCM approach ensures the validity of the diagonal tensor approximation often done in flow simulation. As shown in the results section, LSCM grids ensure right angles between the iso-u and the iso-v with a very good precision. This may have a dramatic impact on both the accuracy and speed of flow simulations performed using LSCM grids. },
 author = { Levy, Bruno AND Petitjean, Sylvain AND Ray, Nicolas },
 booktitle = { 22th gOcad Meeting },
 month = { "june" },
 publisher = { ASGA },
 title = { Least Squares Conformal Maps : A New Parameterization Method for Geo-Modeling },
 year = { 2002 }
}