Texture mapping is crucial to high quality computer graphics. To preserve the initial appearance of the texture, a texture mapping procedure has to meet certain requirements. First, the mapping has to be continuous (for example, no foldovers can exist). Second, the inevitable angular and linear distortions have to be minimized. These requirements, namely providing a continuous mapping while minimizing angular distortion, are met by the angle based flattening (ABF) method. Since ABF only reduces angular distortions, length distortions can be quite large, which impairs the overall quality of the result.

This paper introduces a procedure to reduce linear distortions of a given parameterization. Applied to the results of the ABF, it balances linear and angular distortions to create an improved parameterization (though this balance cannot so far be controlled explicitly). The proposed algorithm is based on weighted Laplacian smoothing.

The authors provide a comprehensive overview of previous work in this field of research. They describe their proposed algorithm in detail, and discuss its properties in terms of computational complexity, accuracy, and validity. A number of examples of parameterizations are included, showing the impressive results of the introduced procedure. Finally, a few suggestions for further improvements are noted.