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Presents a novel technique for texture mapping on arbitrary surfaces with minimal distortion by preserving the local and global structure of the texture. The recent introduction of the fast marching method on triangulated surfaces has made it possible to compute a geodesic distance map from a given surface point in O(n lg n) operations, where n is the number of triangles that represent the surface. We use this method to design a surface flattening approach based on multi-dimensional scaling (MDS). MDS is a family of methods that map a set of points into a finite-dimensional flat (Euclidean) domain, where the only data given is the corresponding distance between every pair of points. The MDS mapping yields minimal changes of the distances between the corresponding points. We then solve an "inverse" problem and map a flat texture patch onto a curved surface while preserving the structure of the texture.