Canadian Conference on Computational Geometry, August 20-22, 2007, Ottawa, Ontario, Canada
We present a heuristic algorithm to compute approximate geodesic distances on triangular manifold S containing n vertices with partially missing data. The proposed method computes an approximation of the geodesic distance between two vertices pi and pj on S and provides an upper bound of the geodesic distance that is shown to be optimal in the worst case. This yields a relative error bound of the estimate that is worst-case optimal. The algorithm approximates the geodesic distance without trying to reconstruct the missing data by embedding the surface in a low dimensional space via multi-dimensional scaling (MDS). Wederive a new heuristic method to add an object to the embedding computed via least-squares MDS.
Canadian Conference on Computational Geometry [Proceedings].