Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Five different algorithms and their modifications were tested on triangular meshes that represent tesselations of synthetic geometric models. The results were compared with the analytically computed values of the Gaussian and mean curvatures of the non uniform rational B-spline (NURBs) surfaces, these meshes originated from. This work manifests the best algorithms suited for total (Gaussian) and mean curvature estimation, and shows that indeed different alogrithms should be employed to compute the Gaussian and mean curvatures.

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Bug algorithms are a class of popular algorithms for autonomous robot navigation in unknown environments with local information. Very natural, with low memory requirements, Bug strategies do not yet allow any competitive analysis. The bound on the robot's path changes from xene to scene depending an the obstades, even though a new obstacle may not alter the length of the shortest path. \Ye propose a new competilive algorithm, CoutiousBug, whose competitive factor has an order of O ( P -' ) , where d is the length of the optimal path from starting point S to a (arget point T. m = and #.Win denote the number of the distance funclion isolated local minima points in the given enviranment. Simulations were performed to study the average competitive factor of the algorithm.