Abstract: An improved algorithm for determining the approximate geodesic path between a source point and a destination point on a triangle mesh is presented. The triangle mesh is represented as a weighted graph, and an initial shortest path is computed. The neighboring edges of the shortest path are iteratively subdivided to construct new weighted graphs to approach the geodesic path. With a subdivision strategy of ‘neighbor extending’, we implement an efficient algorithm which significantly reduce the possibility of being trapped in a local optimum. A new method to deform surfaces using radial basis function is proposed by replacing the Euclidean distance as geodesic distance. Experiments show the good performance of the algorithm.