Surface reconstruction is one of the significant applications of scattered data interpolation and approximation. In practice, it is very much related to the subject of computational geometry and object modelling where curve, surface, solid or object representation is to be sought from a given finite set of data. The obtained mathematical representation is often studied and the reconstructed object is placed in computer graphics environment for viewing, printing, or further manipulation.
Computing the shortest path (optimal collision-free path) between two nodes is a fundamental problem in computational geometry. Real road networks in transportation and industrial automation and motion planning in robotics are amongst the applications of shortest path problem. An optimal shortest path algorithm is often desired for practical implementation on real life problem and to design and develop an optimal shortest path algorithm has always been a challenge!
