Growing 2D manifolds computation
Meng Jia · International Journal of Applied Mathematics & Statistics/International journal of applied mathematics and statistics · 2014
This paper mainly studies the computation of 2D manifolds of maps. An algorithm for computing 1D manifold, which uses a prediction and correction scheme to add new mesh points, is proposed at first. 2D manifold is computed by covering it with 1D sub-manifolds. A generalized Foliation Condition is proposed and used to make sure that the 2D manifold grows uniformly along the 1D sub-manifolds of different directions. The weak point of our algorithm is too much mesh points are generated at the inner part of the 2D manifold, and it is a promising key point where the algorithm can be revised in the future. But inserting 1D sub-manifold has advantages over inserting mesh points, because it avoids searching the preimage of the inserted mesh points on the surface of the 2D manifold.