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An exact conservative remapping scheme requires overlaps between two meshesand a reconstruction scheme on the old cells (Lagrangian mesh). While the areintensive discussion on reconstruction schemes, there are relative sparsediscussion on how to calculate overlaps of two grids. Computing the exactoverlaps was believed complicated and often be avoided. This paper introducesthe mathematical formulation of such a problem and tools to solve the problem.We propose methods to calculate the overlaps of two dismissable generalquadrilateral mesh of the same logically structure in a planar domain. Thequadrilateral polygon intersection problem is reduced to as a problem that howan edge in a new mesh intersects with a local frame which consists at most 7connected edges in the old mesh. As such, locality of the method is persevered.The alternative direction technique is applied to reduce the dimension of thesearching space. It reduces more than 256 possible intersections between a newcell with the old tessellation to 34 (17 when considering symmetry)programmable intersections between an edge and an local frame whenever theintersection between the old and new cell does not degenerate. At the sametime, we shall how the computational amount of the overlaps depends on theunderlying problem in terms of singular intersection points. A simple anddetailed classification on the type of overlaps is presented, according toclassification, degeneracy of an overlap can be easily identified.

Computing Overlaps of Two Quadrilateral Mesh Of the Same Connectivity