Reverse Static Algorithm Segments

Subdivision scheme is a new discrete modeling technology. Subdivision surfacewhich is a limit surface of a sequence of refined meshes can express modeling surfacethrough control mesh and subdivision rules. Nowadays, with more and moresubdivision schemes appearing, subdivision plays an important role in constructingthree dimensional models comparing with traditional parametric way. By subdivision,we can get a sequence of refined meshes gradually so as to get smooth surfaces of athree dimensional model quickly. It has already been used widely in computer graphics.Reverse subdivision is a reverse process that reconstruct a subdivided mesh of amodel into the mesh just before subdivision, that is, the process from a nice model to acoarser one. Because of its wide application in constructing multi-resolution models,data compression, fast transmission and multi-resolution editing, it has become apopular topic in recent years. This thesis reviews all the research and results aboutreverse subdivision in the world and discusses its wide application in the future andfocuses on reversing static subdivision schemes by introducing a new concept calledcharacteristic polygon. In practice, the subdivided meshes are mostly composed ofquadrangles and non-quadrangular polygons. According to this point, we have proposedan algorithm on reversing Doo-Sabin and Midedge subdivision schemes bycharacteristic polygon and subdivision's inheritance. It is proved valid and feasible bysome examples. This algorithm proposed in the thesis can be a good inspire to theresearch in related field.