Planar Parameterization Method Based On Hierarchical Structure

The main object of digital geometric processing(DGP)is the geometric model represented by the data structure(two-dimensional peacekeeping mainly),which is the fourth multimedia transformation experienced by human society.The content of digital geometry processing mainly includes the registration of sur-face mesh,reconstruction,smoothing,parameterization,texture mapping,remeshing and so on,this paper first reviews these important contents in digital geometric process-ing.Parameterization is the basis of digital geometric processing and plays an important role in many subsequent mesh operations.Parameterization is actually an old problem,and a typical application is the drawing of maps.With the development of computer processing ability and storage technology,in recent decades,the research on parameterization is in the ascendant,and many methods of using efficient parameterization are put forward,and the 2nd chapter of this paper introduces the related background work of parameterization,and on the basis of the previous proposed plane Parameterization method based on multi-level structure.Our multi-level algorithm mainly includes simplifying the original mesh and adding two steps to the initial parameterized mesh subdivision.For a triangular mesh with a topol-ogy and embryo on the disk,the grid is simplified and the topological information of the simplified point is stored.Secondly,the simplified mesh is mapped to the disk;Then according to the stored topology information in batches of points until the restoration of all the vertices of the triangle mesh and in this process to continuously optimize the mesh,to prevent triangular flip at the same time so that the grid vertices evenly dis-tributed;Finally,the disk mesh which restores all the vertices is optimized to obtain the final parameterized mesh.The robustness of this algorithm is derived from:1.The simplified mesh is easier to optimize;2.In the add-in process,the mesh vertex does not produce aggregation phenomenon,easy to generate low distortion plane parameter-ization results.Using the processor for Intel(R)Core(TM)i3-2130 CPU@3.40GHz,Memory 4.00GB machine experiments,the experimental results show that the use of multi-level structure for planar parameterization,compared with the latest algorithm,robustness has greatly improved.Our algorithm contains two procedures:decimation and subdivision.For a triangle mesh which is homeomorphic to disk,we decimate it firstly and store the topological information of the decimated vertices.Secondly,we map the decimated mesh into disk,subdivide the mesh and insert vertices flexibly according to the information stored until all of the vertices are restored.We optimize the mesh during the period to avoid flip-ping and make vertices distribute evenly meanwhile.Finally,we optimize the mesh and acquire the parameterized result.The robustness of the algorithm comes from two aspects:1.It's easy to optimize the mesh after decimation.2.Vertices do not clus-ter during subdivision and it's much easy to acquire the low-distortion parameterized mesh.We conducted our experiment on a desktop computer whose processor is Intel(R)Core(TM)i3-2130 CPU@3.40GHz and memory is 4.00GB.Compared with state-of-the-art methods,our algorithm performs better in robustness.