Research On Planarization Reconstruction Of Surface Based On Triangles And Polygons Mixing

In recent years,with the progress of computer aided technology,free-form surface architecture has been vigorously developed,and the nonlinear form has become a trend at present.Although the architect can use modeling software conveniently free surface form,but in the construction of the actual construction faces many challenges,one of the important problems for surface optimization problem,namely how to find a suitable for construction of curved surface fitting is approximated by a ideal surface,which usually means to flat surface reconstruction.At present,most of the practice and research use a single polygon mesh to fit the surface,but there are still many difficulties and challenges in this way of using the same type of polygon plate to cover the surface.In addition to a single polygonal mesh,the use of a mixed mesh of triangles and polygons to fit surfaces provides an alternative option for architects The challenge of flat-free surfaces is to address the complex interplay of different objectives related to geometry,aesthetics,and manufacturing constraints,all of which need to be considered simultaneously.For a single quadrilateral or hexagonal mesh,it is undoubtedly very difficult to maintain a good surface fit while solving the flatness problem,and the generated results often lose a certain degree of grid beauty.Because of the existence of triangles,the hybrid mesh has the natural advantage of flatness,which can achieve the balance among flatness,fitting degree and grid aesthetics,so as to better fit the surface.Therefore,the intervention of hybrid grid is very necessary.The theme of this paper is to use triangle and polygon hybrid mesh to reconstruct free-form surface on a flat surface.Firstly,this paper reviews the relevant literatures and cases of hybrid mesh,and demonstrates the unique value of hybrid mesh,which provides a strong theoretical basis for surface planarization based on hybrid mesh.Then,a hybrid plate mesh generation method is proposed in this paper.Firstly,a method that can transform regular mesh into hybrid plate mesh is obtained by using simple geometric principles.Then,the basic method is extended to obtain a set of hybrid plate generation ideas suitable for irregular Voronoi polygonal mesh.And based on Rhino and Grasshopper platform,the surface mesh reconstruction tools are programmed for these two ideas respectively,which provides the means for architects to quickly generate surface mesh reconstruction.At the end of the paper,the research work is summarized and the prospect of the next step is put forward.The whole thesis contains about 42000 words,89 pictures and charts.