The Symmetry Detection Of Polyhedral Wire-frame Model

Solid model can describe the shape of three-dimensional objects accurately, and arewidely used in biological, physical, medical and aerospace fields. Through thethree-dimensional wireframe model symmetry detection of solid model reconstruction fromthe wireframe model has a more important significance. finding the exact speed of the planeof symmetry is the key of polyhedral symmetry detection. In this paper, by studying thegeometric properties of polyhedral three-dimensional wireframe model to study proposeddetection algorithm based on a wireframe model to detect potential plane of symmetry andvertex polyhedron polyhedron based wireframe model.Point out the significance of symmetry detection and extracting an object from awire-frame, describe the two-dimensional and three-dimensional symmetry detection researchstatus at home and abroad; introduces some symmetry detection algorithms, and mainlydiscusses the current comparison mainstream algorithms, analyse and compare theperformance of these algorithms.According to the analysis of the current algorithms, Summarizes the general steps of thepolygon with polyhedron symmetry detection algorithm, analysis the geometric properties ofpolygon axis of symmetry and polyhedron symmetry plane which is used in each step andpoints out their different roles in the symmetry detection, point out the media of quickly findgeometric properties of polygon axis of symmetry and polyhedron symmetry plane in thesymmetry detection, thus to improve accuracy and efficiency of the polygon axis ofsymmetry and polyhedron symmetry plane detection algorithm.The nature of Polygon axis of symmetry and Skewed axis of symmetry is studied. Basedon the number of polygon vertices and sequence, this paper puts forward a new algorithm ofpolygon symmetry detection. First determine the parity of the number of polygon vertices andthe centroid, and mark the Polygon vertices clockwise; Then, find out the candidates for thepolygons based on the number of vertex and centroid; Lastly, detect whether all the order ofthe vertices is symmetric. The method can be extended to skewed symmetry detection. Due tothe use of the simple properties of polygons, the number and order of vertex, the method iseffective, and experiments have proved the feasibility and veracity.Through the study of the nature of three-dimensional wireframe model plane ofsymmetry,a method which combine the network analysis method is proposed for symmetricand skew detection algorithm of polyhedron potential surface loop wire frame model.Firsttake the polyhedron wireframe model potential surface loop; And then find out the potentialth axis of symmetry on the surface, and based on the potential axis of symmetry on thesurface and edges form a closed loop to as potential symmetry plane; Finally through the detection whether all the vertices of of3d wireframe model is symmetrical about the plane,determine the true plane of symmetry. Using the network analysis and properties whether thecenter of mass is in the symmetry of the surface in the process of testing improves theefficiency of search for the symmetrical surface. The experimental results show that thismethod has higher efficiency and accuracy.Through the research of existing symmetry plane algorithm based on equidistant pointsout the limitation of the algorithm, the limitations of the algorithm is that it is not be suitablefor wire frame model with10below the vertex. the principle and steps of the algorithm isimproved. Firstly calculates the centroid of wire frame model and classified according tonumber of vertex wireframe model; For wire frame model under10vertex the take symmetryplane of the arbitrary vertex as potential symmetry plane, for wire frame model more than10vertices take surface of four vertices in coplanar as a potential surface, take symmetry planeof equidistance three vertices as potential symmetry plane; finally detect whether all thevertices of of3d wireframe model is symmetrical about the potential symmetry plane. Theexperiment respectively according to different types of wire frame model is verified, and itproves the accuracy and feasibility of the algorithm.