Research And Appllication Of Core Algoritham In Folding Paper-cut

With the rapid development of computer technology and digital technology,digital technology is more widely used in traditional art, including traditional paintingand paper cutting. Paper-cut modeling style is widely symmetry, compared with thepattern of asymmetric patterns, symmetrical patterns meet the aesthetic standards,therefore, the digital paper-cut can simulate the traditional paper-cut to generate asymmetrical pattern,a common pattern of symmetry have two kinds,such as theoverall symmetry and local symmetry.So far, there exsit some question with thistechnology that symmetrical patterns are not common and locally symmetric patterncan not be generated. We further study digital folding paper-cut based on the existing.The main study are as follows:We studied digital origami. It includes horizontal symmetry, vertical symmetry,skew symmetry, multiple symmetry,together with some ideas and algorithms ofsymmetrical origami.Futhermore,the paper lay emphsis on how to solve the twotechnical difficulties,that is,to accurately generate origami folding in local symmetryand to display multiple origami cover,and put forward to the digital origamialgorithm based on a kind of segments folding that users input parameters togenerate accurate folding,change origami process into the process of constructing abinary tree plane,and show the folden pattern according to store data of the binarytree.We studied the digital paper cutting.Mainly researched on the ideas andalgorithms of digital paper cutting with different tailoring ways, from outside toinside, from the inside to outside, from the inside to inside cut etc. The coreproblems involved in three crop cut whether the part of the cut forming the innercore(which was tailored part whether can fall off), and put forward line set cuttingpolygon algorithm, is the position of the digital scissors problem into a point andpolygon position, using cutting line set the intersecting lines exist not neighboringprinciple judge whether forms a closed polygon to judge whether inner formation.We studied the paper-cut patterns show of digital folding. Mainly studied thefolding paper-cut patterns show of the overall symmetry and the folding paper-cutpatterns show of the local symmetry. Among deeply researched the folding paper-cutpatterns of the local symmetry according to the levels show,and proposed the methodof merging binary tree node to show the effect of the folded paper cutting, and it isbased on constructing binary tree plane in the process of origami, mergering the childnodes around father node with the binary tree traverse sequence after to show thebinary tree roots node of the storage of paper-cut folding pattern. We designed and developed a digital folding paper-cut platform. the users candesign origami shape, cut the folded paper and preview the effect of paper cuttingdepending on different needs with the platform. Through the platform, showing asquare of paper how to fold into an octagon, and showing the folded paper-cutpatterns and the pattern after the commencement of the folded paper-cut graphics.