Research On Optimization For Triangular Mesh Surface Flattening Technology

Aerospace to insulation, stealth, anti-radiation etc., need to do flexible materiallayer for some three-dimensional product, and flattening the three-dimensionalsurface to two-dimensional plane. With the development of three-dimensional dataacquisition technology, triangular mesh surface is applied more and more widely inthe field of computer graphics and geometric design. Therefore, this article hasconducted in-depth research to the flattening technology of curved surface based ontriangular mesh.Only the developable surface can unfold without any distortion totwo-dimensional plane; for non-developable surface, our goal is to make thedeformation as small as possible. In this paper, based on the topology reconstructionof triangular mesh surface, improving the previous proposed flattening algorithmbased on triangular mesh surfaces, and proposed based on the length of the globaloptimization and equal deformation flattening algorithm, the triangular meshsurface is mapped to a two-dimensional plane topology equivalently by geometricmethod. First, developing basic point and its1-neighbor points, and then throughthe boundary of expanded portion, spread out, until all the mesh surface is expanded.For the triangle does not meet the integrity of topological relations, proposed thecorrection method, and achieved good results.The surface flattening algorithm hasstrong versatility, can expand triangular mesh surfaces as a high rate of speedFor the initial geometric expansion results does not satisfy the accuracyrequirements, this paper presents the mechanical optimization method, establishspring-mass model, using the Lagrange equation of motion to analyze the motion ofparticle, through iterative to obtain optimization triangular mesh surface unfoldingresults. To be able to better simulate the shape deformation of the surface, this papermakes improvement on the spring-mass model proposed by predecessors, adds across spring, and using the implicit Euler method to iterate, avoiding the oscillationand divergence of the iterative process effectively.In this paper, the surface flattening method is only applicable to non-closedsurface, for a closed surface or surface consist of developable and undevelopableparts, first of all to divide or cut, and then expand. This paper presents asegmentation algorithm based on eigenvalues of vertex’ normal tensor voting matrix of triangular mesh, construct the vertex tensor according to the unit normal vectorof the vertex’1-neighborhood triangle, then using the difference of tensoreigenvalues distribute the vertexes, and divides the triangle mesh surface throughregional growth algorithm. For the closed surface of better development ornon-closed surface has large local deformation after expansion, add notchesaccording to its characteristics of boundary. This paper uses Dijkstra algorithm tocalculate the shortest cut path of any points, and achieved good results.Finally, using the MATLAB program verified the effectiveness of the methodfor optimization on trigonometry mesh surface expansion in this paper.