Research On A Mesh-based Approach For Mesh-free Method Planar Shape Deformation

Planar shape deformation has wide applications in computer graphics and geometric processing,and this technology can help users to obtain new shapes according to their own ideas.Planar shape deformation can usually be expressed as a mapping function between Euclidean planes.According to the form of the representation function,these methods can be generally divided into two categories:mesh-based methods and mesh-free methods.Traditional mesh-based methods can flexibly control the distortions of the deformation but has the weakness of non-smooth due to its piecewise-linear nature and their efficiency is largely affected by the mesh resolution.And the mesh-free methods have the feature of smoothness,but most of them are lack of distortion control.Though a few take distortions into consideration,the computation is complicated and time-consuming.In order to keep the shape of local mesh element as much as possible and control the smoothness of the deformation,we research the traditional mesh-based methods and mesh-free methods.The main work of this paper includes the following two aspects:(1)We combine the advantages with the both methods and present a mesh-free method planar shape deformation assisted with mesh-based method.It uses smooth basis functions to represent the deformation and borrows the computational framework of the mesh-based methods.In detail,it constructs a triangle-mesh structure on the deformation domain to flexibly control the distortions and linearly approximates the numerical calculus of deformation energy by using the mesh structure as well as foldover-free constraints to meet different deformation requirements.(2)In order to conveniently and intuitively compare the presented algorithm with the traditional methods,we design and implement a real-time planar shape deformation system based on OpenGL 4.6.It includes the mesh-based methods(ARAP deformation algorithm on the mesh domain,SLIM deformation algorithm on the mesh domain),and the mesh-free method used by AMIPS,and our algorithm.By the system,we show the deformation effects,response times and distortions of different algorithms,thus further verifying the superiority of our algorithm.In this end,we apply our algorithm to Virtual Try-On and you can get different poses of a cloth image by editing it.Experiment shows that our method is simple,efficient controllable,and extendable,and the deformation results are smooth and natural.In addition,it can effectively prevent the mesh element from flipping.