Research On Surface Deformation Technologies Based On Triangular Mesh

With the development of 3D scanning equipment and computer hardware and the integration of computer graphics and modern network technology,the branch of digital geometry processing has been developed.Digital geometry processing focuses on the acquisition and processing of massive 3D geometry data,which is widely used in computer animation,virtual reality,geometric modeling and other fields.Mesh deformation mainly deals with the rigid and non-rigid motions of the object.The only change is the geometric information of the model,and the topology connection information of the model is maintained.Through the deformation operation,the modeler can make good use of the existing three-dimensional model information and greatly improve the modeling efficiency.Because of its simple manipulation and easy implementation,mesh deformation technology has attracted a lot of attention in the industry,and has produced a lot of algorithms.Good mesh deformation technology usually needs to meet the characteristics of fast interaction speed,maintaining local details,simulating the real world object motions,and keeping deformation smooth and so on.we deeply study the mesh deformation technology and propose some new deformation methods from the perspective of performance,shape preserved and physical reality.Main contributions of the dissertation include:(1)This paper proposes a two-level framework mesh deformation technique.At present,there are many algorithms for mesh surface deformation,but most algorithms often exhibit either low performance or shape distortion for dense meshes,such as self-intersection,volume shrinkage,local collapse and so on.To solve these problems,we propose a an efficient and real-time deformation technology.First,we simplify the source model,and transfer the deformation of the simplified mesh to the source model to generate the initial deformation results quickly.Then the dual iterative optimization algorithm is used to adjust the deformed vertex positions to ensure the smoothness and shape-preserved of the final deformation results.The goal of our algorithm is to embed the simplified mesh into the original mesh,and then manipulate the simplified mesh to obtain the final deformation results,so as to maintain the local shape of the source mesh and improve the deformation efficiency.(2)We present a rigidity control mesh deformation technique.Real-world objects are often composed of different materials,their rigidity behavior during deformation varies across the surface.Therefore,during deformation we need to consider the physical material properties of the object,so as to be able to simulate the movement of the object more realistically.In the(1)algorithm,since we do not consider the material properties of the object itself,so it is difficult to simulate the real movement of the object.This paper presents a mesh deformation technique with material properties,which combines global and local stiffness parameters to simulate the real motion of the object.The combination of stiffness coefficients provides an intuitive way for users to specify the material stiffness of objects,and allows users to simulate the shape deformation composed of different materials.Since the algorithm we proposed only needs to solve a non-linear energy function,which is simple and effective.The deformation results not only conform to the physical properties of the object,but also keep the local geometric details.(3)We presents an example-driven mesh deformation technology.Stiffness-controlled mesh deformation technology often requires a lot of physical modeling,and users need to carefully model and analyze objects,thus greatly increasing the amount of manual interaction.In this paper,we propose an example-driven mesh deformation technique.This technique mainly uses some existing deformation models in shape space to guide mesh deformation.The main idea of our algorithm is to define a rotation invariant feature representation and a reconstruction framework to accurately reconstruct the vertex position of the model.Through the combination of feature representation and reconstruction framework,the example-driven mesh deformation technique is formulated as to solve a nonlinear energy function to find the closest model in shape space.By effectively utilizing the knowledge in shape space,our method produces real deformation results and reduces a large number of manual interaction operations.Although the three research works in this paper are independent,they complement each other and deepen layer by layer.A large number of experiments show that the theories proposed in this paper are basically correct,the algorithms are effective and robust.