Research On Approaches Of Deformation Simulation And Collision Detection Driven By Medial Axis Transform For 3D Models

The simulation technology of deformable object on 3D model has been a hot topic in computer graphics.It has in-depth applications in the many fields,such as digital twin,virtual reality and reverse engineering.It contains two key issues.One is how to describe the laws of motion for models based on geometric or physical methods.The other is how to handle collision problem efficiently in a motion's scene.In recent years,with the improvement on the technology of 3D scanning and modeling,the high-resolution models are more and more available that have rich shape's details and complex structures.As the result,there are some new challenges for using the models.The first is that it becomes more and more difficult to balance the computation efficiency and simulation quality.The second is that the hierarchical bounding box method does not perform well in collision detection of deformable object.To make matters worse,deformed calculation's module and collision detection's are independent for each other in the traditional simulation framework.Such a design of framework produces a significant amount of computational overhead.Therefore,the research target of the thesis is to use medial axis transform to solve the above problem.The main contributions of this research are summarized as follows:First,a medial axis-driven skinning deformation method is proposed.The method belongs to the geometry-based mechanism.The method takes the advantage of medial axis transform,and maps the features of 3D mesh to medial mesh.This is the first innovation in the thesis.The medial mesh is deformed according to as-rigid-as-possible deformation,then drive the deformation of mesh by parameter coordinates.Finally,the features are restored on deformed mesh through the iso-surface projection,tangential relaxation and global volume preservation.The results show that the method can preserve the local feature and global volume.Second,how to speed up the computation of deformation and collision detection are researched,while keep up the quality of simulation based on physical mechanism of elastics bodies.On the one hand,a medial axis-driven physical deformation method for elastic bodies is proposed.This method uses model reduction technology to reduce the global step of projective dynamics by medial mesh.Because medial axis transform is a precise shape skeleton,it is able to capture richer deformation features,and significantly improve the solving speed of nonlinear dynamics system.On the other hand,a medial axis-driven collision detection method is proposed.The medial primitives are used as bounding boxes in the method.The thesis presents and proves a closed-form and simple method to test medial primitives are overlapping or not.If they are overlapping,the deepest points can be calculated precisely.Combined with the spatial subdivision grid,the colliding triangle pairs are found.The second innovation is employing medial axis transform on deformation of elastics bodies and collision detection,respectively,and achieves a significant improvement in efficiency.Third,Medial Elastics are presented as a simulation framework in this thesis.Medial Elastics unifies the calculation unit of the deformation and collision detection method on the same medial mesh,and then couples the two calculation modules.This is the third innovation of the thesis.The radii of medial sphere are updated directly by generalized coordinates.As the result,Medial Elastics takes only a less time consume to maintain the model to be enclosed in the union of medial primitives.For the traditional framework,updating a hierarchical tree of bounding box or a spatial hash table is usually the bottleneck of computational efficiency.In addition,Medial Elastics is very friendly to parallel computing.The entire calculations are implemented on the GPU parallel architecture.The results show that Medial Elastics is able to simulate the scenes with multiple high-resolution models at interactive speeds.The scenes include rich and complex collision events and the visual effects are very impressive.