| The simulation of the deformable solids is one of the most important branch of physical-based simulation,which is widely used in many related industries,such as virtual reality,animations and movies,games.At present,the existing fields of the deformable solids simulation have achieved a lot of researches in the material selection,deformable effects,numerical solving methods and efficiency,et al.For the material selection part,we develop the heterogeneous materials and the example-based materials.Considering the numerical simulation method,we utilize the material point method and the finite element method.We extend the animation range of the material point method and we enhance the simulation efficiency of the finite element method for the example-based materials with different topology structures.For recent years,the material point method has been proved to be an important simulation method in the physically-based simulation fields.While it still has some limitations for the elastic materials,especially for the heterogeneous materials which are more general in nature world.Since the interpolation between the background grids and the particles are only based on the geometry position of the particles without considering the material properties,the movement of particles will act as an ―average‖ effect in one grid.To make up for the deficiency,we propose a simulation method for heterogeneous elastic materials.Firstly,in the pre-computation process,the simulation object is discretized as particles,then the material boundaries and the corresponding boundary particles are established according to the distribution of the particles with different properties.The locations of the boundary particles are updated dynamically during the simulation process.And we introduce the particle impact domains to separate different particles which increase the computing DOF(degree of freedom)inside the grid.According to the position of the material boundaries,we present a criterion to judge that the calculation of the simulation particles is on the background computing grids or on the particle domains.Secondly,there are several collision objects are involved in the simulation process.The traditional material point method can automatically deal with collision issues without sliding,while it cannot deal with the sliding or separation situations.To demonstrate more deformation results,we take use of multiple background grids for different simulation objects.In addition,we also propose to increase the collision detection on the particle domains to avoid further penetration issue.The collision process is divided into two stages,which are calculated on the background grids and the particle domains,separately.The colliding objects include rigid body and the deformable solid,which increases the diversity of the simulation effects.Thirdly,we obtain the eigenfunctions by solving the eigenvalue problem of the Laplace-Beltrami Operator on the tetrahedral mesh.Objects with different topological structures achieve unified descriptions in the reduced shape interpolation subspace constructed by the eigenfunctions.The eigenfunctions constructed on the volumetric mesh directly obtain the inner vertices displacements of the simulation object on the projection and reconstruction process between the shape interpolation space and the Euclidean space.While the existing method computed the eigenfunctions on the surface meshes,the distributing displacements of the surface vertices to the inner vertices with a decreasing kernel function,which causes the loss of the computing precision and efficiency to some extent.In addition,we introduce the adding details method for the reconstruction mesh process and the pose transfer method for different topology structure models.Finally,the simulation method with example-based materials shows art-directed deformation effects,we achieve the real-time efficiency on the basis of the existing algorithms with different topology examples.We construct the interpolation shape subspace by the Laplace-Beltrami Operator and the model reduction subspace by the nonlinear modal basis.And we present a direct projection between the two reduced subspaces,which makes the shape interpolation process calculate totally on the subspace.In addition,the model reduction subspace enhances the linear equation solving speed.The experimental results demonstrate that the proposed method guarantees the real-time efficiency and at the same time keeps the different topology structures between the examples and the simulation object. |
