Browsing by Author "Ren, Xiaohua"

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    Biorthogonal Wavelet Surface Reconstruction Using Partial Integrations
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Ren, Xiaohua; Lyu, Luan; He, Xiaowei; Cao, Wei; Yang, Zhixin; Sheng, Bin; Zhang, Yanci; Wu, Enhua; Fu, Hongbo and Ghosh, Abhijeet and Kopf, Johannes
    We introduce a new biorthogonal wavelet approach to creating a water-tight surface defined by an implicit function, from a finite set of oriented points. Our approach aims at addressing problems with previous wavelet methods which are not resilient to missing or nonuniformly sampled data. To address the problems, our approach has two key elements. First, by applying a three-dimensional partial integration, we derive a new integral formula to compute the wavelet coefficients without requiring the implicit function to be an indicator function. It can be shown that the previously used formula is a special case of our formula when the integrated function is an indicator function. Second, a simple yet general method is proposed to construct smooth wavelets with small support. With our method, a family of wavelets can be constructed with the same support size as previously used wavelets while having one more degree of continuity. Experiments show that our approach can robustly produce results comparable to those produced by the Fourier and Poisson methods, regardless of the input data being noisy, missing or nonuniform. Moreover, our approach does not need to compute global integrals or solve large linear systems.
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    Fracture Patterns Design for Anisotropic Models with the Material Point Method
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Cao, Wei; Lyu, Luan; Ren, Xiaohua; Zhang, Bob; Yang, Zhixin; Wu, Enhua; Eisemann, Elmar and Jacobson, Alec and Zhang, Fang-Lue
    Physically plausible fracture animation is a challenging topic in computer graphics. Most of the existing approaches focus on the fracture of isotropic materials. We proposed a frame-field method for the design of anisotropic brittle fracture patterns. In this case, the material anisotropy is determined by two parts: anisotropic elastic deformation and anisotropic damage mechanics. For the elastic deformation, we reformulate the constitutive model of hyperelastic materials to achieve anisotropy by adding additional energy density functions in particular directions. For the damage evolution, we propose an improved phasefield fracture method to simulate the anisotropy by designing a deformation-aware second-order structural tensor. These two parts can present elastic anisotropy and fractured anisotropy independently, or they can be well coupled together to exhibit rich crack effects. To ensure the flexibility of simulation, we further introduce a frame-field concept to assist in setting local anisotropy, similar to the fiber orientation of textiles. For the discretization of the deformable object, we adopt a novel Material Point Method(MPM) according to its fracture-friendly nature. We also give some design criteria for anisotropic models through comparative analysis. Experiments show that our anisotropic method is able to be well integrated with the MPM scheme for simulating the dynamic fracture behavior of anisotropic materials.
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    A Second-Order Explicit Pressure Projection Method for Eulerian Fluid Simulation
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Jiang, Junwei; Shen, Xiangda; Gong, Yuning; Fan, Zeng; Liu, Yanli; Xing, Guanyu; Ren, Xiaohua; Zhang, Yanci; Dominik L. Michels; Soeren Pirk
    In this paper, we propose a novel second-order explicit midpoint method to address the issue of energy loss and vorticity dissipation in Eulerian fluid simulation. The basic idea is to explicitly compute the pressure gradient at the middle time of each time step and apply it to the velocity field after advection. Theoretically, our solver can achieve higher accuracy than the first-order solvers at similar computational cost. On the other hand, our method is twice and even faster than the implicit second-order solvers at the cost of a small loss of accuracy. We have carried out a large number of 2D, 3D and numerical experiments to verify the effectiveness and availability of our algorithm.