Browsing by Author "Chai, Shuangming"

Now showing 1 - 3 of 3
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    Constrained Remeshing Using Evolutionary Vertex Optimization
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Zhang, Wen-Xiang; Wang, Qi; Guo, Jia-Peng; Chai, Shuangming; Liu, Ligang; Fu, Xiao-Ming; Chaine, Raphaëlle; Kim, Min H.
    We propose a simple yet effective method to perform surface remeshing with hard constraints, such as bounding approximation errors and ensuring Delaunay conditions. The remeshing is formulated as a constrained optimization problem, where the variables contain the mesh connectivity and the mesh geometry. To solve it effectively, we adopt traditional local operations, including edge split, edge collapse, edge flip, and vertex relocation, to update the variables. Central to our method is an evolutionary vertex optimization algorithm, which is derivative-free and robust. The feasibility and practicability of our method are demonstrated in two applications, including error-bounded Delaunay mesh simplification and error-bounded angle improvement with a given number of vertices, over many models. Compared to state-of-the-art methods, our method achieves higher remeshing quality.
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    Interactive Editing of Discrete Chebyshev Nets
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Li, Rui-Zeng; Guo, Jia-Peng; Wang, Qi; Chai, Shuangming; Liu, Ligang; Fu, Xiao-Ming; Chaine, Raphaëlle; Kim, Min H.
    We propose an interactive method to edit a discrete Chebyshev net, which is a quad mesh with edges of the same length. To ensure that the edited mesh is always a discrete Chebyshev net, the maximum difference of all edge lengths should be zero during the editing process. Hence, we formulate an objective function using lp-norm (p > 2) to force the maximum length deviation to approach zero in practice. To optimize the nonlinear and non-convex objective function interactively and efficiently, we develop a novel second-order solver. The core of the solver is to construct a new convex majorizer for our objective function to achieve fast convergence. We present two acceleration strategies to further reduce the optimization time, including adaptive p change and adaptive variables reduction. A large number of experiments demonstrate the capability and feasibility of our method for interactively editing complex discrete Chebyshev nets.
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    Precise High-order Meshing of 2D Domains with Rational Bézier Curves
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Yang, Jinlin; Liu, Shibo; Chai, Shuangming; Liu, Ligang; Fu, Xiao-Ming; Campen, Marcel; Spagnuolo, Michela
    We propose a novel method to generate a high-order triangular mesh for an input 2D domain with two key characteristics: (1) the mesh precisely conforms to a set of input piecewise rational domain curves, and (2) the geometric map on each curved triangle is injective. Central to the algorithm is a new sufficient condition for placing control points of a rational Bézier triangle to guarantee that the conformance and injectivity constraints are theoretically satisfied. Taking advantage of this condition, we provide an explicit construct that robustly creates higher-order 2D meshes satisfying the two characteristics. We demonstrate the robustness and effectiveness of our algorithm over a data set containing 2200 examples.