Browsing by Author "Fu, Xiao-Ming"

Now showing 1 - 9 of 9
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    Computing Surface PolyCube-Maps by Constrained Voxelization
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Yang, Yang; Fu, Xiao-Ming; Liu, Ligang; Lee, Jehee and Theobalt, Christian and Wetzstein, Gordon
    We present a novel method to compute bijective PolyCube-maps with low isometric distortion. Given a surface and its preaxis- aligned shape that is not an exact PolyCube shape, the algorithm contains two steps: (i) construct a PolyCube shape to approximate the pre-axis-aligned shape; and (ii) generate a bijective, low isometric distortion mapping between the constructed PolyCube shape and the input surface. The PolyCube construction is formulated as a constrained optimization problem, where the objective is the number of corners in the constructed PolyCube, and the constraint is to bound the approximation error between the constructed PolyCube and the input pre-axis-aligned shape while ensuring topological validity. A novel erasing-and-filling solver is proposed to solve this challenging problem. Centeral to the algorithm for computing bijective PolyCube-maps is a quad mesh optimization process that projects the constructed PolyCube onto the input surface with high-quality quads. We demonstrate the efficacy of our algorithm on a data set containing 300 closed meshes. Compared to state-of-the-art methods, our method achieves higher practical robustness and lower mapping distortion.
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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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    Greedy Cut Construction for Parameterizations
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Zhu, Tianyu; Ye, Chunyang; Chai, Shuangming; Fu, Xiao-Ming; Panozzo, Daniele and Assarsson, Ulf
    We present a novel method to construct short cuts for parameterizations with low isometric distortion. The algorithm contains two steps: (i) detect feature points, where the distortion is usually concentrated; and (ii) construct a cut by connecting the detected feature points. Central to each step is a greedy method. After generating a redundant feature point set, a greedy filtering process is performed to identify the feature points required for low isometric distortion parameterizations. This filtering process discards the feature points that are useless for distortion reduction while still enabling us to obtain low isometric distortion. Next, we formulate the process of connecting the detected feature points as a Steiner tree problem. To find an approximate solution, we first successively and greedily produce a collection of auxiliary points. Then, a cut is constructed by connecting the feature points and auxiliary points. In the 26,299 test cases in which an exact solution to the Steiner tree problem is available, the length of the cut obtained by our method is on average 0.17% longer than optimal. Compared to state-of-the-art cut construction methods, our method is one order of magnitude faster and generates shorter cuts while achieving similar isometric distortion.
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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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    Large-Scale Worst-Case Topology Optimization
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Zhang, Di; Zhai, Xiaoya; Fu, Xiao-Ming; Wang, Heming; Liu, Ligang; Umetani, Nobuyuki; Wojtan, Chris; Vouga, Etienne
    We propose a novel topology optimization method to efficiently minimize the maximum compliance for a high-resolution model bearing uncertain external loads. Central to this approach is a modified power method that can quickly compute the maximum eigenvalue to evaluate the worst-case compliance, enabling our method to be suitable for large-scale topology optimization. After obtaining the worst-case compliance, we use the adjoint variable method to perform the sensitivity analysis for updating the density variables. By iteratively computing the worst-case compliance, performing the sensitivity analysis, and updating the density variables, our algorithm achieves the optimized models with high efficiency. The capability and feasibility of our approach are demonstrated over various large-scale models. Typically, for a model of size 512×170×170 and 69934 loading nodes, our method took about 50 minutes on a desktop computer with an NVIDIA GTX 1080Ti graphics card with 11 GB memory.
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    Memory-Efficient Bijective Parameterizations of Very-Large-Scale Models
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Ye, Chunyang; Su, Jian-Ping; Liu, Ligang; Fu, Xiao-Ming; Eisemann, Elmar and Jacobson, Alec and Zhang, Fang-Lue
    As high-precision 3D scanners become more and more widespread, it is easy to obtain very-large-scale meshes containing at least millions of vertices. However, processing these very-large-scale meshes is still a very challenging task due to memory limitations. This paper focuses on a fundamental geometric processing task, i.e., bijective parameterization construction. To this end, we present a spline-enhanced method to compute bijective and low distortion parameterizations for very-large-scale disk topology meshes. Instead of computing descent directions using the mesh vertices as variables, we estimate descent directions for each vertex by optimizing a proxy energy defined in spline spaces. Since the spline functions contain a small set of control points, it significantly decreases memory requirement. Besides, a divide-and-conquer method is proposed to obtain bijective initializations, and a submesh-based optimization strategy is developed to reduce distortion further. The capability and feasibility of our method are demonstrated over various complex models. Compared to the existing methods for bijective parameterizations of very-large-scale meshes, our method exhibits better scalability and requires much less memory.
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    Practical Fabrication of Discrete Chebyshev Nets
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Liu, Hao-Yu; Liu, Zhong-Yuan; Zhao, Zheng-Yu; Liu, Ligang; Fu, Xiao-Ming; Eisemann, Elmar and Jacobson, Alec and Zhang, Fang-Lue
    We propose a computational and practical technique to allow home users to fabricate discrete Chebyshev nets for various 3D models. The success of our method relies on two key components. The first one is a novel and simple method to approximate discrete integrable, unit-length, and angle-bounded frame fields, used to model discrete Chebyshev nets. Central to our field generation process is an alternating algorithm that takes turns executing one pass to enforce integrability and another pass to approach unit length while bounding angles. The second is a practical fabrication specification. The discrete Chebyshev net is first partitioned into a set of patches to facilitate manufacturing. Then, each patch is assigned a specification on pulling, bend, and fold to fit the nets. We demonstrate the capability and feasibility of our method in various complex models.
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    Practical Foldover-Free Volumetric Mapping Construction
    (The Eurographics Association and John Wiley & Sons Ltd., 2019) Su, Jian-Ping; Fu, Xiao-Ming; Liu, Ligang; Lee, Jehee and Theobalt, Christian and Wetzstein, Gordon
    In this paper, we present a practically robust method for computing foldover-free volumetric mappings with hard linear constraints. Central to this approach is a projection algorithm that monotonically and efficiently decreases the distance from the mapping to the bounded conformal distortion mapping space. After projection, the conformal distortion of the updated mapping tends to be below the given bound, thereby significantly reducing foldovers. Since it is non-trivial to define an optimal bound, we introduce a practical conformal distortion bound generation scheme to facilitate subsequent projections. By iteratively generating conformal distortion bounds and trying to project mappings into bounded conformal distortion spaces monotonically, our algorithm achieves high-quality foldover-free volumetric mappings with strong practical robustness and high efficiency. Compared with existing methods, our method computes mesh-based and meshless volumetric mappings with no prescribed conformal distortion bounds. We demonstrate the efficacy and efficiency of our method through a variety of geometric processing tasks.
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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.