Browsing by Author "Fu, Chi-Wing"

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    Computational Design and Optimization of Non-Circular Gears
    (The Eurographics Association and John Wiley & Sons Ltd., 2020) Xu, Hao; Fu, Tianwen; Song, Peng; Zhou, Mingjun; Fu, Chi-Wing; Mitra, Niloy J.; Panozzo, Daniele and Assarsson, Ulf
    We study a general form of gears known as non-circular gears that can transfer periodic motion with variable speed through their irregular shapes and eccentric rotation centers. To design functional non-circular gears is nontrivial, since the gear pair must have compatible shape to keep in contact during motion, so the driver gear can push the follower to rotate via a bounded torque that the motor can exert. To address the challenge, we model the geometry, kinematics, and dynamics of non-circular gears, formulate the design problem as a shape optimization, and identify necessary independent variables in the optimization search. Taking a pair of 2D shapes as inputs, our method optimizes them into gears by locating the rotation center on each shape, minimally modifying each shape to form the gear's boundary, and constructing appropriate teeth for gear meshing. Our optimized gears not only resemble the inputs but can also drive the motion with relatively small torque. We demonstrate our method's usability by generating a rich variety of non-circular gears from various inputs and 3D printing several of them.
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    Curve Complexity Heuristic KD-trees for Neighborhood-based Exploration of 3D Curves
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Lu, Yucheng; Cheng, Luyu; Isenberg, Tobias; Fu, Chi-Wing; Chen, Guoning; Liu, Hui; Deussen, Oliver; Wang, Yunhai; Mitra, Niloy and Viola, Ivan
    We introduce the curve complexity heuristic (CCH), a KD-tree construction strategy for 3D curves, which enables interactive exploration of neighborhoods in dense and large line datasets. It can be applied to searches of k-nearest curves (KNC) as well as radius-nearest curves (RNC). The CCH KD-tree construction consists of two steps: (i) 3D curve decomposition that takes into account curve complexity and (ii) KD-tree construction, which involves a novel splitting and early termination strategy. The obtained KD-tree allows us to improve the speed of existing neighborhood search approaches by at least an order of magnitude (i. e., 28× for KNC and 12× for RNC with 98% accuracy) by considering local curve complexity. We validate this performance with a quantitative evaluation of the quality of search results and computation time. Also, we demonstrate the usefulness of our approach for supporting various applications such as interactive line queries, line opacity optimization, and line abstraction.
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    Non-Local Low-Rank Normal Filtering for Mesh Denoising
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Li, Xianzhi; Zhu, Lei; Fu, Chi-Wing; Heng, Pheng-Ann; Fu, Hongbo and Ghosh, Abhijeet and Kopf, Johannes
    This paper presents a non-local low-rank normal filtering method for mesh denoising. By exploring the geometric similarity between local surface patches on 3D meshes in the form of normal fields, we devise a low-rank recovery model that filters normal vectors by means of patch groups. In summary, our method has the following key contributions. First, we present the guided normal patch covariance descriptor to analyze the similarity between patches. Second, we pack normal vectors on similar patches into the normal-field patch-group (NPG) matrix for rank analysis. Third, we formulate mesh denoising as a low-rank matrix recovery problem based on the prior that the rank of the NPG matrix is high for raw meshes with noise, but can be significantly reduced for denoised meshes, whose normal vectors across similar patches should be more strongly correlated. Furthermore, we devise an objective function based on an improved truncated 'gamma' norm, and derive an optimization procedure using the alternative direction method of multipliers and iteratively re-weighted least squares techniques.We conducted several experiments to evaluate our method using various 3D models, and compared our results against several state-of-the-art methods. Experimental results show that our method consistently outperforms other methods and better preserves the fine details.
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    Worst-Case Rigidity Analysis and Optimization for Assemblies with Mechanical Joints
    (The Eurographics Association and John Wiley & Sons Ltd., 2022) Liu, Zhenyuan; Hu, Jingyu; Xu, Hao; Song, Peng; Zhang, Ran; Bickel, Bernd; Fu, Chi-Wing; Chaine, Raphaëlle; Kim, Min H.
    We study structural rigidity for assemblies with mechanical joints. Existing methods identify whether an assembly is structurally rigid by assuming parts are perfectly rigid. Yet, an assembly identified as rigid may not be that ''rigid'' in practice, and existing methods cannot quantify how rigid an assembly is. We address this limitation by developing a new measure, worst-case rigidity, to quantify the rigidity of an assembly as the largest possible deformation that the assembly undergoes for arbitrary external loads of fixed magnitude. Computing worst-case rigidity is non-trivial due to non-rigid parts and different joint types. We thus formulate a new computational approach by encoding parts and their connections into a stiffness matrix, in which parts are modeled as deformable objects and joints as soft constraints. Based on this, we formulate worst-case rigidity analysis as an optimization that seeks the worst-case deformation of an assembly for arbitrary external loads, and solve the optimization problem via an eigenanalysis. Furthermore, we present methods to optimize the geometry and topology of various assemblies to enhance their rigidity, as guided by our rigidity measure. In the end, we validate our method on a variety of assembly structures with physical experiments and demonstrate its effectiveness by designing and fabricating several structurally rigid assemblies.