Browsing by Author "Deng, Chongyang"

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    Gauss-Seidel Progressive Iterative Approximation (GS-PIA) for Loop Surface Interpolation
    (The Eurographics Association, 2018) Wang, Zhihao; Li, Yajuan; Ma, Weiyin; Deng, Chongyang; Fu, Hongbo and Ghosh, Abhijeet and Kopf, Johannes
    We propose a Gauss-Seidel progressive iterative approximation (GS-PIA) method for Loop subdivision surface interpolation by combining classical Gauss-Seidel iterative method for linear system and progressive iterative approximation (PIA) for data interpolation. We prove that GS-PIA is convergent by applying matrix theory. GS-PIA algorithm retains the good features of the classical PIA method, such as the resemblance with the given mesh and the advantages of both a local method and a global method. Compared with some existed interpolation methods of subdivision surfaces, GS-PIA algorithm has advantages in three aspects. First, it has a faster convergence rate compared with the PIA and WPIA algorithms. Second, compared with WPIA algorithm, GS-PIA algorithm need not to choose weights. Third, GS-PIA need not to modify the mesh topology compared with other methods with fairness measures. Numerical examples for Loop subdivision surfaces interpolation illustrated in this paper show the efficiency and effectiveness of GS-PIA algorithm.
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    Maximum Likelihood Coordinates
    (The Eurographics Association and John Wiley & Sons Ltd., 2023) Chang, Qingjun; Deng, Chongyang; Hormann, Kai; Memari, Pooran; Solomon, Justin
    Any point inside a d-dimensional simplex can be expressed in a unique way as a convex combination of the simplex's vertices, and the coefficients of this combination are called the barycentric coordinates of the point. The idea of barycentric coordinates extends to general polytopes with n vertices, but they are no longer unique if n>d+1. Several constructions of such generalized barycentric coordinates have been proposed, in particular for polygons and polyhedra, but most approaches cannot guarantee the non-negativity of the coordinates, which is important for applications like image warping and mesh deformation. We present a novel construction of non-negative and smooth generalized barycentric coordinates for arbitrary simple polygons, which extends to higher dimensions and can include isolated interior points. Our approach is inspired by maximum entropy coordinates, as it also uses a statistical model to define coordinates for convex polygons, but our generalization to non-convex shapes is different and based instead on the project-and-smooth idea of iterative coordinates. We show that our coordinates and their gradients can be evaluated efficiently and provide several examples that illustrate their advantages over previous constructions.