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A Fast and Memory-Efficient Direct Rendering Method for Polynomial-Based implicit surfaces

Computer Modeling in Engineering & Sciences 2024年第11期141卷 1033-1046页

作者： Jiayu Ren Susumu Nakata Graduate School of Information Science and Engineering Ritsumeikan UniversityIbarakiOsaka567-8570Japan2 College School of Information Science and Engineering Ritsumeikan UniversityIbarakiOsaka567-8570Japan

Three-dimensional surfaces are typically modeled as implicit ***,direct rendering of implicit surfaces is not simple,especially when such surfaces contain finely detailed *** approach is ray-casting,where the field of the implicit surface is assumed to be piecewise polynomials defined on the grid of a rectangular domain.A critical issue for direct rendering based on ray-casting is the computational cost of finding intersections between surfaces and *** particular,ray-casting requires many function evaluations along each ray,severely slowing the rendering *** this paper,a method is proposed to achieve direct rendering of polynomial-based implicit surfaces in real-time by strategically narrowing the search range and designing the shader to exploit the structure of piecewise *** experiments,the proposed method achieved a high framerate performance for different test cases,with a speed-up factor ranging from 1.1 to *** addition,the proposed method demonstrated better efficiency with high cell *** terms of memory consumption,the proposed method saved between 90.94%and 99.64%in different test ***,the proposed method became more memory-efficient as the cell resolution increased.

关键词： implicit surfaces direct rendering ray marching

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Technologies for implicit surfaces sampling with particle systems

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Computer Aided Drafting,Design and Manufacturing 2012年第3期22卷 65-70页

作者： LI Weitao ZHANG Caiming LIU Qian ZHANG Xin School of Compute Science and Technology Shandong University Jinan 250101 China Shandong Province Key Lab of Digital Media Technology Shandong University of Finance and Economics Jinan 250101 China

Point-based surface has been widely used in computer graphics for modeling, animation, visualization, simulation of liq- uid and so on. Furthermore, particle-based approach can distribute the surface sampling points and control its parameters according to the needs of the application. In this paper, we examine several kinds of algorithms presented over the last decades, with the main focus on particle sampling technologies for implicit surface. Therefore, we classify various algorithms into categories, describe main ideas behind each categories, and compare the advantages and shortcomings of the algorithms in each category.

关键词： implicit surfaces particle sampling minimizing energy

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Interactive Restoration of Three-Dimensional implicit Surface with Irregular Parts

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Computer Modeling in Engineering & Sciences 2023年第9期136卷 2111-2125页

作者： Jiayu Ren Yoshihisa Fujita Susumu Nakata Graduate School of Information Science and Engineering Ritsumeikan UniversityShiga525-8577Japan College of Information Science and Engineering Ritsumeikan UniversityShiga525-8577Japan

implicit surface generation based on the interpolation of surface points is one of the well-known modeling methods in the area of computer *** methods for the implicit surface reconstruction from surface points have been proposed on the basis of radial basis functions,a weighted sum of local functions,splines,wavelets,and combinations of ***,if the surface points contain errors or are sparsely distributed,irregular components,such as curvature-shaped redundant bulges and unexpectedly generated high-frequency components,are commonly *** paper presents a framework for restoring irregular components generated on and around *** are assumed to specify local masks that cover irregular components and parameters that determine the degree of *** algorithm in this paper removes the defects based on the user-specific masks and *** have shown that the proposed methods can effectively remove redundant protrusions and jaggy noise.

关键词： Shape modeling implicit surfaces interactive restoration

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A unified framework for isotropic meshing based on narrowband Euclidean distance transformation

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Computational Visual Media 2015年第3期1卷 239-251页

作者： Yuen-Shan Leung Xiaoning Wang Ying He Yong-Jin Liu Charlie C.L.Wang School of Computer Engineering Nanyang Technological University Department of Computer Science and Technology Tsinghua University Department of Mechanical and Automation Engineering The Chinese University of Hong Kong

In this paper, we propose a simpleyet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation(CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing highquality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient,and can construct the shell space for resolutions up to 20483 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-ofthe-art techniques, but is significantly faster than conventional CPU-based implementations.

关键词： centroidal Voronoi tessellation(CVT) Euclidean distance transformation GPU isotropic meshing polygonal meshes point clouds implicit surfaces

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Developable algebraic surfaces

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Progress in Natural Science:Materials International 2004年第3期 70-76页

作者： CHEN Dongren and WANG Guojin*(Institute of Images and Graphics, State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China)

An algebraic surface can be defined by an implicit polynomial equation F(x,y,z)=0 . In this paper, general characterizations of developable algebraic surfaces of arbitrary degree are presented. Using the shift operators of the subscripts of Bézier ordinates, the uniform apparent discriminants of developable algebraic surfaces to their Bézier ordinates are given directly. To degree 2 algebraic surfaces, which are widely used in computer aided geometric design and graphics, all possible developable surface types are obtained. For more conveniently applying algebraic surfaces of high degree to computer aided geometric design, the notion of ε quasi developable surfaces is introduced, and an example of using a quasi developable algebraic surface of degree 3 to interpolate three curves of degree 2 is given.

关键词： implicit surfaces algebraic surfaces developable surfaces shift operators.

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