Journal Article10.1007/BF02464333
Function representation in geometric modeling : concepts, implementation and applications
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TL;DR: This work uses a high-level geometric language that can extend the interactive modeling system by input symbolic descriptions of primitives, operations, and predicates and supports combinations of representational styles, including constructive geometry, sweeping, soft objects, voxel-based objects, deformable and other animated objects.
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Abstract: Concepts of functionally based geometric modeling including sets of objects, operations, and relations are discussed. Transformations of a defining real function are described for set-theoretic operations, blending, offsetting, bijective mapping, projection, cartesian products, and metamorphosis. Inclusion, point membership, and intersection relations are also described. We use a high-level geometric language that can extend the interactive modeling system by input symbolic descriptions of primitives, operations, and predicates. This approach supports combinations of representational styles, including constructive geometry, sweeping, soft objects, voxel-based objects, deformable and other animated objects. Application examples of aesthetic design, collisions simulation, NC machining, range data processing, and 3D texture generation are given.
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Citations
Laplacian surface editing
Olga Sorkine,Daniel Cohen-Or,Yaron Lipman,Marc Alexa,Christian Rössl,Hans-Peter Seidel +5 more
- 08 Jul 2004
TL;DR: In this paper, the Laplacian of the mesh is enhanced to be invariant to locally linearized rigid transformations and scaling, which can be used to perform surface editing at interactive rates.
Laplacian Surface Editing
Olga Sorkine,Yaron Lipman,Daniel Cohen-Or,Marc Alexa,Christian Rössl,Hans-Peter Seidel,Roberto Scopigno,Denis Zorin,Dieter W. Fellner,Stephen N. Spencer +9 more
- 01 Jan 2004
TL;DR: This work argues that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation, and provides such a representation, based on the Laplacian of the mesh, by encoding each vertex relative to its neighborhood.
826
Modeling video evolution for action recognition
Basura Fernando,Efstratios Gavves,M José Oramas,Amir Ghodrati,Tinne Tuytelaars +4 more
- 07 Jun 2015
TL;DR: The proposed method to capture video-wide temporal information for action recognition postulate that a function capable of ordering the frames of a video temporally captures well the evolution of the appearance within the video.
Fast surface reconstruction using the level set method
Hongkai Zhao,Stanley Osher,Ronald Fedkiw +2 more
- 13 Jul 2001
TL;DR: The level set method and fast sweeping and tagging methods are used to reconstruct surfaces from a scattered data set and the reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density.
Additive manufacturing of functionally graded materials: A review
Chi Zhang,Fei Chen,Zhifeng Huang,Jia Mingyong,Guiyi Chen,Yongqiang Ye,Yaojun Lin,Wei Liu,Bingqing Chen,Qiang Shen,Lianmeng Zhang,Enrique J. Lavernia +11 more
TL;DR: A review of the state-of-the-art in FGM can be found in this paper, where the authors present their current understanding of important issues, such as modeling, processing, microstructures and mechanical properties.
447
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