Periodic surface modeling for computer aided nano design

Wang, Yan

doi:10.1016/j.cad.2006.09.005

Cited by 101 publications

(44 citation statements)

References 24 publications

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“…With the observation that hyperbolic surfaces exist in nature ubiquitously and periodic features are common in condensed materials, we recently proposed an implicit surface modeling approach, periodic surface (PS), to represent geometric structures at nano scales [1,2]. Periodic surfaces are either loci or foci.…”

Section: Introductionmentioning

confidence: 99%

Computing Minkowski Sum of Periodic Surface Models

Wang

2009

Computer-Aided Design and Applications

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Recently we proposed a periodic surface model to assist geometric construction in computer-aided nano-design. This implicit surface model helps create super-porous nano structures parametrically and support crystal packing. In this paper, we study construction methods of Minkowski sums for periodic surfaces. A numerical approximation approach based on the Chebyshev polynomials is developed and can be applied in the formulations of surface normal direction matching and volume translations.

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Section: Introductionmentioning

confidence: 99%

Computing Minkowski Sum of Periodic Surface Models

Wang

2009

Computer-Aided Design and Applications

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“…With the observation that hyperbolic surfaces ubiquitously exist in nature and periodic features are common in condensed materials, we recently proposed an implicit surface modeling approach, periodic surface (herein referred to as PS), to represent geometric structures in nano scales [1,2]. Periodic surfaces are either loci or foci.…”

Section: Introductionmentioning

confidence: 99%

Loci Periodic Surface Reconstruction from Crystals

Wang¹

2007

Computer-Aided Design and Applications

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“…This paper deals with function-based approaches [1][2] [6], which provide solutions to most of the known problems that plague the traditional approaches to modeling in commercial CAD products. An approach to modeling periodical structures based on a triangle wave space mapping was presented in [6].…”

Section: Related Workmentioning

confidence: 99%

“…Recently the computational overhead and handling of complex models invoving microstructures was simplified by using function-based modeling [1] [2]. Precise parametrized constructive modeling based on real functions allows for the procedural definition of multi-scale microstructures, which can undergo blending, deformations, metamorphosis and other geometric operations.…”

Section: Introductionmentioning

confidence: 99%

Multi-scale space-variant FRep cellular structures

Fryazinov

Vilbrandt²,

Pasko

2013

Computer-Aided Design

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Existing mesh and voxel based modeling methods encounter difficulties when dealing with objects containing cellular structures on several scale levels and varying their parameters in space. We describe an alternative approach based on using real functions evaluated procedurally at any given point. This allows for modeling fully parameterized, nested and multi-scale cellular structures with dynamic variations in geometric and cellular properties. The geometry of a base unit cell is defined using Function Representation (FRep) based primitives and operations. The unit cell is then replicated in space using periodic space mappings such as sawtooth and triangle waves. While being replicated, the unit cell can vary its geometry and topology due to the use of dynamic parameterization. We illustrate this approach by several examples of microstructure generation within a given volume or along a given surface. We also outline some methods for direct rendering and fabrication not involving auxiliary mesh and voxel representations.

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Periodic surface modeling for computer aided nano design

Cited by 101 publications

References 24 publications

Computing Minkowski Sum of Periodic Surface Models

Computing Minkowski Sum of Periodic Surface Models

Loci Periodic Surface Reconstruction from Crystals

Multi-scale space-variant FRep cellular structures

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