Degree Operations on Periodic Surfaces

2007 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Surface Model ◽  
Implicit Surface ◽  
Periodic Surface ◽  
Degree Elevation ◽  
Periodic Surfaces ◽  
Computer Aided ◽  
Particle Aggregates

In previous work, a periodic surface model for computer-aided nano-design (CAND) was developed. This implicit surface model can construct Euclidean and hyperbolic nano geometries parametrically and represent morphologies of particle aggregates and polymers. In this paper, we study the characteristics of degree elevation and reduction based on a generalized periodic surface model. Methods of degree elevation and reduction operations are developed in order to support multi-resolution representation and model exchange.

Minkowski Sums of Periodic Surface Models

2009 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Crystal Packing ◽  
Surface Model ◽  
Implicit Surface ◽  
Periodic Surface ◽  
Construction Methods ◽  
Periodic Surfaces ◽  
Nano Structures ◽  
Surface Models ◽  
Minkowski Sums ◽  
Volume Translation

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 both surface normal direction matching and volume translation formulations.

Feature-Based Crystal Construction in Computer-Aided Nano-Design

2008 ◽  
Author(s):  
Cheng Qi ◽  
Yan Wang
Keyword(s):  
Material Design ◽  
Surface Model ◽  
Periodic Surface ◽  
Periodic Surfaces ◽  
Nano Structures ◽  
Rapid Construction ◽  
Computer Aided ◽  
Feature Based ◽  
Basic Features ◽  
Complex Crystal

Providing nano engineers and scientists efficient and easy-to-use tools to create geometry conformations that have minimum energies is highly desirable in material design. Recently we developed a periodic surface model to assist the construction of nano structures parametrically for computeraided nano-design. In this paper, we present a feature-based approach for crystal construction. The proposed approach starts to create models of basic features by the aide of periodic surfaces followed by operations between basic features. The goal is to introduce a rapid construction method for complex crystal structures.

3D Fractals From Periodic Surfaces

2010 ◽  
Author(s):  
Yan Wang
Keyword(s):  
Porous Silicon ◽  
Iterated Function Systems ◽  
Surface Model ◽  
Porous Structures ◽  
Implicit Surface ◽  
Periodic Surface ◽  
Irregular Structures ◽  
Periodic Surfaces ◽  
Iterated Function ◽  
3D Fractals

Fractals are ubiquitous as in natural objects and have been applied in designing porous structures such as micro antenna and porous silicon. The seemingly complex and irregular structures can be generated based on simple principles. In this paper, we present three approaches to construct 3D fractal geometries using a recently proposed periodic surface model. By applying iterated function systems to the implicit surface model in the Euclidean or parameter space, 3D fractals can be constructed efficiently. Porosity is also proposed as a metric in fractal design.

Parting Line Formation by Slicing a Trimmed Surface Model

1996 ◽  
Author(s):  
T. Wong ◽  
S. T. Tan ◽  
W. S. Sze
Keyword(s):  
Product Design ◽  
Free Form ◽  
Surface Model ◽  
Curved Surfaces ◽  
Line Formation ◽  
Planar Surfaces ◽  
Manufacturing Efficiency ◽  
Computer Aided ◽  
Trimmed Surface ◽  
Free Form Surfaces

Abstract The parting line on a product affects the final layout of the mould blocks and hence the manufacturing efficiency. The increased usage of free-form surfaces in product design increases the burden of computer aided parting line and parting surface determination. Previous proposed algorithms may not be sufficient to deal with such situation since most of them were originally designed to deal with products having planar surfaces or simple curved surfaces. A new algorithm is proposed to deal with such situation. The algorithm adopted a recursive uneven slicing on a trimmed surface model. The method provides a quick and efficient way of locating the parting line of a product.

Towards automatic computer-aided knee surgery by innovative methods for processing the femur surface model

2010 ◽  
Vol 6 (3) ◽  
pp. 350-361 ◽  
Author(s):  
Pietro Cerveri ◽  
Mario Marchente ◽  
Ward Bartels ◽  
Kristoff Corten ◽  
Jean-Pierre Simon ◽  
...  
Keyword(s):  
Knee Surgery ◽  
Surface Model ◽  
Automatic Computer ◽  
Innovative Methods ◽  
Computer Aided

Microswimmers near corrugated, periodic surfaces

Soft Matter ◽  
2021 ◽  
Author(s):  
Christina Kurzthaler ◽  
Howard A. Stone
Keyword(s):  
Analytical Theory ◽  
Hydrodynamic Interactions ◽  
Periodic Surface ◽  
Periodic Surfaces ◽  
Corrugated Surfaces ◽  
The Impact

We derive an analytical theory for the hydrodynamic interactions between microswimmers and corrugated surfaces and study the impact of a periodic surface on the velocities of active agents.

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