• Electronics and Telecommunications Trends
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• v.4 no.1
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• pp.93-117
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• 1989

Computational Geometry is concerned with the design and analysis of computational algorithms which solve geometry problems. Geometry problems have a large number of applications areas such as pattern recognition, image processing, computer graphics, VLSI design and statistics since they involve inherently geometric problems for which efficient algorithms have to be developed. Several parallel algorithms, based on various parallel computation models, have been proposed for solving geometric problems. We review the current status of the parallel algorithms in computational geometry.

• 한국전산유체공학회:학술대회논문집
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• 1996.05a
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• pp.111-117
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• 1996

The Delaunay triangulation technique was tested for complicated shapes of computational domain. While a simple geometry, both in topology and in geometry, was discretized well into triangular elements. a complex geometry often failed in triangularization. A complex geometry should be devided into smaller sub-domains whose shape is simple both topologically and geometrically. The present study developed the data structures not only for relationships among neibering elements but also for shape information, and coupled these into the Delaunay triangulation technique. This approach was able to enhance greatly the reliability of triangularization specially in complicated shapes of computational domains. The GUI (Graphic User Interface) and OOP (Object-Oriented Programming) were used in order to develop the user-friendly and efficient computer code.

• Korean Journal of Computational Design and Engineering
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• v.20 no.1
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• pp.44-54
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• 2015

Solving partial differential equations (PDEs) on a manifold setting is frequently faced problem in CAD, CAM and CAE. However, unlikely to a regular grid, solutions for those problems on a triangular mesh are not available in general, as there are no well-established intrinsic differential operators. Considering that a triangular mesh is a powerful tool for representing a highly-complicated geometry, this problem must be tackled for improving the capabilities of many geometry processing algorithms. In this paper, we introduce mathematically well-defined differential operators on a triangular mesh setup, and show some examples of their applications. Through this, it is expected that many CAD/CAM/CAE application will be benefited, as it provides a mathematically rigorous solution for a PDE problem which was not available before.

• Communications of Mathematical Education
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• v.19 no.4 s.24
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• pp.621-631
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• 2005

The purpose of this study is to consider how to restructure the university geometry curriculum and contents in terms of applications to theoretical computer science. We analyzed various topics from computer graphics, CAGD(computer aided geometric design) and computational geometry suitable for geometry students interested in applications. Moreover we discussed about selections of topics for several cases.

• ETRI Journal
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• v.10 no.3
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• pp.125-140
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• 1988

Computational geometry has wide applications in pattern recognition, image processing, VLSI design, and computer graphics. Voronoi diagrams in computational geometry possess many important properites which are related to other geometric structures of a set of point. In this pater the design of systolic algorithms for the static and the dynamic Voronoi diagrams is considered. The major motivation for developing the systolic architecture is for VLSI implementation. A new systematic transform technique for designing systolic arrays, in particular, for the problem in computational geometry has been proposed. Following this procedure, a type T systolic array architecture and associated systolic algorithms have been designed for constructing Voronoi diagrams. The functions of the cells in the array are also specified. The resulting systolic array achieves the maximal throughput with O(n) computational complexity.

• Journal of computational fluids engineering
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• v.2 no.2
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• pp.97-103
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• 1997

A modified Delaunay triangulation technique is tested for complicated computational domain. While a simple geometry. both in topology and geometry, has been well discretized into triangular elements, a complex geometry having difficulty in triangulation had to be divided into small sub-domains of simpler shape. The present study presents a modified Delaunay triangulation method based on the data structure of geometric modeller. This approach greatly enhances the reliability of triangulation, especially in complicated computational domain. We have shown that efficiency of Delaunay triangulation can be much improved by using both the GUI (Graphic User Interface) and OOP (Object-Oriented Programming).

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.10a
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• pp.296-303
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• 1996

This paper proposes a method for shape optimization of trusses. The potential savings offered by shape optimization will certainly be more significant than those resulting from fixed-geometry optimization. On the other hand, difficulties associated with topology and geometry optimization are still in existence. Even with a known topology, the geometry optimization problem is still a difficult task. An evolutionary procedure to be adopted and improved in this work, however, offers a means to achieve optimization in topology and geometry together. A plane truss structure is modelled within a specified domain and made to include a great number of nodes and members. Then the structure is analyzed and those members with stresses below a certain level are progressively eliminated from the structural system In this manner the structure evolves into a truss with a better topology and geometry by removing less important parts. Through the worked examples, we can see that the method presented in this Paper shows much promise.

• Computational Structural Engineering
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• v.20 no.4
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• pp.36-43
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• 2007

• Computational Structural Engineering
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• v.23 no.1
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• pp.75-77
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• 2010

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1481-1488
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• 2009

A construction of Cartesian authentication codes over unitary geometry is presented and its size parameters are computed. Assuming that the encoding rules are chosen according to a uniform probability distribution, the probabilities of success for different types of attacks are also computed.