• 충청수학회지
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• 제34권4호
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• pp.387-395
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• 2021

In this paper, we give a characterization of a Delaunay surface in ℝ³. Let Σ be a CMC-H surface in ℝ³ with H ≠ 0. If Σ meets a plane with constant contact angle along a circle, then it is rotationally symmetric, i.e., Σ is part of a Delaunay surface.

• 산업경영시스템학회지
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• 제41권4호
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• pp.123-130
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• 2018

Triangulation is one of the fundamental problems in computational geometry and computer graphics community, and it has huge application areas such as 3D printing, computer-aided engineering, surface reconstruction, surface visualization, and so on. The Delaunay refinement algorithm is a well-known method to generate quality triangular meshes when point cloud and/or constrained edges are given in two- or three-dimensional space. In this paper, we propose a simple but efficient algorithm to triangulate Voronoi surfaces of Voronoi diagram of spheres in 3-dimensional Euclidean space. The proposed algorithm is based on the Ruppert's Delaunay refinement algorithm, and we modified the algorithm to be applied to the triangulation of Voronoi surfaces in two ways. First, a new method to deciding the location of a newly added vertex on the surface in 3-dimensional space is proposed. Second, a new efficient but effective way of estimating approximation error between Voronoi surface and triangulation. Because the proposed algorithm generates a triangular mesh for Voronoi surfaces with guaranteed quality, users can control the level of quality of the resulting triangulation that their application problems require. We have implemented and tested the proposed algorithm for random non-intersecting spheres, and the experimental result shows the proposed algorithm produces quality triangulations on Voronoi surfaces satisfying the quality criterion.

• 한국정밀공학회지
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• 제17권7호
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• pp.181-188
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• 2000

The objective of this research is to develop an efficient reverse engineering method of 3-dimensional compound surfaces for raped prototyping process. As a first step, several image processing techniques were applied to the measured data obtained using laser scanner. And the boundary information of the compound surface were extracted to divide the surface into several separate regions. As a next step, the Delaunay triangulation method were applied to reconstruct the surface based on the measured data and the boundary information. Finally, the STL file were created for the rapid prototyping process. Required simulations and experiments were performed and the results were analyzed to show the effectiveness of the proposed methods.

• 대한의용생체공학회:의공학회지
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• 제21권3호
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• pp.225-231
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• 2000

표면에 의한 3차원 재구성 방법 중 Delaunay 삼각형 분할 방법은 기존의 기하학적 연결성 문제를 해결하고 영상의 질도 높은 것으로 평가받고 있다. 그러나 이 방법은 윤곽선의 위치에 따른 비 입체적 연결성 문제를 갖고 있다. 본 논문에서는 PC환경에서 이러한 문제를 개선한 Delaunay 삼각형 분할 재구성 방법을 제안하였다. 제안된 방법은 기존의 방법에서 나타나는 '비 입체(non-solid)‘ 사면체의 효과적인 처리를 위하여 수정된 External Voronoi Skeleton(EVS)을 이용한 제거 알고리즘을 사용하였다. 이를 적용한 결과. 원 객체 형태에 영향을 주지 않으면서 '비 입체' 사면체만이 제거됨을 확인할 수 있었다. 그리고 재구성된 영상의 표면이 사면체로 촘촘하게 연결되므로 복잡한 형태를 갖는 입체의 표면을 효과적으로 재구성할 수 있었다.

• 대한기계학회논문집A
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• 제27권5호
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• pp.681-687
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• 2003

Terrain surfaces have to be modeled in very detail and wheel-surface contacting geometry must be well defined in order to obtain proper ground-reaction and friction forces fur realistic simulation of off-road vehicles. Delaunay triangulation is one of the most widely used methods in modeling 3-dimensional terrain surfaces, and the T-search is a relevant algorithm for searching resulting triangular polygons. The T-search method searches polygons in a successive order and may not allow real-time computation of off-road vehicle dynamics if the terrain is modeled with many polygons, depending on the computer performance used in the simulation. The dynamic T-search, which is proposed in this paper, combines conventional T-search and the concept of the dynmaic-window search which uses reduced searching windows or sets of triangular surface polygons at each frame by taking advantage of the information regarding dynamic charactereistics of a simulated vehicle. Numerical tests show improvement of searching speeds by about 5% for randomly distributed triangles. For continuous search following a vehicle path, which occurs in actual vehicle simulation, the searching speed becomes 4 times faster.

• 대한기계학회논문집A
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• 제25권8호
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• pp.1246-1252
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• 2001

Reverse engineering has been widely used for the shape reconstruction of an object without CAD data and the measurement of clay or wood models for the development of new products. To generate a surface from measured points by a laser scanner, typical steps include the scanning of a clay or wood model and the generation of manufacturing data like STL file. A laser scanner has a great potential to get geometrical data of a model for its fast measuring speed and higher precision. The data from a laser scanner are composed of many line stripes of points. A new approach to remove point data with Delaunay triangulation is introduced to deal with problems during reverse engineering process. This approach can be used to reduce a number of measuring data from laser scanner within tolerance, thus it can avoid the time for handling point data during modelling process and the time for verifying and slicing STL model during RP process.

• 한국컴퓨터그래픽스학회논문지
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• 제13권4호
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• pp.21-27
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• 2007

본 논문에서는 3차원 점집합으로부터 3차원 메시를 생성하는 효율적인 기법을 소개한다. 대표적인 3차원 삼각화 방법으로 3차원 딜로니 삼각화 기법이 있으나 물체의 표면만을 고려한 메시 생성을 위한 방법으로 비효율적인 측면이 있다. 본 논문에서는 적은 계산량으로 물체의 표면 메시를 생성하는 기법을 소개한다. 물체의 각 영역을 분할하고 각 영역에 대해서 2차원 딜로니 삼각화를 적용하여 3차원 메시 구조를 얻는다. 3차원 점 집합에 대해 OBB(Oriented Bounding Box)를 계산하고 이를 기준으로 점 집합을 여러 분할 영역으로 나누고 각 부분 점 집합에 대해서 2차원 딜로니 삼각화를 실시한다. 각 2차원 삼각화 결과는 점전적으로 전체 메시에 병합된다. 또한 병합된 메시에서 잘못된 에지의 연결을 제거함으로써 객체의 삼각 분할 결과를 향상시킨다. 제안된 메시 생성 기법은 다양한 영상 기반 모델링 응용에서 효과적으로 적용될 수 있다.

• 한국게임학회 논문지
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• 제2권1호
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• pp.62-68
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• 2002

본 연구에서는 기존의 곡면 삼각화 방법들이 많은 수의 삼각형 메쉬를 사용하면서도 정확하게 표현하기가 힘들었던, 날카로운 모서리를 가지는 곡면을 처리할 수 있는 trammed NURBS곡면 삼각화 방법을 제안, 구현하였다. 기존의 매개변수영역에서의 삼각화의 문제점인 3차원공간상의 삼각형 메쉬를 계산할 때의 왜곡현상을 해결하기 위해서 곡면의 펼친영역을 근사적으로 계산하여 삼각화 하는 방법을 사용했다. 곡선, 곡면의 날카로운 점과 모서리를 자동으로 인식하기 위해서 1차미분 연속조건을 이용하였고, 이를 제약조건으로 constraint Delaunay 삼각화방법을 사용하여 곡면의 날카로운 형상(sharp shape)을 유지하면서 삼각화를 수행할 수 있었다. 제안된 삼각화 방법은 기존의 삼각화 방법에 비하여 적은수의 삼각형 메쉬로 곡면의 날카로운 모서리를 보다 정확하게 표현 할 수 있는 장점을 가지고 있어서 삼각형의 개수에 따라 가시화 성능이 큰 영향을 받는 컴퓨터게임 같은 분야에 도움을 줄 수 있으리라 예상된다.

• 대한기계학회논문집A
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• 제26권5호
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• pp.803-812
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• 2002

Reverse engineering has been widely used for the shape reconstruction of an object without CAD data and the measurement of clay or wood models for the development of new products. To generate a surface from measured points by a laser scanner, typical steps include the scanning of a clay or wood model and the generation of manufacturing data like STL file. A laser scanner has a great potential to get geometrical data of a model for its fast measuring speed and higher precision. The data from a laser scanner are composed of many line stripes of points. A new approach to remove point data with Delaunay triangulation is introduced to deal with problems during reverse engineering process. The selection of group of triangles to be triangulated based on the angle between triangles is used for robust and reliable implementation of Delaunay triangulation as preliminary steps. Developed software enables the user to specify the criteria for the selection of group of triangles either by the angle between triangles or the percentage of triangles reduced. The time and error for handling point data during modelling process can be reduced and thus RP models with accuracy will be helpful to automated process.

• 대한전기학회논문지
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• 제37권12호
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• pp.847-853
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• 1988

A method of three-demensional finite element mesh generation is presented in this paper. This method is based on the Delaunay's triangulation whose dual is Voronoi's diagram. A set of points is given on the boundary surface of the concerning domain and the initial tetrahedra are generated by the given set of points. Then, the quality of every tetrahedron is investigated and the interior points are generated near the tetrahedra which are inferior in quality and the tetrahedra of good quality can be controlled by the density of the initial boundary points. Regions with different material constant can be refined in tetrahedra respectively. To confirm the effectiveness of this algorithm,the total volume of tetrahedra was compared to the true volume and this mesh generator was applied to a three-dimensional electostatic problem.