• Korean Journal of Computational Design and Engineering
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• v.7 no.4
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• pp.248-253
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• 2002

Delaunay triangulation is well balanced in the sense that the triangles tend toward equiangularity. And so, Delaunay triangulation hasn't some slivers triangle. It's commonly used in various field of CAD applications, such as reverse engineering, shape reconstruction, solid modeling and volume rendering. For Example, In this paper, an improved Delaunay triangulation is proposed in 2-dimensions. The suggested algorithm subdivides a uniform grids into sub-quad grids, and so efficient where points are nonuniform distribution. To get the mate from quad-subdivision algorithm, the area where triangulation-patch will be most likely created should be searched first.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.41 no.4
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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.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2000.10a
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• pp.151-156
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• 2000

Delaunay triangulation is well balanced in the sense that the triangles tend toward equiangularity. And so, Delaunay triangulation hasn't some slivers triangle. It's commonly used in various field of CAD applications, such as shape reconstruction, solid modeling and volume rendering. In this paper, an improved Delaunay triangulation is proposed in 2-dimensions. The suggested algorithm subdivides a uniform grids into sub-quad grids, and so efficient where points are non-uniform distribution. To get the mate from quad-subdivision algorithm, the area where triangulation-patch will be most likely created should be searched first.

• The KIPS Transactions:PartB
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• v.15B no.4
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• pp.341-346
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• 2008

Minimum Weight Triangulation (MWT) problem is an optimization problem searching for the triangulation of a given graph with minimum weight. Like many other graph problems this problem is also known to be NP-hard for general graphs. Several heuristic algorithms have been proposed for this problem including simulated annealing and genetic algorithm. In this paper, we propose a new genetic algorithm called GA-FF and show that the performance of the proposed genetic algorithm outperforms the previous one.

• Korean Journal of Computational Design and Engineering
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• v.12 no.6
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• pp.413-421
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• 2007

3D rendering is becoming a common feature of mobile application programs with the rapid advance of mobile devices. Since the existing rendering engines do not provide triangulation functions, mobile 3D programs have focused on an efficient handling with pre-tessellated geometry. In addition, triangulation is comparatively expensive in computation, so it seems that the triangulation cannot be easily implemented on mobile devices with limited resources. Triangulation of 3D geometry is the essential process of visualization of 3D model data and many different triangulation methods have been reported. We developed a light and fast visualization process that involves constrained triangulation based on Voronoi diagram and applied it to a mobile computer application. In this paper, we applied kd-tree to the original incremental construction algorithm and produced new O(nlogn) incremental construction algorithm. And we show a simple and efficient constrained triangulation method based on Voronoi diagram. This paper also describes an implementation of mobile STEP data viewer as an application of our proposed algorithms.

• Communications for Statistical Applications and Methods
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• v.31 no.5
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• pp.557-569
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• 2024

Based on the investigation of logistic regression models utilizing sparse triangulation within a compact domain in ℝ², this study addresses the limited research extending the triogram model to logistic regression. A primary challenge arises from the potential instability induced by a large number of vertices, hindering the effective modeling of complex relationships. To mitigate this challenge, we propose introducing sparsity to boundary vertices of the triangulation based on the Ramer-Douglas-Peucker algorithm and employing the K-means algorithm for adaptive vertex initialization. A second order coordinate-wise descent algorithm is adopted to implement the proposed method. Validation of the proposed algorithm's stability and performance assessment are conducted using synthetic and handwritten digit data (LeCun et al., 1989). Results demonstrate the advantages of our method over existing methodologies, particularly when dealing with non-rectangular data domains.

• Korean Journal of Computational Design and Engineering
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• v.22 no.2
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• pp.110-117
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• 2017

Delaunay refinement algorithm is a classical method to generate quality triangular meshes when point cloud and/or constrained edges are given in two- or three-dimensional space. It computes the Delaunay triangulation for given points and edges to obtain an initial solution, and update the triangulation by inserting steiner points one by one to get an improved quality triangulation. This process repeats until it satisfies given quality criteria. The efficiency of the algorithm depends on the criteria and point insertion method. In this paper, we propose a method to accelerate the Delaunay refinement algorithm by applying geometric hashing technique called bucketing when inserting a new steiner point so that it can localize necessary computation. We have tested the proposed method with a few types of data sets, and the experimental result shows strong linear time behavior.

• Journal of Korean Institute of Industrial Engineers
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• v.26 no.3
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• pp.289-295
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• 2000

The triangulation problem is to make triangles using the given points on the space. The Minimum Weight Triangulation(MWT) is the problem of finding a set of triangles with the minimum weight among possible set of the triangles. In this paper, a modified genetic algorithm(GA) based on an existing genetic algorithm and multispace smoothing technique is proposed. Through the computational results, we can find the tendency that the proposed GA finds good solutions though it needs longer time than the existing GA does as the problem size increases.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.10
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• pp.917-923
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• 2015

In this paper, the TSE (Triangulation based target Size Estimator) algorithm is presented to estimate static target size at IIR (Imaging Infrared) environment. The size information is important factor for accurate IIR target tracking. But the IIR sensor can't generate distance between missile and target to calculate target size. In order to overcome the problem, we propose TSE algorithm which based on triangulation measurement. The performance of proposed method is tested at target intercept scenario. The experiment results show that the proposed algorithm has suitable performance for the accurate static target size estimating.

• The Transactions of the Korea Information Processing Society
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• v.7 no.3
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• pp.943-952
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• 2000

The surface reconstruction problem from a set of wire-frame contours is very important in diverse fields such as medical imaging or computer animation. In this paper, surface triangulation method is proposed for solving the problem. Generally, many optimal triangulation techniques suffer from the large computation time but heuristic approaches may produce very unnatural surface when contours are widely different in shape. To compensate the disadvantages of these approaches, we propose a new heuristic triangulation method which iteratively decomposes the surface generation problem from a band (a pair of vertices chain) into tow subproblems from two sub-bands. Generally, conventional greedy heuristic contour triangulation algorithm, suffer from the drastic error propagation during surface modeling when the adjacent contours are different in shape. Our divide-and-conquer algorithm, called band partitioning algorithm, processes eccentric parts of the contours first with more global information. Consequently, the resulting facet model becomes more stable and natural even though the shapes are widely different. An interesting property of our method is hat it supports multi-resolution capability in surface modeling time. According to experiments, it is proved to be very robust and efficient in many applications.