• Proceedings of the KOSOMBE Conference
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• v.1997 no.05
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• pp.362-365
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• 1997

To visualize electrical activities in the cerebral cortex, we develop the 3D topographic mapping system based on PC. For this work, we utilize OpenGL tool and an optimized interpolation method known as 3D barycentric algotithm, which has a little computational complexity. OpenGL processes the 3D coordinates, and 3D barycentric algotithm interpolates to get overall EEGs with EEGs measured from finite electrodes on 3D. To prove validity of this algorithm on the PC-based system, we developped Windows-based 3D topographic mapping program using the Barycentric algorithm. The result showed that the performance of this system is comparable to that of workstation in terms of speed and precision. Also, the result of clinical test was the same as that of a EEG technician's analysis.

• Proceedings of the KIPE Conference
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• 2015.07a
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• pp.45-46
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• 2015

본 논문에서는 무게중심좌표계에 의한 공간벡터 PWM의 간단한 구현방법을 제안한다. 무게중심좌표계를 사용하면 듀티비를 계산할 때 SIN, COS의 함수계산없이 단순한 사칙연산만을 사용하고 기준벡터가 속한 섹터에 따라 서로 다른 듀티비를 정하는 식을 유도할 필요가 없으며 듀티비가 어떻게 정해지는지에 대한 직관적인 이해를 할 수 있다. 본 논문에서는 무게중심 좌표계에서 공간벡터 PWM의 듀티비를 정하는 원리에 대하여 설명한다.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.7
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• pp.414-420
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• 2004

Among the desirable properties of a piecewise linear parameterization, guaranteeing a one-to-one mapping (i.e., no triangle flips in the parameter plane) is often sought. A one-to-one mapping is accomplished by non-negative coefficients in the affine transformation. In the Floater's method, the coefficients were computed after the 3D mesh was flattened by geodesic polar-mapping. But using this geodesic polar map introduces unnecessary local distortion. In this paper, a simple variant of the original shape-preserving mapping technique by Floater is introduced. A new simple method for calculating barycentric coordinates by using straightest geodesics is proposed. With this method, the non-negative coefficients are computed directly on the mesh, reducing the shape distortion introduced by the previously-used polar mapping. The parameterization is then found by solving a sparse linear system, and it provides a simple and visually-smooth piecewise linear mapping, without foldovers.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.3
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• pp.183-189
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• 2014

In this paper, a polyhedral element is presented to solve three-dimensional problems by developing shape functions based on Wachspress coordinates and moving least square approximation. A subdivision of polyhedrons into tetrahedral domains is performed for the construction of shape functions of polyhedral elements, and numerical integration of the weak form is carried out consistently over the tetrahedral domains. The weight functions for moving least square approximation are defined by solving Laplace equation with boundary values based on Wachspress coordinates on polyhedral element faces. Polyhedral elements presented in this paper have similar properties to conventional finite element regarding the continuity, the completeness, the node-element connectivity and the inter-element compatibility. Numerical examples show the effectiveness of the present method for solving three-dimensional problems using polyhedral elements.

• Journal of Integrative Natural Science
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• v.10 no.1
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• pp.27-32
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• 2017

In this paper we consider the two tangent lines of isogonal and isotomic conjugates of the line at both vertices of a given triangle. We find the necessary and sufficient condition for the two tangent lines of isogonal or isotomic conjugates of the line at both vertices and the median line to be concurrent. We also prove that every line whose isogonal conjugate tangent lines at both vertices are concurrent with the median line intersects at a unique point. Moreover, we show that the three intersection points correspond to the vertices of triangle are collinear.

• ETRI Journal
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• v.38 no.6
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• pp.1095-1103
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• 2016

We present a method for transferring deformation weights of a human character to three-dimensional (3D) scanned clothes. First, clothing vertices are projected onto a character skin. Their deformation weights are determined from the barycentric coordinates of the projection points. For more complicated parts, such as shoulders and armpits, continuously moving planes are constructed and employed as projection reference planes. Clothing vertices on a plane are projected onto the intersection curve of the plane with a character skin to achieve a smooth weight transfer. The proposed method produces an initial deformation for physically based clothing simulations. We demonstrated the effectiveness of our method through several deformation results for 3D scanned clothes.

• 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.

• 한국HCI학회:학술대회논문집
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• 2009.02a
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• pp.469-474
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• 2009

This paper proposes an real time ray tracing system using optimized kd-tree traversal environment and ray/triangle intersection algorithm. The previous kd-tree traversal algorithms search for the upper nodes in a bottom-up manner. In a such way we need to revisit the already visited parent node or use redundant memory after failing to find the intersected primitives in the leaf node. Thus ray tracing for relatively complex scenes become more difficult. The new algorithm contains stacks implemented on GPU's local memory on CUDA framework, thus elegantly eliminate the problems of previous algorithms. After traversing the node we perform the latest CPU-based ray/triangle intersection algorithm 'Plucker coordinate test', which is further accelerated in massively parallel thanks to CUDA. Plucker test can drastically reduce the computational costs since it does not use barycentric coordinates but only simple test using the relations between a ray and the triangle edges. The entire system is consist of a single ray kernel simply and implemented without introduction of complicated synchronization or ray packets. Consequently our experiment shows the new algorithm can is roughly twice as faster as the previous.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.8
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• pp.4072-4089
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• 2018

This paper introduces a scheme for optimizing the material properties of mass-spring systems of different resolutions to provide coherent behavior for reduced level-of-detail in MSS(Mass-Spring System) meshes. The global optimal material coefficients are derived to match the behavior of provided reference mesh. The proposed method also gives us insight into levels of reduction that we can achieve in the systematic behavioral coherency among the different resolution of MSS meshes. We obtain visually acceptable coherent behaviors for cloth models based on our proposed error metric and identify that this method can significantly reduce the resolution levels of simulated objects. In addition, we have confirmed coherent behaviors with different resolutions through various experimental validation tests. We analyzed spring force estimations through triangular Barycentric coordinates based from the reference MSS that uses a Gaussian kernel based distribution. Experimental results show that the displacement difference ratio of the node positions is less than 10% even if the number of nodes of $MSS^{sim}$ decreases by more than 50% compared with $MSS^{ref}$. Therefore, we believe that it can be applied to various fields that are requiring the real-time simulation technology such as VR, AR, surgical simulation, mobile game, and numerous other application domains.