• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.379-390
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• 2024

This study proposes a fuzzy inventory model for managing large-scale production, incorporating cost considerations. The model accounts for two types of expenditure scenarios-parametric and exponential. Uncertainty surrounds holding costs, setup costs, and demand rates. The approach considers a supply chain system with a complex manufacturing process, factoring in transportation costs based on the quantity of goods and distance between the supplier and retailer. The initial crisp model is then transformed into a fuzzy simulation, incorporating specific fuzzy variables affecting inventory costs. The proposed method significantly reduces overall inventory costs for the entire supply chain. Retailer demand is linked to inventory levels, and vendor/distributor storage deteriorates over time. The fuzzy condition assumes hexagonal variables for all associated factors. The study employs the signed distance method for defuzzification to determine the optimal order quantity with hexagonal fuzzy numbers. Mathematical examples are provided to illustrate the practicality of the proposed approach.

• Journal of the Korea Computer Graphics Society
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• v.18 no.1
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• pp.29-34
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• 2012

High-quality tetrahedral meshes are crucial for FEM-based simulation of large elasto-plastic deformation and tetrahedral-mesh-based simulation of fluid flow. This paper proposes a volume meshing method that exploits an octree-based adaptive signed distance field to fill the inside of a polygonal object with tetrahedra, of which dihedral angles are good. The suggested method utilizes an octree structure to reduce the total number of tetrahedra by space-efficiently filling an object with graded tetrahedra. To obtain a high-quality mesh with good dihedral angles, we restrict the octree in such a way that any pair of neighboring cells only differs by one level. In octree-based tetrahedral meshing, the signed distance computation of a point to the surface of a given object is a very important and frequently-called operation. To accelerate this operation, we develop a method that computes a signed distance field directly on the vertices of the octree cells while constructing the octree using a top-down approach. This is the main focus of the paper. The suggested tetrahedral meshing method is fast, stable and easy to implement.

• Journal of the Korean Institute of Intelligent Systems
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• v.7 no.5
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• pp.14-20
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• 1997

This paper proposes a new design method for the SMC-type FLC and shows that a SMC-type LFC is an extension of the SMC with BL. The conventional SMC-type FLC uses error and change-of-error as inputs of the FLC and generates the absolute value of a switching magnitude. Then, the fuzzy rule table is constructed on a two-dimensional space of the phase plane and has commonly the skew symmetric property. In this paper, we introduce a new variable, signed distance, from the skew symmetric property of the rule table. And thd variable becomes only a fuzzy variable that is used to generate the control input of a SMC-type FLC. that is, we design a new SMC-type FLC that uses a signed distance and a control input as the variables representing the contents of the rule-antecedent and the rule-con-sequent, respectively. Then the number of total rules is reduced and the control performance is almost the same as that of the conventional SMC-type FLC. Additionally, we derive the control law of the ordinary SMC with BL from a new SMC-type FLC. Namely, we show that a FLC is an extension of the SMC with BL.

• Journal of Institute of Convergence Technology
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• v.10 no.1
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• pp.7-12
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• 2020

We describe a efficient surface reconstruction method that reconstructs a 3D manifold polygonal mesh approximately passing through a set of 3D oriented points. Our algorithm includes 3D convex hull, octree data structure, signed distance function (SDF), and marching cubes. The 3D convex hull provides us with a fast computation of SDF, octree structure allows us to compute a minimal distance for SDF, and marching cubes lead to iso-surface generation with SDF. Our approach gives us flexibility in the choice of the resolution of the reconstructed surface, and it also enables to use on low-level PCs with minimal peak memory usage. Experimenting with publicly available scan data shows that we can reconstruct a polygonal mesh from point cloud of sizes varying from 10,000 ~ 1,000,000 in about 1~60 seconds.

• Journal of the Korea Society of Computer and Information
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• v.27 no.3
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• pp.63-69
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• 2022

In this paper, we propose a new GPU-based framework for quickly calculating adaptive and continuous SDF(Signed distance fields), and examine cases related to rendering/collision processing using them. The quadtree constructed from the triangle mesh is transferred to the GPU memory, and the Euclidean distance to the triangle is processed in parallel for each thread by using it to find the shortest continuous distance without discontinuity in the adaptive grid space. In this process, it is shown through experiments that the cut-off view of the adaptive distance field, the distance value inquiry at a specific location, real-time raytracing, and collision handling can be performed quickly and efficiently. Using the proposed method, the adaptive sign distance field can be calculated quickly in about 1 second even on a high polygon mesh, so it is a method that can be fully utilized not only for rigid bodies but also for deformable bodies. It shows the stability of the algorithm through various experimental results whether it can accurately sample and represent distance values in various models.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1189-1198
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• 2017

Computer-aided design (CAD)-based Monte Carlo radiation transport is of value to the nuclear engineering community for its ability to conduct transport on high-fidelity models of nuclear systems, but it is more computationally expensive than native geometry representations. This work describes the adaptation of a rendering data structure, the signed distance field, as a geometric query tool for accelerating CAD-based transport in the direct-accelerated geometry Monte Carlo toolkit. Demonstrations of its effectiveness are shown for several problems. The beginnings of a predictive model for the data structure's utilization based on various problem parameters is also introduced.

• Proceedings of the Korean Society of Computer Information Conference
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• 2021.07a
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• pp.655-658
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• 2021

본 논문에서는 GPU 아키텍처를 이용하여 적응형 부호 거리장을 최적화하여 빠르게 구축하고 시각화 할 수 있는 방법에 대해 제안한다. 쿼드트리를 효율적으로 GPU 메모리로 전달하고, 이를 활용하여 삼각형에 대해 유클리디안 거리를 각 스레드 별로 병렬처리하여 최단 거리를 찾는다. 이 과정에서 GPU를 사용하여 삼각형으로 구성된 3D 메쉬로부터 빠르게 적응형 부호 거리장을 계산할 수 있는 최적화 기법과 절단면 보기, 특정 위치의 값 조회, 실시간 레이트레이싱 및 충돌처리 작업을 빠르고 효율적으로 수행할 수 있는지를 보여준다. 또한, 제안하는 프레임워크를 활용하면 하이 폴리곤 메쉬도 1초 내외로 부호 거리장을 계산할 수 있기 때문에 강체뿐만 아니라 변형체에도 충분히 활용될 수 있다.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.723-739
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• 2023

In this paper, we developed three theoretical models based on prey and predator that exhibit holling-type response functions. In both a fuzzy and a crisp environment, we have provided a mathematical formulation for the prey predator concept. We used the signed distance method to defuzzify the triangular fuzzy numbers using the alpha-cut function. We can identify equilibrium points for all three theoretical models using the defuzzification technique. Utilizing a variational matrix, stability is also performed with the two species model through three theoretical models. Results are presented, followed by discussion. MATLAB software is used to provide numerical simulations.

• Journal of the Korea Computer Graphics Society
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• v.17 no.1
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• pp.17-24
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• 2011

In Computer Graphics, interaction between a particle-based fluid and a rigid body is important. In General, this interaction has been simulated in a discrete environment. As a result, there have been lots of errors. The larger the time step is used, the bigger the error is. This paper describes how to minimize the error in a discrete environment. To be specific, the collision handling method is that estimates particle collision using a signed distance function increases continuously according to space. At the time a fluid particle and a rigid body model collide, the exact collision time and the position is estimated. Through this, we propose the method how to be simulated the interaction between a fluid and a rigid body model as a continuous environment.

• Journal of the Korea Computer Graphics Society
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• v.23 no.4
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• pp.11-19
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• 2017

We propose a new pipeline of fluid surface reconstruction that incorporates hybrid SDF(signed distance fields) and adaptive fluid surface techniques to finely reconstruct liquid-solid mixed surfaces. Previous particle-based fluid simulation suffer from a noisy surface problem when the particles are distributed irregularly. If a smoothing scheme is applied to reduce the problem, sharp and detailed features can be lost by over-smoothing artifacts. Our method constructs a hybrid SDF by combining signed distance values from the solid and liquid parts of the object. We also proposed a method of adaptively reconstructing the surface of the fluid to further improve the overall efficiency. This not only shows the detailed surface of the solid and liquid parts, but also the detail of the solid surface and the smooth fluid surface when both materials are mixed. We introduce the concept of guiding shape and propose a method to get signed distance value quickly. In addition, the hybrid SDF and mesh reconstruction techniques are integrated in the adaptive framework. As a result, our method improves the overall efficiency of the pipeline to restore fluid surfaces.