• Structural Engineering and Mechanics
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• v.64 no.6
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• pp.695-701
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• 2017

This paper investigates some general properties in the degenerate scale problem of antiplane elasticity or Laplace equation. For a given configuration, the degenerate scale problem is solved by using conformal mapping technique, or by using the null field BIE (boundary integral equation) numerically. After solving the problem, we can define and evaluate the degenerate area which is defined by the area enclosed by the contour in the degenerate configuration. It is found that the degenerate area is an important parameter in the problem. After using the conformal mapping, the degenerate area can be easily evaluated. The degenerate area for many configurations, from triangle, quadrilles and N-gon configuration are evaluated numerically. Most properties studied can only be found by numerical computation. The investigated properties provide a deeper understanding for the degenerate scale problem.

• Proceedings of the Korean Society of Computer Information Conference
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• 2022.01a
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• pp.341-344
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• 2022

본 논문에서는 삼각형 메쉬 기반에서 변형률 기반 동역학(Strain-based dynamics, SBD)을 안정적으로 표현할 수 있는 굽힘 스프링 구조와 감쇠 기법에 대해 설명한다. SBD는 삼각형 메쉬의 에지 길이(Edge length) 기반의 에너지 대신 변형률(Strain)을 활용하여 에너지를 모델링한다. 하지만, 비정상적인 삼각형(Degenerate triangle)인 경우 변형률이 불안정하게 계산되어 잘못된 방향으로 늘어나는 문제가 발생한다. 본 논문에서는 이러한 문제를 효율적으로 처리할 수 있는 굽힘 스프링(Bending spring) 구조에 대해 소개한다. 결과적으로 본 논문에서 제안하는 기법은 안정적으로 SBD를 처리할 수 있기 때문에 다양한 재질의 옷감 시뮬레이션을 안정적으로 표현할 수 있도록 한다.

• Journal of the Korea Society of Computer and Information
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• v.28 no.9
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• pp.73-79
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• 2023

This paper describes a level of detail (LOD) based bending spring structure and damping technique that can reliably represent strain-based dynamics (SBD) on a triangular mesh. SBD models elastic energy using strain instead of energy based on the edge length of a triangular mesh. However, when a large external force occurs, the process of calculating the elastic energy based on edges results in a degenerate triangle, which stretches in the wrong direction because it calculates an unstable strain. In this paper, we introduce an LOD-based bending spring generation and energy calculation method that can efficiently handle this problem. As a result, the technique proposed in this paper can reliably and efficiently handle SBD based on bending springs, which can provide a stable representation of cloth simulation.

• Korean Journal of Computational Design and Engineering
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• v.9 no.3
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• pp.203-211
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• 2004

In this paper, we present a method of extracting a regular 2-manifold triangular net from a triangular net including degenerate and self-intersected triangles. This method can be applied to obtaining an offset model without degenerate and self-intersected triangles. Then this offset model can be used to generate CL curves and extract machining features for CAPP The robust and efficient algorithm to detect valid triangles by growing regions from an initial valid triangle is presented. The main advantage of the algorithm is that detection of valid triangles is performed only in valid regions and their adjacent selfintersections, and omitted in the rest regions (invalid regions). This advantage increases robustness of the algorithm. As well as a k-d tree bucketing method is used to detect self-intersections efficiently.

• Proceedings of the Korea Information Processing Society Conference
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• 2003.05a
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• pp.393-396
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• 2003

삼각형 스트립은 삼각형 메쉬에 대한 간결한 표현을 제공하는 데이터 구조이다 스킵 스트립은 실시간으로 삼각형 스트립을 이용하여 3차원 모델을 다해상도로 표현하는 효율적인 방법이다. 그렇지만 스킵 스트립은 모델이 점점 단순화될수록 삼각형 스트립의 과정에서 동일한 정점이 여러 번 축적된다. 이 정접들은 렌더렁에 불필요한 정점의 수를 증가시키는 퇴화 삼각형을 만들게 된다. 본 논문에서는 이러한 퇴화된 삼각형을 줄이기 위해서 퇴화 삼각형 제거 필터를 제안하며, 실험결과 단순 삼각형 스트립 스캐너의 방법보다 평균 22.2%의 정점 감소 효과를 얻을 수 있었다.

• Journal of the Korea Computer Graphics Society
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• v.16 no.2
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• pp.9-17
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• 2010

Minkowski sum of two polyedra is an operation to compute the sum of all pairs of points contained in the polyhedra. It has been a very useful tool to solve many geometric problems arising in the areas of robotics, NC machining, solid modeling, and so on. However, very few algorithms have been proposed to compute Minkowski sum of polyhedra, because computing Minkowski sum boundaries is susceptible to roundoff errors. We propose an algorithm to robustly compute the Minkowski sum boundaries by employing the controlled linear perturbation scheme to prevent numerically ambiguous and degenerate cases from occurring. According to our experiments, our algorithm computes the Minkowski sum boundaries with the precision of $10^{-14}$ by perturbing the vertices of the input polyhedra up to $10^{-10}$.