• Proceedings of the Korean Society of Precision Engineering Conference
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• 1992.10a
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• pp.260-265
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• 1992

본 논문에서는 민코스키 합의 기본개념에 기초해서 2D 공간에서 Convex 다각형뿐만 아니라 일반적인 형상의 다각형, 즉 concave 다각형과 폴리라인을 포함한 기본도형 들에 대한 민코스키 합을 구현해 보고 이 결과를 토대로 민코스키 합의 특성과 민코스키 합을 이용해서 물체를 모델링 할 때의 장점 및 문제점들을 알아보고자 한다. 또한 3D 공간으로의 확장시 고려해야할 요소들과 다른 자료에서 소개된 응용가능 분야 이외의 새로운 분야에서의 사용 가능성을 살펴본다.

• 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 $10^{-10}$.

• Journal of the Korea Computer Graphics Society
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• v.17 no.3
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• pp.9-19
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• 2011

Computing triangle-triangle intersections has been a fundamental task required for many 3D geometric problems. We propose a novel robust GPU algorithm to efficiently compute intersections in a large triangle set. The algorithm has three stages:k-d tree construction, triangle pair generation, and exact intersection computation. All three stages are executed on GPU except, for unsafe triangle pairs. Unsafe triangle pairs are robustly handled by CLP(controlled linear perturbation) on a CPU thread. They are identified by floating-point filtering while exact intersection is computed on GPU. Many triangles crossing a split plane are duplicated in k-d tree construction, which form a lot of redundant triangle pairs later. To eliminate them efficiently, we use a split index which can determine redundancy of a pair by a simple bitwise operation. We applied the proposed algorithm to computing 3D Minkowski sum boundaries to verify its efficiency and robustness.