Journal of the Korea Computer Graphics Society (한국컴퓨터그래픽스학회논문지)

Korea Computer Graphics Society (한국컴퓨터그래픽스학회)
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Penetration Depth Computation for Rigid Models using Explicit and Implicit Minkowski Sums

명시적 그리고 암시적 민코우스키 합을 이용한 강체 침투깊이 계산 알고리즘

  • Lee, Youngeun (Department of Computer Science and Engineering, Ewha Womans University) ;
  • Kim, Young J. (Department of Computer Science and Engineering, Ewha Womans University)
  • 이영은 (이화여자대학교 컴퓨터공학과) ;
  • 김영준 (이화여자대학교 컴퓨터공학과)
  • Received : 2017.01.11
  • Accepted : 2017.03.07
  • Published : 2017.03.07
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Abstract

We present penetration depth (PD) computation algorithms using explicit Minkowski sum construction ($PD_e$) and implicit Minkowski sum construction ($PD_i$). Minkowski sum construction is the most time consuming part in fast PD computation. In order to address this issue, we find a candidate solution using a centroid difference and motion coherence. Then, $PD_e$ constructs or updates partial Minkowski sum around the candidate solution. In contrast, $PD_i$ constructs only a tangent plane to the Minkowski sums iteratively. In practice, our algorithms can compute PD for complicated models consisting of thousands of triangles in a few milli-seconds. We also discuss the benefits of using different construction of Minkowski sums in the context of PD.

본 논문에서는 3차원상의 두 강체 사이의 침투깊이 (penetration depth)를 명시적으로 민코우스키 합 (explicit Minkowski sum)을 생성하는 방법 ($PD_e$)과 암시적으로 민코우스키 합 (implicit Minkowski sum)을 생성 하는 방법 ($PD_i$)을 이용하여 계산하는 알고리즘을 제안하고 이들의 성능을 비교한다. 3차원 강체들 간의 침투깊이를 구하는데 성능상에 큰 장애가 되는 것이 민코우스키 합의 생성이다. 본 논문의 알고리즘들은 우선 물체의 중심 차 (centroid difference)와 운동 일관성 (motion coherence)기법을 이용하여 침투깊이를 예측한다. 특히 $PD_e$는 추측된 침투깊이에 부분 민코우스키 합을 명시적으로 생성 혹은 갱신하여 침투깊이를 빠르게 구한다. 반면에 $PD_i$는 민코우스키 합을 명시적으로 생성하기보다는 민코우스키 합에 접하는 접평면만을 반복적으로 생성하여 국소적으로 최적화된 침투깊이를 계산한다. 본 연구의 알고리즘들을 수천 개의 삼각형으로 이루어진 강체를 이용해 실험한 결과 수 밀리초 (millisecond) 이내의 빠른 속도로 침투깊이를 계산할 수 있다는 것을 실험적으로 보인다.

Keywords

Acknowledgement

Supported by : 한국연구재단

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