정보처리학회논문지A (The KIPS Transactions:PartA)

한국정보처리학회 (Korea Information Processing Society)
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Lie-군상에서의 Bezier 곡선과 Bezier곡면의 생성방법

Generation Method of Bezier Curves and Surfaces on Lie Groups

  • 임장환 (중앙대학교 첨단영상대학원) ;
  • 김태은 (남서울대학교 공학부 멀티미디어학과)
  • 발행 : 2002.03.01
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⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 벡터공간 $R_n$에서 정의된 Bezier곡선과 Bezier곡면을 Lie군(Lie group)에서 확장하는 일반적인 새로운 생성방법을 제시한다. 이 방법에 의해서 생성된 Bezier곡선과 Bezier곡면은 Lie군의 성질에 의해서 미분 가능한 구조를 갖는다. 이 방법은 공간상에서 움직이는 물체에 대한 부드러운 움직임을 묘사하거나 궤도생성에 사용할 수 있다.

The goal of this paper is to generalize the concept of Bezier curves and surfaces defined on the vector space $R_n$ to Lie groups, which is a new generation method of curves (called Bezier curves) on Lie groups. The defined Bezier curves and surfaces are alsways smooth because of the properties of Lie groups. We apply this method to smooth motion interpolation or smooth trajectory generation for moving rigid body in space.

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참고문헌

  1. Betten, D. TopologischeTransformationsgruppen, Lecture Note, Tubingen WS 1972/73
  2. Helgason, S. Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, 1978
  3. Hilgert, J., Need, K.-H. Lie-Gruppen und Lie-Algebren, Vieweg, 1991
  4. Faugeras, O. Three Dimensional Compter Vision. MIT Press, 1999
  5. Foley, van Dam, Feiner, Hughes. Computer Graphics, Addison-Wesley Publishing Company, 1997
  6. Kim, M-J., Kim, M-S., Shin, S. Y. A General Construction Scheme for Unite Quaternion Curves with Simple Hight Order Derivatives, (Proc. of SIGGRAPH '95), pp.369-376, 1995 https://doi.org/10.1145/218380.218486
  7. Kim, M-J, Kim, Myung-Soo. A Compact Differential Formula for the First Derivatives of a Unit Quaternion Curve, J. of Visulation and Computer Animation, Vol.7, No.1, pp.43-58, 1996 https://doi.org/10.1002/(SICI)1099-1778(199601)7:1<43::AID-VIS136>3.0.CO;2-T
  8. O'neil, B. Semi-Riemannian Geometry with Application to Relativity, Academic Press, 1983
  9. Shoemake, K. Animating rotation with quaternion curves, Computer Graphiecs (Pro. of SIGGRAPH'85), pp.245-254, 1985 https://doi.org/10.1145/325334.325242
  10. Park, F. C., Ravani, B. Smooth Invariant Interpolation of Rotations, ACM Transation on Graphics, Vol.16, No.3, pp.277-295, 1997 https://doi.org/10.1145/256157.256160
  11. Pobegailo, AP. $C^n$ interpolation on smooth manifolds with one-parameter transformations, Computer-Aided Design, Vol.28, No.12, pp.973-979, 1996 https://doi.org/10.1016/0010-4485(96)00025-5
  12. Varadarajan, V. S. Lie groups, Lie Algebras, and Their Representations, Springer-Verlag, 1984