Abstract
본 논문에서는 벡터공간 <TEX>$R_n$</TEX>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 <TEX>$R_n$</TEX> 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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