Affiliation:
1. Seoul National Univ., Seoul, Korea
2. Univ. of California, Davis
Abstract
We present an algorithm for generating a twice-differentiable curve on the rotation group SO(3) that interpolated a given ordered set of rotation matrices at their specified knot times. In our approach we regard SO(3) as a Lie group with a bi-invariant Riemannian metriac, and apply the coordinate-invariant methods of Riemannian geometry. The resulting rotation curve is easy to compute, invariant with respect to fixed and moving reference frames, and also approximately minimizes angular acceleration.
Publisher
Association for Computing Machinery (ACM)
Subject
Computer Graphics and Computer-Aided Design
Reference15 articles.
1. Smooth interpolation of orientations with angular velocity constraints using quaternions
2. BELINFANTE J. a. AND KOLMAN B. 1972. A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods. SIAM Philadelphia PA. BELINFANTE J. a. AND KOLMAN B. 1972. A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods. SIAM Philadelphia PA.
3. CHEVALLEY C. 1946. Theory of Lie Groups. Princeton University Press Princeton NJ. CHEVALLEY C. 1946. Theory of Lie Groups. Princeton University Press Princeton NJ.
4. Geometric construction of B~zier motions;GE Q. J.;ASME J. Mech. Des.,1994
Cited by
119 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献