Smooth invariant interpolation of rotations

被引：117
|
作者：
Park, FC [1 ]
Ravani, B [1 ]
机构：
[1] UNIV CALIF DAVIS,DEPT AERONAUT & MECH ENGN,DAVIS,CA 95616
来源：
ACM TRANSACTIONS ON GRAPHICS | 1997年 / 16卷 / 03期
关键词：
algorithms; theory; cubic spline; interpolation; Lie algebra; Lie group; mathematics; rotation;
D O I：
10.1145/256157.256160
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We present an algorithm for generating a twice-differentiable curve on the rotation group SO(3) that interpolates 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 metric, 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.
引用
收藏
页码：277 / 295
页数：19
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