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.
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页码：277 / 295
页数：19
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