Smooth invariant interpolation of rotations

被引：120

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

页码：277 / 295

页数：19

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