TY - JOUR

T1 - Real time motion fairing with unit quaternions

AU - Fang, Y. C.

AU - Hsieh, C. C.

AU - Kim, M. J.

AU - Chang, J. J.

AU - Woo, T. C.

N1 - Funding Information:
Tony C. Woo is professor of industrial engineering, adjunct professor of mechanical engineering,a nd holder of the John M. Fluke DistinguishedC hair in Manufacturing Engineering at the University of Washington. His prior associationsw ere with the University of Michigan and the National Science Foundation. His research and teaching is in computationagl eometryfo r design and manufacturingH. e receivedh is education in electrical engineeringa t the University of Illinois.

PY - 1998

Y1 - 1998

N2 - Though it may be tempting to smooth orientation data by filtering the Euler angles directly, it is noted that smoothed Euler angles do not necessarily yield a smooth motion. This is caused by the difference between the metric in the rotation group and that in the Euclidean space. The quaternions, which Hamilton discovered in 1853, provide a means for representing rotation. A unit quaternion, represented as a hypersphere in R4, has the same local topology and geometry as the rotation group. It thus provides a means for interpolating orientations. It is possible to achieve smooth rotation by filtering in quaternions the resulting quaternion may no longer be unitized. Fortunately, a unit quaternion curve, which represents the rotation path, can be derived by integrating the exponential map of the angular velocity. Unity of quaternions is thus maintained by filtering angular velocities. A lowpass filter coupled with an adaptive, mediative filter are employed to achieve smooth rotation motion in real time

AB - Though it may be tempting to smooth orientation data by filtering the Euler angles directly, it is noted that smoothed Euler angles do not necessarily yield a smooth motion. This is caused by the difference between the metric in the rotation group and that in the Euclidean space. The quaternions, which Hamilton discovered in 1853, provide a means for representing rotation. A unit quaternion, represented as a hypersphere in R4, has the same local topology and geometry as the rotation group. It thus provides a means for interpolating orientations. It is possible to achieve smooth rotation by filtering in quaternions the resulting quaternion may no longer be unitized. Fortunately, a unit quaternion curve, which represents the rotation path, can be derived by integrating the exponential map of the angular velocity. Unity of quaternions is thus maintained by filtering angular velocities. A lowpass filter coupled with an adaptive, mediative filter are employed to achieve smooth rotation motion in real time

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U2 - 10.1016/s0010-4485(97)00057-2

DO - 10.1016/s0010-4485(97)00057-2

M3 - Article

AN - SCOPUS:0000677243

VL - 30

SP - 191

EP - 198

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

IS - 3

ER -