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Smooth interpolation of orientations with angular velocity constraints using quaternions

Barr, Alan H. and Currin, Bena and Gabriel, Steven and Hughes, John F. (1992) Smooth interpolation of orientations with angular velocity constraints using quaternions. ACM SIGGRAPH Computer Graphics, 26 (2). pp. 313-320. ISSN 0097-8930. doi:10.1145/142920.134086.

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In this paper we present methods to smoothly interpolate orientations, given N rotational key frames of an object along a trajectory. The methods allow the user to impose constraints on the rotational path, such as the angular velocity at the endpoints of the trajectory. We convert the rotations to quaternions, and then spline in that non-Euclidean space. Analogous to the mathematical foundations of flat-space spline curves, we minimize the net “tangential acceleration” of the quaternion path. We replace the flat-space quantities with curved-space quantities, and numerically solve the resulting equation with finite difference and optimization methods.

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Additional Information:© 1992 ACM. The authors wish to thank Mark Montague, John Snyder, David Laidlaw, and Jeff Goldsmith at the Caltech graphics lab, as well as the Siggraph reviewers, for numerous helpful suggestions. The banana database is a generative model made by John Snyder and Jed Lengyel. This research was supported by the NSF/DARPA STC for Computer Graphics and Scientific Visualization, and by grants from HP, IBM, DEC and NCR to the university laboratories.
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Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
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Record Number:CaltechAUTHORS:20160504-111057823
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Official Citation:Alan H. Barr, Bena Currin, Steven Gabriel, and John F. Hughes. 1992. Smooth interpolation of orientations with angular velocity constraints using quaternions. In Proceedings of the 19th annual conference on Computer graphics and interactive techniques (SIGGRAPH '92), James J. Thomas (Ed.). ACM, New York, NY, USA, 313-320. DOI=
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66654
Deposited On:04 May 2016 20:18
Last Modified:11 Nov 2021 00:01

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