Incremental Spherical Linear Interpolation

Tony Barrera
Barrera Kristiansen AB

Anders Hast
Creative Media Lab, University of Gävle, Sweden

Ewert Bengtsson
Centre for Image Analysis, Uppsala University, Sweden

Ladda ner artikelhttp://www.ep.liu.se/ecp_article/index.en.aspx?issue=013;article=004

Ingår i: The Annual SIGRAD Conference. Special Theme - Environmental Visualization

Linköping Electronic Conference Proceedings 13:4, s. 7-10

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Publicerad: 2004-11-24


ISSN: 1650-3686 (tryckt), 1650-3740 (online)


Animation is often done by setting up a sequence of key orientations; represented by quaternions. The in between orientations are obtained by spherical linear interpolation (SLERP) of the quaternions; which then can be used to rotate the objects. However; SLERP involves the computation of trigonometric functions; which are computationally expensive. Since it is often required that the angle between each quaternion should be the same; we propose that incremental SLERP is used instead. In this paper we demonstrate five different methods for incremental SLERP; whereof one is new; and their pros and cons are discussed.


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T. BARRERA; A. HAST; E. BENGTSSON 2004. Faster shading by equal angle interpolation of vectors IEEE Transactions on Visualization and Computer Graphics; pp. 217-223.

R. L. BURDEN; J. D. FAIRES 2001. Numerical Analysis Brooks/Cole; Thomson Learning; pp. 507-516.

C. F. GERALD; P. O. WHEATLEY 1994. Applied Numerical Analysis; 5:th ed. Addison Wesley; pp. 400-403.

A. GLASSNER 1999. Situation Normal Andrew Glassner’s Notebook- Recreational Computer Graphics; Morgan Kaufmann Publishers; pp. 87-97.

A. HAST; T. BARRERA; E. BENGTSSON 2003. Shading by Spherical Linear Interpolation using DeMoivre’s Formula WSCG’03; Short Paper; pp. 57-60.

J. B. KUIPERS 1999. Quaternions and rotation Sequences - A Primer with Applications to Orbits; Aerospace; and Virtual Reality Princeton University Press; pp. 54-57; 162;163.

J. E. MARSDEN; M. J. HOFFMAN 1996. Basic Complex Analysis W. H. Freeman and Company; pp. 17.

W. K. NICHOLSON 1995. Linear Algebra with Applications PWS Publishing Company; pp. 275;276.

R. PARENT 2002. Computer Animation - Algorithms and Techniques Academic Press; pp. 97;98.

J. SHANKEL 2000. Interpolating Quaternions Game Programming Gems. Edited byM. DeLoura. Charles RiverMedia; pp. 205-213

K. SHOEMAKE 1985. Animating rotation with quaternion curves ACM SIGGRAPH; pp. 245-254.

G. F. SIMMONS 1991. Differential Equations with Applications and Historical Notes; 2:nd ed. MacGraw Hill; pp. 64;65.

J. SVAROVSKY 2000. Quaternions for Game Programming Game Programming Gems. Edited by M. DeLoura. Charles River Media; pp. 195-299.

A. WATT; M. WATT 1992. Advanced Animation and Rendering Techniques - Theory and Practice Addison Wesley; pp. 363.

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