Abstract
This paper develops a geometric construction algorithm for designing a second order geometrically (G 2) continuous motion. It combines results in kinematics with the notion of geometric continuity from the field of Computer Aided Geometric Design and develops geometric conditions for piecing two motion segments smoothly. A complete algorithm is presented for constructing a G 2 continuous piecewise Bézier type motion. The results have applications in mechanical systems animation, computer vision, robot trajectory planning and key framing in computer graphics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barsky, B. A. and DeRose, T. D., 1989, Geometric continuity of parametric curves: three equivalent characterizations. IEEE Computer Graphics and A pplications. 9 (6):60–68.
Boehm, W., 1987, Smooth curves and surfaces. Geometric Modeling: Algorithms and New Trends, edited by G. Farin philadelphia PA. pp. 175–184. , SIAM.
Bottema, O. and B. Roth, 1979, Theoretical Kinematics. North Holland Publ., Amsterdam, 558pp. Pages 51–60, 150–152, 521–523.
Duff, T. TabLaporatories 1986, Quaternion splines for animating orientation. Technical report, AT& T Bel l
Farin, G., 1993, C Curves and Surfaces for Computer Aided Geometric Design. 3rd ed., Academic Press, San Diego, 334pp.
Flanders, H. 1963, Di erential Forms with Application to the Physical Sciences. Academic Press, New York, 205pp.
Ge, Q. J. , and B. Ravani, 1993a, Computer aided geometric design of motion interpolants, ASME J. of Mechanical Design, in press.
Ge, Q. J., and B. Ravani, 1993b, Geometric construction of Bézier Type Motions, ASME J. of Mechanical Desian in press
McCarthy, J. M. , and B. Ravan , 1986, Differential kinematics of spherical and spatial motions using kinematic mapping. Trans. ASME J. of Appl. Mech., 53:15–22.
Pletinckx, D., 1989, Quaternioncalculus as a basic tool in computer graphics. The Visual Computer, 5:2–13.
Ravani, B., and B. Roth, 1984, Mappings of spatial kinematics. Trans. ASME J. of Mech. , Transmissions. , and Auto. in Desion. 106(3) :341–347.
Reeves, W., 1981, Inbetweening for computer animation utilizing moving point constraints. A CM Siggraph, 15 (3) :263–269.
Shoemake, K., 1985, Animating rotation with quaternion curves. ACM Siggraph, 19 (3) : 245–254.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Ge, Q.J., Ravani, B. (1993). Computational Geometry and Motion Approximation. In: Angeles, J., Hommel, G., Kovács, P. (eds) Computational Kinematics. Solid Mechanics and Its Applications, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8192-9_21
Download citation
DOI: https://doi.org/10.1007/978-94-015-8192-9_21
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4342-9
Online ISBN: 978-94-015-8192-9
eBook Packages: Springer Book Archive