Abstract
A brief description of the PDE method of surface generation is given, before looking at the way in which this method can be used to generate and parameterise a complex solid; namely an internal combustion engine piston. This paper demonstrates that because of the nature of the PDE method, the surface patches which are generated are smooth, guaranteed to meet perfectly at the boundaries of the patches, and can be constructed with tangent plane continuity at the boundaries where this is required. Furthermore, the method uses relatively few design parameters which allows us to change the shape of the object easily and opens the possibility of linking directly to numerical optimisation techniques.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Mortenson, M. E.: Geometric modelling. New York: Wiley 1985.
Rockwood, A. P., Owen, J. C.: Blending surfaces in solid modelling. In: Geometric modeling: algorithms and new trends (Farin, G. E., ed.), pp. 367–383. Philadelphia: SIAM 1987.
Vida, J., Martin, R. R., Varady, T.: A survey of blending methods that use parametric surfaces. Comput. Aided Des. 26, 341–365 (1994).
Woodwark, J. R.: Blends in geometric modelling. In: Mathematics of Surfaces II, pp. 225–297. Oxford: OUP, 1987.
Rossignac, J., Requicha, A. A. G.: Constant-radius blending in solid modelling. Comput. Mech. Eng. 3, 65–73 (1985).
Kos, G., Martin, R. R., Varady, T.: Methods to recover constant radius rolling ball blends in reverse engineering. Comp. Aided Geom. Des. 17, 127–160 (2000).
Pratt, M. J.: Cyclides in computer aided geometric design. Comp. Aided Geom. Des. 7, 221–242 (1990).
Pratt, M. J.: Cyclides in computer aided geometric design II. Comp. Aided Geom. Des. 12, 131–152 (1995).
Srinivas, Y. L., Dutta, D.: Blending and joining using cyclides. ASME Trans. J. Mech. Des. 116, 1034–1041 (1994).
Wallner, J., Pottmann, H.: Rational blending surfaces between quadrics. Comp. Aided Geom. Des. 14, 407–419 (1997).
Allen, S., Dutta, D.: Cyclides in pure blending I. Comp. Aided Geom. Des. 14, 51–75 (1997).
Bloor, M. I. G., Wilson, M. J.: Generating blend surfaces using partial differential equations. CAD 21, 165–171 (1989).
Bloor, M. I. G., Wilson, M. J.: Blend design as a boundary-value problem. In: Theory and practise of geometric modelling (Straber, W., Seidel, H.-P., eds.), pp. 221–234. Berlin Heidelberg New York Tokyo: Springer 1989.
Bloor, M. I. G., Wilson, M. J.: Spectral approximations to PDE surfaces. Comput. Aided Des. 28, 145–152 (1996).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Wien
About this paper
Cite this paper
Robinson, M., Bloor, M.I.G., Wilson, M.J. (2001). Parametric Representation of Complex Mechanical Parts Using PDE Surface Generation. In: Brunnett, G., Bieri, H., Farin, G. (eds) Geometric Modelling. Computing, vol 14. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6270-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-7091-6270-5_17
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83603-3
Online ISBN: 978-3-7091-6270-5
eBook Packages: Springer Book Archive