Abstract
Previous papers have examined the method and accuracy of generating B-spline approximations to PDE surfaces; such approximations being obtained using the finite element method with appropriate B-spline basis functions as the basis. This paper looks at the use of multiple knots in the B-spline surface approximation to a PDE surface with a view to allowing discontinuities in the surface normal at certain locations. The method is applied to the surface of a yacht hull where an analytic solution is known, and hence comparison using approximations to the Euclidean and maximum norms can be made.
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References
Bloor, M. I. G., Wilson, M. J.: Generating blend surfaces using partial differential equations. Comput. Aided Des. 21, 165–171 (1989).
Bloor, M. I. G., Wilson, M. J.: Using partial differential equations to generate free form surfaces. Comput. Aided Des. 22, 202–212 (1990).
Lowe, T. W., Bloor, M. I. G., Wilson, M. J.: Functionality in surface design. In: Advances in design automation 1990, vol. 1. Computer aided and computational design (Ravani, B., ed.), pp. 43-50. New York: ASME 1990.
ANSI Y14.26M: Digital representation for communication of product definition Data, Version 4.0, Section 3.17, 126-127 (1988).
ISO 10303 Standard for the Exchange of Product Model Data, Part 42: Integrated resources: geometric and topological representation, and part 205: application protocol for mechanical design using surface representation (1992).
Bartels, R. H., Beatty, J. C., Barsky, B. A.: An introduction to splines for use in computer graphics and geometric modelling. Los Altos: Morgan Kauffmann 1987.
Faux, I. D., Pratt, M. J.: Computational geometry for design and manufacture. Chichester: Ellis Horwood 1979.
Mortenson, M. E.: Geometric modelling. New York: J. Wiley 1985.
Davies, A. J.: The finite element method: a first approach. Oxford: Oxford University Press 1980.
Strang, G., Fix, G. J.: An analysis of the finite element method. Englewood Cliffs: Prentice Hall 1973.
Zienkiewicz, O. C: The finite element method, 3rd edn. New York: McGraw-Hill 1977.
Bloor, M. I. G., Wilson, M. J.: Representing PDE surfaces in terms of B-splines. Comput. Aided Des. 22, 324–330 (1990).
Brown, J. M., Bloor, M. I. G., Bloor, M. S., Wilson, M. J.: Generation and modification of non-uniform B-spline surface approximations to PDE surfaces using the finite element method. In: Advances in design automation, 1. Computer aided and computational design (Ravani, B., ed.), pp. 265–272. New York: ASME 1990.
Brown, J. M., Bloor, M. I. G., Bloor, M. S., Wilson, M. J.: Generating B-spline approximations of PDE surfaces. Math. Engineering Ind. (in press).
Brown, J. M., Bloor, M. I. G., Bloor, M. S., Nowacki, H., Wilson, M. J.: Fairness of B-spline surface approximations to PDE surfaces using the finite element method, In: The Mathematics of Surfaces IV, (Bowyer, A., ed.), pp. 335–348. Oxford: IMA 1994.
Brown, J. M., Bloor, M. I. G., Bloor, M. S., Wilson, M. J.: The accuracy of B-spline finite element approximations to PDE surfaces (in preparation).
Dill, J. C, Rogers, D. F.: Color graphics and ship hull curvature. In: Computer Applications in the Automation of Shipyard Operation and Ship Design IV (Rogers, D. F., Nehrling, B. C, Kuo, C., eds.), pp. 197–205. Amsterdam: North-Holland 1982.
Nowacki, H., Reese, D.: Design and fairing of ship surfaces. In: Surfaces in CAGD (Barnhill, R. E., Boehm, W., eds.), pp. 121–134. Amsterdam: North-Holland 1983.
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Brown, J.M., Bloor, M.S., Bloor, M.I.G., Wilson, M.J. (1995). The Use of Multiple Knots for B-spline Finite Element Approximations to PDE Surfaces. In: Hagen, H., Farin, G., Noltemeier, H. (eds) Geometric Modelling. Computing Supplement, vol 10. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7584-2_6
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DOI: https://doi.org/10.1007/978-3-7091-7584-2_6
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82666-9
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