Abstract
This paper will describe work in which the physical properties of objects defined in terms of PDE surfaces have been calculated and optimized against their functional requirements, subject to pre-specified constraints. The surface properties of such objects are also analysed in terms of some conventional measures of fairness based upon surface curvature, and the results presented. A limited discussion of application areas where fairnesss, or indeed lack of it, may be desirable is also given.
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References
Bloor, M.I.G., Wilson, M.J., “Generating Blend Surfaces using Partial Differential Equations”, CAD, Vol. 21, No 3, pp. 165–171, 1989.
Bloor, M.I.G., Wilson, M.J., “Using Partial Differential Equations to generate Freeform Surfaces”, CAD, Vol. 22, pp. 202–212. 1990.
Lowe, T. W., Bloor, M. I. G. and Wilson, M. J., “The Automatic Functional Design of Hull Surface Geometry”, Journal of Ship Research, Vol 38, No. 4, pp. 319–328, 1994.
Doan, N., Bloor, M. I. G. and Wilson, M. J., “A Strategy for the Automated Design of Mechanical Parts”, eds Rossignac, J., Turner, J. and Allen, G., A., Second Symposium of Solid Modelling and Applications, ACM Press, New York, pp. 15–21, 1993.
Wilson, D. R., Bloor, M. I. G. and Wilson, M. J., “An Automated Method for the Incorporation of Functionality in the Geometric Design of a Shell”, eds Rossignac, J., Turner, J. and Allen, G., A., Second Symposium of Solid Modelling and Applications, ACM Press, New York, pp. 253–259, 1993.
Bloor, M.I.G., Wilson, M.J., `Blend Design as a Boundary-Value Problem’, eds. Straber,W., Seidel 11.-P., in Theory and Practise of Geometric Modelling, Springer-Verlag, Berlin, pp. 221–234, 1989.
Woodwark, J.R., “Blends in Geometric Modelling”, in The Mathematics of Surfaces II, ed. Martin,R R, Oxford University Press, Oxford, UK, pp. 255–297, 1987.
Mortenson, M.E., “Geometric Modeling”, Wiley-Interscience, New York, 1985.
Celniker, G. and Gossard, D. “Energy-based models for free-form surface shape design”, ASME Design Automation Conference, 107–112. 1988.
Williams, C.J.K, “Use of structural analogy in generation of smooth surfaces for engineering purposes”, CAD, Vol. 19, pp. 310–322, 1987.
Nowacki, H. and Reese, D., “Design and Fairing of Ship Surfaces”, in: Barnhill, R.E. and Boehm, W., eds., Surfaces in CAGD, North-Holland, pp. 121–134, 1983.
Hagen, H., and G. Schulze, “Automatic Smoothing with geometric surface patches”, Computer Aided Geometric Design 4, pp. 231–235, 1987. 1987.
Terzopoulos, D. and Witkin, A., “Physically Based Models with Rigid and Deformable Components”, IEEE Computer Graphics, Applications, pp. 41–51, 1988.
Platt, J.C. and Barr, A.H., “Constraint Methods for Flexible Models”, Computer Graphics, Vol. 22, No. 4, pp. 279–288, 1988.
Nowacki, H., Dingyuan, L., and Xinmin, L., “Mesh Fairing GC Surface Generation Method”, in: Straber, W. and H.-P. Seidel, H.-P., eds., Theory and Practise of Geometric Modeling, Springer-Verlag, Berlin, pp. 93–103, 1989.
Hagen, H. and Schulze, G., “Variational Principles in Curve and Surface Design”, in: Hagen, H. and Roller, D., eds., Geometric Modelling, Springer, pp. 161–184, 1990.
Hagen, H. and Santarelli, P., “Variational Design of Smooth B-Spline Surfaces”, in: Hagen, H., ed., Topics in Surface Modelling, SIAM, pp. 85–94, 1992.
Moreton, H. and Sequin, C., “Functional Optimization for Fair Surface Design”, ACM Computer Graphics 26, pp. 167–176, 1992.
Hagen, H. and Bonneau G.-P. (1993), “Variational Design of Smooth Rational Bezier Surfaces”, Computing Suppl. 8, pp. 133–138, 1993.
Welch, W. and Witkin, A., “Variational Surface Modeling”, Computer Graphics, Vol. 26, 157–166.
Zipps, J.M., “Untersuchung der analyytischen Beziehungen zwischen Variationsformuliezungen und elliptischen Differential gleichungen zur Generierung von Freiform-flachen”, Diplomarbeit un Fache Schiffstheorie, T.U.Berlin, 1991.
Bloor, M.I.G., Wilson, M.J. and Hagen, H., “The Smoothing Properties of Variational Schemes for Surface Design”, Computer Aided Geometric Design, Vol 12, No. 4, pp. 381394, 1995.
Klass, R., Correction of local surface irregularities using reflection lines, Computer Aided Design, Vol. 12, pp. 73–77, 1980.
Kaufmann, E., Klass, R., “Smoothing surfaces using reflection lines for families of spline”, Computer Aided Design, Vol. 20, pp. 312–316, 1988.
Lowe, T., Bloor, M.I.G., Wilson, M.J., “Functionality in Blend Design”, CAD, Vol. 22, pp. 655–665, 1990.
Nowacki, H., in Computational Geometry for Ships, eds. Nowacki, H., Bloor, M.I.G. and Oleksiewicz, B., World Scientific, Singapore, 1995.
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© 1996 B. G. Teubner Stuttgart
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Bloor, M.I.G., Wilson, M.J. (1996). Functional Aspects of Fairness. In: Hoschek, J., Kaklis, P.D. (eds) Advanced Course on FAIRSHAPE. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-82969-6_9
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DOI: https://doi.org/10.1007/978-3-322-82969-6_9
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-519-02634-1
Online ISBN: 978-3-322-82969-6
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