Abstract
Computer Aided Geometric Design has emerged from the needs of free form curves and surfaces in CAD/CAM technologies. Rational schemes are now replacing polynomial schemes in CAGD. This paper presents several methods to generate weights of rational Bézier curves and surfaces. The main idea is to find weights which minimize functional measuring a technical smoothness of the curves and surfaces. These functional are related to the energy of beams and plates in the sense of elasticity theory. A new result on the reparameterization of rational Bézier curves is also presented. This allows to find efficient algorithms minimizing the smoothing functional.
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Bonneau, GP. (1995). Weight Estimation of Rational Bézier Curves and 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_5
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DOI: https://doi.org/10.1007/978-3-7091-7584-2_5
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82666-9
Online ISBN: 978-3-7091-7584-2
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