Abstract
The Bézier formulation for parametric curves has many qualities, among them the intuitive relationship between the shape of the control polygon and the shape of the curve, and the ease of computation and subdivision. Other formulations, however, have become more popular because they offer local control, or because they are interpolating, or even more recently because they provide the added flexibility of shape parameters.
We present here techniques to use the Bézier formulation to interpolate the two-dimensional points given by a user with cubic piecewise Bézier curves, while maintaining up to G121 continuity, and to interactively manipulate the bias and tension of each span, with geometric entities clearly related to the curve, while preserving the degree of geometric continuity prescribed by the user.
Resume
La méthode de Bézier pour définir des courbes paramétriques a de nombreuses qualités, parmi lesquelles la relation intuitive entre la forme de la courbe et la forme du polygone de contrôle, et la facelité avec laquelle les courbes sont calculées et subdivisées. D’autes méthodes, cependant, sont devenus plus populaires parce qu’elles permettent le contrôle local, parce qu’elles interpolent, ou bien plus récemment parce qu’elles permettent de plus la possibilité de paramétres de formes.
Nous présentons ici des techniques pour utiliser la méthode de Bézier pour interpoler les points en deux dimensions donnés par l’utilisateur avec des arcs de courbes de Bézier, tout en maintenat la continuité gémétrique jusqu’à G[2]. Le systéme permet aussi à l’utilisateur de manipuler de facon interactive par l’intermédaire d’objects géométriques intuitivement reliés aux propriétés dsirées lc biais et la tension de la courbe obtenue.
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References
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© 1985 Springer-Verlag Tokyo
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Fournier, A., Barsky, B.A. (1985). Geometric Continuity with Interpolating Bézier Curves. In: Magnenat-Thalmann, N., Thalmann, D. (eds) Computer-Generated Images. Springer, Tokyo. https://doi.org/10.1007/978-4-431-68033-8_14
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DOI: https://doi.org/10.1007/978-4-431-68033-8_14
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-68035-2
Online ISBN: 978-4-431-68033-8
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