In this paper, in addition to these definitions we have also defined a new classification by applying angular curvature used for planar curves in computational geometry to Bézier control polygon.
📌 3 Key Takeaways
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Objective & Hypothesis:The role of differential geometry in describing a curve can not be denied.
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Key Findings & Data:The differential forms defined for Bézier curves which are widely used in computer aided geometric design, plays a significant role in classification and image processing of curves.
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Conclusion & Impact:In this paper, in addition to these definitions we have also defined a new classification by applying angular curvature used for planar curves in computational geometry to Bézier control polygon.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
The role of differential geometry in describing a curve can not be denied. The differential forms defined for Bézier curves which are widely used in computer aided geometric design, plays a significant role in classification and image processing of curves. For this reason, the definitions such as Serret-Frenet frame, curvature and torsion which are described for Bézier curves are very important in computer aided geometric design. In this paper, in addition to these definitions we have also defined a new classification by applying angular curvature used for planar curves in computational geometry to Bézier control polygon.
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Cite This Article
TANTAY, B., TAŞ, F. (2011). The curvature of a Bezier control polyline. Mathematical and Computational Applications, Cilt: 16 - Sayı: 2, 350–358. https://ajindex.com/articles/279872
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Boissonnat, J.D., Teillaud,M., Effective Computational Geometry for Curves and Surfaces, Springer, 2006
Marsh,D., Applied Geometry for Computer Graphics and CAD, Springer, 2005
Ramsay, A., Richtmyer, R.D., Introduction to Hyperbolic Geometry, Springer, 1995.