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 Maddede Bu Makale
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Amaç & Hipotez:The role of differential geometry in describing a curve can not be denied.
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Temel Bulgular & Veri: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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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
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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Bu Makaleye Atıf Yap
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
Zorin, D., Bézier Curves and B-splines, Blossoming, Geometric Modeling, New York University,G22.3033-002: Topics in Computer Graphics: Lecture #2, 2002
Chen, X., An Introduction to Blossoming of Bsplines, School of Computing, University of Utah, Salt Lake City, UT 84112
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.