Bézier Curve with a Minimal Jerk Energy

Temel Bulgular & Veri:By way of an application, we show that the unknown control points of the Bézier curve having a minimal jerk energy can be written as a linear combination of the known control points.

💡

Sonuç & Katkı:Furthermore, for such a Bézier curve we obtain a general form of its matrix represention.

🔬Tür:Araştırma Makalesi

📍Kapsam:Genişletilmiş Akademik Örneklem

⚙️Değişkenler:Bézier curve · minimal jerk energy · control points

Abstract

We provide a method in order to determine a Bézier curve with a minimal jerk energy by means of associated matrices. By way of an application, we show that the unknown control points of the Bézier curve having a minimal jerk energy can be written as a linear combination of the known control points. Furthermore, for such a Bézier curve we obtain a general form of its matrix represention.

Anahtar kelimeler

Bézier curve minimal jerk energy control points

🔖

Bu Makaleye Atıf Yap

ERİŞKİN, H., YÜCESAN, A. (2016). Bézier Curve with a Minimal Jerk Energy. Mathematical Sciences and Applications E-Notes, Cilt: 4 - Sayı: 2, 139–148. https://ajindex.com/articles/690749

📄 Tam Metin PDF Okuyucu

Yeni Sekmede Aç ↗

↗Yeni Sekme

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (18)

Ahn, Y. J., Hoffmann, C., Rosen, P., Geometric constraints on quadratic Bézier curves using minimal length and energy. J. Comput. Appl. Math. 255(2014), 887-897
Brunnett, G., Hagen, H., Santarelli, P., Variational design of curves and surfaces. Surv. Math. Indust. 3(1993), no. 3, 1-27
Brunnett, G., Kiefer, J., Interpolation with minimal-energy splines. Comput. Aided Design 26(1994), no.2, 137-144
Eberly, D., A relationship between minimum bending energy and degree elevation for Bézier curves.
Farin, G., Curves and surfaces for CAGD: A Practical Guide, fifth ed. Morgan Kaufmann, San Francisco, 2002
Farin, G., Class a Bézier curves. Comput. Aided Geom. Design 23(2006), no.7, 573-581
Gravesen, J., Differential geometry and design of shape and motion.
Hagen, H., Bézier-curves with curvature and torsion continuity. Rocky Mtn. J. of Math. 16(1986), no.3, 629-638
Meier, H., Nowacki, H., Interpolating curves with gradual changes in curvature. Comput. Aided Geom. Design 4(1987), no.4, 297-305
Moreton, H. P., Séquin, C. H., Minimum variation curves and surfaces for computer aided geometric design. In: Designing Fair Curves and Surfaces-Shape Quality in Geometric Modeling and Computer Aided Design. SIAM, Philadelphia, USA, 1994
Roulier, J., Bézier curves of positive curvature. Comput. Aided Geom. Design 5(1988), no.1, 59-70
Saxena, A., Sahay, B., Computer aided engineering design. Anamaya Publishers, 2005
Tawiwat, V., Jumnong, P., Combining minimum energy and minimum direct jerk of linear dynamic systems. World Academy of Science, Engineering and Technology, 47(2008), 252-257
Veltkamp, R. C., Wesselink, W., Modeling 3D curves of minimal energy. In: Eurographics 95, Maastricht, the Netherlands, 1995, 97-110
Weinstock, R., Calculus of variations with applications to physics&engineering. Dover Publications, Inc 1974
Xu, G., Wang, G., Chen, W., Geometric construction of energy-minimizing Bézier curves. Sci. China Inf. Sci. 54(2011), no. 7, 1395-1406
Yong, J. H., Cheng, F., Geometric Hermite curves with minimum strain energy. Comput. Aided Geom. Design 21(2004), no.3, 281-301
Zhang, C. M., Zhang, P. F., Cheng, F., Fairing spline curves and surfaces by minimizing energy. Comput. Aided Design 33(2001), no.13, 913-923.