KaydedilenlerDerginizi ekleyin

Dergiler / Sigma Mühendislik ve Fen Bilimleri Dergisi / 2018 / Cilt: 36 - Sayı: 2

QUASI-HARMONIC CONSTRAINTS FOR TORIC BEZIER SURFACES

Daud AHMAD
Saba NAEEM
Sayfa
325–340
Yayın Tarihi
2018-06-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

This gives us the solution of the Plateau toric Bezier problem for these illustrative instances for known convex hull domains.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Toric Bezier patches generalize the classical tensor-product triangular and rectangular Bezier surfaces, extensively used in CAGD.
📊
Temel Bulgular & Veri:The construction of toric Bezier surfaces corresponding to multi-sided convex hulls for known boundary mass-points with integer coordinates (in particular for trapezoidal and hexagonal convex hulls) is given.
💡
Sonuç & Katkı:This gives us the solution of the Plateau toric Bezier problem for these illustrative instances for known convex hull domains.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Harmonicity · minimal surfaces · toric bezier patches

Abstract

Toric Bezier patches generalize the classical tensor-product triangular and rectangular Bezier surfaces, extensively used in CAGD. The construction of toric Bezier surfaces corresponding to multi-sided convex hulls for known boundary mass-points with integer coordinates (in particular for trapezoidal and hexagonal convex hulls) is given. For these toric Bezier surfaces, we find approximate minimal surfaces obtained by extremizing the quasi-harmonic energy functional. We call these approximate minimal surfaces as the quasi-harmonic toric Bezier surfaces. This is achieved by imposing the vanishing condition of gradient of the quasi-harmonic functional and obtaining a set of linear constraints on the unknown inner mass-points of the toric Bezier patch for the above mentioned convex hull domains, under which they are quasi-harmonic toric Bezier patches. This gives us the solution of the Plateau toric Bezier problem for these illustrative instances for known convex hull domains.

🔖

Bu Makaleye Atıf Yap

AHMAD, D., NAEEM, S. (2018). QUASI-HARMONIC CONSTRAINTS FOR TORIC BEZIER SURFACES. Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt: 36 - Sayı: 2, 325–340. https://ajindex.com/articles/419169

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (19)

  1. R. Osserman. A survey of Minimal Surfaces. Dover Publications Inc., 1986
  2. J. C. C. Nitsche. Lectures on Minimal Surfaces. Cambridge University Press, 1989
  3. J.A.F Plateau. Statique exprimentale et thorique des liquides soumis aux seules forces molculaires. Gauthier-Villars, Paris, 1873
  4. H.A. Schwarz. Gesammelte Mathematische Abhandlungen. 2 Bande. Springer, 1890
  5. R. Garnier. Le problme de Plateau. Annales Scienti_ques de l'E.N.S., 3(45):53-144, 1928
  6. J. Douglas. Solution of the problem of Plateau. Trans. Amer. Math. Soc., 33(1):263-321, 1931
  7. T. Rad_o. On Plateau's problem. Ann. Of Math., (2)31(3):457-469, 1930
  8. C. Coppin and D. Greenspan. A contribution to the particle modeling of soap films. Applied Mathematics and Computation, 26(4):315-331, 1988
  9. K. Koohestani. Nonlinear force density method for the form-finding of minimal surface membrane structures. Communications in Nonlinear Science and Numerical Simulation, 19(6):2071-2087, 2014
  10. Kenneth A. Brakke. The surface evolver. Experiment. Math., 1(2):141-165, 1992
  11. D. L. Chopp. Computing minimal surfaces via level set curvature ow. Journal of Computational Physics, 106(1):77-91, 1993
  12. Y.Jung, K.T.Chu, and S.Torquato. A variational level set approach for surface area minimization of triply-periodic surfaces. J. Comput. Phys., 223(2):711-730, May 2007. [13]. Trasdahl and E.M. Ronquist. High order numerical approximation of minimal surfaces. Journal of Computational Physics, 230(12):4795-4810, 2011
  13. C. Y. Li, R. H. Wang, and C. G. Zhu. Designing approximation minimal parametric surfaces with geodesics. Applied Mathematical Modelling, 37(9):6415-6424, 2013
  14. O. Kassabov. Transition to canonical principal parameters on minimal surfaces. Computer Aided Geometric Design, 31(78):441-450, 2014
  15. Gang Xu, Yaguang Zhu, Guozhao Wang, Andr_e Galligo, Li Zhang, and Kin-chuen Hui. Explicit form of parametric polynomial minimal surfaces with arbitrary degree. Appl. Math. Comput., 259(C):124-131, May 2015
  16. J. Monterde. Bezier surfaces of minimal area: The Dirichlet approach. Computer Aided Geometric Design, 21:117-136, 2004
  17. X. D. Chen, G. Xua, and Y. Wanga. Approximation methods for the Plateau-Bezier problem. In 2009 11th IEEE International Conference on Computer-Aided Design and Computer Graphics, 2009
  18. Y. X. Hao, R. H. Wang, and C. J. Li. Minimal quasi-Bezier surface. Applied Mathematical Modelling, 36:5751-5757, 2012
  19. G. Xu and G. Wan