\(\hbox {GC}^{1}\) Shape-Preserving Trigonometric Surfaces

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• 作者：Maria Hussain ; Malik Zawwar Hussain…
• 关键词：Shape ; preservation ; $$GC^{1}$$ G C 1 bi ; quadratic trigonometric function ; Free parameters ; 68U05 ; 65D05 ; 65D07 ; 65D18
• 刊名：Journal of Mathematical Imaging and Vision
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：53
• 期：1
• 页码：21-41
• 全文大小：7,715 KB
• 参考文献：1.Beatson, R.K., Ziegler, Z.: Monotonicity preserving surface interpolation. SIAM J. Numer. Anal. 22(2), 401鈥?11 (1985)MATH MathSciNet View Article
  2.Brodlie, K., Mashwama, P., Butt, S.: Visualization of surface data to preserve positivity and other simple constraints. Comput. Graph. 19(4), 585鈥?94 (1995)View Article
  3.Carlson, R.E., Fritsch, F.N.: Monotone piecewise bicubic interpolation. SIAM J. Numer. Anal. 22(2), 386鈥?00 (1985)MATH MathSciNet View Article
  4.Costantini, P., Manni, C.: A bicubic shape-preserving blending scheme. Comput. Aided Geom. Des. 13, 307鈥?31 (1996)MATH MathSciNet View Article
  5.Delgado, J., Pe帽a, J.M.: Are rational B茅zier surfaces monotonicity preserving? Comput. Aided Geom. Des. 24(5), 303鈥?06 (2007)MATH View Article
  6.Fujioka, H., Kano, H.: Optimal smoothing spline surfaces with constraints on derivatives, In: Proceedings of the \(50^{\rm th}\) IEEE Conference on Decision and Control and European Control Conference, Orlando, FL December 12鈥?5 (2011)
  7.Han, X.: Quadratic trigonometric polynomial curves with a shape parameter. Comput. Aided Geom. Des. 19, 503鈥?12 (2002)MATH View Article
  8.Han, X.: Cubic trigonometric polynomial curves with a shape parameter. Comput. Aided Geom. Des. 21, 535鈥?48 (2004)MATH View Article
  9.Han, X.: \(C^{2}\) quadratic trigonometric polynomial curves with local basis. J. Comput. Appl. Math. 180, 161鈥?72 (2005)MATH MathSciNet View Article
  10.Han, X.: Quadratic trigonometric polynomial curves concerning local control. Appl. Numer. Math. 56, 105鈥?15 (2006)MATH MathSciNet View Article
  11.Han, X., Ma, Y., Huang, X.: The cubic trigonometric B茅zier curve with two shape parameters. Appl. Math. Lett. 22, 226鈥?31 (2009)MATH MathSciNet View Article
  12.Han, X., Huang, X., Ma, Y.: Shape analysis of cubic trigonometric B茅zier curve with a shape parameter. Appl. Math. Comput. 217(6), 2527鈥?533 (2010)MATH MathSciNet View Article
  13.Hoschek, J., Lasser, D.: Fundam. Comput. Aided Geom. Des. AK Peters, Natick, MA (1993)
  14.Hussain, M.Z., Bashir, S.: Shape preserving surface data visualization using rational bi-cubic functions. J. Numer. Math. 19(4), 267鈥?07 (2011)MATH MathSciNet View Article
  15.Hussain, M.Z., Sarfraz, M.: Positivity-preserving interpolation of positive data by rational cubics. J. Comput. Appl. Math. 218, 446鈥?58 (2008)
  16.Hussain, M.Z., Hussain, M., Waseem, A.: Shape-preserving trigonometric functions. Comput. Appl. Math. 33, 411鈥?31 (2014)MATH MathSciNet View Article
  17.Luo, Z., Peng, X.: A \(C^{1}\) -rational spline in range restricted interpolation of scattered data. J. Comput. Appl. Math. 194(2), 255鈥?66 (2006)MATH MathSciNet View Article
  18.Lyche, T., Merrien, J.-L.: Hermite subdivision with shape constraints on a rectangular mesh. BIT Numer. Math. 46, 831鈥?59 (2006)MATH MathSciNet View Article
  19.Mulansky, B., Schmidt, J.W.: Powell鈥揝abin splines in range restricted interpolation of scattered data. Computing 53(2), 137鈥?54 (1994)MATH MathSciNet View Article
  20.Nazir, F.: \(C^{1}\) Rational Coons Patches. M.Phil Thesis, Department of Mathematics, Lahore College for Women University, Lahore (2013)
  21.Peng, X., Li, Z., Sun, Q.: Non-negativity preserving interpolation by \(C^{1}\) bivariate rational spline surface. J. Appl. Math. 2012, 1鈥?2 (2012)MathSciNet
  22.Qi, G., Kuanquan, W., Yongfeng, Y., Yongtian, Y.: Applications of trigonometric spline wavelets in ECG detection. Chin. J. Electron. 18(1), 117鈥?19 (2009)
  23.Schumaker, L.L.: Spline Functions: Basic Theory, 3rd edn. Cambridge University Press, Cambridge (2007)View Article
  24.Simon, D., Isik, C.: Optimal trigonometric robot joint trajectories. Robotica 9, 379鈥?86 (1991)View Article
  25.Xie, J., Liu, X., Xu, L.: The applications of cardinal trigonometric splines in solving nonlinear integral equations. ISRN Applied Mathematics (2014). doi:10.鈥?155/鈥?014/鈥?13909
  
• 作者单位：Maria Hussain (1)
  Malik Zawwar Hussain (2)
  Amna Waseem (2)
  Moshayyadah Javaid (2)
  
  1. Department of Mathematics, Lahore College for Women University, Lahore, Pakistan
  2. Department of Mathematics, University of the Punjab, Lahore, Pakistan
  
• 刊物类别：Computer Science
• 刊物主题：Computer Imaging, Vision, Pattern Recognition and Graphics
  Image Processing and Computer Vision
  Artificial Intelligence and Robotics
  Automation and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-7683

文摘

A \(GC^{1}\) bi-quadratic trigonometric interpolation scheme with four free parameters in each rectangular patch is developed. The free parameters are constrained to avoid unnecessary oscillations, resulting in smooth positive and monotone surfaces for the positive and monotone 3D data. The formulated schemes are local and the degree of the interpolant is unique over the whole domain.