**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32009

##### Fast and Efficient Algorithms for Evaluating Uniform and Nonuniform Lagrange and Newton Curves

**Authors:**
Taweechai Nuntawisuttiwong,
Natasha Dejdumrong

**Abstract:**

**Keywords:**
Newton interpolation,
Lagrange interpolation,
linear
complexity.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.3455677

**References:**

[1] I. Newton, Philosophiae Naturalis Principia Mathematica. London, 1687.

[2] I. Newton, Letter to Oldenburg (24 october 1676). in The Correspondence of Isaac Newton, vol. 2, pp.110-161, 1960.

[3] G. Farin, Curves and Surfaces for Computer Aided Geometric Design, 5th ed. Academic Press, Morgan Kaufman Publishers, San Francisco, 2002.

[4] H. B. Said, Generalized Ball Curve and Its Recursive Algorithm. ACM Transactions on Graphics, vol. 8, pp. 360-371, 1989.

[5] G. J. Wang, Ball Curve of High Degree and Its Geometric Properties. Appl. Math.: A Journal of Chinese Universities, vol. 2, pp. 126-140, 1987.

[6] J. Delgado and J. M. Pe˜na, A Shape Preserving Representation with an Evaluation Algorithm of Linear Complexity. Computer Aided Geometric Design, vol. 20(1), pp. 1-20, 2008.

[7] W. Hongyi, Unifying Representation of B´ezier Curve And Genaralized Ball Curves. Appl. Math. J. Chinese Univ. Ser. B, vol. 5(1), pp. 109-121, 2000.

[8] Y. Dan and C. Xinmeng, Another Type Of Generalized Ball Curves And Surfaces. Acta Mathematica Scientia, vol. 27B(4), pp. 897-907, 2007.

[9] N. Dejdumrong, Efficient Algorithms for Non-rational and Rational B´ezier Curves. Fifth International Conference on Computer Graphics, Imaging and Visualisation, 2008.