PROJECTING A HYDROGRAPHIC MAP OF THE REPUBLIC OF MACEDONIA

Abstract

Bezier and B-spline curves are among the most powerful tools used for complex graphical approximation. In this paper, we will use them to recreate the hydrographic map of the Republic of Macedonia. The results obtained in this paper show that cubic spline curves have smaller average deviation in respect to B-spline curves, in contrast to Bezier curves. The results and the images are obtained by using the software package Wolfram Mathematica. Key words: Bezier curves; B-spline; cubic spline REFERENCES [1] Vera B. Anand: Computer Graphics and Geometric Modeling for Engineers, John Wiley & Sons Inc. 1996. [2] V. Andova, S. Atanasova, K. Bacev, Gj. Peev, G.Kostov: Approximation of map borders using Mathematica, ETAI (2015). [3] R. H. Bartels, J. C. Beatty, B. A. Barsky: An Introduction to Splines for Use in Computer Graphics and Geometric Modeling, Morgan Kaufmann Publishers Inc. 1987. [4] R. C. Beach: An Introduction to the Curves and Surfaces of Computer-Aided Design, Van Nostrand Reinhold, 1991. [5] E. Cohen: Discrete B-splines and Subdivision Techniques in Computer Aided Geometric Design and Computer Graphics, International Association for Bridge and Structural Engineering, 1979. [6] C. De Boor: A Practical Guide to Splines, Revised Edition, Springer, 1978. [7] G. Farin: Curves and Surfaces for CAGD. A Practical Guide, fifth edition, Academic Press, 2002. [8] G. Farin, J. Hoschek, M.-S. Kim: Handbook of Computer Aided Geometric Design, Elsevier, 2002. [9] G. Farin: NURBS: From Projective Geometry to Practical Use, 2nd edition, AK Peters, 1999. [10] J. Fiorot, P. Jeannin: Rational Curves and Surfaces, Wiley, 1992. [11] J. Gallier: Curves and Surfaces. In: Geometric Modeling:Theory and Algorithms, Morgan Kofman Publishers,2000. [12] G. G. Lorentz: Bernstein Polynomials, University of Toronto Press, 1953. [13] R. F. Riesenfeld: Applications of B-spline Approximation to Geometric Problems of Computer-Aided Design, Syracuse University, 1973. [14] D. Rogers: An Introduction to NURBS with Historical Perspective, Elsevier, 2001. [15] W. Rudin: Real and Complex Analysis, McGraw-Hill Higher Education, 1986. [16] D. Salomon: Curves and Surfaces for Computer Graphic, Springer, 2006. [17] S. Wagon: Mathematica in Action Problem Solving Through Visualization and Computation, Springer, 2010. [18] S. Wolfram: The Mathematica Book, Fifth Edition, Wolfram Media, 2003.