A simple 2D interpolation model for analysis of nonlinear data
Author(s)
Mehdi Zamani
ABSTRACT
To determination the volume and weight of non uniform bodies, such as in ore deposits evaluation for mining and rock cutting for construction, the methods of interpolation are usually used. The classic curves, which are frequently used to interpolate onedimensional data are cubic spl ine, Bspline and Bezier curves. These methods have good efficiency for determination of geom etric characteristics of nonregular masses. They have some limitations and problems with two dimensional interpolation analysis such as for ming large linear systems of equations with a lot of entries and difficulty encounter with their solutions. In this research the twodimensional splines are used, which have the advantages of simplicity and less computational operations ef fort. The spline functions that are applied have the continuity of C1 at elements boundaries. The presented model has suitable efficiency for vo lumes of large extents governing to lots of data.
To determination the volume and weight of non uniform bodies, such as in ore deposits evaluation for mining and rock cutting for construction, the methods of interpolation are usually used. The classic curves, which are frequently used to interpolate onedimensional data are cubic spl ine, Bspline and Bezier curves. These methods have good efficiency for determination of geom etric characteristics of nonregular masses. They have some limitations and problems with two dimensional interpolation analysis such as for ming large linear systems of equations with a lot of entries and difficulty encounter with their solutions. In this research the twodimensional splines are used, which have the advantages of simplicity and less computational operations ef fort. The spline functions that are applied have the continuity of C1 at elements boundaries. The presented model has suitable efficiency for vo lumes of large extents governing to lots of data.
KEYWORDS
Simulation; Approximation; Least square; Cubic Spline; Optimization; Curve Fitting; Prediction
Simulation; Approximation; Least square; Cubic Spline; Optimization; Curve Fitting; Prediction
Cite this paper
Zamani, M. (2010) A simple 2D interpolation model for analysis of nonlinear data. Natural Science, 2, 641-645. doi: 10.4236/ns.2010.26080.
Zamani, M. (2010) A simple 2D interpolation model for analysis of nonlinear data. Natural Science, 2, 641-645. doi: 10.4236/ns.2010.26080.
References
[1] Salmon, D. (2006) Curves and surfaces for computer graphics. Springer, New York. [2] Saxena, A. and Sahay, B. (2005) Computer aided engineering design. Springer, Anamaya Publisher, New Delhi. [3] Conte, S.D. and de Boor, C. (1981) Elementary numerical analysis, an algorithm approach. Kin Keong Printing Co. Pte. Ltd., Singapore. [4] Burden, R. and Fairs, D. (1989) Numerical analysis. PWSKent Publishing Company, Boston. [5] March, D. (2005) Applied geometry for compute graphics and CAD. 2nd Edition, SpringerVerlag, New York. [6] Todd, D.K. (1959) Groundwater hydrology. John Wily & Sons, Inc., New York.
[1] Salmon, D. (2006) Curves and surfaces for computer graphics. Springer, New York. [2] Saxena, A. and Sahay, B. (2005) Computer aided engineering design. Springer, Anamaya Publisher, New Delhi. [3] Conte, S.D. and de Boor, C. (1981) Elementary numerical analysis, an algorithm approach. Kin Keong Printing Co. Pte. Ltd., Singapore. [4] Burden, R. and Fairs, D. (1989) Numerical analysis. PWSKent Publishing Company, Boston. [5] March, D. (2005) Applied geometry for compute graphics and CAD. 2nd Edition, SpringerVerlag, New York. [6] Todd, D.K. (1959) Groundwater hydrology. John Wily & Sons, Inc., New York.