BIMOND: Piecewise Bicubic Interpolation

These files provide MATLAB implementations of the BIMOND3 and BIMOND4 algorithms presented by Carlson and Fritsch in [1] and [2], respectively. The BIMOND algorithms are a 2D extension of PCHIP (Piecewise Cubic Hermite Interpolating Polynomial), preserving monotonicity in the underlying data.

This package depends on the MATLAB Curve Fitting Toolbox. Additionally, these functions assume that the following files are available in the user's MATLAB path:

• pchci.m
• pchcs.m
• pchic.m
• pchst.m
• pchsw.m
• r1mach.m

These files are included in this repository but can also be obtained as part of the slatec MATLAB package.

I/O

Both BIMOND3 and BIMOND4 take as input vectors x and y, and a matrix of function values p where the rows index x and the columns indexy.

The functions output a ppform spline that can be evaluated with functions from the MATLAB Curve Fitting Toolbox.

The function get_coefs will reformat the ppform spline to a cell of coefficient vectors specifying each piecewise polynomial.

BIMOND3

The BIMOND3 algorithm presented in [1] provides two-dimensional interpolation of data that is monotone in both variables. BIMOND3_example.m reproduces the numeric example given in Appendix B.

BIMOND4

The BIMOND4 algorithm presented in [2] provides two-dimensional interpolation of data that is monotone in only one variable. BIMOND4_example.m reproduces the numeric example given in Section 5.

References.

[1] Carlson, R. E., & Fritsch, F. N. (1989). An algorithm for monotone piecewise bicubic interpolation. SIAM Journal on Numerical Analysis, 26(1), 230-238.

[2] Carlson, R. E., & Fritsch, F. N. (1991). A bivariate interpolation algorithm for data that are monotone in one variable. SIAM Journal on Scientific and Statistical Computing, 12(4), 859-866.