### Chapter 8: Curve and Surface Fitting

 Chapter Introduction Module 8.1: nag_pch_interp - Piecewise Cubic Hermite Interpolation nag_pch_monot_interp Generates a monotonicity-preserving piecewise cubic Hermite interpolant nag_pch_eval Computes values and optionally derivatives of a piecewise cubic Hermite interpolant nag_pch_intg Computes the definite integral of a piecewise cubic Hermite interpolant nag_pch_extract Extracts details of a piecewise cubic Hermite interpolant from a structure of type nag_pch_comm_wp nag_pch_comm_wp Represents a piecewise cubic Hermite interpolant (type) Examples Module 8.2: nag_spline_1d - One-dimensional Spline Fitting nag_spline_1d_auto_fit Generates a cubic spline approximation to an arbitrary 1-d data set, with automatic knot selection nag_spline_1d_lsq_fit Generates a weighted least-squares cubic spline fit to an arbitrary 1-d data set, with given interior knots nag_spline_1d_interp Generates a cubic spline interpolant to an arbitrary 1-d data set nag_spline_1d_eval Computes values of a cubic spline and optionally its first three derivatives nag_spline_1d_intg Computes the definite integral of a cubic spline nag_spline_1d_set Initializes a cubic spline with given interior knots and B-spline coefficients nag_spline_1d_extract Extracts details of a cubic spline from a structure of type nag_spline_1d_comm_wp nag_spline_1d_comm_wp Represents a 1-d cubic spline in B-spline series form (type) Examples Module 8.3: nag_spline_2d - Two-dimensional Spline Fitting nag_spline_2d_auto_fit Generates a bicubic spline approximation to a 2-d data set, with automatic knot selection nag_spline_2d_lsq_fit Generates a minimal, weighted least-squares bicubic spline surface fit to a given set of data points, with given interior knots nag_spline_2d_interp Generates a bicubic spline interpolating surface through a set of data values, given on a rectangular grid of the xy plane nag_spline_2d_eval Computes values of a bicubic spline nag_spline_2d_intg Computes the definite integral of a bicubic spline nag_spline_2d_set Initializes a bicubic spline with given interior knots and B-spline coefficients nag_spline_2d_extract Extracts details of a bicubic spline from a structure of type nag_spline_2d_comm_wp nag_spline_2d_comm_wp Represents a 2-d bicubic spline in B-spline series form (type) Examples Module 8.4: nag_scat_interp - Interpolation of Scattered Data nag_scat_2d_interp Generates a 2-d interpolating function using a modified Shepard method nag_scat_2d_eval Computes values of the interpolant generated by nag_scat_2d_interp and its partial derivatives nag_scat_3d_interp Generates a 3-d interpolating function using a modified Shepard method nag_scat_3d_eval Computes values of the interpolant generated by nag_scat_3d_interp and its partial derivatives nag_scat_2d_set Initializes a structure of type nag_scat_comm_wp to represent a 2-d scattered data interpolant nag_scat_3d_set Initializes a structure of type nag_scat_comm_wp to represent a 3-d scattered data interpolant nag_scat_extract Extracts details of a scattered data interpolant from a structure of derived type nag_scat_comm_wp nag_scat_comm_wp Represents a scattered data interpolant generated either by nag_scat_2d_interp or nag_scat_3d_interp (type) Examples Module 8.5: nag_cheb_1d - Chebyshev Series nag_cheb_1d_fit Finds the least-squares fit using arbitrary data points nag_cheb_1d_interp Generates the coefficients of the Chebyshev polynomial which interpolates (passes exactly through) data at a special set of points nag_cheb_1d_fit_con Finds the least-squares fit using arbitrary data points with constraints on some data points nag_cheb_1d_eval Evaluation of fitted polynomial in one variable, from Chebyshev series form nag_cheb_1d_deriv Derivatives of fitted polynomial in Chebyshev series form nag_cheb_1d_intg Integral of fitted polynomial in Chebyshev series form Examples