fitpack — Modern Fortran Spline Fitting

fitpack is a Modern Fortran (2008+) library for curve and surface fitting with splines, based on the FITPACK package by Paul Dierckx.

It provides an object-oriented API with derived types for all major fitting tasks: smoothing, interpolation, least-squares approximation, and constrained fitting. All routines support spline degrees 1 through 5 (cubic by default) and return B-spline representations that can be evaluated, differentiated, integrated, and root-found efficiently.

Type Hierarchy

All fitter types extend the abstract base fitpack_fitter:

fitpack_fitter (abstract base)
├── fitpack_curve                   — 1D spline: y = s(x)
│   ├── fitpack_periodic_curve      — periodic boundary conditions
│   └── fitpack_convex_curve        — convexity-constrained fitting
├── fitpack_parametric_curve        — parametric curves: x_i = s_i(u)
│   ├── fitpack_closed_curve        — closed parametric curves
│   └── fitpack_constrained_curve   — endpoint derivative constraints
├── fitpack_surface                 — 2D spline from scattered data
├── fitpack_grid_surface            — 2D spline from gridded data
├── fitpack_parametric_surface      — parametric surfaces
├── fitpack_polar                   — polar-domain fitting (scattered)
├── fitpack_grid_polar              — polar-domain fitting (gridded)
├── fitpack_sphere                  — spherical-domain fitting (scattered)
└── fitpack_grid_sphere             — spherical-domain fitting (gridded)

Quick Start

Fit a curve

use fitpack, only: fitpack_curve
 
type(fitpack_curve) :: curve
integer :: ierr
 
! Create a smoothing spline from data
curve = fitpack_curve(x, y, ierr=ierr)
 
! Evaluate at new points
y_new = curve%eval(x_new, ierr)
 
! Compute derivative, integral, zeros
dydx  = curve%dfdx(x_new, ierr)
area  = curve%integral(x(1), x(size(x)), ierr)
roots = curve%zeros(ierr)

Fit a surface

use fitpack, only: fitpack_grid_surface
 
type(fitpack_grid_surface) :: surf
integer :: ierr
 
! Create a smoothing spline from gridded data
surf = fitpack_grid_surface(x, y, z, ierr=ierr)
 
! Evaluate on a new grid
z_new = surf%eval(x_new, y_new, ierr)

Building

fitpack uses fpm (Fortran Package Manager):

fpm build          # build the library
fpm test           # run all tests

Spline Theory

• B-Spline Foundations — B-spline basis functions, de Boor evaluation, derivatives, integration, knot insertion
• Curve Fitting Theory — Smoothing criterion, adaptive knot placement, periodic and parametric curves
• Surface Fitting Theory — Tensor product splines, scattered vs. gridded fitting, Kronecker product efficiency
• Polar and Spherical Domains — Polar coordinate transform, spherical coordinates, pole boundary conditions

Tutorials

Curves

• Univariate Curve Fitting with fitpack_curve — Univariate smoothing and interpolation with fitpack_curve
• Periodic Curve Fitting — Periodic splines with fitpack_periodic_curve
• Parametric, Closed, and Constrained Curves — Parametric, closed, and constrained curves
• Convexity-Constrained Curve Fitting — Shape-preserving fitting with convexity constraints

Surfaces

• Scattered Surface Fitting Tutorial — Scattered bivariate data with fitpack_surface
• Grid and Parametric Surface Tutorial — Gridded data and parametric surfaces

Special Domains

• Polar Domain Fitting Tutorial — Disc-shaped domains with fitpack_polar and fitpack_grid_polar
• Spherical Spline Fitting Tutorial — Spherical data with fitpack_sphere and fitpack_grid_sphere

Examples

Compilable example programs are in the examples/ directory. Build and run with:

fpm run --example example_curve
fpm run --example example_periodic_curve
fpm run --example example_parametric_curves
fpm run --example example_convex_curve
fpm run --example example_surface
fpm run --example example_grid_surface
fpm run --example example_polar
fpm run --example example_sphere

Reference

• Book Reference Index — Quick-reference table mapping routines to book chapters and equations

The algorithms are described in:

P. Dierckx, Curve and Surface Fitting with Splines, Oxford University Press, 1993.

Each routine's documentation references the relevant book chapter, section, and equation numbers.