Quick-reference table mapping FITPACK routines to chapters, sections, and equations in the primary reference:
P. Dierckx, Curve and Surface Fitting with Splines, Oxford University Press, 1993.
Core Algorithms
| Routine | Book Reference | Description |
fpbspl | Ch. 1, Eq. 1.11 | B-spline basis evaluation (de Boor–Cox recurrence) |
fprati | Ch. 5, §5.2.4 | Rational interpolation for smoothing parameter update |
fpdisc | Ch. 4, §4.3 | Discontinuity jumps of B-spline derivatives at knots |
fpgivs | Ch. 4, §4.2 | Givens rotation computation |
fprota | Ch. 4, §4.2 | Apply Givens rotation to matrix rows |
fpback | Ch. 4, §4.2 | Back-substitution for upper triangular systems |
fprank | Ch. 4, §4.3 | Rank-deficient least-squares via Householder |
fporde | Ch. 5, §5.3 | Assign scattered data to knot intervals |
fpchec | Ch. 4, §4.1 | Check knot sequence validity |
fpchep | Ch. 4, §4.1 | Check periodic knot sequence |
fppara | Ch. 9, §9.1 | Compute chord-length parameterization |
Curve Fitting (1D)
| Routine | Book Reference | Description |
curfit | Ch. 5, §5.2 (pp. 67–84) | Automatic-knot curve fitting |
percur | Ch. 6, §6.1 (pp. 105–114) | Periodic curve fitting |
parcur | Ch. 9, §9.1 (pp. 199–212) | Open parametric curve fitting |
clocur | Ch. 9, §9.2 (pp. 213–216) | Closed parametric curve fitting |
concur | Ch. 9, §9.3 (pp. 217–228) | Constrained parametric curve fitting |
concon | Ch. 8, §8.3 (pp. 173–188) | Convexity-constrained fitting (auto knots) |
cocosp | Ch. 8, §8.4 (pp. 189–196) | Convexity-constrained fitting (given knots) |
insert | Ch. 6, §6.2 (pp. 114–118) | Knot insertion (Oslo algorithm) |
Curve Evaluation
| Routine | Book Reference | Description |
splev | Ch. 1, Eq. 1.11 | Evaluate spline at given points |
splder | Ch. 1, §1.3 | Evaluate spline derivatives |
splint | Ch. 1, §1.4 | Definite integral of spline |
sproot | Ch. 6, §6.3 (pp. 118–123) | Zeros of a cubic spline |
fourco | Ch. 7, §7.3 (pp. 153–165) | Fourier coefficients of spline |
curev | Ch. 9 | Evaluate parametric spline curve |
cualde | Ch. 9 | All derivatives of parametric curve |
Surface Fitting (2D)
| Routine | Book Reference | Description |
surfit | Ch. 5, §5.3 (pp. 85–98) | Scattered bivariate fitting |
regrid | Ch. 5, §5.4 (pp. 98–103) | Gridded bivariate fitting |
parsur | Ch. 10, §10.2 (pp. 241–254) | Parametric surface fitting |
Surface Evaluation
| Routine | Book Reference | Description |
bispev | Ch. 1, §1.5 | Evaluate bivariate spline on grid |
bispeu | Ch. 1, §1.5 | Evaluate bivariate spline at scattered points |
parder | Ch. 1, §1.5 | Partial derivatives on grid |
pardeu | Ch. 1, §1.5 | Partial derivatives at scattered points |
pardtc | — | Transform coefficients for derivative spline |
dblint | Ch. 1, §1.5 | Double integral over rectangle |
profil | — | Cross-section at fixed x or y |
surev | Ch. 10 | Evaluate parametric surface on grid |
evapol | — | Evaluate polar-domain spline |
Polar and Spherical Domains
| Routine | Book Reference | Description |
polar | Ch. 11, §11.1 (pp. 255–263) | Scattered polar fitting |
pogrid | Ch. 11, §11.1 (pp. 255–263) | Gridded polar fitting |
sphere | Ch. 11, §11.2 (pp. 263–269) | Scattered spherical fitting |
spgrid | Ch. 11, §11.2 (pp. 263–269) | Gridded spherical fitting |
1.13.2