GOffice Reference Manual: Cubic splines

Cubic splines

Functions

void	go_cspline_destroy ()
void	go_cspline_destroyl ()
double	go_cspline_get_deriv ()
long double	go_cspline_get_derivl ()
double *	go_cspline_get_derivs ()
long double *	go_cspline_get_derivsl ()
double *	go_cspline_get_integrals ()
long double *	go_cspline_get_integralsl ()
double	go_cspline_get_value ()
long double	go_cspline_get_valuel ()
double *	go_cspline_get_values ()
long double *	go_cspline_get_valuesl ()
GOCSpline *	go_cspline_init ()
GOCSplinel *	go_cspline_initl ()

Types and Values

enum	GOCSplineType

Object Hierarchy

    GBoxed
    ├── GOCSpline
    ╰── GOCSplinel

Description

Functions

go_cspline_destroy ()

void
go_cspline_destroy (GOCSpline *sp);

Frees the spline structure when done.

Parameters

a spline structure returned by go_cspline_init.

go_cspline_destroyl ()

void
go_cspline_destroyl (GOCSplinel *sp);

go_cspline_get_deriv ()

double
go_cspline_get_deriv (GOCSpline const *sp,
                      double x);

sp must be a valid spline structure as returned by go_cspline_init.

Parameters

sp	a spline structure returned by go_cspline_init.
x	the value

Returns

the interpolated derivative at x, or 0 if an error occurred.

go_cspline_get_derivl ()

long double
go_cspline_get_derivl (GOCSplinel const *sp,
                       long double x);

Returns

go_cspline_get_derivs ()

double *
go_cspline_get_derivs (GOCSpline const *sp,
                       double const *x,
                       int n);

sp must be a valid spline structure as returned by go_cspline_init. The x values must be sorted in increasing order.

Parameters

sp	a spline structure returned by go_cspline_init.
x	a vector a values at which interpolation is requested.
n	the number of interpolation requested.

Returns

a newly allocated array of the n interpolated derivatives which should be destroyed by a call to g_free when not anymore needed, or NULL if an error occurred.

go_cspline_get_derivsl ()

long double *
go_cspline_get_derivsl (GOCSplinel const *sp,
                        long double const *x,
                        int n);

Returns

go_cspline_get_integrals ()

double *
go_cspline_get_integrals (GOCSpline const *sp,
                          double const *x,
                          int n);

sp must be a valid spline structure as returned by go_cspline_init. The x values must be sorted in increasing order.

Parameters

sp	a spline structure returned by go_cspline_init.
x	a vector a values at which interpolation is requested.
n	the number of interpolation requested.

Returns

a newly allocated array of the n-1 integrals on the intervals between two consecutive values stored in x. which should be destroyed by a call to g_free when not anymore needed, or NULL if an error occurred.

go_cspline_get_integralsl ()

long double *
go_cspline_get_integralsl (GOCSplinel const *sp,
                           long double const *x,
                           int n);

Returns

go_cspline_get_value ()

double
go_cspline_get_value (GOCSpline const *sp,
                      double x);

sp must be a valid spline structure as returned by go_cspline_init.

Parameters

sp	a spline structure returned by go_cspline_init.
x	The value

Returns

the interpolated value for x, or 0 if an error occurred.

go_cspline_get_valuel ()

long double
go_cspline_get_valuel (GOCSplinel const *sp,
                       long double x);

Returns

go_cspline_get_values ()

double *
go_cspline_get_values (GOCSpline const *sp,
                       double const *x,
                       int n);

sp must be a valid spline structure as returned by go_cspline_init. The x values must be sorted in increasing order.

Parameters

sp	a spline structure returned by go_cspline_init.
x	a vector a values at which interpolation is requested.
n	the number of interpolation requested.

Returns

a newly allocated array of interpolated values which should be destroyed by a call to g_free when not anymore needed, or NULL if an error occurred.

go_cspline_get_valuesl ()

long double *
go_cspline_get_valuesl (GOCSplinel const *sp,
                        long double const *x,
                        int n);

Returns

go_cspline_init ()

GOCSpline *
go_cspline_init (double const *x,
                 double const *y,
                 int n,
                 unsigned  limits,
                 double c0,
                 double cn);

Creates a spline structure, and computes the coefficients associated with the polynoms. The ith polynome (between x[i-1] and x[i] is: y(x) = y[i-1] + (c[i-1] + (b[i-1] + a[i] * (x - x[i-1])) * (x - x[i-1])) * (x - x[i-1]) where a[i-1], b[i-1], c[i-1], x[i-1] and y[i-1] are the corresponding members of the new structure.

Parameters

x	the x values
y	the y values
n	the number of x and y values
limits	how the limits must be treated, four values are allowed: GO_CSPLINE_NATURAL: first and least second derivatives are 0. GO_CSPLINE_PARABOLIC: the curve will be a parabole arc outside of the limits. GO_CSPLINE_CUBIC: the curve will be cubic outside of the limits. GO_CSPLINE_CLAMPED: the first and last derivatives are imposed.
c0	the first derivative when using clamped splines, not used in the other limit types.
cn	the first derivative when using clamped splines, not used in the other limit types.

Returns

a newly created GOCSpline instance which should be destroyed by a call to go_bezier_spline_destroy.

go_cspline_initl ()

GOCSplinel *
go_cspline_initl (long double const *x,
                  long double const *y,
                  int n,
                  unsigned  limits,
                  long double a0,
                  long double a1);

Returns

Types and Values

enum GOCSplineType

Members

GO_CSPLINE_NATURAL	natural.
GO_CSPLINE_PARABOLIC	parabolic.
GO_CSPLINE_CUBIC	cubic.
GO_CSPLINE_CLAMPED	clamped.