#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include "cubic_spline.h"
#include "mbs_1D_array.h"
#include "mbs_matrix.h"
#include "mbs_message.h"

Functions
CubicSpline *	cubic_spline_new_from_file (const char *filename)
	Load the coefficient of the cubic splines from a file. More...

int	cubic_spline_get_index (CubicSpline *cs, double x_in)
	Retrieve the index (starting at zero) in the spline coefficient table corresponding to the specified coordinate. More...

double	cubic_spline_comp_value (CubicSpline *cs, double x_in, int index)
	Compute the value of the cubic spline at the specified coordinate. More...

double	cubic_spline_comp_firstder (CubicSpline *cs, double x_in, int index)
	Compute the value of the first derivative of the cubic spline at the specified coordinate. More...

double	cubic_spline_comp_secondder (CubicSpline *cs, double x_in, int index)
	Compute the value of the second derivative of the cubic spline at the specified coordinate. More...

void	cubic_spline_comp_val_and_der (CubicSpline cs, double x_in, int index, double y, double yp, double ypp)
	Compute the value of the cubic spline and its first and second derivatives at the specified coordinate. More...

void	cubic_spline_delete (CubicSpline *cs)
	Free the memory of cubic spline. More...

Detailed Description

This c file implements utilities functions about cubic spline interpolation.

Creation date: 2022

Author: Robotran team

(c) Universite catholique de Louvain

Function Documentation

◆ cubic_spline_comp_firstder()

double cubic_spline_comp_firstder	(	CubicSpline *	cs,
		double	x_in,
		int	index
	)

Compute the value of the first derivative of the cubic spline at the specified coordinate.

Parameters

cs	cubic spline.
x_in	evaluated coordinate.
index	corresponding to the evaluated coordinate. Use cubic_spline_get_index to get the index corresponding to the coordinate or use -99 to let the function evaluating the index by itself. Other negative values are invalid index.

Returns: the value of the cubic spline.

◆ cubic_spline_comp_secondder()

double cubic_spline_comp_secondder	(	CubicSpline *	cs,
		double	x_in,
		int	index
	)

Compute the value of the second derivative of the cubic spline at the specified coordinate.

Parameters

cs	cubic spline.
x_in	evaluated coordinate.
index	corresponding to the evaluated coordinate. Use cubic_spline_get_index to get the index corresponding to the coordinate or use -99 to let the function evaluating the index by itself. Other negative values are invalid index.

Returns: the value of the cubic spline.

◆ cubic_spline_comp_val_and_der()

void cubic_spline_comp_val_and_der	(	CubicSpline *	cs,
		double	x_in,
		int	index,
		double *	y,
		double *	yp,
		double *	ypp
	)

Compute the value of the cubic spline and its first and second derivatives at the specified coordinate.

Parameters

cs	cubic spline.
x_in	evaluated coordinate.
index	corresponding to the evaluated coordinate. Use cubic_spline_get_index to get the index corresponding to the coordinate or use -99 to let the function evaluating the index by itself. Ohter negative value are invalid index.
y	a pointer to the memory where to store the value of the cubic spline.
yp	a pointer to the memory where to store the 1st derivative.
ypp	a pointer to the memory where to store the 2nd derivative.

◆ cubic_spline_comp_value()

double cubic_spline_comp_value	(	CubicSpline *	cs,
		double	x_in,
		int	index
	)

Compute the value of the cubic spline at the specified coordinate.

Parameters

cs	cubic spline.
x_in	evaluated coordinate.
index	corresponding to the evaluated coordinate. Use cubic_spline_get_index to get the index corresponding to the coordinate or use -99 to let the function evaluating the index by itself. Other negative values are invalid index.

Returns: the value of the cubic spline.

◆ cubic_spline_delete()

void cubic_spline_delete ( CubicSpline * cs )

Free the memory of cubic spline.

Parameters

cs	cubic spline to be deleted.

◆ cubic_spline_get_index()

int cubic_spline_get_index	(	CubicSpline *	cs,
		double	x_in
	)

Retrieve the index (starting at zero) in the spline coefficient table corresponding to the specified coordinate.

The index is the lower value of the interval.

Parameters

cs	cubic spline.
x_in	coordinate for which to retrieve the index.

Returns: the correct value of the index where coefficients corresponding to the value x_in are located.

◆ cubic_spline_new_from_file()

CubicSpline* cubic_spline_new_from_file ( const char * filename )

Load the coefficient of the cubic splines from a file.

Allocate also the memory corresponding to this spline structure.

The file contains 5 columns, denoted: $x_{beg}$ , $a$ , $b$ , $c$ , $d$ . Each column must be separated by a space character. Each line defines a segment. The signification of each column is:

$x_{beg}$ : Value of the interpolation variable at the beginning of the current segment;
, , , : coefficients of the cubic spline for the current segment;

The spline is computed as: $spline(x) = a y^3 + b y^2 + c y + d$ with $y = (x-x_{beg})$

The last line of the file must contains five column, even if only the first value is used as the end of the cubic spline interpolation range.

To generate the input file, an example of Python script is provided with the sources of MBsysC. The file named cubic_spline_compute_coefficients.py is located in the folder MBsysC/scripts.

Parameters

[in] filename File name (with the path and extension) that contains the coefficients of the spline

Returns: an allocated structure

Functions

Detailed Description

Function Documentation

◆ cubic_spline_comp_firstder()

◆ cubic_spline_comp_secondder()

◆ cubic_spline_comp_val_and_der()

◆ cubic_spline_comp_value()

◆ cubic_spline_delete()

◆ cubic_spline_get_index()

◆ cubic_spline_new_from_file()