g1_fitting.hpp File Reference

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Functions
void	g1_fit::calc_clothoid (double x0, double y0, double theta0, double x1, double y1, double theta1, double &k, double &dk, double &l)
void	g1_fit::calc_std_fresnel_integral (double y, double &int_c, double &int_s)

Function Documentation

calc_clothoid()

void g1_fit::calc_clothoid	(	double	x0,
		double	y0,
		double	theta0,
		double	x1,
		double	y1,
		double	theta1,
		double &	k,
		double &	dk,
		double &	L
	)

Compute clothoid parameters from a start and an endpoint. The clothoid curve is defined as x(s) = x0 + \int_0^s cos( 0.5*dk*t^2 + k*t + theta0 ) dt y(s) = y0 + \int_0^s sin( 0.5*dk*t^2 + k*t + theta0 ) dt

Refer to Eq. 1 in https://arxiv.org/pdf/1209.0910.pdf.

Parameters

x0	x(0) in equation above [m].
y0	y(0) in equation above [m].
theta0	Curve angle at s=0 [rad], theta(s)= 0.5*dk*t^2 + k*t + theta0.
x1	x(L) in equation above [m].
y1	y(L) in equation above [m].
theta1	Curve angle at s=L [rad].
k	Curvature at s=0 [1/m], see equation above.
dk	Curvature change [1/m^2], see equation above.
L	Clothoid length [m] from (x0, y0) to (x1, y1).

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calc_std_fresnel_integral()

void g1_fit::calc_std_fresnel_integral	(	double	y,
		double &	int_c,
		double &	int_s
	)

Compute standard Fresnel integrals: c(y) = \int_0^y cos( (pi/2)*x^2 ) dx s(y) = \int_0^y sin( (pi/2)*x^2 ) dx

Refer to Eq. 14 in https://arxiv.org/pdf/1209.0910.pdf.

The present algorithm is described in Thompson, W. J., 1997. Atlas for Computing Mathematical Functions: An Illustrated Guide for Practitioners with Programs in C and Mathematica with CDrom, 1st Edition. John Wiley & Sons, Inc., New York, NY, USA,

using the modifications proposed by Venkata Sivakanth Telasula (2023). Fresnel Cosine and Sine Integral Function (https://www.mathworks.com/matlabcentral/fileexchange/9017-fresnel-cosine-and-sine-integral-function), MATLAB Central File Exchange.

Parameters

y	See equation above.
int_c	Fresnel cosine integral.
int_s	Fresnel sine integral.

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