Clothoid2d.h

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#pragma once
 
#include <vector>
#include <Geom/Pnt2d.h>  // for Pnt2d
 
namespace Geom { class Ax2d; }
 
namespace Geom
{
/*
    "The clothoid is the standard transition curve used in railroad engineering/highway engineering for connecting a straight and a circular curve.
    A clothoid has a CONSTANT INCREASING curvature proportional to its curve length.
    Two input parameters are required : the radius R and the parameter A. Suggested values of A : R / 3 <= A <= R.
    All clothoids are geometrically similar : as with the radius R, the parameter A serves as a modification factor(enlargement / reduction).
    For practical applications, a clothoid is viewed in the *1st quadrant* of the coordinate system."
    The smaller the parameter A is, the faster the curvature increases.The length of the transition arc L grows with the parameter A.
    (Source "Fundamentals of Road Design" - ISBN 9781845643362)
*/
class LX_GEOM_EXPORT Clothoid2d
{
public:
    Clothoid2d();
    Clothoid2d(const double& R, const double& A);
    Clothoid2d(const Clothoid2d& other);
    Clothoid2d(Clothoid2d&& other);
    Clothoid2d& operator=(const Clothoid2d& other);
    Clothoid2d& operator=(Clothoid2d&& other);
    ~Clothoid2d() = default;
 
    double getR() const;
    void setR(const double& R);
    double getA() const;
    void setA(const double& A);
 
    double computeTauFromRA() const;
 
    double getDeltaR(const double& tau) const;
    double getLength(const double& tau) const;
    double getTau(const double& L) const;
 
    Geom::XY getCoordinate(const double& L) const;
    Geom::XY getCenter(const double& L) const;
 
    double computeTk() const;
    double computeTl() const;
 
    std::vector<Geom::XY> approximate(const unsigned int& segments) const;
 
private:
    double _R;  // Radius
    double _A;  // Constant A
 
    // Helper function to compute the angle between Ax2d-Direction and the X-Axis.
    static double getAngle(const Geom::Ax2d& position);
    // Helper function to compute a Pnt2d given an Ax2d (origin, direction) and a distance u along the direction.
    static Geom::Pnt2d lineValue(const double& u, const Geom::Ax2d& ax2);
    // Helper function to rotate a XY coordinate around (0., 0.) about angle.
    static Geom::XY rotate2D(const Geom::XY& xy, const double& angle);
};
}  // namespace Geom