# Class BaseCurve

- Defined in File BaseCurve.hxx

## Inheritance Relationships

### Derived Types

- `public G2lib::Biarc` (Class Biarc)

- `public G2lib::BiarcList` (Class BiarcList)

- `public G2lib::CircleArc` (Class CircleArc)

- `public G2lib::ClothoidCurve` (Class ClothoidCurve)

- `public G2lib::ClothoidList` (Class ClothoidList)

- `public G2lib::LineSegment` (Class LineSegment)

- `public G2lib::PolyLine` (Class PolyLine)

## Class Documentation

class G2lib::BaseCurve

  Base classe for all the curve ìn in the library.

  Subclassed by G2lib::Biarc, G2lib::BiarcList, G2lib::CircleArc, G2lib::ClothoidCurve, G2lib::ClothoidList, G2lib::LineSegment, G2lib::PolyLine

  Public Functions

  inline BaseCurve(CurveType const &type)

    Initialize the class storing the curve type.

  inline virtual ~BaseCurve()
  inline CurveType type() const

    The name of the curve type

  virtual real_type length() const = 0

    The length of the curve

  virtual real_type length_ISO(real_type offs) const = 0

    The length of the curve with offset (ISO)

  inline real_type length_SAE(real_type offs) const

    The length of the curve with offset (SAE)

  virtual void bbox(real_type &xmin, real_type &ymin, real_type &xmax, real_type &ymax) const = 0

    Compute the bounding box of the curve.

    Parameters

      - xmin – [out] left bottom

      - ymin – [out] left bottom

      - xmax – [out] right top

      - ymax – [out] right top

  virtual void bbox_ISO(real_type offs, real_type &xmin, real_type &ymin, real_type &xmax, real_type &ymax) const = 0

    Compute the bounding box of the curve with offset (ISO).

    Parameters

      - offs – [in] curve offset

      - xmin – [out] left bottom

      - ymin – [out] left bottom

      - xmax – [out] right top

      - ymax – [out] right top

  inline void bbox_SAE(real_type offs, real_type &xmin, real_type &ymin, real_type &xmax, real_type &ymax) const

    Compute the bounding box of the curve (SAE).

    Parameters

      - offs – [in] curve offset

      - xmin – [out] left bottom

      - ymin – [out] left bottom

      - xmax – [out] right top

      - ymax – [out] right top

  virtual void bbTriangles(std::vector<Triangle2D> &tvec, real_type max_angle = Utils::m_pi / 18, real_type max_size = 1e100, int_type icurve = 0) const = 0

    Build a cover with triangles of the curve.

    Parameters

      - tvec – [out] list of covering triangles

      - max_angle – [out] maximum angle variation of the curve covered by a triangle

      - max_size – [out] maximum admissible size of the covering tirnagles

      - icurve – [out] index of the covering triangles

  virtual void bbTriangles_ISO(real_type offs, std::vector<Triangle2D> &tvec, real_type max_angle = Utils::m_pi / 18, real_type max_size = 1e100, int_type icurve = 0) const = 0

    Build a cover with triangles of the curve with offset (ISO).

    Parameters

      - offs – [out] curve offset

      - tvec – [out] list of covering triangles

      - max_angle – [out] maximum angle variation of the curve covered by a triangle

      - max_size – [out] maximum admissible size of the covering tirnagles

      - icurve – [out] index of the covering triangles

  virtual void bbTriangles_SAE(real_type offs, std::vector<Triangle2D> &tvec, real_type max_angle = Utils::m_pi / 18, real_type max_size = 1e100, int_type icurve = 0) const = 0

    Build a cover with triangles of the curve with offset (SAE).

    Parameters

      - offs – [out] curve offset

      - tvec – [out] list of covering triangles

      - max_angle – [out] maximum angle variation of the arc covered by a triangle

      - max_size – [out] maximum admissible size of the covering tirnagles

      - icurve – [out] index of the covering triangles

  inline virtual real_type thetaBegin() const

    Initial angle of the curve.

  inline virtual real_type thetaEnd() const

    Final angle of the curve.

  inline virtual real_type kappaBegin() const

    Initial curvature.

  inline virtual real_type kappaEnd() const

    Final curvature.

  inline virtual real_type xBegin() const

    Initial x-coordinate.

  inline virtual real_type yBegin() const

    Initial y-coordinate.

  inline virtual real_type xEnd() const

    Final x-coordinate.

  inline virtual real_type yEnd() const

    Final y-coordinate.

  inline virtual real_type xBegin_ISO(real_type offs) const

    Initial x-coordinate with offset (ISO standard).

  inline virtual real_type yBegin_ISO(real_type offs) const

    Initial y-coordinate with offset (ISO standard).

  inline virtual real_type xEnd_ISO(real_type offs) const

    Final x-coordinate with offset (ISO standard).

  inline virtual real_type yEnd_ISO(real_type offs) const

    Final y-coordinate with offset (ISO standard).

  inline real_type xBegin_SAE(real_type offs) const

    Initial x-coordinate with offset (SAE standard).

  inline real_type yBegin_SAE(real_type offs) const

    Initial y-coordinate with offset (SAE standard).

  inline real_type xEnd_SAE(real_type offs) const

    Final y-coordinate with offset (SAE standard).

  inline real_type yEnd_SAE(real_type offs) const

    Final y-coordinate with offset (ISO standard).

  inline virtual real_type tx_Begin() const

    Initial tangent x-coordinate.

  inline virtual real_type ty_Begin() const

    Initial tangent y-coordinate.

  inline virtual real_type tx_End() const

    Final tangent x-coordinate.

  inline virtual real_type ty_End() const

    Final tangent y-coordinate.

  inline virtual real_type nx_Begin_ISO() const

    Intial normal x-coordinate (ISO).

  inline virtual real_type ny_Begin_ISO() const

    Intial normal y-coordinate (ISO).

  inline virtual real_type nx_End_ISO() const

    Final normal x-coordinate (ISO).

  inline virtual real_type ny_End_ISO() const

    Final normal y-coordinate (ISO).

  inline real_type nx_Begin_SAE() const

    Intial normal x-coordinate (SAE).

  inline real_type ny_Begin_SAE() const

    Intial normal y-coordinate (SAE).

  inline real_type nx_End_SAE() const

    Final normal x-coordinate (SAE).

  inline real_type ny_End_SAE() const

    Intial normal y-coordinate (SAE).

  virtual real_type theta(real_type s) const = 0

    Angle at curvilinear coodinate `s`.

  virtual real_type theta_D(real_type s) const = 0

    Angle derivative (curvature) at curvilinear coodinate `s`.

  virtual real_type theta_DD(real_type s) const = 0

    Angle second derivative (devitive of curvature) at curvilinear coodinate `s`.

  virtual real_type theta_DDD(real_type s) const = 0

    Angle third derivative at curvilinear coodinate `s`.

  inline real_type kappa(real_type s) const

    Ccurvature at curvilinear coodinate `s`.

  inline real_type kappa_D(real_type s) const

    Curvature derivative at curvilinear coodinate `s`.

  inline real_type kappa_DD(real_type s) const

    Curvature second derivative at curvilinear coodinate `s`.

  virtual real_type tx(real_type s) const

    Tangent x-coordinate at curvilinear coodinate `s`.

  virtual real_type ty(real_type s) const

    Tangent y-coordinate at curvilinear coodinate `s`.

  virtual real_type tx_D(real_type s) const

    Tangent derivative x-coordinate at curvilinear coodinate `s`.

  virtual real_type ty_D(real_type s) const

    Tangent derivative y-coordinate at curvilinear coodinate `s`.

  virtual real_type tx_DD(real_type s) const

    Tangent second derivative x-coordinate at curvilinear coodinate `s`.

  virtual real_type ty_DD(real_type s) const

    Tangent second derivative y-coordinate at curvilinear coodinate `s`.

  virtual real_type tx_DDD(real_type s) const

    Tangent third derivative x-coordinate at curvilinear coodinate `s`.

  virtual real_type ty_DDD(real_type s) const

    Tangent third derivative y-coordinate at curvilinear coodinate `s`.

  inline real_type nx_ISO(real_type s) const

    Normal x-coordinate at curvilinear coodinate `s` (ISO).

  inline real_type nx_ISO_D(real_type s) const

    Normal derivative x-coordinate at curvilinear coodinate `s` (ISO).

  inline real_type nx_ISO_DD(real_type s) const

    Normal second derivative x-coordinate at curvilinear coodinate `s` (ISO).

  inline real_type nx_ISO_DDD(real_type s) const

    Normal third derivative x-coordinate at curvilinear coodinate `s` (ISO).

  inline real_type ny_ISO(real_type s) const

    Normal y-coordinate at curvilinear coodinate `s` (ISO).

  inline real_type ny_ISO_D(real_type s) const

    Normal derivative y-coordinate at curvilinear coodinate `s` (ISO).

  inline real_type ny_ISO_DD(real_type s) const

    Normal second derivative y-coordinate at curvilinear coodinate `s` (ISO).

  inline real_type ny_ISO_DDD(real_type s) const

    Normal third derivative y-coordinate at curvilinear coodinate `s` (ISO).

  inline real_type nx_SAE(real_type s) const

    Normal x-coordinate at curvilinear coodinate `s` (SAE).

  inline real_type nx_SAE_D(real_type s) const

    Normal derivative x-coordinate at curvilinear coodinate `s` (SAE).

  inline real_type nx_SAE_DD(real_type s) const

    Normal second derivative x-coordinate at curvilinear coodinate `s` (SAE).

  inline real_type nx_SAE_DDD(real_type s) const

    Normal third derivative x-coordinate at curvilinear coodinate `s` (SAE).

  inline real_type ny_SAE(real_type s) const

    Normal y-coordinate at curvilinear coodinate `s` (ISO)

  inline real_type ny_SAE_D(real_type s) const

    Normal derivative y-coordinate at curvilinear coodinate `s` (SAE).

  inline real_type ny_SAE_DD(real_type s) const

    Normal second derivative x-coordinate at curvilinear coodinate `s` (SAE).

  inline real_type ny_SAE_DDD(real_type s) const

    Normal third derivative y-coordinate at curvilinear coodinate `s` (SAE).

  inline virtual void tg(real_type s, real_type &tg_x, real_type &tg_y) const

    Tangent at curvilinear coodinate `s`.

  inline virtual void tg_D(real_type s, real_type &tg_x_D, real_type &tg_y_D) const

    Tangent derivative at curvilinear coodinate `s`.

  inline virtual void tg_DD(real_type s, real_type &tg_x_DD, real_type &tg_y_DD) const

    Tangent second derivative at curvilinear coodinate `s`.

  inline virtual void tg_DDD(real_type s, real_type &tg_x_DDD, real_type &tg_y_DDD) const

    Tangent third derivative at curvilinear coodinate `s`.

  inline void nor_ISO(real_type s, real_type &nx, real_type &ny) const

    Normal at curvilinear coodinate `s` (ISO).

  inline void nor_ISO_D(real_type s, real_type &nx_D, real_type &ny_D) const

    Normal derivative at curvilinear coodinate `s` (ISO).

  inline void nor_ISO_DD(real_type s, real_type &nx_DD, real_type &ny_DD) const

    Normal second derivative at curvilinear coodinate `s` (ISO).

  inline void nor_ISO_DDD(real_type s, real_type &nx_DDD, real_type &ny_DDD) const

    Normal third derivative at curvilinear coodinate `s` (ISO).

  inline void nor_SAE(real_type s, real_type &nx, real_type &ny) const

    Normal at curvilinear coodinate `s` (SAE).

  inline void nor_SAE_D(real_type s, real_type &nx_D, real_type &ny_D) const

    Normal derivative at curvilinear coodinate `s` (SAE).

  inline void nor_SAE_DD(real_type s, real_type &nx_DD, real_type &ny_DD) const

    Normal second derivative at curvilinear coodinate `s` (SAE).

  inline void nor_SAE_DDD(real_type s, real_type &nx_DDD, real_type &ny_DDD) const

    Normal third at curvilinear coodinate `s` (SAE).

  inline virtual void evaluate(real_type s, real_type &th, real_type &k, real_type &x, real_type &y) const

    Evaluate curve at curvilinear coordinate `s`.

    Parameters

      - s – [in] curvilinear coordinate

      - th – [out] angle

      - k – [out] curvature

      - x – [out] x-coordinate

      - y – [out] y-coordinate

  inline virtual void evaluate_ISO(real_type s, real_type offs, real_type &th, real_type &k, real_type &x, real_type &y) const

    Evaluate curve with offset at curvilinear coordinate `s` (ISO).

    Parameters

      - s – [in] curvilinear coordinate

      - offs – [in] offset

      - th – [out] angle

      - k – [out] curvature

      - x – [out] x-coordinate

      - y – [out] y-coordinate

  inline virtual void evaluate_SAE(real_type s, real_type offs, real_type &th, real_type &k, real_type &x, real_type &y) const

    Evaluate curve with offset at curvilinear coordinate `s` (SAE).

    Parameters

      - s – [in] curvilinear coordinate

      - offs – [in] offset

      - th – [out] angle

      - k – [out] curvature

      - x – [out] x-coordinate

      - y – [out] y-coordinate

  virtual real_type X(real_type s) const = 0

    x-coordinate at curvilinear coordinate `s`.

  virtual real_type Y(real_type s) const = 0

    y-coordinate at curvilinear coordinate `s`.

  virtual real_type X_D(real_type s) const = 0

    x-coordinate derivative at curvilinear coordinate `s`.

  virtual real_type Y_D(real_type s) const = 0

    y-coordinate derivative at curvilinear coordinate `s`.

  virtual real_type X_DD(real_type s) const = 0

    x-coordinate second derivative at curvilinear coordinate `s`.

  virtual real_type Y_DD(real_type s) const = 0

    y-coordinate second derivative at curvilinear coordinate `s`.

  virtual real_type X_DDD(real_type s) const = 0

    x-coordinate third derivative at curvilinear coordinate `s`.

  virtual real_type Y_DDD(real_type s) const = 0

    y-coordinate third derivative at curvilinear coordinate `s`.

  virtual void eval(real_type s, real_type &x, real_type &y) const = 0

    x and y-coordinate at curvilinear coordinate `s`.

  virtual void eval_D(real_type s, real_type &x_D, real_type &y_D) const = 0

    x and y-coordinate derivative at curvilinear coordinate `s`.

  virtual void eval_DD(real_type s, real_type &x_DD, real_type &y_DD) const = 0

    x and y-coordinate second derivative at curvilinear coordinate `s`.

  virtual void eval_DDD(real_type s, real_type &x_DDD, real_type &y_DDD) const = 0

    x and y-coordinate third derivative at curvilinear coordinate `s`.

  virtual real_type X_ISO(real_type s, real_type offs) const

    x-coordinate at curvilinear coordinate `s` with offset `offs` (ISO).

  virtual real_type Y_ISO(real_type s, real_type offs) const

    y-coordinate at curvilinear coordinate `s` with offset `offs` (ISO).

  virtual real_type X_ISO_D(real_type s, real_type offs) const

    x-coordinate derivative at curvilinear coordinate `s` with offset `offs` (ISO).

  virtual real_type Y_ISO_D(real_type s, real_type offs) const

    y-coordinate derivative at curvilinear coordinate `s` with offset `offs` (ISO).

  virtual real_type X_ISO_DD(real_type s, real_type offs) const

    x-coordinate second derivative at curvilinear coordinate `s` with offset `offs` (ISO).

  virtual real_type Y_ISO_DD(real_type s, real_type offs) const

    y-coordinate second derivative at curvilinear coordinate `s` with offset `offs` (ISO).

  virtual real_type X_ISO_DDD(real_type s, real_type offs) const

    x-coordinate third derivative at curvilinear coordinate `s` with offset `offs` (ISO).

  virtual real_type Y_ISO_DDD(real_type s, real_type offs) const

    y-coordinate third derivative at curvilinear coordinate `s` with offset `offs` (ISO).

  inline real_type X_SAE(real_type s, real_type offs) const

    x-coordinate at curvilinear coordinate `s` with offset `offs` (SAE).

  inline real_type Y_SAE(real_type s, real_type offs) const

    y-coordinate at curvilinear coordinate `s` with offset `offs` (SAE).

  inline real_type X_SAE_D(real_type s, real_type offs) const

    x-coordinate derivative at curvilinear coordinate `s` with offset `offs` (SAE).

  inline real_type Y_SAE_D(real_type s, real_type offs) const

    y-coordinate derivative at curvilinear coordinate `s` with offset `offs` (SAE).

  inline real_type X_SAE_DD(real_type s, real_type offs) const

    x-coordinate second derivative at curvilinear coordinate `s` with offset `offs` (SAE).

  inline real_type Y_SAE_DD(real_type s, real_type offs) const

    y-coordinate second derivative at curvilinear coordinate `s` with offset `offs` (SAE).

  inline real_type X_SAE_DDD(real_type s, real_type offs) const

    x-coordinate third derivative at curvilinear coordinate `s` with offset `offs` (SAE).

  inline real_type Y_SAE_DDD(real_type s, real_type offs) const

    y-coordinate third derivative at curvilinear coordinate `s` with offset `offs` (SAE).

  virtual void eval_ISO(real_type s, real_type offs, real_type &x, real_type &y) const

    Compute curve at position `s` with offset `offs` (ISO).

    Parameters

      - s – [in] parameter on the curve

      - offs – [in] offset of the curve

      - x – [out] coordinate

      - y – [out] coordinate

  inline void eval_SAE(real_type s, real_type offs, real_type &x, real_type &y) const

    Compute curve at position `s` with offset `offs` (SAE).

    Parameters

      - s – [in] parameter on the curve

      - offs – [in] offset of the curve

      - x – [out] coordinate

      - y – [out] coordinate

  virtual void eval_ISO_D(real_type s, real_type offs, real_type &x_D, real_type &y_D) const

    Compute derivative curve at position `s` with offset `offs` (ISO).

    Parameters

      - s – [in] parameter on the curve

      - offs – [in] offset of the curve

      - x_D – [out] x-coordinate

      - y_D – [out] y-coordinate

  inline void eval_SAE_D(real_type s, real_type offs, real_type &x_D, real_type &y_D) const

    Compute derivative curve at position `s` with offset `offs` (SAE).

    Parameters

      - s – [in] parameter on the curve

      - offs – [in] offset of the curve

      - x_D – [out] x-coordinate first derivative

      - y_D – [out] y-coordinate first derivative

  virtual void eval_ISO_DD(real_type s, real_type offs, real_type &x_DD, real_type &y_DD) const

    Compute second derivative curve at position `s` with offset `offs` (ISO).

    Parameters

      - s – [in] parameter on the curve

      - offs – [in] offset of the curve

      - x_DD – [out] x-coordinate second derivative

      - y_DD – [out] y-coordinate second derivative

  inline void eval_SAE_DD(real_type s, real_type offs, real_type &x_DD, real_type &y_DD) const

    Compute second derivative curve at position `s` with offset `offs` (SAE).

    Parameters

      - s – [in] parameter on the curve

      - offs – [in] offset of the curve

      - x_DD – [out] x-coordinate second derivative

      - y_DD – [out] y-coordinate second derivative

  virtual void eval_ISO_DDD(real_type s, real_type offs, real_type &x_DDD, real_type &y_DDD) const

    Compute third derivative curve at position `s` with offset `offs` (ISO).

    Parameters

      - s – [in] parameter on the curve

      - offs – [in] offset of the curve

      - x_DDD – [out] x-coordinate third derivative

      - y_DDD – [out] y-coordinate third derivative

  inline void eval_SAE_DDD(real_type s, real_type offs, real_type &x_DDD, real_type &y_DDD) const

    Compute third derivative curve at position `s` with offset `offs` (SAE).

    Parameters

      - s – [in] parameter on the curve

      - offs – [in] offset of the curve

      - x_DDD – [out] x-coordinate third derivative

      - y_DDD – [out] y-coordinate third derivative

  virtual void translate(real_type tx, real_type ty) = 0

    translate curve by \( (t_x,t_y) \)

  virtual void rotate(real_type angle, real_type cx, real_type cy) = 0

    Rotate curve by angle \( theta \) centered at point \( (c_x,c_y)\).

    Parameters

      - angle – [in] angle \( theta \)

      - cx – [in] \( c_x\)

      - cy – [in] \( c_y\)

  virtual void scale(real_type sc) = 0

    Scale curve by factor `sc`.

  virtual void reverse() = 0

    Reverse curve parameterization.

  virtual void changeOrigin(real_type newx0, real_type newy0) = 0

    Translate curve so that origin will be (`newx0`, `newy0`).

  virtual void trim(real_type s_begin, real_type s_end) = 0

    Cut curve at parametrix coordinate `s_begin` and `s_end`.

  inline bool collision(BaseCurve const &C) const

    Check collision with another curve.

  inline bool collision_ISO(real_type offs, BaseCurve const &C, real_type offs_C) const

    Check collision with another curve with offset (ISO).

    Parameters

      - offs – [in] curve offset

      - C – [in] second curve to check collision

      - offs_C – [in] curve offset of the second curve

    Returns

      true if collision is detected

  inline bool collision_SAE(real_type offs, BaseCurve const &C, real_type offs_C) const

    Check collision with another curve with offset (SAE).

    Parameters

      - offs – [in] curve offset

      - C – [in] second curve to check collision

      - offs_C – [in] curve offset of the second curve

    Returns

      true if collision is detected

  inline void intersect(BaseCurve const &C, IntersectList &ilist, bool swap_s_vals) const

    Intersect the curve with another curve.

    Parameters

      - C – [in] second curve intersect

      - ilist – [out] list of the intersection (as parameter on the curves)

      - swap_s_vals – [in] if true store `(s2,s1)` instead of `(s1,s2)` for each intersection

  inline void intersect_ISO(real_type offs, BaseCurve const &C, real_type offs_C, IntersectList &ilist, bool swap_s_vals) const

    Intersect the curve with another curve with offset (ISO)

    Parameters

      - offs – [in] offset first curve

      - C – [in] second curve intersect

      - offs_C – [in] offset second curve

      - ilist – [out] list of the intersection (as parameter on the curves)

      - swap_s_vals – [in] if true store `(s2,s1)` instead of `(s1,s2)` for each intersection

  inline void intersect_SAE(real_type offs, BaseCurve const &C, real_type offs_C, IntersectList &ilist, bool swap_s_vals) const

    Intersect the curve with another curve with offset (SAE).

    Parameters

      - offs – [in] offset first curve

      - C – [in] second curve intersect

      - offs_C – [in] offset second curve

      - ilist – [out] list of the intersection (as parameter on the curves)

      - swap_s_vals – [in] if true store `(s2,s1)` instead of `(s1,s2)` for each intersection

  virtual int_type closestPoint_ISO(real_type qx, real_type qy, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst) const = 0

    Given a point find closest point on the curve.

    Parameters

      - qx – x-coordinate of the point

      - qy – y-coordinate of the point

      - x – x-coordinate of the projected point on the curve

      - y – y-coordinate of the projected point on the curve

      - s – parameter on the curve of the projection

      - t – curvilinear coordinate of the point x,y (if orthogonal projection)

      - dst – distance point projected point

    Returns

      1 = point is projected orthogonal 0 = more than one projection (first returned) -1 = minimum point is not othogonal projection to curve

  inline int_type closestPoint_SAE(real_type qx, real_type qy, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst) const

    Given a point find closest point on the curve.

    Parameters

      - qx – x-coordinate of the point

      - qy – y-coordinate of the point

      - x – x-coordinate of the projected point on the curve

      - y – y-coordinate of the projected point on the curve

      - s – parameter on the curve of the projection

      - t – curvilinear coordinate of the point x,y (if orthogonal projection)

      - dst – distance point projected point

    Returns

      1 = point is projected orthogonal 0 = more than one projection (first returned) -1 = minimum point is not othogonal projection to curve

  virtual int_type closestPoint_ISO(real_type qx, real_type qy, real_type offs, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst) const = 0

    Given a point find closest point on the curve.

    Parameters

      - qx – x-coordinate of the point

      - qy – y-coordinate of the point

      - offs – offset of the curve

      - x – x-coordinate of the projected point on the curve

      - y – y-coordinate of the projected point on the curve

      - s – parameter on the curve of the projection

      - t – curvilinear coordinate of the point x,y (if orthogonal projection)

      - dst – distance point projected point

    Returns

      1 = point is projected orthogonal 0 = more than one projection (first returned) -1 = minimum point is not othogonal projection to curve

  inline int_type closestPoint_SAE(real_type qx, real_type qy, real_type offs, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst) const

    Given a point find closest point on the curve.

    Parameters

      - qx – x-coordinate of the point

      - qy – y-coordinate of the point

      - offs – offset of the curve

      - x – x-coordinate of the projected point on the curve

      - y – y-coordinate of the projected point on the curve

      - s – parameter on the curve of the projection

      - t – curvilinear coordinate of the point x,y (if orthogonal projection)

      - dst – distance point projected point

    Returns

      1 = point is projected orthogonal 0 = more than one projection (first returned) -1 = minimum point is not othogonal projection to curve

  inline virtual real_type distance(real_type qx, real_type qy) const

    Compute the distance between a point \( q=(q_x,q_y) \) and the curve.

    Parameters

      - qx – [in] component \( q_x \)

      - qy – [in] component \( q_y \)

    Returns

      the computed distance

  inline real_type distance_ISO(real_type qx, real_type qy, real_type offs) const

    Compute the distance between a point \( q=(q_x,q_y) \) and the curve with offset (ISO).

    Parameters

      - qx – [in] component \( q_x \)

      - qy – [in] component \( q_y \)

      - offs – [in] offset of the curve

    Returns

      the computed distance

  inline real_type distance_SAE(real_type qx, real_type qy, real_type offs) const

    Compute the distance between a point \( q=(q_x,q_y) \) and the curve with offset (SAE).

    Parameters

      - qx – [in] component \( q_x \)

      - qy – [in] component \( q_y \)

      - offs – [in] offset of the curve

    Returns

      the computed distance

  inline bool findST_ISO(real_type x, real_type y, real_type &s, real_type &t) const

    Find the curvilinear coordinate of point \( P=(x,y) \) respect to the curve (ISO), i.e.

    \[ P = C(s)+N(s)t \]

    where \( C(s) \) is the curve position respect to the curvilinear coordinates and \( C(s) \) is the normal at the point \( C(s) \).

    Parameters

      - x – [in] component \( x \)

      - y – [in] component \( y \)

      - s – [out] curvilinear coordinate

      - t – [out] offset respect to the curve of \( (x,y) \)

    Returns

      true if the coordinate are found

  inline bool findST_SAE(real_type x, real_type y, real_type &s, real_type &t) const

    Find the curvilinear coordinate of point \( (x,y) \) respect to the curve (SAE), i.e.

    \[ P = C(s)+N(s)t \]

    where \( C(s) \) is the curve position respect to the curvilinear coordinates and \( C(s) \) is the normal at the point \( C(s) \).

    Parameters

      - x – [in] component \( x \)

      - y – [in] component \( y \)

      - s – [out] curvilinear coordinate

      - t – [out] offset respect to the curve of \( (x,y) \)

    Returns

      true if the coordinate are found

  virtual void info(ostream_type &stream) const = 0

    Pretty print of the curve data.