Class CircleArc

• Defined in File Circle.hxx

Inheritance Relationships

Base Type

• public G2lib::BaseCurve (Class BaseCurve)

Class Documentation

class G2lib::CircleArc : public G2lib::BaseCurve

Class to manage a circle arc

Public Functions

inline CircleArc()

Build an empty circle

inline CircleArc(CircleArc const &s)

Build a copy of an existing circle arc.

inline explicit CircleArc(real_type x0, real_type y0, real_type theta0, real_type k, real_type L)

Construct a circle arc with the standard parameters.

Parameters

• x0 – [in] starting position x-coordinate

• y0 – [in] starting position y-coordinate

• theta0 – [in] initial angle

• k – [in] curvature

• L – [in] length

inline explicit CircleArc(LineSegment const &LS)

Construct a circle arc from a line segment (degenerate circle).

inline void copy(CircleArc const &c)

Make a copy of an existing circle arc.

explicit CircleArc(BaseCurve const &C)

Build a circle arc from a generic curve (if possibile).

inline CircleArc const &operator=(CircleArc const &s)

Make a copy of an existing circle arc.

inline void build(real_type x0, real_type y0, real_type theta0, real_type k, real_type L)

Construct a circle arc with the standard parameters.

Parameters

• x0 – [in] starting position x-coordinate

• y0 – [in] starting position y-coordinate

• theta0 – [in] initial angle

• k – [in] curvature

• L – [in] length

bool build_G1(real_type x0, real_type y0, real_type theta0, real_type x1, real_type y1)

Build a circle by solving the hermite G1 problem.

Parameters

• x0 – [in] starting position x-coordinate

• y0 – [in] starting position y-coordinate

• theta0 – [in] initial angle

• x1 – [in] final position x-coordinate

• y1 – [in] final position y-coordinate

Returns

true if success

bool build_3P(real_type x0, real_type y0, real_type x1, real_type y1, real_type x2, real_type y2)

Build a circle passing by 3 points.

Parameters

• x0 – [in] starting point x-coordinate

• y0 – [in] starting point y-coordinate

• x1 – [in] intermediate point x-coordinate

• y1 – [in] intermediate point y-coordinate

• x2 – [in] final point x-coordinate

• y2 – [in] final point y-coordinate

Returns

true if success

bool bbTriangle(real_type &x0, real_type &y0, real_type &x1, real_type &y1, real_type &x2, real_type &y2) const

Get the bounding box triangle (if angle variation less that pi/3).

Parameters

• x0 – [out] first triangle point x-coordinate

• y0 – [out] first triangle point y-coordinate

• x1 – [out] second triangle point x-coordinate

• y1 – [out] second triangle point y-coordinate

• x2 – [out] third triangle point x-coordinate

• y2 – [out] third triangle point y-coordinate

Returns

true if success

bool bbTriangle_ISO(real_type offs, real_type &x0, real_type &y0, real_type &x1, real_type &y1, real_type &x2, real_type &y2) const

Get the bounding box triangle of the circle arc with offset (if angle variation less that \( \pi/3 \)).

Parameters

• offs – [in] offset

• x0 – [out] first triangle point x-coordinate

• y0 – [out] first triangle point y-coordinate

• x1 – [out] second triangle point x-coordinate

• y1 – [out] second triangle point y-coordinate

• x2 – [out] third triangle point x-coordinate

• y2 – [out] third triangle point y-coordinate

Returns

true if success

inline bool bbTriangle_SAE(real_type offs, real_type &x0, real_type &y0, real_type &x1, real_type &y1, real_type &x2, real_type &y2) const

Get the bounding box triangle of the circle arc with offset if angle variation less that \( \pi/3 \)).

Parameters

• offs – [in] offset

• x0 – [out] first triangle point x-coordinate

• y0 – [out] first triangle point y-coordinate

• x1 – [out] second triangle point x-coordinate

• y1 – [out] second triangle point y-coordinate

• x2 – [out] third triangle point x-coordinate

• y2 – [out] third triangle point y-coordinate

Returns

true if success

inline bool bbTriangle(real_type *p0, real_type *p1, real_type *p2) const

Get the bounding box triangle of the circle (if angle variation less that \( \pi/3 \)).

Parameters

• p0 – [out] first triangle point

• p1 – [out] second triangle point

• p2 – [out] third triangle point

Returns

true if success

inline bool bbTriangle_ISO(real_type offs, real_type *p0, real_type *p1, real_type *p2) const

Get the bounding box triangle of the circle arc with offset (if angle variation less that \( \pi/3 \)).

Parameters

• offs – [in] offset

• p0 – [out] first triangle point

• p1 – [out] second triangle point

• p2 – [out] third triangle point

Returns

true if success

inline bool bbTriangle_SAE(real_type offs, real_type *p0, real_type *p1, real_type *p2) const

Get the bounding box triangle of the circle arc with offset (if angle variation less that \( \pi/3 \)).

Parameters

• offs – [in] offset

• p0 – [out] first triangle point

• p1 – [out] second triangle point

• p2 – [out] third triangle point

Returns

true if success

inline bool bbTriangle(Triangle2D &t, real_type ss0 = 0, real_type ss1 = 0, int_type icurve = 0) const

Get the bounding box triangle list of the circle arc.

Parameters

• t – [out] the bounding triangle

• ss0 – [in] s0 stored in the triangle class

• ss1 – [in] s1 stored in the triangle class

• icurve – [in] id stored in the triangle class

Returns

true if success

inline bool bbTriangle_ISO(real_type offs, Triangle2D &t, real_type ss0 = 0, real_type ss1 = 0, int_type icurve = 0) const

Get the bounding box triangle list of the circle arc with offset.

Parameters

• offs – [in] offset

• t – [out] the bounding triangle

• ss0 – [in] s0 stored in the triangle class

• ss1 – [in] s1 stored in the triangle class

• icurve – [in] id stored in the triangle class

Returns

true if success

inline bool bbTriangle_SAE(real_type offs, Triangle2D &t, real_type ss0 = 0, real_type ss1 = 0, int_type icurve = 0) const

Get the bounding box triangle list of the circle arc with offset.

Parameters

• offs – [in] offset

• t – [out] the bounding triangle

• ss0 – [in] s0 stored in the triangle class

• ss1 – [in] s1 stored in the triangle class

• icurve – [in] id stored in the triangle class

Returns

true if success

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 override

Get the bounding box triangle list of the circle arc with offset.

Parameters

• tvec – [out] the bounding triangle list

• max_angle – [in] maximum angle variation admitted for all splitted segment

• max_size – [in] maximum size admitted for all splitted segment

• icurve – [in] id stored in the 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 override

Get the bounding box triangle list of the circle arc with offset.

Parameters

• offs – [in] offset

• tvec – [out] the bounding triangle list

• max_angle – [in] maximum angle variation admitted for all splitted segment

• max_size – [in] maximum size admitted for all splitted segment

• icurve – [in] id stored in the triangles

inline 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 override

Get the bounding box triangle list of the circle arc with offset.

Parameters

• offs – [in] offset

• tvec – [out] the bounding triangle list

• max_angle – [in] maximum angle variation admitted for all splitted segment

• max_size – [in] maximum size admitted for all splitted segment

• icurve – [in] id stored in the triangles

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

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 override

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 virtual real_type length() const override

The length of the curve

inline virtual real_type length_ISO(real_type offs) const override

The length of the curve with offset (ISO)

inline virtual real_type thetaBegin() const override

Initial angle of the curve.

inline virtual real_type kappaBegin() const override

Initial curvature.

inline virtual real_type kappaEnd() const override

Final curvature.

inline virtual real_type xBegin() const override

Initial x-coordinate.

inline virtual real_type yBegin() const override

Initial y-coordinate.

inline virtual real_type tx_Begin() const override

Initial tangent x-coordinate.

inline virtual real_type ty_Begin() const override

Initial tangent y-coordinate.

inline virtual real_type nx_Begin_ISO() const override

Intial normal x-coordinate (ISO).

inline virtual real_type ny_Begin_ISO() const override

Intial normal y-coordinate (ISO).

inline virtual real_type theta(real_type s) const override

Angle at curvilinear coodinate s.

inline virtual real_type theta_D(real_type) const override

Angle derivative (curvature) at curvilinear coodinate s.

inline virtual real_type theta_DD(real_type) const override

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

inline virtual real_type theta_DDD(real_type) const override

Angle third derivative at curvilinear coodinate s.

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

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

virtual real_type X(real_type s) const override

x-coordinate at curvilinear coordinate s.

virtual real_type Y(real_type s) const override

y-coordinate at curvilinear coordinate s.

virtual real_type X_D(real_type) const override

x-coordinate derivative at curvilinear coordinate s.

virtual real_type Y_D(real_type) const override

y-coordinate derivative at curvilinear coordinate s.

virtual real_type X_DD(real_type) const override

x-coordinate second derivative at curvilinear coordinate s.

virtual real_type Y_DD(real_type) const override

y-coordinate second derivative at curvilinear coordinate s.

virtual real_type X_DDD(real_type) const override

x-coordinate third derivative at curvilinear coordinate s.

virtual real_type Y_DDD(real_type) const override

y-coordinate third derivative at curvilinear coordinate s.

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

x and y-coordinate at curvilinear coordinate s.

virtual void eval_D(real_type, real_type &x_D, real_type &y_D) const override

x and y-coordinate derivative at curvilinear coordinate s.

virtual void eval_DD(real_type, real_type &x_DD, real_type &y_DD) const override

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

virtual void eval_DDD(real_type, real_type &x_DDD, real_type &y_DDD) const override

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

inline virtual real_type tx(real_type s) const override

Tangent x-coordinate at curvilinear coodinate s.

inline virtual real_type tx_D(real_type s) const override

Tangent derivative x-coordinate at curvilinear coodinate s.

inline virtual real_type tx_DD(real_type s) const override

Tangent second derivative x-coordinate at curvilinear coodinate s.

inline virtual real_type tx_DDD(real_type s) const override

Tangent third derivative x-coordinate at curvilinear coodinate s.

inline virtual real_type ty(real_type s) const override

Tangent y-coordinate at curvilinear coodinate s.

inline virtual real_type ty_D(real_type s) const override

Tangent derivative y-coordinate at curvilinear coodinate s.

inline virtual real_type ty_DD(real_type s) const override

Tangent second derivative y-coordinate at curvilinear coodinate s.

inline virtual real_type ty_DDD(real_type s) const override

Tangent third derivative y-coordinate at curvilinear coodinate s.

virtual void tg(real_type s, real_type &tx, real_type &ty) const override

Tangent at curvilinear coodinate s.

virtual void tg_D(real_type s, real_type &tx_D, real_type &ty_D) const override

Tangent derivative at curvilinear coodinate s.

virtual void tg_DD(real_type s, real_type &tx_DD, real_type &ty_DD) const override

Tangent second derivative at curvilinear coodinate s.

virtual void tg_DDD(real_type s, real_type &tx_DDD, real_type &ty_DDD) const override

Tangent third derivative at curvilinear coodinate s.

inline virtual void translate(real_type tx, real_type ty) override

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

virtual void rotate(real_type angle, real_type cx, real_type cy) override

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 reverse() override

Reverse curve parameterization.

inline virtual void changeOrigin(real_type newx0, real_type newy0) override

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

virtual void scale(real_type s) override

Scale curve by factor sc.

virtual void trim(real_type s_begin, real_type s_end) override

Cut curve at parametrix coordinate s_begin and s_end.

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 override

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 override

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 void info(ostream_type &stream) const override

Pretty print of the curve data.

bool collision(CircleArc const&) const

Detect a collision with another circle arc.

bool collision_ISO(real_type offs, CircleArc const &C, real_type offs_obj) const

Detect a collision with another circle arc with offset.

Parameters

• offs – [in] offset of first circle arc

• C – [in] second circle arc

• offs_obj – [in] offset of second circle arc

void intersect(CircleArc const &obj, IntersectList &ilist, bool swap_s_vals) const

Intersect a circle arc with another circle arc.

Parameters

• obj – [in] second biarc

• 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

void intersect_ISO(real_type offs, CircleArc const &C, real_type offs_obj, IntersectList &ilist, bool swap_s_vals) const

Intersect a circle arc with another circle arc with offset (ISO).

Parameters

• offs – [in] offset of first circle arc

• C – [in] second circle arc

• offs_obj – [in] offset of second circle arc

• 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 real_type sinTheta0() const

Return \( \sin \theta_0 \) where \( \theta_0 \) is the initial tangent angle.

inline real_type cosTheta0() const

Return \( \cos \theta_0 \) where \( \theta_0 \) is the initial tangent angle.

inline real_type curvature() const

Return curvature of the circle arc.

real_type lenTolerance(real_type tol) const

Return the length of the arc that can approximated by a line segment.

inline real_type delta_theta() const

Return the tangent angle variation in the circle arc.

inline real_type thetaTotalVariation() const

Return the absolute value of the tangent angle variation in the circle arc.

real_type thetaMinMax(real_type &thMin, real_type &thMax) const

Minimum and maximum tangent angle.

Parameters

• thMin – [out] mimimum tangent angle

• thMax – [out] maximum tangent angle

Returns

thMax-thMin

inline real_type deltaTheta() const

Minimum and maximum tangent angle.

Parameters

• thMin – [out] mimimum tangent angle

• thMax – [out] maximum tangent angle

Returns

thMax-thMin

void changeCurvilinearOrigin(real_type s0, real_type newL)

Change the origin of the circle arc at \( s_0 \) and the length of the arc to \( L \).

Parameters

• s0 – [in] \( s_0 \)

• newL – [in] \( L \)

void center(real_type &cx, real_type &cy) const

Get the center of the circle arc \( (c_x,c_y) \).

Parameters

• cx – [in] \( c_x \)

• cy – [in] \( c_y \)

inline real_type ray() const

Get the ray of the circle arc.

void paramNURBS(int_type &n_knots, int_type &n_pnts) const

Get the parameters to build a NURBS for the circle ars.

Parameters

• n_knots – [out] number of knots for the NURBS

• n_pnts – [out] number of point of the polygon of the NURBS

void toNURBS(real_type *knots, real_type Poly[][3]) const

Get the parameters to build a NURBS for the circle ars.

Parameters

• knots – [out] vector of the knots

• Poly – [out] points of the polygon of the NURBS

inline CurveType type() const

The name of the curve type

inline real_type length_SAE(real_type offs) const

The length of the curve with offset (SAE)

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

inline virtual real_type thetaEnd() const

Final angle of the curve.

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_End() const

Final tangent x-coordinate.

inline virtual real_type ty_End() const

Final tangent y-coordinate.

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).

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.

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 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_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_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

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

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

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

Friends

friend class ClothoidCurve

friend ostream_type &operator<<(ostream_type &stream, CircleArc const &c)

Pretty print circle arc.