Class ClothoidList¶

Defined in File ClothoidList.hxx

Inheritance Relationships¶

Base Type¶

public G2lib::BaseCurve (Class BaseCurve)

Class Documentation¶

class G2lib::ClothoidList : public G2lib::BaseCurve ¶

Manage a piecewise clothoids \( G(s) \) composed by n clothoids (not necessarily G2 or G1 connected)

Public Functions

inline ClothoidList()¶: Build an empty clothoid list

inline ~ClothoidList() override¶

inline ClothoidList(ClothoidList const &s)¶: Build a copy of an existing clothoid list

void init()¶: Initialize the clothoid list

void reserve(int_type n)¶: Reserve memory for n clothoid

void copy(ClothoidList const &L)¶: Build a clothoid list copying an existing one

inline ClothoidList const &operator=(ClothoidList const &s)¶: Copy an existing clothoid list

explicit ClothoidList(LineSegment const &LS)¶: Build a clothoid from a line segment

explicit ClothoidList(CircleArc const &C)¶: Build a clothoid from a circle arc

explicit ClothoidList(Biarc const &B)¶: Build a clothoid from a biarc

explicit ClothoidList(BiarcList const &BL)¶: Build a clothoid from a list of biarc

explicit ClothoidList(ClothoidCurve const &CL)¶: Build a clothoid from a clothoid curve

explicit ClothoidList(PolyLine const &PL)¶: Build a clothoid from a list line segment

explicit ClothoidList(BaseCurve const &C)¶: Build a clothoid from a curve

void push_back(LineSegment const &c)¶: Add a line segment to the tail of clothoid list

void push_back(CircleArc const &c)¶: Add a circle arc to the tail of clothoid list

void push_back(Biarc const &c)¶: Add a biarc to the tail of clothoid list

void push_back(BiarcList const &c)¶: Add a biarc list to the tail of clothoid list

void push_back(ClothoidCurve const &c)¶: Add a clothoid curve to the tail of clothoid list

void push_back(ClothoidList const &c)¶: Add a clothoid list to the tail of clothoid list

void push_back(PolyLine const &c)¶: Add a list of line segment to the tail of clothoid list

void push_back(real_type kappa0, real_type dkappa, real_type L)¶

Add a clothoid to the tail of the clothoid list.

Parameters

kappa0 – initial curvature
dkappa – derivative of the curvature
L – length of the segment

void push_back(real_type x0, real_type y0, real_type theta0, real_type kappa0, real_type dkappa, real_type L)¶

Add a clothoid to the tail of the clothoid list. The builded clothoid is translated to the tail of the clothioid list.

Parameters

x0 – initial x
y0 – initial y
theta0 – initial angle
kappa0 – initial curvature
dkappa – derivative of the curvature
L – length of the segment

void push_back_G1(real_type x1, real_type y1, real_type theta1)¶

Add a clothoid to the tail of the clothoid list solving the G1 problem. The initial point and angle are taken from the tail of the clothoid list.

Parameters

x1 – final x
y1 – final y
theta1 – final angle

void push_back_G1(real_type x0, real_type y0, real_type theta0, real_type x1, real_type y1, real_type theta1)¶

Add a clothoid to the tail of the clothoid list solving the G1 problem. The initial point and angle are taken from the tail of the clothoid list. The builded clothoid is translated to the tail of the clothioid list.

Parameters

x0 – initial x
y0 – initial y
theta0 – initial angle
x1 – final x
y1 – final y
theta1 – final angle

inline bool is_closed() const¶: True if curve is closed

inline void make_closed()¶: Set clousure flag to true

inline void make_open()¶: Set clousure flag to false

inline real_type closure_gap_x() const¶: Difference initial final point x component

inline real_type closure_gap_y() const¶: Difference initial final point y component

inline real_type closure_gap_tx() const¶: Difference initial final tangent x component

inline real_type closure_gap_ty() const¶: Difference initial final tangent y component

inline bool closure_check(real_type tol_xy = 1e-6, real_type tol_tg = 1e-6) const¶

check if clothoid list is closed

Parameters

tol_xy – [in] position tolerance
tol_tg – [in] angle (tangent) tolerance

Returns

true if curve is closed

bool build_G1(int_type n, real_type const *x, real_type const *y)¶

Build clothoid list passing to a list of points solving a series of G1 fitting problems. The angle at points are estimated using the routine xy_to_guess_angle

Parameters

n – [in] number of points
x – [in] x-coordinates
y – [in] y-coordinates

Returns

false if routine fails

bool build_G1(int_type n, real_type const *x, real_type const *y, real_type const *theta)¶

Build clothoid list passing to a list of points solving a series of G1 fitting problems.

Parameters

n – [in] number of points
x – [in] x-coordinates
y – [in] y-coordinates
theta – [in] angles at the points

Returns

false if routine fails

bool build(real_type x0, real_type y0, real_type theta0, int_type n, real_type const *s, real_type const *kappa)¶

Build clothoid list with G2 continuity. The vector s contains the breakpoints of the curve. Between two breakpoint the curvature change linearly (is a clothoid)

Parameters

x0 – [in] initial x
y0 – [in] initial y
theta0 – [in] initial angle
n – [in] number of segments
s – [in] break point of the piecewise curve
kappa – [in] curvature at the break point

Returns

true if curve is closed

inline bool build(real_type x0, real_type y0, real_type theta0, vector<real_type> const &s, vector<real_type> const &kappa)¶

Build clothoid list with G2 continuity. The vector s contains the breakpoints of the curve. Between two breakpoint the curvature change linearly (is a clothoid)

Parameters

x0 – [in] initial x
y0 – [in] initial y
theta0 – [in] initial angle
s – [in] break point of the piecewise curve
kappa – [in] curvature at the break point

Returns

true if curve is closed

bool build_raw(int_type n, real_type const *x, real_type const *y, real_type const *abscissa, real_type const *theta, real_type const *kappa)¶

Build clothoid listy using raw data.

Parameters

n – [in] number of points
x – [in] x-coordinates
y – [in] y-coordinates
abscissa – [in] break point of the piecewise curve
theta – [in] angles at breakpoints
kappa – [in] curvature at the break point

Returns

false if fails

inline bool build_raw(vector<real_type> const &x, vector<real_type> const &y, vector<real_type> const &abscissa, vector<real_type> const &theta, vector<real_type> const &kappa)¶

Build clothoid listy using raw data.

Parameters

x – [in] x-coordinates
y – [in] y-coordinates
abscissa – [in] break point of the piecewise curve
theta – [in] angles at breakpoints
kappa – [in] curvature at the break point

Returns

false if fails

ClothoidCurve const &get(int_type idx) const¶: Get the idx-th clothoid of the list

ClothoidCurve const &getAtS(real_type s) const¶: Get the idx-th clothoid of the list where idx is the clothoid at parameter s

inline int_type numSegments() const¶: Return the numbber of clothoid of the list

void wrap_in_range(real_type &s) const¶: The list of clothoid has total length \( L \) the parameter \( s \) us recomputed as \( s+kL\) in such a way \( s+kL\in[0,L)\) with \( k\in\mathbb{Z} \).

int_type findAtS(real_type &s) const¶: Find the clothoid segment whose definiton range contains s

virtual real_type length() const override¶: The length of the curve

virtual real_type length_ISO(real_type offs) const override¶: The length of the curve with offset (ISO)

real_type segment_length(int_type nseg) const¶: Return the length of the nseg-th clothoid of the list

real_type segment_length_ISO(int_type nseg, real_type offs) const¶: Return the length of the nseg-th clothoid of the list with offset

inline real_type segment_length_SAE(int_type nseg, real_type offs) const¶: Return the length of the nseg-th clothoid of the list with offset

virtual void bbTriangles(std::vector<Triangle2D> &tvec, real_type max_angle = Utils::m_pi / 6, real_type max_size = 1e100, int_type icurve = 0) const override¶

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 / 6, real_type max_size = 1e100, int_type icurve = 0) const override¶

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

inline virtual void bbTriangles_SAE(real_type offs, std::vector<Triangle2D> &tvec, real_type max_angle = Utils::m_pi / 6, real_type max_size = 1e100, int_type icurve = 0) const override¶

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 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 thetaBegin() const override¶: Initial angle of the curve.

inline virtual real_type thetaEnd() const override¶: Final angle of the curve.

inline virtual real_type xBegin() const override¶: Initial x-coordinate.

inline virtual real_type yBegin() const override¶: Initial y-coordinate.

inline virtual real_type xEnd() const override¶: Final x-coordinate.

inline virtual real_type yEnd() const override¶: Final y-coordinate.

inline virtual real_type xBegin_ISO(real_type offs) const override¶: Initial x-coordinate with offset (ISO standard).

inline virtual real_type yBegin_ISO(real_type offs) const override¶: Initial y-coordinate with offset (ISO standard).

inline virtual real_type xEnd_ISO(real_type offs) const override¶: Final x-coordinate with offset (ISO standard).

inline virtual real_type yEnd_ISO(real_type offs) const override¶: Final y-coordinate with offset (ISO standard).

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 tx_End() const override¶: Final tangent x-coordinate.

inline virtual real_type ty_End() const override¶: Final 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 nx_End_ISO() const override¶: Final normal x-coordinate (ISO).

inline virtual real_type ny_End_ISO() const override¶: Final normal y-coordinate (ISO).

virtual real_type theta(real_type s) const override¶: Angle at curvilinear coodinate s.

virtual real_type theta_D(real_type s) const override¶: Angle derivative (curvature) at curvilinear coodinate s.

virtual real_type theta_DD(real_type s) const override¶: Angle second derivative (devitive of curvature) at curvilinear coodinate s.

virtual real_type theta_DDD(real_type s) const override¶: Angle third derivative at curvilinear coodinate s.

virtual real_type tx(real_type s) const override¶: Tangent x-coordinate at curvilinear coodinate s.

virtual real_type ty(real_type s) const override¶: Tangent y-coordinate at curvilinear coodinate s.

virtual real_type tx_D(real_type s) const override¶: Tangent derivative x-coordinate at curvilinear coodinate s.

virtual real_type ty_D(real_type s) const override¶: Tangent derivative y-coordinate at curvilinear coodinate s.

virtual real_type tx_DD(real_type s) const override¶: Tangent second derivative x-coordinate at curvilinear coodinate s.

virtual real_type ty_DD(real_type s) const override¶: Tangent second derivative y-coordinate at curvilinear coodinate s.

virtual real_type tx_DDD(real_type s) const override¶: Tangent third derivative x-coordinate at curvilinear coodinate s.

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 &tg_x, real_type &tg_y) const override¶: Tangent at curvilinear coodinate s.

virtual void tg_D(real_type s, real_type &tg_x_D, real_type &tg_y_D) const override¶: Tangent derivative at curvilinear coodinate s.

virtual void tg_DD(real_type s, real_type &tg_x_DD, real_type &tg_y_DD) const override¶: Tangent second derivative at curvilinear coodinate s.

virtual void tg_DDD(real_type s, real_type &tg_x_DDD, real_type &tg_y_DDD) const override¶: Tangent third derivative at curvilinear coodinate s.

virtual void evaluate(real_type s, real_type &th, real_type &k, 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 void evaluate_ISO(real_type s, real_type offs, real_type &th, real_type &k, real_type &x, real_type &y) const override¶

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

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 s) const override¶: x-coordinate derivative at curvilinear coordinate s.

virtual real_type Y_D(real_type s) const override¶: y-coordinate derivative at curvilinear coordinate s.

virtual real_type X_DD(real_type s) const override¶: x-coordinate second derivative at curvilinear coordinate s.

virtual real_type Y_DD(real_type s) const override¶: y-coordinate second derivative at curvilinear coordinate s.

virtual real_type X_DDD(real_type s) const override¶: x-coordinate third derivative at curvilinear coordinate s.

virtual real_type Y_DDD(real_type s) 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 s, 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 s, 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 s, real_type &x_DDD, real_type &y_DDD) const override¶: x and y-coordinate third derivative at curvilinear coordinate s.

virtual real_type X_ISO(real_type s, real_type offs) const override¶: x-coordinate at curvilinear coordinate s with offset offs (ISO).

virtual real_type Y_ISO(real_type s, real_type offs) const override¶: y-coordinate at curvilinear coordinate s with offset offs (ISO).

virtual real_type X_ISO_D(real_type s, real_type offs) const override¶: x-coordinate derivative at curvilinear coordinate s with offset offs (ISO).

virtual real_type Y_ISO_D(real_type s, real_type offs) const override¶: y-coordinate derivative at curvilinear coordinate s with offset offs (ISO).

virtual real_type X_ISO_DD(real_type s, real_type offs) const override¶: 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 override¶: 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 override¶: 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 override¶: y-coordinate third derivative at curvilinear coordinate s with offset offs (ISO).

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

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

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

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

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

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

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

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

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 scale(real_type sc) override¶: Scale curve by factor sc.

virtual void reverse() override¶: Reverse curve parameterization.

virtual void changeOrigin(real_type newx0, real_type newy0) override¶: Translate curve so that origin will be (newx0, newy0).

virtual void trim(real_type s_begin, real_type s_end) override¶: Cut curve at parametrix coordinate s_begin and s_end.

void trim(real_type s_begin, real_type s_end, ClothoidList &newCL) const¶

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¶

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

n >= 0 point is projected orthogonal, n is the number of the segment at minimum distance

-(n+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¶

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

n > 0 point is projected orthogonal, n-1 is the number of the segment at minimum distance

-(n+1) minimum point is not othogonal projection to curve

int_type closestSegment(real_type qx, real_type qy) const¶

Parameters

qx – x-coordinate of the point
qy – y-coordinate of the point

Returns

the segment at minimal distance from point (qx,qy)

int_type closestPointInRange_ISO(real_type qx, real_type qy, int_type icurve_begin, int_type icurve_end, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst, int_type &icurve) const¶

Parameters

qx – x-coordinate of the point
qy – y-coordinate of the point
icurve_begin – index of the initial segment
icurve_end – index of the past to the last segment
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
icurve – number of the segment with the 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 closestPointInRange_SAE(real_type qx, real_type qy, int_type icurve_begin, int_type icurve_end, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst, int_type &icurve) const¶

Parameters

qx – x-coordinate of the point
qy – y-coordinate of the point
icurve_begin – index of the initial segment
icurve_end – index of the past to the last segment
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
icurve – number of the segment with the projected point

Returns

1 point is projected orthogonal

0 = more than one projection (first returned)

-1 = minimum point is not othogonal projection to curve

int_type closestPointInSRange_ISO(real_type qx, real_type qy, real_type s_begin, real_type s_end, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst, int_type &icurve) const¶

Parameters

qx – x-coordinate of the point
qy – y-coordinate of the point
s_begin – initial curvilinear coordinate of the search range
s_end – final curvilinear coordinate of the search range
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
icurve – number of the segment with the projected point

Returns

1 ok -1 projection failed

inline int_type closestPointInSRange_SAE(real_type qx, real_type qy, int_type s_begin, int_type s_end, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst, int_type &icurve) const¶

Parameters

qx – x-coordinate of the point
qy – y-coordinate of the point
s_begin – initial curvilinear coordinate of the search range
s_end – final curvilinear coordinate of the search range
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
icurve – number of the segment with the projected point

Returns

1 ok -1 projection failed

inline virtual void info(ostream_type &stream) const override¶: Pretty print of the curve data.

void getSK(real_type *s, real_type *kappa) const¶

Return the clothoid list as a list of nodes and curvatures

Parameters

s – [out] nodes
kappa – [out] curvature

inline void getSK(std::vector<real_type> &s, std::vector<real_type> &kappa) const¶

Return the clothoid list as a list of nodes and curvatures

Parameters

s – [out] nodes
kappa – [out] curvature

void getSTK(real_type *s, real_type *theta, real_type *kappa) const¶

Return the clothoid list as a list of nodes angles and curvatures

Parameters

s – [out] nodes
theta – [out] angles
kappa – [out] curvature

inline void getSTK(std::vector<real_type> &s, std::vector<real_type> &theta, std::vector<real_type> &kappa) const¶

Return the clothoid list as a list of nodes angles and curvatures

Parameters

s – [out] nodes
theta – [out] angles
kappa – [out] curvature

void getXY(real_type *x, real_type *y) const¶

Return the points of the clothoid list at breakpoints

Parameters

x – [out] x-coordinates
y – [out] y-coordinates

void getDeltaTheta(real_type *deltaTheta) const¶

void getDeltaKappa(real_type *deltaKappa) const¶

int_type findST1(real_type x, real_type y, real_type &s, real_type &t) const¶

Find parametric coordinate.

Parameters

x – x-coordinate point
y – y-coordinate point
s – value \( s \)
t – value \( t \)

Returns

idx the segment with point at minimal distance, otherwise -(idx+1) if (x,y) cannot be projected orthogonally on the segment

int_type findST1(int_type ibegin, int_type iend, real_type x, real_type y, real_type &s, real_type &t) const¶

Find parametric coordinate.

Parameters

ibegin – initial segment to compute the distance
iend – final segment to compute the distance
x – x-coordinate point
y – y-coordinate point
s – value \( s \)
t – value \( t \)

Returns

idx the segment with point at minimal distance, otherwise -(idx+1) if (x,y) cannot be projected orthogonally on the segment

bool collision(ClothoidList const &C) const¶: Detect a collision with another clothoid list

bool collision_ISO(real_type offs, ClothoidList const &CL, real_type offs_C) const¶

Detect a collision with another clothoid list with offset

Parameters

offs – [in] offset of first clothoid list
CL – [in] second clothoid list
offs_C – [in] offset of second clothoid list

inline void intersect(ClothoidList const &CL, IntersectList &ilist, bool swap_s_vals) const¶

Intersect a clothoid list with another clothoid list

Parameters

CL – [in] second clothoid list
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, ClothoidList const &CL, real_type offs_obj, IntersectList &ilist, bool swap_s_vals) const¶

Intersect a clothoid list with another clothoid list with offset (ISO)

Parameters

offs – [in] offset of first clothoid list
CL – [in] second clothoid list
offs_obj – [in] offset of second clothoid list
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 export_table(ostream_type &stream) const¶

Save Clothoid list to a stream

Parameters: stream – stream to save

void export_ruby(ostream_type &stream) const¶

Save Clothoid list to a stream

Parameters: stream – streamstream to save

void save(ostream_type &stream) const¶

Save the clothoid list on a stream. The data is saved as follows

  # x y theta kappa
  x0 y0 theta0 kappa0
  x1 y1 theta1 kappa1
  ...
  xn yn thetan kappan

void load(istream_type &stream, real_type epsi = 1e-8)¶

Read the clothoid list from a stream. The data is assumed to be saved as follows

  # x y theta kappa
  x0 y0 theta0 kappa0
  x1 y1 theta1 kappa1
  ...
  xn yn thetan kappan

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 kappaBegin() const¶: Initial curvature.

inline virtual real_type kappaEnd() const¶: Final curvature.

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 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_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

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).

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

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

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

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 ostream_type &operator<<(ostream_type &stream, ClothoidList const &CL)¶