Biarc Class Reference

Clothoids: G2lib::Biarc Class Reference
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G2lib::Biarc Class Reference

#include <Biarc.hxx>

Inheritance diagram for G2lib::Biarc:
G2lib::BaseCurve

Public Member Functions

 Biarc ()=delete
 
 Biarc (string const &name)
 
void setup (GenericContainer const &gc) override
 
 Biarc (Biarc const &ba)
 
 Biarc (real_type x0, real_type y0, real_type theta0, real_type x1, real_type y1, real_type theta1, string const &name)
 
 Biarc (LineSegment const &LS)
 
 Biarc (CircleArc const &C)
 
 Biarc (BaseCurve const *pC)
 
void copy (Biarc const &c)
 
CurveType type () const override
 
Biarc const & operator= (Biarc const &ba)
 
CircleArc const & C0 () const
 
CircleArc const & C1 () const
 
bool build (real_type x0, real_type y0, real_type theta0, real_type x1, real_type y1, real_type theta1)
 
bool build_3P (real_type x0, real_type y0, real_type x1, real_type y1, real_type x2, real_type y2)
 
void build (LineSegment const &LS)
 
void build (CircleArc const &C)
 
void build (Biarc const &)
 
void build (ClothoidCurve const &)
 
void build (PolyLine const &)
 
void build (BiarcList const &)
 
void build (ClothoidList const &)
 
void build (Dubins const &)
 
void build (Dubins3p const &)
 
void bbox (real_type &xmin, real_type &ymin, real_type &xmax, real_type &ymax) const override
 
void bbox_ISO (real_type offs, real_type &xmin, real_type &ymin, real_type &xmax, real_type &ymax) const override
 
real_type length () const override
 
real_type length_ISO (real_type offs) const override
 
real_type theta_begin () const override
 
real_type theta_end () const override
 
real_type kappa_begin () const override
 
real_type kappa_end () const override
 
real_type x_begin () const override
 
real_type x_end () const override
 
real_type y_begin () const override
 
real_type y_end () const override
 
real_type tx_begin () const override
 
real_type tx_end () const override
 
real_type ty_begin () const override
 
real_type ty_end () const override
 
real_type nx_begin_ISO () const override
 
real_type nx_end_ISO () const override
 
real_type ny_begin_ISO () const override
 
real_type ny_end_ISO () const override
 
real_type theta (real_type) const override
 
real_type theta_D (real_type) const override
 
real_type theta_DD (real_type) const override
 
real_type theta_DDD (real_type) const override
 
void evaluate (real_type s, real_type &th, real_type &k, real_type &x, real_type &y) const override
 
real_type X (real_type s) const override
 
real_type Y (real_type s) const override
 
real_type X_D (real_type) const override
 
real_type Y_D (real_type) const override
 
real_type X_DD (real_type) const override
 
real_type Y_DD (real_type) const override
 
real_type X_DDD (real_type) const override
 
real_type Y_DDD (real_type) const override
 
real_type X_ISO (real_type s, real_type offs) const override
 
real_type Y_ISO (real_type s, real_type offs) const override
 
real_type X_ISO_D (real_type, real_type offs) const override
 
real_type Y_ISO_D (real_type, real_type offs) const override
 
real_type X_ISO_DD (real_type, real_type offs) const override
 
real_type Y_ISO_DD (real_type, real_type offs) const override
 
real_type X_ISO_DDD (real_type, real_type offs) const override
 
real_type Y_ISO_DDD (real_type, real_type offs) const override
 
void eval (real_type s, real_type &x, real_type &y) const override
 
void eval_D (real_type s, real_type &x_D, real_type &y_D) const override
 
void eval_DD (real_type s, real_type &x_DD, real_type &y_DD) const override
 
void eval_DDD (real_type s, real_type &x_DDD, real_type &y_DDD) const override
 
void eval_ISO (real_type s, real_type offs, real_type &x, real_type &y) const override
 
void eval_ISO_D (real_type s, real_type offs, real_type &x_D, real_type &y_D) const override
 
void eval_ISO_DD (real_type s, real_type offs, real_type &x_DD, real_type &y_DD) const override
 
void eval_ISO_DDD (real_type s, real_type offs, real_type &x_DDD, real_type &y_DDD) const override
 
real_type tx (real_type s) const override
 
real_type tx_D (real_type s) const override
 
real_type tx_DD (real_type s) const override
 
real_type tx_DDD (real_type s) const override
 
real_type ty (real_type s) const override
 
real_type ty_D (real_type s) const override
 
real_type ty_DD (real_type s) const override
 
real_type ty_DDD (real_type s) const override
 
void tg (real_type s, real_type &tx, real_type &ty) const override
 
void tg_D (real_type s, real_type &tx_D, real_type &ty_D) const override
 
void tg_DD (real_type s, real_type &tx_DD, real_type &ty_DD) const override
 
void tg_DDD (real_type s, real_type &tx_DDD, real_type &ty_DDD) const override
 
void translate (real_type tx, real_type ty) override
 translate curve by \((t_x,t_y)\)
 
void rotate (real_type angle, real_type cx, real_type cy) override
 
void reverse () override
 
void change_origin (real_type newx0, real_type newy0) override
 
void trim (real_type s_begin, real_type s_end) override
 
void scale (real_type s) override
 
integer closest_point_ISO (real_type qx, real_type qy, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst) const override
 
integer closest_point_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
 
real_type x_middle () const
 
real_type y_middle () const
 
real_type theta_middle () const
 
real_type kappa0 () const
 
real_type length0 () const
 
real_type kappa1 () const
 
real_type length1 () const
 
real_type delta_theta () const
 
void bb_triangles (vector< Triangle2D > &tvec, real_type max_angle=Utils::m_pi/18, real_type max_size=1e100, integer icurve=0) const override
 
void bb_triangles_ISO (real_type offs, vector< Triangle2D > &tvec, real_type max_angle=Utils::m_pi/18, real_type max_size=1e100, integer icurve=0) const override
 
void bb_triangles_SAE (real_type offs, vector< Triangle2D > &tvec, real_type max_angle=Utils::m_pi/18, real_type max_size=1e100, integer icurve=0) const override
 
bool collision (Biarc const &B) const
 
bool collision_ISO (real_type offs, Biarc const &B, real_type offs_B) const
 
bool collision (BaseCurve const *pC) const override
 
bool collision_ISO (real_type offs, BaseCurve const *pC, real_type offs_C) const override
 
void intersect (Biarc const &B, IntersectList &ilist) const
 
void intersect_ISO (real_type offs, Biarc const &B, real_type offs_B, IntersectList &ilist) const
 
void intersect (BaseCurve const *pC, IntersectList &ilist) const override
 
void intersect_ISO (real_type offs, BaseCurve const *pC, real_type offs_LS, IntersectList &ilist) const override
 
string info () const
 
void info (ostream_type &stream) const override
 
virtual real_type x_begin_ISO (real_type offs) const
 
virtual real_type y_begin_ISO (real_type offs) const
 
virtual real_type x_end_ISO (real_type offs) const
 
virtual real_type y_end_ISO (real_type offs) const
 
real_type x_begin_SAE (real_type offs) const
 
real_type y_begin_SAE (real_type offs) const
 
real_type x_end_SAE (real_type offs) const
 
real_type y_end_SAE (real_type offs) const
 
real_type nx_begin_SAE () const
 
real_type ny_begin_SAE () const
 
real_type nx_end_SAE () const
 
real_type ny_end_SAE () const
 
real_type X_SAE (real_type s, real_type offs) const
 
real_type X_SAE_D (real_type s, real_type offs) const
 
real_type X_SAE_DD (real_type s, real_type offs) const
 
real_type X_SAE_DDD (real_type s, real_type offs) const
 
real_type Y_SAE (real_type s, real_type offs) const
 
real_type Y_SAE_D (real_type s, real_type offs) const
 
real_type Y_SAE_DD (real_type s, real_type offs) const
 
real_type Y_SAE_DDD (real_type s, real_type offs) const
 
virtual void evaluate_ISO (real_type s, real_type offs, real_type &th, real_type &k, real_type &x, real_type &y) const
 
virtual void evaluate_SAE (real_type s, real_type offs, real_type &th, real_type &k, real_type &x, real_type &y) const
 
void eval_SAE (real_type s, real_type offs, real_type &x, real_type &y) const
 
void eval_SAE_D (real_type s, real_type offs, real_type &x_D, real_type &y_D) const
 
void eval_SAE_DD (real_type s, real_type offs, real_type &x_DD, real_type &y_DD) const
 
void eval_SAE_DDD (real_type s, real_type offs, real_type &x_DDD, real_type &y_DDD) const
 
integer closest_point_SAE (real_type qx, real_type qy, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst) const
 
integer closest_point_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
 
real_type distance_ISO (real_type qx, real_type qy, real_type offs) const
 
real_type distance_SAE (real_type qx, real_type qy, real_type offs) const
 
- Public Member Functions inherited from G2lib::BaseCurve
 BaseCurve (BaseCurve const &)=delete
 
BaseCurve const & operator= (BaseCurve const &)=delete
 
 BaseCurve (string const &name)
 
void build (GenericContainer const &gc)
 
string name () const
 
string type_name () const
 
real_type length_SAE (real_type offs) const
 
void bbox_SAE (real_type offs, real_type &xmin, real_type &ymin, real_type &xmax, real_type &ymax) const
 
real_type x_begin_SAE (real_type offs) const
 
real_type y_begin_SAE (real_type offs) const
 
real_type x_end_SAE (real_type offs) const
 
real_type y_end_SAE (real_type offs) const
 
real_type nx_begin_SAE () const
 
real_type ny_begin_SAE () const
 
real_type nx_end_SAE () const
 
real_type ny_end_SAE () const
 
real_type kappa (real_type s) const
 
real_type kappa_D (real_type s) const
 
real_type kappa_DD (real_type s) const
 
real_type nx_ISO (real_type s) const
 
real_type nx_ISO_D (real_type s) const
 
real_type nx_ISO_DD (real_type s) const
 
real_type nx_ISO_DDD (real_type s) const
 
real_type ny_ISO (real_type s) const
 
real_type ny_ISO_D (real_type s) const
 
real_type ny_ISO_DD (real_type s) const
 
real_type ny_ISO_DDD (real_type s) const
 
real_type nx_SAE (real_type s) const
 
real_type nx_SAE_D (real_type s) const
 
real_type nx_SAE_DD (real_type s) const
 
real_type nx_SAE_DDD (real_type s) const
 
real_type ny_SAE (real_type s) const
 
real_type ny_SAE_D (real_type s) const
 
real_type ny_SAE_DD (real_type s) const
 
real_type ny_SAE_DDD (real_type s) const
 
void nor_ISO (real_type s, real_type &nx, real_type &ny) const
 
void nor_ISO_D (real_type s, real_type &nx_D, real_type &ny_D) const
 
void nor_ISO_DD (real_type s, real_type &nx_DD, real_type &ny_DD) const
 
void nor_ISO_DDD (real_type s, real_type &nx_DDD, real_type &ny_DDD) const
 
void nor_SAE (real_type s, real_type &nx, real_type &ny) const
 
void nor_SAE_D (real_type s, real_type &nx_D, real_type &ny_D) const
 
void nor_SAE_DD (real_type s, real_type &nx_DD, real_type &ny_DD) const
 
void nor_SAE_DDD (real_type s, real_type &nx_DDD, real_type &ny_DDD) const
 
real_type X_SAE (real_type s, real_type offs) const
 
real_type Y_SAE (real_type s, real_type offs) const
 
real_type X_SAE_D (real_type s, real_type offs) const
 
real_type Y_SAE_D (real_type s, real_type offs) const
 
real_type X_SAE_DD (real_type s, real_type offs) const
 
real_type Y_SAE_DD (real_type s, real_type offs) const
 
real_type X_SAE_DDD (real_type s, real_type offs) const
 
real_type Y_SAE_DDD (real_type s, real_type offs) const
 
void eval_SAE (real_type s, real_type offs, real_type &x, real_type &y) const
 
void eval_SAE_D (real_type s, real_type offs, real_type &x_D, real_type &y_D) const
 
void eval_SAE_DD (real_type s, real_type offs, real_type &x_DD, real_type &y_DD) const
 
void eval_SAE_DDD (real_type s, real_type offs, real_type &x_DDD, real_type &y_DDD) const
 
bool collision_SAE (real_type offs, BaseCurve const *pC, real_type offs_C) const
 
void intersect_SAE (real_type offs, BaseCurve const *pC, real_type offs_C, IntersectList &ilist) const
 
integer closest_point_SAE (real_type qx, real_type qy, real_type &x, real_type &y, real_type &s, real_type &t, real_type &dst) const
 
integer closest_point_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
 
virtual real_type distance (real_type qx, real_type qy) const
 
real_type distance_ISO (real_type qx, real_type qy, real_type offs) const
 
real_type distance_SAE (real_type qx, real_type qy, real_type offs) const
 
bool findST_ISO (real_type x, real_type y, real_type &s, real_type &t) const
 
bool findST_SAE (real_type x, real_type y, real_type &s, real_type &t) const
 

Friends

ostream_type & operator<< (ostream_type &stream, Biarc const &bi)
 

Detailed Description

Compute biarc fitting by Hemite data

'

Constructor & Destructor Documentation

◆ Biarc() [1/3]

G2lib::Biarc::Biarc ( )
delete

eof: BaseCurve_using.hxx Construct and empty biarc

◆ Biarc() [2/3]

G2lib::Biarc::Biarc ( Biarc const & ba)
inline

Make a copy of an existing biarc

◆ Biarc() [3/3]

G2lib::Biarc::Biarc ( real_type x0,
real_type y0,
real_type theta0,
real_type x1,
real_type y1,
real_type theta1,
string const & name )
explicit

Construct a biarc passing from the points \((x_0,y_0)\) to the point \((x_1,y_1)\) with initial angle \(\theta_0\) and final angle \(\theta_1\)

Parameters
[in]x0\( x_0 \)
[in]y0\( y_0 \)
[in]theta0\( \theta_0 \)
[in]x1\( x_1 \)
[in]y1\( y_1 \)
[in]theta1\( \theta_1 \)
[in]namename of the biarc

Member Function Documentation

◆ bb_triangles()

void G2lib::Biarc::bb_triangles ( vector< Triangle2D > & tvec,
real_type max_angle = Utils::m_pi/18,
real_type max_size = 1e100,
integer icurve = 0 ) const
inlineoverridevirtual

Build a cover with triangles of the curve.

Parameters
[out]tveclist of covering triangles
[out]max_anglemaximum angle variation of the curve covered by a triangle
[out]max_sizemaximum admissible size of the covering tirnagles
[out]icurveindex of the covering triangles
'

Implements G2lib::BaseCurve.

◆ bb_triangles_ISO()

void G2lib::Biarc::bb_triangles_ISO ( real_type offs,
vector< Triangle2D > & tvec,
real_type max_angle = Utils::m_pi/18,
real_type max_size = 1e100,
integer icurve = 0 ) const
inlineoverridevirtual

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

Parameters
[out]offscurve offset
[out]tveclist of covering triangles
[out]max_anglemaximum angle variation of the curve covered by a triangle
[out]max_sizemaximum admissible size of the covering tirnagles
[out]icurveindex of the covering triangles

Implements G2lib::BaseCurve.

◆ bb_triangles_SAE()

void G2lib::Biarc::bb_triangles_SAE ( real_type offs,
vector< Triangle2D > & tvec,
real_type max_angle = Utils::m_pi/18,
real_type max_size = 1e100,
integer icurve = 0 ) const
inlineoverridevirtual

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

Parameters
[out]offscurve offset
[out]tveclist of covering triangles
[out]max_anglemaximum angle variation of the arc covered by a triangle
[out]max_sizemaximum admissible size of the covering tirnagles
[out]icurveindex of the covering triangles

Implements G2lib::BaseCurve.

◆ bbox()

void G2lib::Biarc::bbox ( real_type & xmin,
real_type & ymin,
real_type & xmax,
real_type & ymax ) const
overridevirtual

Compute the bounding box of the curve.

Parameters
[out]xminleft bottom
[out]yminleft bottom
[out]xmaxright top
[out]ymaxright top

Implements G2lib::BaseCurve.

◆ bbox_ISO()

void G2lib::Biarc::bbox_ISO ( real_type offs,
real_type & xmin,
real_type & ymin,
real_type & xmax,
real_type & ymax ) const
overridevirtual

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

Parameters
[in]offscurve offset
[out]xminleft bottom
[out]yminleft bottom
[out]xmaxright top
[out]ymaxright top

Implements G2lib::BaseCurve.

◆ build() [1/3]

void G2lib::Biarc::build ( CircleArc const & C)

Build a biarc from a circle arc.

◆ build() [2/3]

void G2lib::Biarc::build ( LineSegment const & LS)

Build a biarc from a line segment

◆ build() [3/3]

bool G2lib::Biarc::build ( real_type x0,
real_type y0,
real_type theta0,
real_type x1,
real_type y1,
real_type theta1 )

Construct a biarc passing from the points \( (x_0,y_0) \) to the point \( (x_1,y_1) \) with initial angle \( \theta_0 \) and final angle \( \theta_1 \)

Parameters
[in]x0\( x_0 \)
[in]y0\( y_0 \)
[in]theta0\( \theta_0 \)
[in]x1\( x_1 \)
[in]y1\( y_1 \)
[in]theta1\( \theta_1 \)
Returns
false if biarc cannot be computed

◆ build_3P()

bool G2lib::Biarc::build_3P ( real_type x0,
real_type y0,
real_type x1,
real_type y1,
real_type x2,
real_type y2 )

Construct a biarc by 3 point at "minimum energy"

  • Planar point set fairing and fitting by arc splines
  • Xunnian Yang and Guozhao Wang
  • Computer-Aided Design, vol 33, 2001

◆ C0()

CircleArc const & G2lib::Biarc::C0 ( ) const
inline

Return the first circle arc of the biarc.

◆ C1()

CircleArc const & G2lib::Biarc::C1 ( ) const
inline

Return the first circle arc of the biarc.

◆ change_origin()

void G2lib::Biarc::change_origin ( real_type newx0,
real_type newy0 )
overridevirtual

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

Implements G2lib::BaseCurve.

◆ closest_point_ISO() [1/2]

integer G2lib::Biarc::closest_point_ISO ( real_type qx,
real_type qy,
real_type & x,
real_type & y,
real_type & s,
real_type & t,
real_type & dst ) const
overridevirtual

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
sparameter on the curve of the projection
tcurvilinear coordinate of the point x,y (if orthogonal projection)
dstdistance 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

Implements G2lib::BaseCurve.

◆ closest_point_ISO() [2/2]

integer G2lib::Biarc::closest_point_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
overridevirtual

Given a point find closest point on the curve.

Parameters
qx\(x\)-coordinate of the point
qy\(y\)-coordinate of the point
offsoffset of the curve
x\(x\)-coordinate of the projected point on the curve
y\(y\)-coordinate of the projected point on the curve
sparameter on the curve of the projection
tcurvilinear coordinate of the point x,y (if orthogonal projection)
dstdistance 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

Implements G2lib::BaseCurve.

◆ closest_point_SAE() [1/2]

integer G2lib::BaseCurve::closest_point_SAE ( real_type qx,
real_type qy,
real_type & x,
real_type & y,
real_type & s,
real_type & t,
real_type & dst ) const
inline

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
sparameter on the curve of the projection
tcurvilinear coordinate of the point x,y (if orthogonal projection)
dstdistance 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

◆ closest_point_SAE() [2/2]

integer G2lib::BaseCurve::closest_point_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
inline

Given a point find closest point on the curve.

Parameters
qx\(x\)-coordinate of the point
qy\(y\)-coordinate of the point
offsoffset of the curve
x\(x\)-coordinate of the projected point on the curve
y\(y\)-coordinate of the projected point on the curve
sparameter on the curve of the projection
tcurvilinear coordinate of the point x,y (if orthogonal projection)
dstdistance 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

◆ collision() [1/2]

bool G2lib::Biarc::collision ( BaseCurve const * pC) const
overridevirtual

Check collision with another curve.

Implements G2lib::BaseCurve.

◆ collision() [2/2]

bool G2lib::Biarc::collision ( Biarc const & B) const
inline

Detect a collision with another biarc.

◆ collision_ISO() [1/2]

bool G2lib::Biarc::collision_ISO ( real_type offs,
BaseCurve const * pC,
real_type offs_C ) const
overridevirtual

Check collision with another curve with offset (ISO).

Parameters
[in]offscurve offset
[in]pCsecond curve to check collision
[in]offs_Ccurve offset of the second curve
Returns
true if collision is detected

Implements G2lib::BaseCurve.

◆ collision_ISO() [2/2]

bool G2lib::Biarc::collision_ISO ( real_type offs,
Biarc const & B,
real_type offs_B ) const
inline

Detect a collision with another biarc with offset.

Parameters
[in]offsoffset of first biarc
[in]Bsecond biarc
[in]offs_Boffset of second biarc

◆ copy()

void G2lib::Biarc::copy ( Biarc const & c)
inline

Make a copy of an existing biarc.

◆ delta_theta()

real_type G2lib::Biarc::delta_theta ( ) const
inline

Change of the angle of the biarc ( \( \theta_1-\theta_0 \)).

◆ distance_ISO()

real_type G2lib::BaseCurve::distance_ISO ( real_type qx,
real_type qy,
real_type offs ) const
inline

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

Parameters
[in]qxcomponent \(q_x\)
[in]qycomponent \(q_y\)
[in]offsoffset of the curve
Returns
the computed distance

◆ distance_SAE()

real_type G2lib::BaseCurve::distance_SAE ( real_type qx,
real_type qy,
real_type offs ) const
inline

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

Parameters
[in]qxcomponent \(q_x\)
[in]qycomponent \(q_y\)
[in]offsoffset of the curve
Returns
the computed distance

◆ eval()

void G2lib::Biarc::eval ( real_type s,
real_type & x,
real_type & y ) const
overridevirtual

x and \(y\)-coordinate at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ eval_D()

void G2lib::Biarc::eval_D ( real_type s,
real_type & x_D,
real_type & y_D ) const
overridevirtual

x and \(y\)-coordinate derivative at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ eval_DD()

void G2lib::Biarc::eval_DD ( real_type s,
real_type & x_DD,
real_type & y_DD ) const
overridevirtual

x and \(y\)-coordinate second derivative at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ eval_DDD()

void G2lib::Biarc::eval_DDD ( real_type s,
real_type & x_DDD,
real_type & y_DDD ) const
overridevirtual

x and \(y\)-coordinate third derivative at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ eval_ISO()

void G2lib::Biarc::eval_ISO ( real_type s,
real_type offs,
real_type & x,
real_type & y ) const
overridevirtual

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

Parameters
[in]sparameter on the curve
[in]offsoffset of the curve
[out]xcoordinate
[out]ycoordinate

Reimplemented from G2lib::BaseCurve.

◆ eval_ISO_D()

void G2lib::Biarc::eval_ISO_D ( real_type s,
real_type offs,
real_type & x_D,
real_type & y_D ) const
overridevirtual

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

Parameters
[in]sparameter on the curve
[in]offsoffset of the curve
[out]x_D\(x\)-coordinate
[out]y_D\(y\)-coordinate

Reimplemented from G2lib::BaseCurve.

◆ eval_ISO_DD()

void G2lib::Biarc::eval_ISO_DD ( real_type s,
real_type offs,
real_type & x_DD,
real_type & y_DD ) const
overridevirtual

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

Parameters
[in]sparameter on the curve
[in]offsoffset of the curve
[out]x_DD\(x\)-coordinate second derivative
[out]y_DD\(y\)-coordinate second derivative

Reimplemented from G2lib::BaseCurve.

◆ eval_ISO_DDD()

void G2lib::Biarc::eval_ISO_DDD ( real_type s,
real_type offs,
real_type & x_DDD,
real_type & y_DDD ) const
overridevirtual

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

Parameters
[in]sparameter on the curve
[in]offsoffset of the curve
[out]x_DDD\(x\)-coordinate third derivative
[out]y_DDD\(y\)-coordinate third derivative

Reimplemented from G2lib::BaseCurve.

◆ eval_SAE()

void G2lib::BaseCurve::eval_SAE ( real_type s,
real_type offs,
real_type & x,
real_type & y ) const
inline

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

Parameters
[in]sparameter on the curve
[in]offsoffset of the curve
[out]xcoordinate
[out]ycoordinate

◆ eval_SAE_D()

void G2lib::BaseCurve::eval_SAE_D ( real_type s,
real_type offs,
real_type & x_D,
real_type & y_D ) const
inline

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

Parameters
[in]sparameter on the curve
[in]offsoffset of the curve
[out]x_D\(x\)-coordinate first derivative
[out]y_D\(y\)-coordinate first derivative

◆ eval_SAE_DD()

void G2lib::BaseCurve::eval_SAE_DD ( real_type s,
real_type offs,
real_type & x_DD,
real_type & y_DD ) const
inline

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

Parameters
[in]sparameter on the curve
[in]offsoffset of the curve
[out]x_DD\(x\)-coordinate second derivative
[out]y_DD\(y\)-coordinate second derivative

◆ eval_SAE_DDD()

void G2lib::BaseCurve::eval_SAE_DDD ( real_type s,
real_type offs,
real_type & x_DDD,
real_type & y_DDD ) const
inline

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

Parameters
[in]sparameter on the curve
[in]offsoffset of the curve
[out]x_DDD\(x\)-coordinate third derivative
[out]y_DDD\(y\)-coordinate third derivative

◆ evaluate()

void G2lib::Biarc::evaluate ( real_type s,
real_type & th,
real_type & k,
real_type & x,
real_type & y ) const
overridevirtual

Evaluate curve at curvilinear coordinate \(s\).

Parameters
[in]scurvilinear coordinate
[out]thangle
[out]kcurvature
[out]x\(x\)-coordinate
[out]y\(y\)-coordinate

Reimplemented from G2lib::BaseCurve.

◆ evaluate_ISO()

virtual void G2lib::BaseCurve::evaluate_ISO ( real_type s,
real_type offs,
real_type & th,
real_type & k,
real_type & x,
real_type & y ) const
inlinevirtual

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

Parameters
[in]scurvilinear coordinate
[in]offsoffset
[out]thangle
[out]kcurvature
[out]x\(x\)-coordinate
[out]y\(y\)-coordinate

Reimplemented from G2lib::BaseCurve.

◆ evaluate_SAE()

virtual void G2lib::BaseCurve::evaluate_SAE ( real_type s,
real_type offs,
real_type & th,
real_type & k,
real_type & x,
real_type & y ) const
inlinevirtual

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

Parameters
[in]scurvilinear coordinate
[in]offsoffset
[out]thangle
[out]kcurvature
[out]x\(x\)-coordinate
[out]y\(y\)-coordinate

Reimplemented from G2lib::BaseCurve.

◆ info()

void G2lib::Biarc::info ( ostream_type & stream) const
inlineoverridevirtual

Pretty print of the curve data.

Implements G2lib::BaseCurve.

◆ intersect() [1/2]

void G2lib::Biarc::intersect ( BaseCurve const * pC,
IntersectList & ilist ) const
overridevirtual

Intersect the curve with another curve.

Parameters
[in]pCsecond curve intersect
[out]ilistlist of the intersection (as parameter on the curves)

Implements G2lib::BaseCurve.

◆ intersect() [2/2]

void G2lib::Biarc::intersect ( Biarc const & B,
IntersectList & ilist ) const

Intersect a biarc with another biarc.

Parameters
[in]Bsecond biarc
[out]ilistlist of the intersection (as parameter on the curves)

◆ intersect_ISO() [1/2]

void G2lib::Biarc::intersect_ISO ( real_type offs,
BaseCurve const * pC,
real_type offs_C,
IntersectList & ilist ) const
overridevirtual

Intersect the curve with another curve with offset (ISO)

Parameters
[in]offsoffset first curve
[in]pCsecond curve intersect
[in]offs_Coffset second curve
[out]ilistlist of the intersection (as parameter on the curves)

Implements G2lib::BaseCurve.

◆ intersect_ISO() [2/2]

void G2lib::Biarc::intersect_ISO ( real_type offs,
Biarc const & B,
real_type offs_B,
IntersectList & ilist ) const

Intersect a biarc with another biarc with offset (ISO).

Parameters
[in]offsoffset of first biarc
[in]Bsecond biarc
[in]offs_Boffset of second biarc
[out]ilistlist of the intersection (as parameter on the curves)

◆ kappa0()

real_type G2lib::Biarc::kappa0 ( ) const
inline

Return the curvature of the first arc of the biarc.

◆ kappa1()

real_type G2lib::Biarc::kappa1 ( ) const
inline

Return the curvature of the first arc of the biarc.

◆ kappa_begin()

real_type G2lib::Biarc::kappa_begin ( ) const
inlineoverridevirtual

Initial curvature.

Reimplemented from G2lib::BaseCurve.

◆ kappa_end()

real_type G2lib::Biarc::kappa_end ( ) const
inlineoverridevirtual

Final curvature.

Reimplemented from G2lib::BaseCurve.

◆ length()

real_type G2lib::Biarc::length ( ) const
inlineoverridevirtual

The length of the curve

Implements G2lib::BaseCurve.

◆ length0()

real_type G2lib::Biarc::length0 ( ) const
inline

Intial angle of the biarc.

◆ length1()

real_type G2lib::Biarc::length1 ( ) const
inline

Final angle of the biarc.

◆ length_ISO()

real_type G2lib::Biarc::length_ISO ( real_type offs) const
inlineoverridevirtual

The length of the curve with offset (ISO)

Implements G2lib::BaseCurve.

◆ nx_begin_ISO()

real_type G2lib::Biarc::nx_begin_ISO ( ) const
inlineoverridevirtual

Intial normal \(x\)-coordinate (ISO).

Reimplemented from G2lib::BaseCurve.

◆ nx_begin_SAE()

real_type G2lib::BaseCurve::nx_begin_SAE ( ) const
inline

Intial normal \(x\)-coordinate (SAE).

◆ nx_end_ISO()

real_type G2lib::Biarc::nx_end_ISO ( ) const
inlineoverridevirtual

Final normal \(x\)-coordinate (ISO).

Reimplemented from G2lib::BaseCurve.

◆ nx_end_SAE()

real_type G2lib::BaseCurve::nx_end_SAE ( ) const
inline

Final normal \(x\)-coordinate (SAE).

◆ ny_begin_ISO()

real_type G2lib::Biarc::ny_begin_ISO ( ) const
inlineoverridevirtual

Intial normal \(y\)-coordinate (ISO).

Reimplemented from G2lib::BaseCurve.

◆ ny_begin_SAE()

real_type G2lib::BaseCurve::ny_begin_SAE ( ) const
inline

Intial normal \(y\)-coordinate (SAE).

◆ ny_end_ISO()

real_type G2lib::Biarc::ny_end_ISO ( ) const
inlineoverridevirtual

Final normal \(y\)-coordinate (ISO).

Reimplemented from G2lib::BaseCurve.

◆ ny_end_SAE()

real_type G2lib::BaseCurve::ny_end_SAE ( ) const
inline

Intial normal \(y\)-coordinate (SAE).

◆ operator=()

Biarc const & G2lib::Biarc::operator= ( Biarc const & ba)
inline

Make a copy of an existing biarc.

◆ reverse()

void G2lib::Biarc::reverse ( )
overridevirtual

Reverse curve parameterization.

Implements G2lib::BaseCurve.

◆ rotate()

void G2lib::Biarc::rotate ( real_type angle,
real_type cx,
real_type cy )
inlineoverridevirtual

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

Parameters
[in]angleangle \(\theta\)
[in]cx\(c_x\)
[in]cy\(c_y\)

Implements G2lib::BaseCurve.

◆ scale()

void G2lib::Biarc::scale ( real_type sc)
overridevirtual

Scale curve by factor sc.

Implements G2lib::BaseCurve.

◆ setup()

void G2lib::Biarc::setup ( GenericContainer const & gc)
overridevirtual

Implements G2lib::BaseCurve.

◆ tg()

void G2lib::Biarc::tg ( real_type s,
real_type & tg_x,
real_type & tg_y ) const
overridevirtual

Tangent at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ tg_D()

void G2lib::Biarc::tg_D ( real_type s,
real_type & tg_x_D,
real_type & tg_y_D ) const
overridevirtual

Tangent derivative at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ tg_DD()

void G2lib::Biarc::tg_DD ( real_type s,
real_type & tg_x_DD,
real_type & tg_y_DD ) const
overridevirtual

Tangent second derivative at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ tg_DDD()

void G2lib::Biarc::tg_DDD ( real_type s,
real_type & tg_x_DDD,
real_type & tg_y_DDD ) const
overridevirtual

Tangent third derivative at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ theta()

real_type G2lib::Biarc::theta ( real_type s) const
overridevirtual

Angle at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ theta_begin()

real_type G2lib::Biarc::theta_begin ( ) const
inlineoverridevirtual

Initial angle of the curve.

Reimplemented from G2lib::BaseCurve.

◆ theta_D()

real_type G2lib::Biarc::theta_D ( real_type s) const
overridevirtual

Angle derivative (curvature) at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ theta_DD()

real_type G2lib::Biarc::theta_DD ( real_type s) const
inlineoverridevirtual

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

Implements G2lib::BaseCurve.

◆ theta_DDD()

real_type G2lib::Biarc::theta_DDD ( real_type s) const
inlineoverridevirtual

Angle third derivative at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ theta_end()

real_type G2lib::Biarc::theta_end ( ) const
inlineoverridevirtual

Final angle of the curve.

Reimplemented from G2lib::BaseCurve.

◆ theta_middle()

real_type G2lib::Biarc::theta_middle ( ) const
inline

Return the angle of the juction point of the biarc.

◆ translate()

void G2lib::Biarc::translate ( real_type tx,
real_type ty )
inlineoverridevirtual

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

Implements G2lib::BaseCurve.

◆ trim()

void G2lib::Biarc::trim ( real_type s_begin,
real_type s_end )
overridevirtual

Cut curve at parametric coordinate s_begin and s_end.

Implements G2lib::BaseCurve.

◆ tx()

real_type G2lib::Biarc::tx ( real_type s) const
overridevirtual

Tangent \(x\)-coordinate at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ tx_begin()

real_type G2lib::Biarc::tx_begin ( ) const
inlineoverridevirtual

Initial tangent \(x\)-coordinate.

Reimplemented from G2lib::BaseCurve.

◆ tx_D()

real_type G2lib::Biarc::tx_D ( real_type s) const
overridevirtual

Tangent derivative \(x\)-coordinate at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ tx_DD()

real_type G2lib::Biarc::tx_DD ( real_type s) const
overridevirtual

Tangent second derivative \(x\)-coordinate at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ tx_DDD()

real_type G2lib::Biarc::tx_DDD ( real_type s) const
overridevirtual

Tangent third derivative \(x\)-coordinate at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ tx_end()

real_type G2lib::Biarc::tx_end ( ) const
inlineoverridevirtual

Final tangent \(x\)-coordinate.

Reimplemented from G2lib::BaseCurve.

◆ ty()

real_type G2lib::Biarc::ty ( real_type s) const
overridevirtual

Tangent \(y\)-coordinate at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ ty_begin()

real_type G2lib::Biarc::ty_begin ( ) const
inlineoverridevirtual

Initial tangent \(y\)-coordinate.

Reimplemented from G2lib::BaseCurve.

◆ ty_D()

real_type G2lib::Biarc::ty_D ( real_type s) const
overridevirtual

Tangent derivative \(y\)-coordinate at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ ty_DD()

real_type G2lib::Biarc::ty_DD ( real_type s) const
overridevirtual

Tangent second derivative \(y\)-coordinate at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ ty_DDD()

real_type G2lib::Biarc::ty_DDD ( real_type s) const
overridevirtual

Tangent third derivative \(y\)-coordinate at curvilinear coordinate \(s\).

Reimplemented from G2lib::BaseCurve.

◆ ty_end()

real_type G2lib::Biarc::ty_end ( ) const
inlineoverridevirtual

Final tangent \(y\)-coordinate.

Reimplemented from G2lib::BaseCurve.

◆ type()

CurveType G2lib::Biarc::type ( ) const
inlineoverridevirtual

The name of the curve type

Implements G2lib::BaseCurve.

◆ X()

real_type G2lib::Biarc::X ( real_type s) const
overridevirtual

\(x\)-coordinate at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ x_begin()

real_type G2lib::Biarc::x_begin ( ) const
inlineoverridevirtual

Initial \(x\)-coordinate.

Reimplemented from G2lib::BaseCurve.

◆ x_begin_ISO()

virtual real_type G2lib::BaseCurve::x_begin_ISO ( real_type offs) const
inlinevirtual

Initial \(x\)-coordinate with offset (ISO standard).

Reimplemented from G2lib::BaseCurve.

◆ x_begin_SAE()

real_type G2lib::BaseCurve::x_begin_SAE ( real_type offs) const
inline

Initial \(x\)-coordinate with offset (SAE standard).

◆ X_D()

real_type G2lib::Biarc::X_D ( real_type s) const
overridevirtual

\(x\)-coordinate derivative at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ X_DD()

real_type G2lib::Biarc::X_DD ( real_type s) const
overridevirtual

\(x\)-coordinate second derivative at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ X_DDD()

real_type G2lib::Biarc::X_DDD ( real_type s) const
overridevirtual

\(x\)-coordinate third derivative at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ x_end()

real_type G2lib::Biarc::x_end ( ) const
inlineoverridevirtual

Final \(x\)-coordinate.

Reimplemented from G2lib::BaseCurve.

◆ x_end_ISO()

virtual real_type G2lib::BaseCurve::x_end_ISO ( real_type offs) const
inlinevirtual

Final \(x\)-coordinate with offset (ISO standard).

Reimplemented from G2lib::BaseCurve.

◆ x_end_SAE()

real_type G2lib::BaseCurve::x_end_SAE ( real_type offs) const
inline

Final \(y\)-coordinate with offset (SAE standard).

◆ X_ISO()

real_type G2lib::Biarc::X_ISO ( real_type s,
real_type offs ) const
overridevirtual

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

Reimplemented from G2lib::BaseCurve.

◆ X_ISO_D()

real_type G2lib::Biarc::X_ISO_D ( real_type s,
real_type offs ) const
overridevirtual

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

Reimplemented from G2lib::BaseCurve.

◆ X_ISO_DD()

real_type G2lib::Biarc::X_ISO_DD ( real_type s,
real_type offs ) const
overridevirtual

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

Reimplemented from G2lib::BaseCurve.

◆ X_ISO_DDD()

real_type G2lib::Biarc::X_ISO_DDD ( real_type s,
real_type offs ) const
overridevirtual

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

Reimplemented from G2lib::BaseCurve.

◆ x_middle()

real_type G2lib::Biarc::x_middle ( ) const
inline

Return the \(x\)-coordinate of the juction point of the biarc.

◆ X_SAE()

real_type G2lib::BaseCurve::X_SAE ( real_type s,
real_type offs ) const
inline

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

◆ X_SAE_D()

real_type G2lib::BaseCurve::X_SAE_D ( real_type s,
real_type offs ) const
inline

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

◆ X_SAE_DD()

real_type G2lib::BaseCurve::X_SAE_DD ( real_type s,
real_type offs ) const
inline

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

◆ X_SAE_DDD()

real_type G2lib::BaseCurve::X_SAE_DDD ( real_type s,
real_type offs ) const
inline

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

◆ Y()

real_type G2lib::Biarc::Y ( real_type s) const
overridevirtual

\(y\)-coordinate at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ y_begin()

real_type G2lib::Biarc::y_begin ( ) const
inlineoverridevirtual

Initial \(y\)-coordinate.

Reimplemented from G2lib::BaseCurve.

◆ y_begin_ISO()

virtual real_type G2lib::BaseCurve::y_begin_ISO ( real_type offs) const
inlinevirtual

Initial \(y\)-coordinate with offset (ISO standard).

Reimplemented from G2lib::BaseCurve.

◆ y_begin_SAE()

real_type G2lib::BaseCurve::y_begin_SAE ( real_type offs) const
inline

Initial \(y\)-coordinate with offset (SAE standard).

◆ Y_D()

real_type G2lib::Biarc::Y_D ( real_type s) const
overridevirtual

\(y\)-coordinate derivative at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ Y_DD()

real_type G2lib::Biarc::Y_DD ( real_type s) const
overridevirtual

\(y\)-coordinate second derivative at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ Y_DDD()

real_type G2lib::Biarc::Y_DDD ( real_type s) const
overridevirtual

\(y\)-coordinate third derivative at curvilinear coordinate \(s\).

Implements G2lib::BaseCurve.

◆ y_end()

real_type G2lib::Biarc::y_end ( ) const
inlineoverridevirtual

Final \(y\)-coordinate.

Reimplemented from G2lib::BaseCurve.

◆ y_end_ISO()

virtual real_type G2lib::BaseCurve::y_end_ISO ( real_type offs) const
inlinevirtual

Final \(y\)-coordinate with offset (ISO standard).

Reimplemented from G2lib::BaseCurve.

◆ y_end_SAE()

real_type G2lib::BaseCurve::y_end_SAE ( real_type offs) const
inline

Final \(y\)-coordinate with offset (ISO standard).

◆ Y_ISO()

real_type G2lib::Biarc::Y_ISO ( real_type s,
real_type offs ) const
overridevirtual

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

Reimplemented from G2lib::BaseCurve.

◆ Y_ISO_D()

real_type G2lib::Biarc::Y_ISO_D ( real_type s,
real_type offs ) const
overridevirtual

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

Reimplemented from G2lib::BaseCurve.

◆ Y_ISO_DD()

real_type G2lib::Biarc::Y_ISO_DD ( real_type s,
real_type offs ) const
overridevirtual

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

Reimplemented from G2lib::BaseCurve.

◆ Y_ISO_DDD()

real_type G2lib::Biarc::Y_ISO_DDD ( real_type s,
real_type offs ) const
overridevirtual

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

Reimplemented from G2lib::BaseCurve.

◆ y_middle()

real_type G2lib::Biarc::y_middle ( ) const
inline

Return the \(y\)-coordinate of the juction point of the biarc.

◆ Y_SAE()

real_type G2lib::BaseCurve::Y_SAE ( real_type s,
real_type offs ) const
inline

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

◆ Y_SAE_D()

real_type G2lib::BaseCurve::Y_SAE_D ( real_type s,
real_type offs ) const
inline

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

◆ Y_SAE_DD()

real_type G2lib::BaseCurve::Y_SAE_DD ( real_type s,
real_type offs ) const
inline

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

◆ Y_SAE_DDD()

real_type G2lib::BaseCurve::Y_SAE_DDD ( real_type s,
real_type offs ) const
inline

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

Friends And Related Symbol Documentation

◆ operator<<

ostream_type & operator<< ( ostream_type & stream,
Biarc const & bi )
friend

Print on strem the Biarc object

Parameters
streamthe output stream
bian instance of Biarc object
Returns
the output stream
The documentation for this class was generated from the following files:
  • /Users/enrico/Ricerca/develop/PINS/pins-mechatronix/LibSources/submodules/Clothoids/src/Clothoids/Biarc.hxx
  • /Users/enrico/Ricerca/develop/PINS/pins-mechatronix/LibSources/submodules/Clothoids/src/Biarc.cc
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