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Clothoid.hh
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/*--------------------------------------------------------------------------*\
| |
| Copyright (C) 2017 |
| |
| , __ , __ |
| /|/ \ /|/ \ |
| | __/ _ ,_ | __/ _ ,_ |
| | \|/ / | | | | \|/ / | | | |
| |(__/|__/ |_/ \_/|/|(__/|__/ |_/ \_/|/ |
| /| /| |
| \| \| |
| |
| Enrico Bertolazzi |
| Dipartimento di Ingegneria Industriale |
| Universita` degli Studi di Trento |
| email: enrico.bertolazzi@unitn.it |
| |
\*--------------------------------------------------------------------------*/
///
/// file: Clothoid.hh
///
#ifndef CLOTHOID_HH
#define CLOTHOID_HH
#include "Fresnel.hh"
#include "Line.hh"
#include "Circle.hh"
#include "Triangle2D.hh"
#include "AABBtree.hh"
#include <string>
#include <vector>
#include <algorithm>
#include <iterator>
#include <iostream>
//! Clothoid computations routine
namespace G2lib {
using std::vector;
/*\
| ____ _ _ _ _ _ ____
| / ___| | ___ | |_| |__ ___ (_) __| |/ ___| _ _ ____ _____
| | | | |/ _ \| __| '_ \ / _ \| |/ _` | | | | | | '__\ \ / / _ \
| | |___| | (_) | |_| | | | (_) | | (_| | |__| |_| | | \ V / __/
| \____|_|\___/ \__|_| |_|\___/|_|\__,_|\____\__,_|_| \_/ \___|
\*/
//! \brief Class to manage Clothoid Curve
class ClothoidCurve : public BaseCurve {
friend class ClothoidList;
private:
ClothoidData CD; //!< clothoid data
real_type L; //!< length of clothoid segment
void
optimized_sample_internal_ISO(
real_type s_begin,
real_type s_end,
real_type offs,
real_type ds,
real_type max_angle,
vector<real_type> & s
) const;
void
bbTriangles_internal_ISO(
real_type offs,
vector<Triangle2D> & tvec,
real_type s0,
real_type s1,
real_type max_angle,
real_type max_size,
int_type icurve
) const;
void
closestPoint_internal_ISO(
real_type s_begin,
real_type s_end,
real_type qx,
real_type qy,
real_type offs,
real_type & x,
real_type & y,
real_type & s,
real_type & dst
) const;
static int_type max_iter;
static real_type tolerance;
mutable bool aabb_done;
mutable AABBtree aabb_tree;
mutable real_type aabb_offs;
mutable real_type aabb_max_angle;
mutable real_type aabb_max_size;
mutable vector<Triangle2D> aabb_tri;
bool
aabb_intersect_ISO(
Triangle2D const & T1,
real_type offs,
ClothoidCurve const * pC,
Triangle2D const & T2,
real_type C_offs,
real_type & ss1,
real_type & ss2
) const;
class T2D_approximate_collision {
ClothoidCurve const * pC1;
ClothoidCurve const * pC2;
public:
T2D_approximate_collision(
ClothoidCurve const * _pC1,
ClothoidCurve const * _pC2
)
: pC1(_pC1)
, pC2(_pC2)
{}
bool
operator () ( BBox::PtrBBox ptr1, BBox::PtrBBox ptr2 ) const {
Triangle2D const & T1 = pC1->aabb_tri[size_t(ptr1->Ipos())];
Triangle2D const & T2 = pC2->aabb_tri[size_t(ptr2->Ipos())];
return T1.overlap(T2);
}
};
class T2D_collision_ISO {
ClothoidCurve const * pC1;
real_type const offs1;
ClothoidCurve const * pC2;
real_type const offs2;
public:
T2D_collision_ISO(
ClothoidCurve const * _pC1,
real_type const _offs1,
ClothoidCurve const * _pC2,
real_type const _offs2
)
: pC1(_pC1)
, offs1(_offs1)
, pC2(_pC2)
, offs2(_offs2)
{}
bool
operator () ( BBox::PtrBBox ptr1, BBox::PtrBBox ptr2 ) const {
Triangle2D const & T1 = pC1->aabb_tri[size_t(ptr1->Ipos())];
Triangle2D const & T2 = pC2->aabb_tri[size_t(ptr2->Ipos())];
real_type ss1, ss2;
return pC1->aabb_intersect_ISO( T1, offs1, pC2, T2, offs2, ss1, ss2 );
}
};
public:
#include "BaseCurve_using.hxx"
//explicit
ClothoidCurve()
: BaseCurve(G2LIB_CLOTHOID)
, aabb_done(false)
{
CD.x0 = 0;
CD.y0 = 0;
CD.theta0 = 0;
CD.kappa0 = 0;
CD.dk = 0;
L = 0;
}
//explicit
ClothoidCurve( ClothoidCurve const & s )
: BaseCurve(G2LIB_CLOTHOID)
, aabb_done(false)
{ copy(s); }
//! construct a clothoid with the standard parameters
explicit
ClothoidCurve(
real_type _x0,
real_type _y0,
real_type _theta0,
real_type _k,
real_type _dk,
real_type _L
)
: BaseCurve(G2LIB_CLOTHOID)
, aabb_done(false)
{
CD.x0 = _x0;
CD.y0 = _y0;
CD.theta0 = _theta0;
CD.kappa0 = _k;
CD.dk = _dk;
L = _L;
}
//! construct a clothoid by solving the hermite G1 problem
explicit
ClothoidCurve(
real_type const P0[],
real_type theta0,
real_type const P1[],
real_type theta1
)
: BaseCurve(G2LIB_CLOTHOID)
, aabb_done(false)
{
build_G1( P0[0], P0[1], theta0, P1[0], P1[1], theta1 );
}
void
copy( ClothoidCurve const & c ) {
CD = c.CD;
L = c.L;
aabb_done = false;
aabb_tree.clear();
}
explicit
ClothoidCurve( LineSegment const & LS )
: BaseCurve(G2LIB_CLOTHOID)
, aabb_done(false)
{
CD.x0 = LS.x0;
CD.y0 = LS.y0;
CD.theta0 = LS.theta0;
CD.kappa0 = 0;
CD.dk = 0;
L = LS.L;
}
explicit
ClothoidCurve( CircleArc const & C )
: BaseCurve(G2LIB_CLOTHOID)
, aabb_done(false)
{
CD.x0 = C.x0;
CD.y0 = C.y0;
CD.theta0 = C.theta0;
CD.kappa0 = C.k;
CD.dk = 0;
L = C.L;
}
explicit
ClothoidCurve( BaseCurve const & C );
ClothoidCurve const & operator = ( ClothoidCurve const & s )
{ copy(s); return *this; }
/*\
| _ _ _ _
| | |__ _ _(_) |__| |
| | '_ \ || | | / _` |
| |_.__/\_,_|_|_\__,_|
\*/
//! construct a clothoid with the standard parameters
void
build(
real_type _x0,
real_type _y0,
real_type _theta0,
real_type _k,
real_type _dk,
real_type _L
) {
CD.x0 = _x0;
CD.y0 = _y0;
CD.theta0 = _theta0;
CD.kappa0 = _k;
CD.dk = _dk;
L = _L;
aabb_done = false;
aabb_tree.clear();
}
/*!
* \brief build a clothoid by solving the hermite G1 problem
*
* \param x0 initial x position \f$ x_0 \f$
* \param y0 initial y position \f$ y_0 \f$
* \param theta0 initial angle \f$ \theta_0 \f$
* \param x1 final x position \f$ x_1 \f$
* \param y1 final y position \f$ y_1 \f$
* \param theta1 final angle \f$ \theta_1 \f$
* \return number of iteration performed
*/
int
build_G1(
real_type x0,
real_type y0,
real_type theta0,
real_type x1,
real_type y1,
real_type theta1,
real_type tol = 1e-12
) {
aabb_done = false;
aabb_tree.clear();
return CD.build_G1( x0, y0, theta0, x1, y1, theta1, tol, L );
}
/*!
* \brief build a clothoid by solving the hermite G1 problem
*
* \param x0 initial x position \f$ x_0 \f$
* \param y0 initial y position \f$ y_0 \f$
* \param theta0 initial angle \f$ \theta_0 \f$
* \param x1 final x position \f$ x_1 \f$
* \param y1 final y position \f$ y_1 \f$
* \param theta1 final angle \f$ \theta_1 \f$
* \return number of iteration performed
*/
int
build_G1_D(
real_type x0,
real_type y0,
real_type theta0,
real_type x1,
real_type y1,
real_type theta1,
real_type L_D[2],
real_type k_D[2],
real_type dk_D[2],
real_type tol = 1e-12
) {
aabb_done = false;
aabb_tree.clear();
return CD.build_G1( x0, y0, theta0, x1, y1, theta1, tol, L,
true, L_D, k_D, dk_D );
}
/*!
* \brief build a clothoid by solving the forward problem
*
* \param x0 initial x position \f$ x_0 \f$
* \param y0 initial y position \f$ y_0 \f$
* \param theta0 initial angle \f$ \theta_0 \f$
* \param kappa0 initial curvature \f$ \kappa_0 \f$
* \param x1 final x position \f$ x_1 \f$
* \param y1 final y position \f$ y_1 \f$
*/
bool
build_forward(
real_type x0,
real_type y0,
real_type theta0,
real_type kappa0,
real_type x1,
real_type y1,
real_type tol = 1e-12
) {
aabb_done = false;
aabb_tree.clear();
return CD.build_forward( x0, y0, theta0, kappa0, x1, y1, tol, L );
}
/*!
* \brief build a clothoid from a line segment
*
* \param LS line segment object
*/
void
build( LineSegment const & LS ) {
CD.x0 = LS.x0;
CD.y0 = LS.y0;
CD.theta0 = LS.theta0;
CD.kappa0 = 0;
CD.dk = 0;
L = LS.L;
aabb_done = false;
aabb_tree.clear();
}
/*!
* \brief build a clothoid from a line segment
*
* \param C line segment object
*/
void
build( CircleArc const & C ) {
CD.x0 = C.x0;
CD.y0 = C.y0;
CD.theta0 = C.theta0;
CD.kappa0 = C.k;
CD.dk = 0;
L = C.L;
aabb_done = false;
aabb_tree.clear();
}
void
Pinfinity( real_type & x, real_type & y, bool plus = true ) const
{ CD.Pinfinity( x, y, plus ); }
real_type
dkappa() const
{ return CD.dk; }
/*!
* \return clothoid total variation
*/
real_type
thetaTotalVariation() const;
real_type
thetaMinMax( real_type & thMin, real_type & thMax ) const;
/*!
* \return clothoid angle range
*/
real_type
deltaTheta() const
{ real_type thMin, thMax; return thetaMinMax( thMin, thMax ); }
real_type
curvatureMinMax( real_type & kMin, real_type & kMax ) const;
/*!
* \return clothoid total curvature variation
*/
real_type curvatureTotalVariation() const;
real_type integralCurvature2() const;
real_type integralJerk2() const;
real_type integralSnap2() const;
/*!
* Return a vector of optimized sample parameters
* \param offs offset of the sampled curve
* \param npts suggested minimum number of sampled points
* \param max_angle maximum angle variation between two sampled points
* \param s vector of computed parameters
*/
void
optimized_sample_ISO(
real_type offs,
int_type npts,
real_type max_angle,
std::vector<real_type> & s
) const;
void
optimized_sample_SAE(
real_type offs,
int_type npts,
real_type max_angle,
std::vector<real_type> & s
) const {
optimized_sample_ISO( -offs, npts, max_angle, s );
}
/*\
| _ _ _
| __| (_)__| |_ __ _ _ _ __ ___
| / _` | (_-< _/ _` | ' \/ _/ -_)
| \__,_|_/__/\__\__,_|_||_\__\___|
\*/
/*!
* \brief Compute the point on clothoid at minimal distance from a given point
*
* \param qx x-coordinate of the given point
* \param qy y-coordinate of the given point
* \param X x-coordinate of the point on clothoid at minimal distance
* \param Y y-coordinate of the point on clothoid at minimal distance
* \param S curvilinear coordinate of the point (X,Y) on the clothoid
* \return the distance of the
*
*/
real_type
closestPointBySample(
real_type ds,
real_type qx,
real_type qy,
real_type & X,
real_type & Y,
real_type & S
) const;
real_type
distanceBySample(
real_type ds,
real_type qx,
real_type qy,
real_type & S
) const {
real_type X, Y;
return closestPointBySample( ds, qx, qy, X, Y, S );
}
real_type
distanceBySample(
real_type ds,
real_type qx,
real_type qy
) const {
real_type X, Y, S;
return closestPointBySample( ds, qx, qy, X, Y, S );
}
/*\
| _ _ _____ _ _
| | |__| |_|_ _| _(_)__ _ _ _ __ _| |___
| | '_ \ '_ \| || '_| / _` | ' \/ _` | / -_)
| |_.__/_.__/|_||_| |_\__,_|_||_\__, |_\___|
| |___/
\*/
//! get the triangle bounding box (if angle variation less that pi/2)
bool
bbTriangle(
real_type & xx0, real_type & yy0,
real_type & xx1, real_type & yy1,
real_type & xx2, real_type & yy2
) const {
return CD.bbTriangle( L, xx0, yy0, xx1, yy1, xx2, yy2 );
}
//! get the triangle bounding box (if angle variation less that pi/2)
bool
bbTriangle_ISO(
real_type offs,
real_type & xx0, real_type & yy0,
real_type & xx1, real_type & yy1,
real_type & xx2, real_type & yy2
) const {
return CD.bbTriangle_ISO( L, offs, xx0, yy0, xx1, yy1, xx2, yy2 );
}
//! get the triangle bounding box (if angle variation less that pi/2)
bool
bbTriangle_SAE(
real_type offs,
real_type & xx0, real_type & yy0,
real_type & xx1, real_type & yy1,
real_type & xx2, real_type & yy2
) const {
return CD.bbTriangle_SAE( L, offs, xx0, yy0, xx1, yy1, xx2, yy2 );
}
bool
bbTriangle( Triangle2D & t, int_type icurve = 0 ) const {
real_type x0, y0, x1, y1, x2, y2;
bool ok = CD.bbTriangle( L, x0, y0, x1, y1, x2, y2 );
if ( ok ) t.build( x0, y0, x1, y1, x2, y2, 0, 0, icurve );
return ok;
}
bool
bbTriangle_ISO( real_type offs, Triangle2D & t, int_type icurve = 0 ) const {
real_type x0, y0, x1, y1, x2, y2;
bool ok = CD.bbTriangle_ISO( L, offs, x0, y0, x1, y1, x2, y2 );
if ( ok ) t.build( x0, y0, x1, y1, x2, y2, 0, 0, icurve );
return ok;
}
bool
bbTriangle_SAE( real_type offs, Triangle2D & t, int_type icurve = 0 ) const {
real_type x0, y0, x1, y1, x2, y2;
bool ok = CD.bbTriangle_SAE( L, offs, x0, y0, x1, y1, x2, y2 );
if ( ok ) t.build( x0, y0, x1, y1, x2, y2, 0, 0, icurve );
return ok;
}
void
bbTriangles_ISO(
real_type offs,
std::vector<Triangle2D> & tvec,
real_type max_angle = m_pi/6, // 30 degree
real_type max_size = 1e100,
int_type icurve = 0
) const;
void
bbTriangles_SAE(
real_type offs,
std::vector<Triangle2D> & tvec,
real_type max_angle = m_pi/6, // 30 degree
real_type max_size = 1e100,
int_type icurve = 0
) const {
this->bbTriangles_ISO( -offs, tvec, max_angle, max_size, icurve );
}
void
bbTriangles(
std::vector<Triangle2D> & tvec,
real_type max_angle = m_pi/6, // 30 degree
real_type max_size = 1e100,
int_type icurve = 0
) const {
this->bbTriangles_ISO( 0, tvec, max_angle, max_size, icurve );
}
// . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
virtual
void
bbox(
real_type & xmin,
real_type & ymin,
real_type & xmax,
real_type & ymax
) const G2LIB_OVERRIDE {
bbox_ISO( 0, xmin, ymin, xmax, ymax );
}
virtual
void
bbox_ISO(
real_type offs,
real_type & xmin,
real_type & ymin,
real_type & xmax,
real_type & ymax
) const G2LIB_OVERRIDE;
// . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
virtual
real_type
length() const G2LIB_OVERRIDE
{ return L; }
virtual
real_type
length_ISO( real_type ) const G2LIB_OVERRIDE {
G2LIB_DO_ERROR( "Offset length not available for Clothoids" )
return 0;
}
virtual
real_type
thetaBegin() const G2LIB_OVERRIDE
{ return CD.theta0; }
virtual
real_type
thetaEnd() const G2LIB_OVERRIDE
{ return CD.theta(L); }
virtual
real_type
xBegin() const G2LIB_OVERRIDE
{ return CD.x0; }
virtual
real_type
xEnd() const G2LIB_OVERRIDE
{ return CD.X(L); }
virtual
real_type
yBegin() const G2LIB_OVERRIDE
{ return CD.y0; }
virtual
real_type
yEnd() const G2LIB_OVERRIDE
{ return CD.Y(L); }
virtual
real_type
tx_Begin() const G2LIB_OVERRIDE
{ return CD.tg0_x(); }
virtual
real_type
ty_Begin() const G2LIB_OVERRIDE
{ return CD.tg0_y(); }
virtual
real_type
nx_Begin_ISO() const G2LIB_OVERRIDE
{ return CD.nor0_x_ISO(); }
virtual
real_type
ny_Begin_ISO() const G2LIB_OVERRIDE
{ return CD.nor0_y_ISO(); }
// . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
/*\
| _____ _ _ _
| |_ _| __ _ _ __ __| | | \ | |
| | | / _` | '_ \ / _` | | \| |
| | | | (_| | | | | (_| | | |\ |
| |_| \__,_|_| |_|\__,_| |_| \_|
\*/
virtual
real_type
tx( real_type s ) const G2LIB_OVERRIDE
{ return CD.tg_x( s ); }
virtual
real_type
ty( real_type s ) const G2LIB_OVERRIDE
{ return CD.tg_y( s ); }
virtual
real_type
tx_D( real_type s ) const G2LIB_OVERRIDE
{ return CD.tg_x_D( s ); }
virtual
real_type
ty_D( real_type s ) const G2LIB_OVERRIDE
{ return CD.tg_y_D( s ); }
virtual
real_type
tx_DD( real_type s ) const G2LIB_OVERRIDE
{ return CD.tg_x_DD( s ); }
virtual
real_type
ty_DD( real_type s ) const G2LIB_OVERRIDE
{ return CD.tg_y_DD( s ); }
virtual
real_type
tx_DDD( real_type s ) const G2LIB_OVERRIDE
{ return CD.tg_x_DDD( s ); }
virtual
real_type
ty_DDD( real_type s ) const G2LIB_OVERRIDE
{ return CD.tg_y_DDD( s ); }
// . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
virtual
void
tg(
real_type s,
real_type & tx,
real_type & ty
) const G2LIB_OVERRIDE
{ CD.tg( s, tx, ty ); }
virtual
void
tg_D(
real_type s,
real_type & tx_D,
real_type & ty_D
) const G2LIB_OVERRIDE
{ CD.tg_D( s, tx_D, ty_D ); }
virtual
void
tg_DD(
real_type s,
real_type & tx_DD,
real_type & ty_DD
) const G2LIB_OVERRIDE
{ CD.tg_DD( s, tx_DD, ty_DD ); }
virtual
void
tg_DDD(
real_type s,
real_type & tx_DDD,
real_type & ty_DDD
) const G2LIB_OVERRIDE
{ CD.tg_DDD( s, tx_DDD, ty_DDD ); }
// . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
/*!
* \brief get clothoid angle at curvilinear cooordinate `s`
*
* \param s curvilinear cooordinate
* \return angle (radiant) at curvilinear cooordinate `s`
*/
real_type
theta( real_type s ) const G2LIB_OVERRIDE
{ return CD.theta(s); }
/*!
* \brief get clothoid angle derivative (=curvature) at curvilinear cooordinate `s`
*
* \param s curvilinear cooordinate
* \return angle derivative (radiant/s) at curvilinear cooordinate `s`
*/
real_type
theta_D( real_type s ) const G2LIB_OVERRIDE
{ return CD.kappa(s); }
/*!
* \brief get clothoid angle second derivative at curvilinear cooordinate `s`
*
* \return angle second derivative (radiant/s^2) at curvilinear cooordinate `s`
*/
real_type
theta_DD( real_type ) const G2LIB_OVERRIDE
{ return CD.dk; }
/*!
* \brief get clothoid angle third derivative at curvilinear cooordinate `s`
*
* \return angle third derivative (radiant/s^3) at curvilinear cooordinate `s`
*/
real_type
theta_DDD( real_type ) const G2LIB_OVERRIDE
{ return 0; }
// . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#ifdef G2LIB_COMPATIBILITY_MODE
virtual
void
evaluate(
real_type s,
real_type & th,
real_type & k,
real_type & x,
real_type & y
) const G2LIB_OVERRIDE
{ CD.evaluate( s, th, k, x, y ); }
#endif
// . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
/*!
* \brief clothoid X coordinate at curvilinear coordinate `s`
* \param s curvilinear coordinate
* \return clothoid X coordinate
*/
real_type
X( real_type s ) const G2LIB_OVERRIDE
{ return CD.X(s); }
real_type
X_D( real_type s ) const G2LIB_OVERRIDE
{ return CD.X_D(s); }
real_type
X_DD( real_type s ) const G2LIB_OVERRIDE
{ return CD.X_DD(s); }
real_type
X_DDD( real_type s ) const G2LIB_OVERRIDE
{ return CD.X_DDD(s); }
/*!
* \brief clothoid Y coordinate at curvilinear coordinate `s`
* \param s curvilinear coordinate
* \return clothoid Y coordinate
*/
real_type
Y( real_type s ) const G2LIB_OVERRIDE
{ return CD.Y(s); }
real_type
Y_D( real_type s ) const G2LIB_OVERRIDE
{ return CD.Y_D(s); }
real_type
Y_DD ( real_type s ) const G2LIB_OVERRIDE
{ return CD.Y_DD(s); }
real_type
Y_DDD( real_type s ) const G2LIB_OVERRIDE
{ return CD.Y_DDD(s); }
/*!
* \brief clothoid X coordinate at curvilinear coordinate `s`
* \param s curvilinear coordinate
* \param offs lateral offset
* \return clothoid X coordinate
*/
real_type
X_ISO( real_type s, real_type offs ) const G2LIB_OVERRIDE
{ return CD.X_ISO(s,offs); }
real_type
X_ISO_D( real_type s, real_type offs ) const G2LIB_OVERRIDE
{ return CD.X_ISO_D(s,offs); }
real_type
X_ISO_DD( real_type s, real_type offs ) const G2LIB_OVERRIDE
{ return CD.X_ISO_DD(s,offs); }
real_type
X_ISO_DDD( real_type s, real_type offs ) const G2LIB_OVERRIDE
{ return CD.X_ISO_DDD(s,offs); }
/*!
* \brief clothoid Y coordinate at curvilinear coordinate `s`
* \param s curvilinear coordinate
* \param offs lateral offset
* \return clothoid Y coordinate
*/
real_type
Y_ISO( real_type s, real_type offs ) const G2LIB_OVERRIDE
{ return CD.Y_ISO(s,offs); }
real_type
Y_ISO_D( real_type s, real_type offs ) const G2LIB_OVERRIDE
{ return CD.Y_ISO_D(s,offs); }
real_type
Y_ISO_DD( real_type s, real_type offs ) const G2LIB_OVERRIDE
{ return CD.Y_ISO_DD(s,offs); }
real_type
Y_ISO_DDD( real_type s, real_type offs ) const G2LIB_OVERRIDE
{ return CD.Y_ISO_DDD(s,offs); }
// . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
virtual
void
eval(
real_type s,
real_type & x,
real_type & y
) const G2LIB_OVERRIDE
{ CD.eval( s, x, y ); }
virtual
void
eval_D(
real_type s,
real_type & x_D,
real_type & y_D
) const G2LIB_OVERRIDE
{ CD.eval_D( s, x_D, y_D ); }
virtual
void
eval_DD(
real_type s,
real_type & x_DD,
real_type & y_DD
) const G2LIB_OVERRIDE
{ CD.eval_DD( s, x_DD, y_DD ); }
virtual
void
eval_DDD(
real_type s,
real_type & x_DDD,
real_type & y_DDD
) const G2LIB_OVERRIDE
{ CD.eval_DDD( s, x_DDD, y_DDD ); }
virtual
void
eval_ISO(
real_type s,
real_type offs,
real_type & x,
real_type & y
) const G2LIB_OVERRIDE
{ CD.eval_ISO( s, offs, x, y ); }
virtual
void
eval_ISO_D(
real_type s,
real_type offs,
real_type & x_D,
real_type & y_D
) const G2LIB_OVERRIDE
{ CD.eval_ISO_D( s, offs, x_D, y_D ); }
virtual
void
eval_ISO_DD(
real_type s,
real_type offs,
real_type & x_DD,
real_type & y_DD
) const G2LIB_OVERRIDE
{ CD.eval_ISO_DD( s, offs, x_DD, y_DD ); }
virtual
void
eval_ISO_DDD(
real_type s,
real_type offs,
real_type & x_DDD,
real_type & y_DDD
) const G2LIB_OVERRIDE
{ CD.eval_ISO_DDD( s, offs, x_DDD, y_DDD ); }