ClothoidCurve Class Reference
|
Clothoids
|
#include <Clothoid.hxx>
Public Member Functions inherited from Friends | |
| class | ClothoidList |
| ostream_type & | operator<< (ostream_type &stream, ClothoidCurve const &c) |
Detailed Description
Class to manage Clothoid Curve. A clothoid curve is described by the following generalized Fresnel integrals
\[ \begin{cases} x(s) = x_0 + \displaystyle\int_0^s \cos(as^2+bs+c)\,\mathrm{d}t \\[1em] y(s) = y_0 + \displaystyle\int_0^s \sin(as^2+bs+c)\,\mathrm{d}t \end{cases} \]
Constructor & Destructor Documentation
◆ ClothoidCurve() [1/7]
| G2lib::ClothoidCurve::ClothoidCurve | ( | string const & | name | ) |
eof: BaseCurve_using.hxx Build an empty clothoid curve
◆ ClothoidCurve() [2/7]
| G2lib::ClothoidCurve::ClothoidCurve | ( | ClothoidCurve const & | s | ) |
Build a copy of an existing clothoid curve
◆ ClothoidCurve() [3/7]
|
explicit |
Construct a clothoid with the standard parameters.
- Parameters
-
[in] x0 starting position \(x\)-coordinate [in] y0 starting position \(y\)-coordinate [in] theta0 initial angle [in] k curvature [in] dk curvature derivative [in] L length [in] name name of the clothoid curve
◆ ClothoidCurve() [4/7]
|
explicit |
Construct a clothoid \( G(s) \) solving the \( G^1 \) problem.
\[ \begin{array}{rcl} G(0) &=& \mathbf{p}_0 \\[1em] G(L) &=& \mathbf{p}_1 \\[1em] G'(0) &=& (\cos\theta_0,\sin\theta_0)^T \\[1em] G'(L) &=& (\cos\theta_1,\sin\theta_1)^T \\[1em] \end{array} \]
- Parameters
-
[in] P0 initial point \( \mathbf{p}_0 \) [in] theta0 initial angle \( \theta_0 \) [in] P1 final point \( \mathbf{p}_1 \) [in] theta1 final angle \( \theta_1 \) [in] name name of the clothoid curve
◆ ClothoidCurve() [5/7]
|
explicit |
Build a clothoid copying an existing line segment.
◆ ClothoidCurve() [6/7]
|
explicit |
Build a clothoid copying an existing circle arc.
◆ ClothoidCurve() [7/7]
|
explicit |
Build a clothoid copying an existing curve.
Member Function Documentation
◆ approximate_collision_ISO()
| bool G2lib::ClothoidCurve::approximate_collision_ISO | ( | real_type | offs, |
| ClothoidCurve const & | C, | ||
| real_type | offs_C, | ||
| real_type | max_angle, | ||
| real_type | max_size ) const |
Collision detection
- Parameters
-
[in] offs curve offset [in] C curve to compare for collision detection [in] offs_C curve offset [in] max_angle maximum angle variation [in] max_size if the segment is larger then this parameter is split
◆ bb_triangles()
|
inlineoverridevirtual |
Build a cover with triangles of the curve.
- Parameters
-
[out] tvec list of covering triangles [out] max_angle maximum angle variation of the curve covered by a triangle [out] max_size maximum admissible size of the covering tirnagles [out] icurve index of the covering triangles
Implements G2lib::BaseCurve.
◆ bb_triangles_ISO()
|
overridevirtual |
Build a cover with triangles of the curve with offset (ISO).
- Parameters
-
[out] offs curve offset [out] tvec list of covering triangles [out] max_angle maximum angle variation of the curve covered by a triangle [out] max_size maximum admissible size of the covering tirnagles [out] icurve index of the covering triangles
Implements G2lib::BaseCurve.
◆ bb_triangles_SAE()
|
inlineoverridevirtual |
Build a cover with triangles of the curve with offset (SAE).
- Parameters
-
[out] offs curve offset [out] tvec list of covering triangles [out] max_angle maximum angle variation of the arc covered by a triangle [out] max_size maximum admissible size of the covering tirnagles [out] icurve index of the covering triangles
Implements G2lib::BaseCurve.
◆ bbox()
|
inlineoverridevirtual |
Compute the bounding box of the curve.
- Parameters
-
[out] xmin left bottom [out] ymin left bottom [out] xmax right top [out] ymax right top
Implements G2lib::BaseCurve.
◆ bbox_ISO()
|
overridevirtual |
Compute the bounding box of the curve with offset (ISO).
- Parameters
-
[in] offs curve offset [out] xmin left bottom [out] ymin left bottom [out] xmax right top [out] ymax right top
Implements G2lib::BaseCurve.
◆ bbTriangle()
|
inline |
Get the triangle bounding box (if angle variation less that \( \pi/2 \) )
◆ bbTriangle_ISO()
|
inline |
Get the triangle bounding box (if angle variation less that \( \pi/2 \))
◆ bbTriangle_SAE()
|
inline |
Get the triangle bounding box (if angle variation less that \( \pi/2 \))
◆ build() [1/3]
| void G2lib::ClothoidCurve::build | ( | CircleArc const & | C | ) |
Build a clothoid from a circle arc.
◆ build() [2/3]
| void G2lib::ClothoidCurve::build | ( | LineSegment const & | LS | ) |
Build a clothoid from a line segment.
◆ build() [3/3]
| void G2lib::ClothoidCurve::build | ( | real_type | x0, |
| real_type | y0, | ||
| real_type | theta0, | ||
| real_type | k, | ||
| real_type | dk, | ||
| real_type | L ) |
Build a clothoid with the standard parameters
- Parameters
-
[in] x0 starting position \(x\)-coordinate [in] y0 starting position \(y\)-coordinate [in] theta0 initial angle [in] k curvature [in] dk curvature derivative [in] L length
◆ build_forward()
| bool G2lib::ClothoidCurve::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 ) |
Build a clothoid by solving the forward problem.
- Parameters
-
[in] x0 initial \(x\)-position \( x_0 \) [in] y0 initial \(y\)-position \( y_0 \) [in] theta0 initial angle \( \theta_0 \) [in] kappa0 initial curvature \( \kappa_0 \) [in] x1 final \(x\)-position \( x_1 \) [in] y1 final \(y\)-position \( y_1 \) [in] tol tolerance of the forward problem
◆ build_G1()
| int G2lib::ClothoidCurve::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 ) |
Build a clothoid by solving the hermite \( G^1 \) problem.
- Parameters
-
[in] x0 initial x position \( x_0 \) [in] y0 initial y position \( y_0 \) [in] theta0 initial angle \( \theta_0 \) [in] x1 final x position \( x_1 \) [in] y1 final y position \( y_1 \) [in] theta1 final angle \( \theta_1 \) [in] tol tolerance
- Returns
- number of iteration performed
◆ build_G1_D()
| int G2lib::ClothoidCurve::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 ) |
Build a clothoid by solving the hermite \( G^1 \) problem.
- Parameters
-
[in] x0 initial x position \( x_0 \) [in] y0 initial y position \( y_0 \) [in] theta0 initial angle \( \theta_0 \) [in] x1 final x position \( x_1 \) [in] y1 final y position \( y_1 \) [in] theta1 final angle \( \theta_1 \) [out] L_D derivative of the length \( L(\theta_0,\theta_1) \) [out] k_D derivative of the curvature \( \kappa(\theta_0,\theta_1) \) [out] dk_D derivative of the curvature variation \( \kappa'(\theta_0,\theta_1) \) [out] tol = \(10^{-12}\)
- Returns
- number of iteration performed
◆ change_curvilinear_origin()
change the origin of the clothoid at \( s_0 \) and the length to \( L \).
- Parameters
-
[in] s0 \( s_0 \) [in] newL \( L \)
◆ change_origin()
Translate curve so that origin will be (newx0, newy0).
Implements G2lib::BaseCurve.
◆ closest_point_by_sample()
| real_type G2lib::ClothoidCurve::closest_point_by_sample | ( | real_type | ds, |
| real_type | qx, | ||
| real_type | qy, | ||
| real_type & | X, | ||
| real_type & | Y, | ||
| real_type & | S ) const |
Compute the point on clothoid at minimal distance from a given point.
- Parameters
-
ds sampling step qx \( x \)-coordinate of the given point qy \( y \)-coordinate of the given point X \( x \)-coordinate of the point on clothoid at minimal distance Y \( y \)-coordinate of the point on clothoid at minimal distance S curvilinear coordinate of the point (X,Y) on the clothoid
- Returns
- the distance of the point from the clothoid
◆ closest_point_ISO() [1/2]
|
overridevirtual |
Compute the point on clothoid at minimal distance from a given point using the optimized algorithm described in the publication:
- E.Bertolazzi, M.Frego, Point-Clothoid distance and projection computation SIAM J. Scientific Computing, Vol. 41, No. 5, pp. A3326-A3353
- Parameters
-
qx \(x\)-coordinate of the given point qy \(y\)-coordinate of the given point x \(x\)-coordinate of the point on clothoid at minimal distance y \(y\)-coordinate of the point on clothoid at minimal distance s curvilinear coordinate of the point (X,Y) on the clothoid t normal coordinate of the point (X,Y) on the clothoid dst the distance of the point from the clothoid
- 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]
|
overridevirtual |
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
Implements G2lib::BaseCurve.
◆ closest_point_SAE() [1/2]
|
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 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
◆ closest_point_SAE() [2/2]
|
inline |
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
◆ collision()
|
overridevirtual |
Check collision with another curve.
Implements G2lib::BaseCurve.
◆ collision_ISO()
|
overridevirtual |
Check collision with another curve with offset (ISO).
- Parameters
-
[in] offs curve offset [in] pC second curve to check collision [in] offs_C curve offset of the second curve
- Returns
- true if collision is detected
Implements G2lib::BaseCurve.
◆ copy()
| void G2lib::ClothoidCurve::copy | ( | ClothoidCurve const & | c | ) |
Build a clothoid copying an existing one.
◆ curvature_min_max()
Max and min of the curvatire of the clothoid curve.
◆ curvature_total_variation()
| real_type G2lib::ClothoidCurve::curvature_total_variation | ( | ) | const |
Clothoid total curvature variation.
◆ delta_theta()
|
inline |
Clothoid angle range.
◆ distance_by_sample() [1/2]
|
inline |
Approximate the point on clothoid at minimal distance from a given point using simple sampling.
- Parameters
-
ds sampling step qx \(x\)-coordinate of the given point qy \(y\)-coordinate of the given point
- Returns
- the distance of the point from the clothoid
◆ distance_by_sample() [2/2]
|
inline |
Approximate the point on clothoid at minimal distance from a given point using simple sampling.
- Parameters
-
ds sampling step qx \( x \)-coordinate of the given point qy \( y \)-coordinate of the given point S curvilinear coordinate of the point (X,Y) on the clothoid
- Returns
- the distance of the point from the clothoid
◆ distance_ISO()
|
inline |
Compute the distance between a point \(q=(q_x,q_y)\) and the curve with offset (ISO).
- Parameters
-
[in] qx component \(q_x\) [in] qy component \(q_y\) [in] offs offset of the curve
- Returns
- the computed distance
◆ distance_SAE()
|
inline |
Compute the distance between a point \(q=(q_x,q_y)\) and the curve with offset (SAE).
- Parameters
-
[in] qx component \(q_x\) [in] qy component \(q_y\) [in] offs offset of the curve
- Returns
- the computed distance
◆ dkappa()
|
inline |
Derivative of the curvature of the clothoid.
◆ eval()
|
inlineoverridevirtual |
x and \(y\)-coordinate at curvilinear coordinate \(s\).
Implements G2lib::BaseCurve.
◆ eval_D()
|
inlineoverridevirtual |
x and \(y\)-coordinate derivative at curvilinear coordinate \(s\).
Implements G2lib::BaseCurve.
◆ eval_DD()
|
inlineoverridevirtual |
x and \(y\)-coordinate second derivative at curvilinear coordinate \(s\).
Implements G2lib::BaseCurve.
◆ eval_DDD()
|
inlineoverridevirtual |
x and \(y\)-coordinate third derivative at curvilinear coordinate \(s\).
Implements G2lib::BaseCurve.
◆ eval_ISO()
|
inlineoverridevirtual |
Compute curve at position s with offset offs (ISO).
- Parameters
-
[in] s parameter on the curve [in] offs offset of the curve [out] x coordinate [out] y coordinate
Reimplemented from G2lib::BaseCurve.
◆ eval_ISO_D()
|
inlineoverridevirtual |
Compute derivative curve at position s with offset offs (ISO).
- Parameters
-
[in] s parameter on the curve [in] offs offset of the curve [out] x_D \(x\)-coordinate [out] y_D \(y\)-coordinate
Reimplemented from G2lib::BaseCurve.
◆ eval_ISO_DD()
|
inlineoverridevirtual |
Compute second derivative curve at position s with offset offs (ISO).
- Parameters
-
[in] s parameter on the curve [in] offs offset of the curve [out] x_DD \(x\)-coordinate second derivative [out] y_DD \(y\)-coordinate second derivative
Reimplemented from G2lib::BaseCurve.
◆ eval_ISO_DDD()
|
inlineoverridevirtual |
Compute third derivative curve at position s with offset offs (ISO).
- Parameters
-
[in] s parameter on the curve [in] offs offset of the curve [out] x_DDD \(x\)-coordinate third derivative [out] y_DDD \(y\)-coordinate third derivative
Reimplemented from G2lib::BaseCurve.
◆ eval_SAE()
|
inline |
Compute curve at position s with offset offs (SAE).
- Parameters
-
[in] s parameter on the curve [in] offs offset of the curve [out] x coordinate [out] y coordinate
◆ eval_SAE_D()
|
inline |
Compute derivative curve at position s with offset offs (SAE).
- Parameters
-
[in] s parameter on the curve [in] offs offset of the curve [out] x_D \(x\)-coordinate first derivative [out] y_D \(y\)-coordinate first derivative
◆ eval_SAE_DD()
|
inline |
Compute second derivative curve at position s with offset offs (SAE).
- Parameters
-
[in] s parameter on the curve [in] offs offset of the curve [out] x_DD \(x\)-coordinate second derivative [out] y_DD \(y\)-coordinate second derivative
◆ eval_SAE_DDD()
|
inline |
Compute third derivative curve at position s with offset offs (SAE).
- Parameters
-
[in] s parameter on the curve [in] offs offset of the curve [out] x_DDD \(x\)-coordinate third derivative [out] y_DDD \(y\)-coordinate third derivative
◆ evaluate_ISO()
|
inlinevirtual |
Evaluate curve with offset at curvilinear coordinate \(s\) (ISO).
- Parameters
-
[in] s curvilinear coordinate [in] offs offset [out] th angle [out] k curvature [out] x \(x\)-coordinate [out] y \(y\)-coordinate
Reimplemented from G2lib::BaseCurve.
◆ evaluate_SAE()
|
inlinevirtual |
Evaluate curve with offset at curvilinear coordinate \(s\) (SAE).
- Parameters
-
[in] s curvilinear coordinate [in] offs offset [out] th angle [out] k curvature [out] x \(x\)-coordinate [out] y \(y\)-coordinate
Reimplemented from G2lib::BaseCurve.
◆ info()
|
inlineoverridevirtual |
Pretty print of the curve data.
Implements G2lib::BaseCurve.
◆ integral_curvature2()
| real_type G2lib::ClothoidCurve::integral_curvature2 | ( | ) | const |
Given the clothoid curve \( P(s) \) compute.
\[ \int_0^L |P''(s)|^2 \mathrm{d}s \]
◆ integral_jerk2()
| real_type G2lib::ClothoidCurve::integral_jerk2 | ( | ) | const |
Given the clothoid curve \( P(s) \) compute.
\[ \int_0^L |P'''(s)|^2 \mathrm{d}s \]
◆ integral_snap2()
| real_type G2lib::ClothoidCurve::integral_snap2 | ( | ) | const |
Given the clothoid curve \( P(s) \) compute.
\[ \int_0^L |P''''(s)|^2 \mathrm{d}s \]
◆ intersect()
|
overridevirtual |
Intersect the curve with another curve.
- Parameters
-
[in] pC second curve intersect [out] ilist list of the intersection (as parameter on the curves)
Implements G2lib::BaseCurve.
◆ intersect_ISO()
|
overridevirtual |
Intersect the curve with another curve with offset (ISO)
- Parameters
-
[in] offs offset first curve [in] pC second curve intersect [in] offs_C offset second curve [out] ilist list of the intersection (as parameter on the curves)
Implements G2lib::BaseCurve.
◆ kappa_begin()
|
inlineoverridevirtual |
Initial curvature.
Reimplemented from G2lib::BaseCurve.
◆ length()
|
inlineoverridevirtual |
The length of the curve
Implements G2lib::BaseCurve.
◆ length_ISO()
The length of the curve with offset (ISO)
Implements G2lib::BaseCurve.
◆ nx_begin_ISO()
|
inlineoverridevirtual |
Intial normal \(x\)-coordinate (ISO).
Reimplemented from G2lib::BaseCurve.
◆ nx_begin_SAE()
|
inline |
Intial normal \(x\)-coordinate (SAE).
◆ nx_end_ISO()
|
inlinevirtual |
Final normal \(x\)-coordinate (ISO).
Reimplemented from G2lib::BaseCurve.
◆ nx_end_SAE()
|
inline |
Final normal \(x\)-coordinate (SAE).
◆ ny_begin_ISO()
|
inlineoverridevirtual |
Intial normal \(y\)-coordinate (ISO).
Reimplemented from G2lib::BaseCurve.
◆ ny_begin_SAE()
|
inline |
Intial normal \(y\)-coordinate (SAE).
◆ ny_end_ISO()
|
inlinevirtual |
Final normal \(y\)-coordinate (ISO).
Reimplemented from G2lib::BaseCurve.
◆ ny_end_SAE()
|
inline |
Intial normal \(y\)-coordinate (SAE).
◆ operator=()
|
inline |
Copy an existing clothoid.
◆ optimized_sample_ISO()
| void G2lib::ClothoidCurve::optimized_sample_ISO | ( | real_type | offs, |
| integer | npts, | ||
| real_type | max_angle, | ||
| vector< real_type > & | s ) const |
Return a vector of optimized sample parameters for plotting.
- Parameters
-
offs offset of the sampled curve npts suggested minimum number of sampled points max_angle maximum angle variation between two sampled points s vector of computed parameters
◆ optimized_sample_SAE()
|
inline |
Return a vector of optimized sample parameters for plotting.
- Parameters
-
offs offset of the sampled curve npts suggested minimum number of sampled points max_angle maximum angle variation between two sampled points s vector of computed parameters
◆ Pinfinity()
|
inline |
Return the point at infinity of the clothoids \( P(s) \).
- Parameters
-
[out] x \(x\)-coordinate of the \(\infty\) point [out] y \(y\)-coordinate of the \(\infty\) point [out] plus it true return \( \lim_{s\to+\infty} P(s) \) otherwise return \( \lim_{s\to-\infty} P(s) \)
◆ reverse()
|
inlineoverridevirtual |
Reverse curve parameterization.
Implements G2lib::BaseCurve.
◆ rotate()
|
inlineoverridevirtual |
Rotate curve by angle \(\theta\) centered at point \((c_x,c_y)\).
- Parameters
-
[in] angle angle \(\theta\) [in] cx \(c_x\) [in] cy \(c_y\)
Implements G2lib::BaseCurve.
◆ scale()
|
inlineoverridevirtual |
Scale curve by factor sc.
Implements G2lib::BaseCurve.
◆ setup()
|
overridevirtual |
Implements G2lib::BaseCurve.
◆ tg()
|
inlineoverridevirtual |
Tangent at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ tg_D()
|
inlineoverridevirtual |
Tangent derivative at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ tg_DD()
|
inlineoverridevirtual |
Tangent second derivative at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ tg_DDD()
|
inlineoverridevirtual |
Tangent third derivative at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ theta()
Get clothoid angle at curvilinear cooordinate s.
- Parameters
-
s curvilinear cooordinate
- Returns
- angle (radiant) at curvilinear cooordinate
s
Implements G2lib::BaseCurve.
◆ theta_begin()
|
inlineoverridevirtual |
Initial angle of the curve.
Reimplemented from G2lib::BaseCurve.
◆ theta_D()
Get clothoid angle derivative (=curvature) at curvilinear cooordinate s.
- Parameters
-
s curvilinear cooordinate
- Returns
- angle derivative (radiant/s) at curvilinear cooordinate
s
Implements G2lib::BaseCurve.
◆ theta_DD()
Get clothoid angle second derivative at curvilinear cooordinate s.
- Returns
- angle second derivative (radiant/s^2) at curvilinear cooordinate
s
Implements G2lib::BaseCurve.
◆ theta_DDD()
Get clothoid angle third derivative at curvilinear cooordinate s.
- Returns
- angle third derivative (radiant/s^3) at curvilinear cooordinate
s
Implements G2lib::BaseCurve.
◆ theta_end()
|
inlinevirtual |
Final angle of the curve.
Reimplemented from G2lib::BaseCurve.
◆ theta_min_max()
Max and min angle of the curve.
◆ theta_total_variation()
| real_type G2lib::ClothoidCurve::theta_total_variation | ( | ) | const |
Clothoid curve total variation of the angle.
◆ translate()
translate curve by \((t_x,t_y)\)
Implements G2lib::BaseCurve.
◆ trim()
Cut curve at parametric coordinate s_begin and s_end.
Implements G2lib::BaseCurve.
◆ tx()
Tangent \(x\)-coordinate at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ tx_begin()
|
inlineoverridevirtual |
Initial tangent \(x\)-coordinate.
Reimplemented from G2lib::BaseCurve.
◆ tx_D()
Tangent derivative \(x\)-coordinate at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ tx_DD()
Tangent second derivative \(x\)-coordinate at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ tx_DDD()
Tangent third derivative \(x\)-coordinate at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ tx_end()
|
inlinevirtual |
Final tangent \(x\)-coordinate.
Reimplemented from G2lib::BaseCurve.
◆ ty()
Tangent \(y\)-coordinate at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ ty_begin()
|
inlineoverridevirtual |
Initial tangent \(y\)-coordinate.
Reimplemented from G2lib::BaseCurve.
◆ ty_D()
Tangent derivative \(y\)-coordinate at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ ty_DD()
Tangent second derivative \(y\)-coordinate at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ ty_DDD()
Tangent third derivative \(y\)-coordinate at curvilinear coordinate \(s\).
Reimplemented from G2lib::BaseCurve.
◆ ty_end()
|
inlinevirtual |
Final tangent \(y\)-coordinate.
Reimplemented from G2lib::BaseCurve.
◆ type()
|
inlineoverridevirtual |
The name of the curve type
Implements G2lib::BaseCurve.
◆ X()
Clothoid \(x\) coordinate at curvilinear coordinate \(s\).
- Parameters
-
s curvilinear coordinate
- Returns
- clothoid \(x\) coordinate
Implements G2lib::BaseCurve.
◆ x_begin()
|
inlineoverridevirtual |
Initial \(x\)-coordinate.
Reimplemented from G2lib::BaseCurve.
◆ x_begin_ISO()
Initial \(x\)-coordinate with offset (ISO standard).
Reimplemented from G2lib::BaseCurve.
◆ x_begin_SAE()
Initial \(x\)-coordinate with offset (SAE standard).
◆ X_D()
\(x\)-coordinate derivative at curvilinear coordinate \(s\).
Implements G2lib::BaseCurve.
◆ X_DD()
\(x\)-coordinate second derivative at curvilinear coordinate \(s\).
Implements G2lib::BaseCurve.
◆ X_DDD()
\(x\)-coordinate third derivative at curvilinear coordinate \(s\).
Implements G2lib::BaseCurve.
◆ x_end()
|
inlineoverridevirtual |
Final \(x\)-coordinate.
Reimplemented from G2lib::BaseCurve.
◆ x_end_ISO()
Final \(x\)-coordinate with offset (ISO standard).
Reimplemented from G2lib::BaseCurve.
◆ x_end_SAE()
Final \(y\)-coordinate with offset (SAE standard).
◆ X_ISO()
Clothoid \(x\) coordinate at curvilinear coordinate \(s\).
- Parameters
-
s curvilinear coordinate offs lateral offset
- Returns
- clothoid \(x\) coordinate
Reimplemented from G2lib::BaseCurve.
◆ X_ISO_D()
\(x\)-coordinate derivative at curvilinear coordinate \(s\) with offset offs (ISO).
Reimplemented from G2lib::BaseCurve.
◆ X_ISO_DD()
|
inlineoverridevirtual |
\(x\)-coordinate second derivative at curvilinear coordinate \(s\) with offset offs (ISO).
Reimplemented from G2lib::BaseCurve.
◆ X_ISO_DDD()
|
inlineoverridevirtual |
\(x\)-coordinate third derivative at curvilinear coordinate \(s\) with offset offs (ISO).
Reimplemented from G2lib::BaseCurve.
◆ X_SAE()
\(x\)-coordinate at curvilinear coordinate \(s\) with offset offs (SAE).
◆ X_SAE_D()
\(x\)-coordinate derivative at curvilinear coordinate \(s\) with offset offs (SAE).
◆ X_SAE_DD()
\(x\)-coordinate second derivative at curvilinear coordinate \(s\) with offset offs (SAE).
◆ X_SAE_DDD()
\(x\)-coordinate third derivative at curvilinear coordinate \(s\) with offset offs (SAE).
◆ Y()
Clothoid \(y\) coordinate at curvilinear coordinate \(s\).
- Parameters
-
s curvilinear coordinate
- Returns
- clothoid \(y\) coordinate
Implements G2lib::BaseCurve.
◆ y_begin()
|
inlineoverridevirtual |
Initial \(y\)-coordinate.
Reimplemented from G2lib::BaseCurve.
◆ y_begin_ISO()
Initial \(y\)-coordinate with offset (ISO standard).
Reimplemented from G2lib::BaseCurve.
◆ y_begin_SAE()
Initial \(y\)-coordinate with offset (SAE standard).
◆ Y_D()
\(y\)-coordinate derivative at curvilinear coordinate \(s\).
Implements G2lib::BaseCurve.
◆ Y_DD()
\(y\)-coordinate second derivative at curvilinear coordinate \(s\).
Implements G2lib::BaseCurve.
◆ Y_DDD()
\(y\)-coordinate third derivative at curvilinear coordinate \(s\).
Implements G2lib::BaseCurve.
◆ y_end()
|
inlineoverridevirtual |
Final \(y\)-coordinate.
Reimplemented from G2lib::BaseCurve.
◆ y_end_ISO()
Final \(y\)-coordinate with offset (ISO standard).
Reimplemented from G2lib::BaseCurve.
◆ y_end_SAE()
Final \(y\)-coordinate with offset (ISO standard).
◆ Y_ISO()
Clothoid \(y\) coordinate at curvilinear coordinate \(s\).
- Parameters
-
s curvilinear coordinate offs lateral offset
- Returns
- clothoid \(y\) coordinate
Reimplemented from G2lib::BaseCurve.
◆ Y_ISO_D()
\(y\)-coordinate derivative at curvilinear coordinate \(s\) with offset offs (ISO).
Reimplemented from G2lib::BaseCurve.
◆ Y_ISO_DD()
|
inlineoverridevirtual |
\(y\)-coordinate second derivative at curvilinear coordinate \(s\) with offset offs (ISO).
Reimplemented from G2lib::BaseCurve.
◆ Y_ISO_DDD()
|
inlineoverridevirtual |
\(y\)-coordinate third derivative at curvilinear coordinate \(s\) with offset offs (ISO).
Reimplemented from G2lib::BaseCurve.
◆ Y_SAE()
\(y\)-coordinate at curvilinear coordinate \(s\) with offset offs (SAE).
◆ Y_SAE_D()
\(y\)-coordinate derivative at curvilinear coordinate \(s\) with offset offs (SAE).
◆ Y_SAE_DD()
\(y\)-coordinate second derivative at curvilinear coordinate \(s\) with offset offs (SAE).
◆ Y_SAE_DDD()
\(y\)-coordinate third derivative at curvilinear coordinate \(s\) with offset offs (SAE).
Friends And Related Symbol Documentation
◆ operator<<
|
friend |
Print on strem the ClothoidCurve object
- Parameters
-
stream the output stream c an instance of ClothoidCurveobject
- 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/Clothoid.hxx
- /Users/enrico/Ricerca/develop/PINS/pins-mechatronix/LibSources/submodules/Clothoids/src/Clothoid.cc
- /Users/enrico/Ricerca/develop/PINS/pins-mechatronix/LibSources/submodules/Clothoids/src/ClothoidDistance.cc
Generated by
1.12.0