Detailed Description

Defines a class for a path in a Segment object surface.

The path is defined by an elevation and superelevation Function objects and a GroundCurve reference curve. The latter is a C1 function in the z=0 plane. Its domain is constrained in \( [GroundCurve::p0(); GroundCurve::p1()] \) interval and it should map a ℝ² curve. As per notation, \( p \) is the parameter of the reference curve, not necessarily arc length \( s \), and function interpolations and function derivatives as well as headings and heading derivatives are expressed in INERTIAL Frame coordinates.

The geometry here revolves around an abstract "world function"

\( W: (p,r,h) \mapsto (x,y,z) ∈ ℝ³ \)

which maps a Lane-frame position to its corresponding representation in world coordinates (with the caveat that instead of the lane's native longitudinal coordinate 's', the reference curve parameter 'p' is used).

W is derived from three functions which define the lane:

G: p --> (x,y) = the reference ground curve. Z: p --> z = the elevation function. Θ: p --> θ = the superelevation function.

as:

(x,y,z) = W(p,r,h) = (G(p), Z(p)) + R_αβγ*(0, r, h)

where:

R_αβγ is the roll/pitch/yaw rotation given by angles:

α = Θ(p) β = -atan2(dZ/dp, sqrt((dG_x/dp)^2 + (dG_y/dp)^2)) at p γ = atan2(dG_y/dp, dG_x/dp) at p

(R_αβγ is essentially the orientation of the (s,r,h) Lane-frame at a location (s,0,0) on the reference-line of the lane. However, it is not necessarily the correct orientation at r != 0 or h != 0.)

The W(p,r,h) "world function" is defined by the RoadCurve referenced by a Lane's Segment. A Lane is also defined by a r0 lateral offset with respect to the reference curve of the RoadCurve. Thus, a mapping from the local (s,r,h) lane-frame of the Lane becomes:

(x,y,z) = L(s,r,h) = W(P(s, r0), r + r0, h),

where P:(s, r0) --> (p) is a (potentially non-linear) function dependent on the RoadCurve's reference-curve, elevation, and superelevation functions.

#include <src/maliput_malidrive/road_curve/road_curve.h>

Public Member Functions
	MALIDRIVE_NO_COPY_NO_MOVE_NO_ASSIGN (RoadCurve)

	RoadCurve (double linear_tolerance, double scale_length, std::unique_ptr< GroundCurve > ground_curve, std::unique_ptr< Function > elevation, std::unique_ptr< Function > superelevation, bool assert_contiguity)
	Constructs a RoadCurve. More...

	~RoadCurve ()=default

double	p0 () const

double	p1 () const

double	LMax () const

double	linear_tolerance () const

double	scale_length () const

maliput::math::Vector3	W (const maliput::math::Vector3 &prh) const
	Evaluates \( W(p, r, h) \). More...

maliput::math::Vector3	WDot (const maliput::math::Vector3 &prh) const
	Evaluates \( W'(p, r, h) \) with respect to \( p \). More...

maliput::math::Vector3	WDot (const maliput::math::Vector3 &prh, const Function *lane_offset) const
	Evaluates \( W'(p, r, h) \) with respect to \( p \). More...

maliput::math::RollPitchYaw	Orientation (double p) const
	Evaluates the orientation in the INERTIAL Frame of the RoadCurve at `p`, i.e. More...

maliput::math::RollPitchYaw	Orientation (const maliput::math::Vector3 &prh) const
	Evaluates the orientation in the INERTIAL Frame of the RoadCurve at `prh`. More...

maliput::math::RollPitchYaw	Orientation (const maliput::math::Vector3 &prh, const Function *lane_offset) const
	Evaluates the orientation in the INERTIAL Frame of the RoadCurve at `prh`. More...

maliput::math::Vector3	WInverse (const maliput::math::Vector3 &xyz) const
	Evaluates \( W⁻¹(x, y, z) \). More...

maliput::math::Vector3	SHat (const maliput::math::Vector3 &prh, const Function *lane_offset) const
	Evaluates \( W'(p, r, h) / \|W'(p, r, h)\|` with respect to \) p \(. @param prh A vector in the RoadCurve domain. @return A normalized tangent vector in the direction of increasing \) p \( at @p prh. maliput::math::Vector3 SHat(const maliput::math::Vector3& prh) const; Evaluates \) W'(p, r, h) / \|W'(p, r, h)\|` with respect to \( p \). More...

maliput::math::Vector3	RHat (const maliput::math::Vector3 &prh) const
	Evaluates the r-axis unit vector at \( (p, r, h) \). More...

maliput::math::Vector3	RHat (const maliput::math::Vector3 &prh, const Function *lane_offset) const
	Evaluates the r-axis unit vector at \( (p, r, h) \). More...

maliput::math::Vector3	HHat (double p, const maliput::math::Vector3 &s_hat) const
	Evaluates the h-axis unit vector at \( (p, r, h) \). More...

double	PFromP (double xodr_p) const
	Calculates the \( p \) value that matches with the \( p \) value in the XODR description. More...

Constructor & Destructor Documentation

◆ RoadCurve()

RoadCurve	(	double	linear_tolerance,
		double	scale_length,
		std::unique_ptr< GroundCurve >	ground_curve,
		std::unique_ptr< Function >	elevation,
		std::unique_ptr< Function >	superelevation,
		bool	assert_contiguity
	)

Constructs a RoadCurve.

Parameters

linear_tolerance	It is expected to be the same as maliput::api::RoadGeometry::linear_tolerance(). It must be non negative. It is used to integrate an offset RoadCurve's arc length and adjust integration parameters accordingly.
scale_length	It is expected to be the same as maliput::api::RoadGeometry::scale_length(). It must be non negative. It is used to integrate an offset RoadCurve's arc length and adjust integration parameters accordingly.
ground_curve	The reference GroundCurve of this RoadCurve. It must not be nullptr and must be G¹.
elevation	The elevation Function of this RoadCurve. It must not be nullptr.
superelevation	The superelevation Function of this RoadCurve. It must not be nullptr.
assert_contiguity	True for assert contiguity for `elevation` and `superelevation` functions.

Exceptions

maliput::common::assertion_error	When `linear_tolerance` or `scale_length` are negative.
maliput::common::assertion_error	When `ground_curve` or `elevation` or `superelevation` are nullptr.
maliput::common::assertion_error	When `ground_curve` or `elevation` or `superelevation` are not G¹.
maliput::common::assertion_error	When `ground_curve` is not G¹.
maliput::common::assertion_error	When `ground_curve`, `elevation` and `superelevation` do not share the same range within `linear_tolerance`.

◆ ~RoadCurve()

~RoadCurve ( )

default

Member Function Documentation

◆ HHat()

maliput::math::Vector3 HHat	(	double	p,
		const maliput::math::Vector3 &	s_hat
	)		const

Evaluates the h-axis unit vector at \( (p, r, h) \).

Parameters

p	The GroundCurve parameter.
s_hat	A normalized tangent vector in the direction of increasing \( p \).

Returns: A normalized tangent vector in the direction of increasing \( h \) at p, i.e. at \( (p, 0, 0) \). It is orthogonal to s_hat by construction.

Exceptions

maliput::common::assertion_error	When `lane_offset` is nullptr.
maliput::common::assertion_error	When `p` is not in range [p0, p1].

◆ linear_tolerance()

double linear_tolerance ( ) const

Returns: The linear tolerance used to compute all the methods.

See also: maliput::api::RoadGeometry::linear_tolerance().

◆ LMax()

double LMax ( ) const

◆ MALIDRIVE_NO_COPY_NO_MOVE_NO_ASSIGN()

MALIDRIVE_NO_COPY_NO_MOVE_NO_ASSIGN ( RoadCurve )

◆ Orientation() [1/3]

maliput::math::RollPitchYaw Orientation ( const maliput::math::Vector3 & prh ) const

Evaluates the orientation in the INERTIAL Frame of the RoadCurve at prh.

Parameters

prh	A vector in the RoadCurve domain.

Returns: The orientation in the INERTIAL Frame of the RoadCurve at prh.

◆ Orientation() [2/3]

maliput::math::RollPitchYaw Orientation	(	const maliput::math::Vector3 &	prh,
		const Function *	lane_offset
	)		const

Evaluates the orientation in the INERTIAL Frame of the RoadCurve at prh.

Parameters

prh	A vector in the RoadCurve domain.
lane_offset	Holds the function, \( r(p) \), that describes the lateral offset at p. Used to calculate the derivative at `prh`.

Returns: The orientation in the INERTIAL Frame of the RoadCurve at prh.

Exceptions

maliput::common::assertion_error	When `lane_offset` is nullptr.
maliput::common::assertion_error	When `prh` .x() is not in range [p0, p1].

◆ Orientation() [3/3]

maliput::math::RollPitchYaw Orientation ( double p ) const

Evaluates the orientation in the INERTIAL Frame of the RoadCurve at p, i.e.

at \( (p, 0, 0) \).

Parameters

p	The GroundCurve parameter.

Returns: The orientation in the INERTIAL Frame of the RoadCurve at p.

◆ p0()

double p0 ( ) const

◆ p1()

double p1 ( ) const

◆ PFromP()

double PFromP ( double xodr_p ) const

Calculates the \( p \) value that matches with the \( p \) value in the XODR description.

Parameters

xodr_p The parameter in the XODR description.

Returns: The \( p \) value in the GroundCurve domain.

◆ RHat() [1/2]

maliput::math::Vector3 RHat ( const maliput::math::Vector3 & prh ) const

Evaluates the r-axis unit vector at \( (p, r, h) \).

Parameters

prh	A vector in the RoadCurve domain.

Returns: A normalized vector pointing in the direction of increasing \( r \) coordinate at prh.

◆ RHat() [2/2]

maliput::math::Vector3 RHat	(	const maliput::math::Vector3 &	prh,
		const Function *	lane_offset
	)		const

Evaluates the r-axis unit vector at \( (p, r, h) \).

Parameters

prh	A vector in the RoadCurve domain.
lane_offset	Holds the function, \( r(p) \), that describes the lateral offset at p. Used to calculate the derivative at `prh`.

Returns: A normalized tangent vector in the direction of increasing \( r \) at prh.

Exceptions

maliput::common::assertion_error	When `lane_offset` is nullptr.
maliput::common::assertion_error	When `prh` .x() is not in range [p0, p1].

◆ scale_length()

double scale_length ( ) const

Returns: The scale length of the tolerance used to compute all the methods.

See also: maliput::api::RoadGeometry::scale_length().

◆ SHat()

maliput::math::Vector3 SHat	(	const maliput::math::Vector3 &	prh,
		const Function *	lane_offset
	)		const

Evaluates \( W'(p, r, h) / |W'(p, r, h)|` with respect to \) p \(. @param prh A vector in the RoadCurve domain. @return A normalized tangent vector in the direction of increasing \) p \( at @p prh. maliput::math::Vector3 SHat(const maliput::math::Vector3& prh) const; Evaluates \) W'(p, r, h) / |W'(p, r, h)|` with respect to \( p \).

Parameters

prh	A vector in the RoadCurve domain.
lane_offset	Holds the function, \( r(p) \), that describes the lateral offset at p. Used to calculate the derivative at `prh`.

Returns: A normalized tangent vector in the direction of increasing \( p \) at prh.

Exceptions

maliput::common::assertion_error	When `lane_offset` is nullptr.
maliput::common::assertion_error	When `prh` .x() is not in range [p0, p1].

◆ W()

maliput::math::Vector3 W ( const maliput::math::Vector3 & prh ) const

Evaluates \( W(p, r, h) \).

Parameters

prh	A vector in the RoadCurve domain.

Returns: A vector in the INERTIAL Frame which is the image of the RoadCurve.

◆ WDot() [1/2]

maliput::math::Vector3 WDot ( const maliput::math::Vector3 & prh ) const

Evaluates \( W'(p, r, h) \) with respect to \( p \).

Parameters

prh	A vector in the RoadCurve domain.

Returns: The derivative of \( W \) with respect to \( p \) at prh.

◆ WDot() [2/2]

maliput::math::Vector3 WDot	(	const maliput::math::Vector3 &	prh,
		const Function *	lane_offset
	)		const

Evaluates \( W'(p, r, h) \) with respect to \( p \).

Note: Recall that W is the lane-to-world transform, defined by \( (x,y,z) = W(p,r,h) = (G(p), Z(p)) + R_{αβγ}*(0,r(p),h) \)
where \( G \) is the reference curve, \( Z \) is the elevation profile, and \( R_{αβγ} \) is a rotation matrix derived from reference curve (heading), elevation, and superelevation. Thus:; \( ∂W/∂p = (∂G(p)/∂p, ∂Z(p)/∂p) + (∂R_{αβγ}/∂p)*(0,r(p),h) + R_{αβγ}*∂(0,r(p),0)/∂p \),
where:
\( ∂G(p)/∂p = G'(p) \)
\( ∂Z(p)/∂p = Z'(p) \)
\( ∂R_{αβγ}/∂p = (∂R_{αβγ}/∂α ∂R_{αβγ}/∂β ∂R_{αβγ}/∂γ)*(dα/dp, dβ/dp, dγ/dp) \)

Parameters

prh	A vector in the RoadCurve domain.
lane_offset	Holds the function, \( r(p) \), that describes the lateral offset at p. Used to calculate the derivative at `prh`.

Returns: The derivative of \( W \) with respect to \( p \) at prh.

Exceptions

maliput::common::assertion_error	When `lane_offset` is nullptr.
maliput::common::assertion_error	When `prh` .x() is not in range [p0, p1].
maliput::common::assertion_error	When `lane_offset` ->p0() is not in range [p0, p1].
maliput::common::assertion_error	When `lane_offset` ->p1() is not in range [p0, p1].

◆ WInverse()

maliput::math::Vector3 WInverse ( const maliput::math::Vector3 & xyz ) const

Evaluates \( W⁻¹(x, y, z) \).

Parameters

xyz	A point in ℝ³ that would be used to minimize the Euclidean distance the image of \( W \).

Returns: A vector in RoadCurve's domain whose image through \( W \) would minimize the Euclidean distance to xyz.

The documentation for this class was generated from the following files:

Detailed Description

Public Member Functions

Constructor & Destructor Documentation

◆ RoadCurve()

◆ ~RoadCurve()

Member Function Documentation

◆ HHat()

◆ linear_tolerance()

◆ LMax()

◆ MALIDRIVE_NO_COPY_NO_MOVE_NO_ASSIGN()

◆ Orientation() [1/3]

◆ Orientation() [2/3]

◆ Orientation() [3/3]

◆ p0()

◆ p1()

◆ PFromP()

◆ RHat() [1/2]

◆ RHat() [2/2]

◆ scale_length()

◆ SHat()

◆ W()

◆ WDot() [1/2]

◆ WDot() [2/2]

◆ WInverse()