API

API

Curve Types

Curve
LineSegment
ArcSegment
Clothoid
PolyCurve

SmoothCurves.Curve — Type.

Abstract base class for all specialized curve types.

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SmoothCurves.LineSegment — Type.
LineSegment(p0, p1)

A line segment starting from p0 and ending at p1. Besides the Curve protocol, also a direction function is implemented, which calculates the unit vector pointing from p0 in direction of p1.

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SmoothCurves.ArcSegment — Type.
ArcSegment(origin, radius, angle0, angle1)

ArcSegment centered at origin with the given radius going from the first to the second angle. As parametrization the angle difference to the starting angle is used.

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SmoothCurves.Clothoid — Type.
Clothoid(origin, shift, rotation, λ, l0, l1)

Describes a clothoid which in standard orientation.

It is here defined as

\[x(s) = \int_0^s \cos(λ t^2) \mathrm{d}t \\ y(s) = \int_0^s \sin(λ t^2) \mathrm{d}t\]

for parameter $s ∈ [l0, l1]$. (Note that l1 may also be smaller to l0). It is placed at origin, shifted along the x-axis and rotated around the origin by the given angle.

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SmoothCurves.PolyCurve — Type.
PolyCurve(curves...)

Collection of curves joined at their start and endpoints.

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Curve Interface

smax
point
startpoint
endpoint
dpoint
length
dlength
curvature
dcurvature
tangentangle
radialangle

SmoothCurves.smax — Function.
smax(C::Curve)

Maximum parameter $s$ for which the given curve $\mathcal{C}$ is defined.

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SmoothCurves.point — Function.
point(C::Curve, s)

Point (x, y) of the curve $\mathcal{C}$ at $s$. Returns a StaticArrays.SVector.

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SmoothCurves.startpoint — Function.
startpoint(C::Curve)

Return the first point $C(0)$ of the curve.

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SmoothCurves.endpoint — Function.
endpoint(C::Curve)

Return the last point $C(s_\mathrm{max}$ of the curve.

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SmoothCurves.dpoint — Function.
dpoint(C::Curve, s)

Derivative $\frac{dC(s)}{ds}$ of the curve $\mathcal{C}$ at $s$. Returns a StaticArrays.SVector.

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Base.length — Function.
length(C::Curve, s)

Length of the given curve $\mathcal{C}$ between $0$ and $s$.

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length(C::Curve)

Total length of the given curve. Equal to length(C, smax(C)).

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SmoothCurves.dlength — Function.
dlength(C::Curve, s)

Derivative $\frac{dl}{ds}$ at $s$.

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SmoothCurves.curvature — Function.
curvature(C::Curve, s)

Curvature of the Curve $\mathcal{C}$ at $s$.

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SmoothCurves.dcurvature — Function.
dcurvature(C::Curve, s)

Derivative $\frac{dκ}{ds}$ of the curve $\mathcal{C}$ at $s$.

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SmoothCurves.tangentangle — Function.
tangentangle(C::Curve, s)

Angle between the tangent of the curve $\mathcal{C}$ at $s$ and the $x$-axis. Always between $-π$ and $π$.

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SmoothCurves.radialangle — Function.
radialangle(C::Curve, s)

Angle between the radial vector of the curve $\mathcal{C}$ at $s$ and the $x$-axis. Always between $-π$ and $π$.

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Curve specific functions

LineSegment

SmoothCurves.direction — Method.
direction(C::LineSegment)

Returns the unitvector from the start point to the endpoint of the line segment.

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ArcSegment

Base.sign — Method.
sign(C::ArcSegment)

Sign of the curvature of the ArcSegment.

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Clothoid

SmoothCurves.fresnel — Function.
fresnel(λ, s)

Solve the generalized Fresnel integrals

\[x(s) = \int_0^s \cos(λ t^2) \mathrm{d}t \\ y(s) = \int_0^s \sin(λ t^2) \mathrm{d}t\]
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SmoothCurves.standardlength — Function.
l(C::Clothoid, s)

Signed distance to the origin of the Clothoid.

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PolyCurve

SmoothCurves.subcurveindex — Function.
subcurveindex(C::PolyCurve, s)

Index of the subcurve reached at the given parameter s.

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SmoothCurves.subcurveparameter — Function.
subcurveparameter(C::PolyCurve, s)

Parameter $s_i$ for which $C(s)=C_i(s_i)$

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SmoothCurves.dispatch — Function.
dispatch(f, C::PolyCurve, s::Real)

Apply function f to appropriate subcurve i.e. $f(C_i, s_i)$.

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Frenet Frame

SmoothCurves.frenet.coordinates — Function.
frenet.coordinates(p0::Pose, p::Pose)

Coordinates of p in the Frenet frame defined by p0.

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frenet.coordinates(C::Curve, s, p::Pose)

Coordinates of p in the Frenet frame at $C(s)$.

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