CubicSpline2d

A CubicSpline2d is a cubic Bézier curve in 2D defined by a start point, end point and two control points. This module contains functionality for

Constructing splines
Evaluating points and tangent directions along a spline
Scaling, rotating, translating or mirroring a spline
Converting a spline between local and global coordinates in different reference frames

type alias CubicSpline2d =

CubicSpline2d

Constructors

with :

{ startPoint : Point2d

, startControlPoint : Point2d

, endControlPoint : Point2d

, endPoint : Point2d

}

-> CubicSpline2d

fromEndpoints :

{ startPoint : Point2d

, startDerivative : Vector2d

, endPoint : Point2d

, endDerivative : Vector2d

}

-> CubicSpline2d

fromQuadraticSpline : QuadraticSpline2d -> CubicSpline2d

Properties

startPoint : CubicSpline2d -> Point2d

endPoint : CubicSpline2d -> Point2d

startControlPoint : CubicSpline2d -> Point2d

endControlPoint : CubicSpline2d -> Point2d

startDerivative : CubicSpline2d -> Vector2d

endDerivative : CubicSpline2d -> Vector2d

boundingBox : CubicSpline2d -> BoundingBox2d

Evaluation

pointOn : CubicSpline2d -> ParameterValue -> Point2d

pointsAt : List ParameterValue -> CubicSpline2d -> List Point2d

type Nondegenerate

nondegenerate : CubicSpline2d -> Result Point2d Nondegenerate

fromNondegenerate : Nondegenerate -> CubicSpline2d

tangentDirection : Nondegenerate -> ParameterValue -> Direction2d

tangentDirectionsAt : List ParameterValue -> Nondegenerate -> List Direction2d

sample : Nondegenerate -> ParameterValue -> ( Point2d, Direction2d )

samplesAt :

List ParameterValue

-> Nondegenerate

-> List ( Point2d, Direction2d )

Transformations

reverse : CubicSpline2d -> CubicSpline2d

scaleAbout : Point2d -> Float -> CubicSpline2d -> CubicSpline2d

rotateAround : Point2d -> Float -> CubicSpline2d -> CubicSpline2d

translateBy : Vector2d -> CubicSpline2d -> CubicSpline2d

translateIn : Direction2d -> Float -> CubicSpline2d -> CubicSpline2d

mirrorAcross : Axis2d -> CubicSpline2d -> CubicSpline2d

Coordinate conversions

relativeTo : Frame2d -> CubicSpline2d -> CubicSpline2d

placeIn : Frame2d -> CubicSpline2d -> CubicSpline2d

Subdivision

bisect : CubicSpline2d -> ( CubicSpline2d, CubicSpline2d )

splitAt : ParameterValue -> CubicSpline2d -> ( CubicSpline2d, CubicSpline2d )

Arc length parameterization

type ArcLengthParameterized

arcLengthParameterized : { maxError : Float } -> CubicSpline2d -> ArcLengthParameterized

arcLength : ArcLengthParameterized -> Float

pointAlong : ArcLengthParameterized -> Float -> Maybe Point2d

tangentDirectionAlong : ArcLengthParameterized -> Float -> Maybe Direction2d

sampleAlong : ArcLengthParameterized -> Float -> Maybe ( Point2d, Direction2d )

Low level

An ArcLengthParameterized value is a combination of an ArcLengthParameterization and an underlying CubicSpline2d. If you need to do something fancy, you can extract these two values separately.

arcLengthParameterization : ArcLengthParameterized -> ArcLengthParameterization

fromArcLengthParameterized : ArcLengthParameterized -> CubicSpline2d

Differentiation

You are unlikely to need to use these functions directly, but they are useful if you are writing low-level geometric algorithms.

firstDerivative : CubicSpline2d -> ParameterValue -> Vector2d

firstDerivativesAt : List ParameterValue -> CubicSpline2d -> List Vector2d

secondDerivative : CubicSpline2d -> ParameterValue -> Vector2d

secondDerivativesAt : List ParameterValue -> CubicSpline2d -> List Vector2d

thirdDerivative : CubicSpline2d -> Vector2d

maxSecondDerivativeMagnitude : CubicSpline2d -> Float

opensolid/geometry/3.0.1

CubicSpline2d

Constructors

Properties

Evaluation

Transformations

Coordinate conversions

Subdivision

Arc length parameterization

Low level

Differentiation

Modules