CubicSpline3d

A CubicSpline3d is a cubic Bézier curve in 3D defined by a start point, end point and two control points. This module contains functionality for

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

type alias CubicSpline3d =

CubicSpline3d

Constructors

with :

{ startPoint : Point3d

, startControlPoint : Point3d

, endControlPoint : Point3d

, endPoint : Point3d

}

-> CubicSpline3d

fromEndpoints :

{ startPoint : Point3d

, startDerivative : Vector3d

, endPoint : Point3d

, endDerivative : Vector3d

}

-> CubicSpline3d

on : SketchPlane3d -> CubicSpline2d -> CubicSpline3d

fromQuadraticSpline : QuadraticSpline3d -> CubicSpline3d

Properties

startPoint : CubicSpline3d -> Point3d

endPoint : CubicSpline3d -> Point3d

startControlPoint : CubicSpline3d -> Point3d

endControlPoint : CubicSpline3d -> Point3d

startDerivative : CubicSpline3d -> Vector3d

endDerivative : CubicSpline3d -> Vector3d

boundingBox : CubicSpline3d -> BoundingBox3d

Evaluation

pointOn : CubicSpline3d -> ParameterValue -> Point3d

pointsAt : List ParameterValue -> CubicSpline3d -> List Point3d

type Nondegenerate

nondegenerate : CubicSpline3d -> Result Point3d Nondegenerate

fromNondegenerate : Nondegenerate -> CubicSpline3d

tangentDirection : Nondegenerate -> ParameterValue -> Direction3d

tangentDirectionsAt : List ParameterValue -> Nondegenerate -> List Direction3d

sample : Nondegenerate -> ParameterValue -> ( Point3d, Direction3d )

samplesAt :

List ParameterValue

-> Nondegenerate

-> List ( Point3d, Direction3d )

Transformations

reverse : CubicSpline3d -> CubicSpline3d

scaleAbout : Point3d -> Float -> CubicSpline3d -> CubicSpline3d

rotateAround : Axis3d -> Float -> CubicSpline3d -> CubicSpline3d

translateBy : Vector3d -> CubicSpline3d -> CubicSpline3d

translateIn : Direction3d -> Float -> CubicSpline3d -> CubicSpline3d

mirrorAcross : Plane3d -> CubicSpline3d -> CubicSpline3d

projectOnto : Plane3d -> CubicSpline3d -> CubicSpline3d

Coordinate conversions

relativeTo : Frame3d -> CubicSpline3d -> CubicSpline3d

placeIn : Frame3d -> CubicSpline3d -> CubicSpline3d

projectInto : SketchPlane3d -> CubicSpline3d -> CubicSpline2d

Subdivision

bisect : CubicSpline3d -> ( CubicSpline3d, CubicSpline3d )

splitAt : ParameterValue -> CubicSpline3d -> ( CubicSpline3d, CubicSpline3d )

Arc length parameterization

type ArcLengthParameterized

arcLengthParameterized : { maxError : Float } -> CubicSpline3d -> ArcLengthParameterized

arcLength : ArcLengthParameterized -> Float

pointAlong : ArcLengthParameterized -> Float -> Maybe Point3d

tangentDirectionAlong : ArcLengthParameterized -> Float -> Maybe Direction3d

sampleAlong : ArcLengthParameterized -> Float -> Maybe ( Point3d, Direction3d )

Low level

An ArcLengthParameterized value is a combination of an ArcLengthParameterization and an underlying CubicSpline3d. If you need to do something fancy, you can extract these two values separately.

arcLengthParameterization : ArcLengthParameterized -> ArcLengthParameterization

fromArcLengthParameterized : ArcLengthParameterized -> CubicSpline3d

Differentiation

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

firstDerivative : CubicSpline3d -> ParameterValue -> Vector3d

firstDerivativesAt : List ParameterValue -> CubicSpline3d -> List Vector3d

secondDerivative : CubicSpline3d -> ParameterValue -> Vector3d

secondDerivativesAt : List ParameterValue -> CubicSpline3d -> List Vector3d

thirdDerivative : CubicSpline3d -> Vector3d

maxSecondDerivativeMagnitude : CubicSpline3d -> Float

ianmackenzie/elm-geometry/1.0.0

CubicSpline3d

Constructors

Properties

Evaluation

Transformations

Coordinate conversions

Subdivision

Arc length parameterization

Low level

Differentiation

Modules