Navigation/com.amarcolini.joos.path/ParametricCurve

ParametricCurve

abstract class ParametricCurve

Parametric curve with two components (x and y). These curves are reparameterized from an internal parameter (t) to the arc length parameter (s). Note that the arc length reparameterization is lazy, meaning that it is computed only when needed. To precompute, use reparameterize.

Inheritors

Constructors

ParametricCurve

constructor()

Types

ArcLengthParameterization

inner class ArcLengthParameterization(tLo: Double, tHi: Double, maxSegmentLength: Double = 0.25, maxDepth: Int = 15, maxDeltaK: Double = 0.01)

Automatically reparameterizes this curve by computing many small samples. This is computationally expensive and should be avoided unless no faster way is available.

Functions

fun curvature(s: Double, t: Double = reparam(s)): Double

Computes the curvature of a parametric curve at the internal parameter t.

fun deriv(s: Double, t: Double = reparam(s)): Vector2d

Returns the derivative s units along the curve.

fun end(): Vector2d

Returns the end vector.

fun endDeriv(): Vector2d

Returns the end derivative.

fun endSecondDeriv(): Vector2d

Returns the end second derivative.

fun endThirdDeriv(): Vector2d

Returns the end third derivative.

operator fun get(s: Double, t: Double = reparam(s)): Vector2d

Returns the vector s units along the curve.

abstract fun length(): Double

Returns the length of the curve.

open fun project(query: Vector2d): Double

Returns the nearest point on the curve in terms of the internal parameter t.

abstract fun reparameterize()

If this curve can not trivially be reparameterized to an arc length parameter, it should be done here.

fun secondDeriv(s: Double, t: Double = reparam(s)): Vector2d

Returns the second derivative s units along the curve.

fun start(): Vector2d

Returns the start vector.

fun startDeriv(): Vector2d

Returns the start vector.

startSecondDeriv

fun startSecondDeriv(): Vector2d

Returns the start second derivative.

startThirdDeriv

fun startThirdDeriv(): Vector2d

Returns the start third derivative.

fun tangentAngle(s: Double, t: Double = reparam(s)): Angle

Returns the angle of the tangent line s units along the curve.

tangentAngleDeriv

fun tangentAngleDeriv(s: Double, t: Double = reparam(s)): Angle

Returns the derivative of the tangent angle s units along the curve.

tangentAngleSecondDeriv

fun tangentAngleSecondDeriv(s: Double, t: Double = reparam(s)): Angle

Returns the second derivative of the tangent angle s units along the curve.

fun thirdDeriv(s: Double, t: Double = reparam(s)): Vector2d

Returns the third derivative s units along the curve.