Class ExMLerps

See ExM. This class contains functions related to lerping and smoothing.

Inheritance
System.Object
ExMLerps
Inherited Members
System.Object.ToString()
System.Object.Equals(System.Object)
System.Object.Equals(System.Object, System.Object)
System.Object.ReferenceEquals(System.Object, System.Object)
System.Object.GetHashCode()
System.Object.GetType()
System.Object.MemberwiseClone()
Namespace: Danmokou.DMath.Functions
Assembly: cs.temp.dll.dll
Syntax
public static class ExMLerps

Methods

Bezier<T>(TEx<T>, TEx<T>, TEx<T>, TEx<Single>)

Perform a quadratic bezier interpolation.

Declaration
public static TEx<T> Bezier<T>(TEx<T> start, TEx<T> ctrl, TEx<T> end, TEx<float> time)
Parameters
Type Name Description
TEx<T> start

Starting point
TEx<T> ctrl

Control point
TEx<T> end

Ending point
TEx<System.Single> time

0-1 lerp controller (automatically clamped)
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

Bezier3<T>(TEx<T>, TEx<T>, TEx<T>, TEx<T>, TEx<Single>)

Perform a cubic bezier interpolation between points in N-dimensional space.
This is the same as CalcBezier in BagoumLib when start=0 and end=1.
This is not the same as the cubic bezier interpolation used in CSS and most animation engines. For that functionality, use CubicBezier.

Declaration
public static TEx<T> Bezier3<T>(TEx<T> start, TEx<T> ctrl1, TEx<T> ctrl2, TEx<T> end, TEx<float> time)
Parameters
Type Name Description
TEx<T> start

Starting point
TEx<T> ctrl1

First control point
TEx<T> ctrl2

Second control point
TEx<T> end

Ending point
TEx<System.Single> time

0-1 lerp controller (automatically clamped)
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

CubicBezier(ExBPY, ExBPY, ExBPY, ExBPY, ExBPY)

Perform a cubic bezier easing interpolation using the same logic as cubic-bezier in CSS.
This is significantly more computationally expensive than other bezier methods since it requires calculating the roots of the bezier function.
For optimization purposes, it is required that both control coordinates reduce to constants.

Declaration
public static ExBPY CubicBezier(ExBPY time1, ExBPY prog1, ExBPY time2, ExBPY prog2, ExBPY time)
Parameters
Type Name Description
ExBPY time1

Time of first control point
ExBPY prog1

Progression of first control point
ExBPY time2

Time of first control point
ExBPY prog2

Progression of first control point
ExBPY time

0-1 lerp controller (automatically clamped)
Returns
Type Description
ExBPY

CubicBezierLerp<T>(ExBPY, ExBPY, ExBPY, ExBPY, ExBPY, Func<TExArgCtx, TEx<T>>, Func<TExArgCtx, TEx<T>>)

Declaration
public static Func<TExArgCtx, TEx<T>> CubicBezierLerp<T>(ExBPY time1, ExBPY prog1, ExBPY time2, ExBPY prog2, ExBPY time, Func<TExArgCtx, TEx<T>> f1, Func<TExArgCtx, TEx<T>> f2)
Parameters
Type Name Description
ExBPY time1
ExBPY prog1
ExBPY time2
ExBPY prog2
ExBPY time
System.Func<TExArgCtx, TEx<T>> f1
System.Func<TExArgCtx, TEx<T>> f2
Returns
Type Description
System.Func<TExArgCtx, TEx<T>>
Type Parameters
Name Description
T

Damp(tfloat, tfloat, tfloat)

Provide a soft ceiling for the value, multiplying any excess by the value RATIO.

Declaration
public static tfloat Damp(tfloat ceiling, tfloat ratio, tfloat value)
Parameters
Type Name Description
tfloat ceiling
tfloat ratio
tfloat value
Returns
Type Description
tfloat

Ease<T>(Func<TExArgCtx, TEx<Func<Single, Single>>>, Single, Func<TExArgCtx, TEx<T>>)

Apply a ease function on top of a target function that uses time as a controller.

Declaration
public static Func<TExArgCtx, TEx<T>> Ease<T>(Func<TExArgCtx, TEx<Func<float, float>>> smoother, float maxTime, Func<TExArgCtx, TEx<T>> f)
Parameters
Type Name Description
System.Func<TExArgCtx, TEx<System.Func<System.Single, System.Single>>> smoother

Smoothing function (ExMEasers)
System.Single maxTime

Time over which to perform easing
System.Func<TExArgCtx, TEx<T>> f

Target parametric (describing offset)
Returns
Type Description
System.Func<TExArgCtx, TEx<T>>
Type Parameters
Name Description
T

EaseD<T>(String, Single, Func<TExArgCtx, TEx<T>>)

Apply a ease function on top of a target derivative function that uses time as a controller. Primarily used for velocity parametrics.

Declaration
public static Func<TExArgCtx, TEx<T>> EaseD<T>(string smoother, float maxTime, Func<TExArgCtx, TEx<T>> f)
Parameters
Type Name Description
System.String smoother

Name of a float->float smoothing function (ExMEasers)
System.Single maxTime

Time over which to perform easing
System.Func<TExArgCtx, TEx<T>> f

Target parametric (describing velocity)
Returns
Type Description
System.Func<TExArgCtx, TEx<T>>
Type Parameters
Name Description
T

EQuad0m10(tfloat, tfloat, tfloat)

Quadratic function that joins an ease-out and an ease-in, ie. two joined parabolas.

Declaration
public static tfloat EQuad0m10(tfloat midp, tfloat period, tfloat controller)
Parameters
Type Name Description
tfloat midp
tfloat period
tfloat controller
Returns
Type Description
tfloat

Lerp<T>(tfloat, tfloat, tfloat, TEx<T>, TEx<T>)

Lerp between two functions.
Note: Unless marked otherwise, all lerp functions clamp the controller.

Declaration
public static TEx<T> Lerp<T>(tfloat zeroBound, tfloat oneBound, tfloat controller, TEx<T> f1, TEx<T> f2)
Parameters
Type Name Description
tfloat zeroBound

Lower bound for lerp controller
tfloat oneBound

Upper bound for lerp controller
tfloat controller

Lerp controller
TEx<T> f1

First function (when controller leq zeroBound, return this)
TEx<T> f2

Second function (when controller geq oneBound, return this)
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

Lerp01<T>(tfloat, TEx<T>, TEx<T>)

Lerp between two functions with 0-1 as the bounds for the controller.

Declaration
public static TEx<T> Lerp01<T>(tfloat controller, TEx<T> f1, TEx<T> f2)
Parameters
Type Name Description
tfloat controller
TEx<T> f1
TEx<T> f2
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

Lerp01U<T>(tfloat, TEx<T>, TEx<T>)

Lerp between two functions with 0-1 as the bounds for the controller. The controller is not clamped.

Declaration
public static TEx<T> Lerp01U<T>(tfloat controller, TEx<T> f1, TEx<T> f2)
Parameters
Type Name Description
tfloat controller
TEx<T> f1
TEx<T> f2
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

Lerp3<T>(tfloat, tfloat, tfloat, tfloat, tfloat, TEx<T>, TEx<T>, TEx<T>)

Lerp between three functions. Between zeroBound and oneBound, lerp from the first to the second. Between zeroBound2 and oneBound2, lerp from the second to the third.

Declaration
public static TEx<T> Lerp3<T>(tfloat zeroBound, tfloat oneBound, tfloat zeroBound2, tfloat oneBound2, tfloat controller, TEx<T> f1, TEx<T> f2, TEx<T> f3)
Parameters
Type Name Description
tfloat zeroBound
tfloat oneBound
tfloat zeroBound2
tfloat oneBound2
tfloat controller
TEx<T> f1
TEx<T> f2
TEx<T> f3
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

Lerp3c<T>(tfloat, tfloat, tfloat, tfloat, TEx<T>, TEx<T>, TEx<T>)

Lerp between three functions. Between zeroBound and oneBound, lerp from the first to the second. Between oneBound and twoBound, lerp from the second to the third.

Declaration
public static TEx<T> Lerp3c<T>(tfloat zeroBound, tfloat oneBound, tfloat twoBound, tfloat controller, TEx<T> f1, TEx<T> f2, TEx<T> f3)
Parameters
Type Name Description
tfloat zeroBound
tfloat oneBound
tfloat twoBound
tfloat controller
TEx<T> f1
TEx<T> f2
TEx<T> f3
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

Lerp4<T>(tfloat, tfloat, tfloat, tfloat, tfloat, tfloat, tfloat, TEx<T>, TEx<T>, TEx<T>, TEx<T>)

Lerp between four functions. Between zeroBound and oneBound, lerp from the first to the second. Between zeroBound2 and oneBound2, lerp from the second to the third. Between zeroBound3 and oneBound3, lerp from the third to the fourth.

Declaration
public static TEx<T> Lerp4<T>(tfloat zeroBound, tfloat oneBound, tfloat zeroBound2, tfloat oneBound2, tfloat zeroBound3, tfloat oneBound3, tfloat controller, TEx<T> f1, TEx<T> f2, TEx<T> f3, TEx<T> f4)
Parameters
Type Name Description
tfloat zeroBound
tfloat oneBound
tfloat zeroBound2
tfloat oneBound2
tfloat zeroBound3
tfloat oneBound3
tfloat controller
TEx<T> f1
TEx<T> f2
TEx<T> f3
TEx<T> f4
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

LerpBack<T>(tfloat, tfloat, tfloat, tfloat, tfloat, TEx<T>, TEx<T>)

Lerp between two functions. Between zeroBound and oneBound, lerp from the first to the second. Between oneBound2 and zeroBound2, lerp from the second back to the first.

Declaration
public static TEx<T> LerpBack<T>(tfloat zeroBound, tfloat oneBound, tfloat oneBound2, tfloat zeroBound2, tfloat controller, TEx<T> f1, TEx<T> f2)
Parameters
Type Name Description
tfloat zeroBound

Lower bound for lerp controller
tfloat oneBound

Upper bound for lerp controller
tfloat oneBound2

Upper bound for lerp controller
tfloat zeroBound2

Lower bound for lerp controller
tfloat controller

Lerp controller
TEx<T> f1

First function (when controller leq zeroBound, return this)
TEx<T> f2

Second function (when controller geq oneBound, return this)
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

LerpD<T>(TEx<T>, TEx<T>)

Lerp between a value for easy difficulty and lunatic difficulty.

Declaration
public static TEx<T> LerpD<T>(TEx<T> f1, TEx<T> f2)
Parameters
Type Name Description
TEx<T> f1
TEx<T> f2
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

LerpMany<T>((UncompiledCode<Single> bd, UncompiledCode<T> val)[], Func<TExArgCtx, TEx<Single>>)

Lerp between many functions.

Declaration
public static Func<TExArgCtx, TEx<T>> LerpMany<T>((UncompiledCode<float> bd, UncompiledCode<T> val)[] points, Func<TExArgCtx, TEx<float>> controller)
Parameters
Type Name Description
System.ValueTuple<UncompiledCode<System.Single>, UncompiledCode<T>>[] points
System.Func<TExArgCtx, TEx<System.Single>> controller
Returns
Type Description
System.Func<TExArgCtx, TEx<T>>
Type Parameters
Name Description
T

LerpR<T>(TEx<T>, TEx<T>)

Lerp between a value for minimum rank and maximum rank.

Declaration
public static TEx<T> LerpR<T>(TEx<T> f1, TEx<T> f2)
Parameters
Type Name Description
TEx<T> f1
TEx<T> f2
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

LerpSmooth<T>(TEx<Func<Single, Single>>, tfloat, tfloat, tfloat, TEx<T>, TEx<T>)

Lerp between two functions with smoothing applied to the controller.

Declaration
public static TEx<T> LerpSmooth<T>(TEx<Func<float, float>> smoother, tfloat zeroBound, tfloat oneBound, tfloat controller, TEx<T> f1, TEx<T> f2)
Parameters
Type Name Description
TEx<System.Func<System.Single, System.Single>> smoother
tfloat zeroBound
tfloat oneBound
tfloat controller
TEx<T> f1
TEx<T> f2
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

LerpT<T>(ExBPY, ExBPY, Func<TExArgCtx, TEx<T>>, Func<TExArgCtx, TEx<T>>)

Lerp between f1 and f2 using time (t) as a controller.

Declaration
public static Func<TExArgCtx, TEx<T>> LerpT<T>(ExBPY zeroBound, ExBPY oneBound, Func<TExArgCtx, TEx<T>> f1, Func<TExArgCtx, TEx<T>> f2)
Parameters
Type Name Description
ExBPY zeroBound

Lower bound for time. When t=zeroBound, return f1.
ExBPY oneBound

Upper bound for time. When t=oneBound, return f2.
System.Func<TExArgCtx, TEx<T>> f1

First lerp value
System.Func<TExArgCtx, TEx<T>> f2

Second lerp value
Returns
Type Description
System.Func<TExArgCtx, TEx<T>>
Type Parameters
Name Description
T

LerpT3<T>(ExBPY, ExBPY, ExBPY, ExBPY, Func<TExArgCtx, TEx<T>>, Func<TExArgCtx, TEx<T>>, Func<TExArgCtx, TEx<T>>)

Declaration
public static Func<TExArgCtx, TEx<T>> LerpT3<T>(ExBPY zeroBound, ExBPY oneBound, ExBPY twoBound, ExBPY threeBound, Func<TExArgCtx, TEx<T>> f1, Func<TExArgCtx, TEx<T>> f2, Func<TExArgCtx, TEx<T>> f3)
Parameters
Type Name Description
ExBPY zeroBound
ExBPY oneBound
ExBPY twoBound
ExBPY threeBound
System.Func<TExArgCtx, TEx<T>> f1
System.Func<TExArgCtx, TEx<T>> f2
System.Func<TExArgCtx, TEx<T>> f3
Returns
Type Description
System.Func<TExArgCtx, TEx<T>>
Type Parameters
Name Description
T

LerpU<T>(tfloat, tfloat, tfloat, TEx<T>, TEx<T>)

Lerp between two functions. The controller is not clamped.

Declaration
public static TEx<T> LerpU<T>(tfloat zeroBound, tfloat oneBound, tfloat controller, TEx<T> f1, TEx<T> f2)
Parameters
Type Name Description
tfloat zeroBound

Lower bound for lerp controller
tfloat oneBound

Upper bound for lerp controller
tfloat controller

Lerp controller
TEx<T> f1

First function
TEx<T> f2

Second function
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

Ratio(tfloat, tfloat, tfloat)

Get the value t such that LerpUnclamped(a, b, t) = x. Do not use if a = b.

Declaration
public static tfloat Ratio(tfloat a, tfloat b, tfloat x)
Parameters
Type Name Description
tfloat a

Lower lerp bound
tfloat b

Upper lerp bound
tfloat x

Resulting lerp value
Returns
Type Description
tfloat

RotateLerp(tfloat, tfloat, tfloat, tv2, tv2)

Declaration
public static tv2 RotateLerp(tfloat zeroBound, tfloat oneBound, tfloat controller, tv2 source, tv2 target)
Parameters
Type Name Description
tfloat zeroBound
tfloat oneBound
tfloat controller
tv2 source
tv2 target
Returns
Type Description
tv2

RotateLerpCCW(tfloat, tfloat, tfloat, tv2, tv2)

Declaration
public static tv2 RotateLerpCCW(tfloat zeroBound, tfloat oneBound, tfloat controller, tv2 source, tv2 target)
Parameters
Type Name Description
tfloat zeroBound
tfloat oneBound
tfloat controller
tv2 source
tv2 target
Returns
Type Description
tv2

RotateLerpCW(tfloat, tfloat, tfloat, tv2, tv2)

Declaration
public static tv2 RotateLerpCW(tfloat zeroBound, tfloat oneBound, tfloat controller, tv2 source, tv2 target)
Parameters
Type Name Description
tfloat zeroBound
tfloat oneBound
tfloat controller
tv2 source
tv2 target
Returns
Type Description
tv2

Select<T>(Func<TExArgCtx, TEx<Single>>, UncompiledCode<T>[])

Select one of an array of values. If OOB, selects the last element. Note: this expands to (if i = 0) arr[0] (if i = 1) arr[1] .... This may sound stupid, but since each value is a function, there's no way to actually store it in an array.

Declaration
public static Func<TExArgCtx, TEx<T>> Select<T>(Func<TExArgCtx, TEx<float>> index, UncompiledCode<T>[] points)
Parameters
Type Name Description
System.Func<TExArgCtx, TEx<System.Single>> index
UncompiledCode<T>[] points
Returns
Type Description
System.Func<TExArgCtx, TEx<T>>
Type Parameters
Name Description
T

SelectDC<T>(TEx<T>, TEx<T>, TEx<T>, TEx<T>)

Select a value according to the current difficulty counter.

Declaration
public static TEx<T> SelectDC<T>(TEx<T> easy, TEx<T> normal, TEx<T> hard, TEx<T> lunatic)
Parameters
Type Name Description
TEx<T> easy
TEx<T> normal
TEx<T> hard
TEx<T> lunatic
Returns
Type Description
TEx<T>
Type Parameters
Name Description
T

Smooth(TEx<Func<Single, Single>>, tfloat)

Apply a contortion to a 0-1 range. This returns an approximately linear function.

Declaration
[Obsolete("Instead of running 'smooth(eiosine, t)', you may simply run 'eiosine(t)'.")]
public static tfloat Smooth(TEx<Func<float, float>> smoother, tfloat controller)
Parameters
Type Name Description
TEx<System.Func<System.Single, System.Single>> smoother

Smoothing function (ExMEasers)
tfloat controller

0-1 value
Returns
Type Description
tfloat

SmoothC(TEx<Func<Single, Single>>, tfloat)

Apply a contortion to a clamped 0-1 range. This returns an approximately linear function.

Declaration
public static tfloat SmoothC(TEx<Func<float, float>> smoother, tfloat controller)
Parameters
Type Name Description
TEx<System.Func<System.Single, System.Single>> smoother

Smoothing function (ExMEasers)
tfloat controller

0-1 value (clamped if outside)
Returns
Type Description
tfloat

SmoothIO(TEx<Func<Single, Single>>, TEx<Func<Single, Single>>, tfloat, tfloat, tfloat, tfloat)

Apply a contortion to a 0-x range, returning:
0-1 in the range [0,s1]
1 in the range [s1,x-s2]
1-0 in the range [x-s2,x]

Declaration
public static tfloat SmoothIO(TEx<Func<float, float>> smoother1, TEx<Func<float, float>> smoother2, tfloat total, tfloat smth1, tfloat smth2, tfloat controller)
Parameters
Type Name Description
TEx<System.Func<System.Single, System.Single>> smoother1

First Smoothing function (ExMEasers)
TEx<System.Func<System.Single, System.Single>> smoother2

Second Smoothing function (ExMEasers)
tfloat total

Total time
tfloat smth1

Smooth-in time
tfloat smth2

Smooth-out time
tfloat controller

0-x value
Returns
Type Description
tfloat

SmoothIOe(TEx<Func<Single, Single>>, tfloat, tfloat, tfloat)

Apply SmoothIO where name=name1=name2 and smth=smth1=smth2.

Declaration
public static tfloat SmoothIOe(TEx<Func<float, float>> smoother, tfloat total, tfloat smth, tfloat controller)
Parameters
Type Name Description
TEx<System.Func<System.Single, System.Single>> smoother
tfloat total
tfloat smth
tfloat controller
Returns
Type Description
tfloat

SmoothLoop(TEx<Func<Single, Single>>, tfloat)

Get the value of an easer at a given point between 0 and 1. The return value is periodized, so if the input is 5.4, then the output is 5 + ease(0.4).

Declaration
public static tfloat SmoothLoop(TEx<Func<float, float>> smoother, tfloat controller)
Parameters
Type Name Description
TEx<System.Func<System.Single, System.Single>> smoother

Smoothing function (ExMEasers)
tfloat controller
Returns
Type Description
tfloat

SmoothLoopR(TEx<Func<Single, Single>>, tfloat, tfloat)

Returns R * SmoothLoop(name, controller/R).

Declaration
public static tfloat SmoothLoopR(TEx<Func<float, float>> smoother, tfloat range, tfloat controller)
Parameters
Type Name Description
TEx<System.Func<System.Single, System.Single>> smoother
tfloat range
tfloat controller
Returns
Type Description
tfloat

SmoothR(TEx<Func<Single, Single>>, tfloat, tfloat)

Apply a contortion to a 0-R range, returning R * Smooth(name, controller/R). This returns an approximately linear function.

Declaration
public static tfloat SmoothR(TEx<Func<float, float>> smoother, tfloat range, tfloat controller)
Parameters
Type Name Description
TEx<System.Func<System.Single, System.Single>> smoother

Smoothing function (ExMEasers)
tfloat range

Range
tfloat controller

0-R value
Returns
Type Description
tfloat

SStep(tfloat, tfloat, tfloat)

Return 0 if the controller is leq the lower bound, 1 if the controller is geq the lower bound, and a linear interpolation in between.

Declaration
public static tfloat SStep(tfloat zeroBound, tfloat oneBound, tfloat controller)
Parameters
Type Name Description
tfloat zeroBound
tfloat oneBound
tfloat controller
Returns
Type Description
tfloat

SwitchH<T>(ExBPY, ExBPY, Func<TExArgCtx, TEx<T>>, Func<TExArgCtx, TEx<T>>)

Return one of two functions depending on the input, adjusting the switch variable by the reference switch amount if returning the latter function.

Declaration
public static Func<TExArgCtx, TEx<T>> SwitchH<T>(ExBPY switchVar, ExBPY at, Func<TExArgCtx, TEx<T>> f1, Func<TExArgCtx, TEx<T>> f2)
Parameters
Type Name Description
ExBPY switchVar

The variable upon which pivoting is performed. Should be either "p" (firing index) or "t" (time).
ExBPY at

Reference
System.Func<TExArgCtx, TEx<T>> f1

Function when t \leq at
System.Func<TExArgCtx, TEx<T>> f2

Function when t \gt at
Returns
Type Description
System.Func<TExArgCtx, TEx<T>>
Type Parameters
Name Description
T