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Easing Functions for Unity3D
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EasingFunctions.cs
/*
* Created by C.J. Kimberlin
*
* The MIT License (MIT)
*
* Copyright (c) 2019
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*
*
* TERMS OF USE - EASING EQUATIONS
* Open source under the BSD License.
* Copyright (c)2001 Robert Penner
* All rights reserved.
* Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
* Neither the name of the author nor the names of contributors may be used to endorse or promote products derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
* THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
*
* ============= Description =============
*
* Below is an example of how to use the easing functions in the file. There is a getting function that will return the function
* from an enum. This is useful since the enum can be exposed in the editor and then the function queried during Start().
*
* EasingFunction.Ease ease = EasingFunction.Ease.EaseInOutQuad;
* EasingFunction.EasingFunc func = GetEasingFunction(ease);
*
* float value = func(0, 10, 0.67f);
*
* EasingFunction.EaseingFunc derivativeFunc = GetEasingFunctionDerivative(ease);
*
* float derivativeValue = derivativeFunc(0, 10, 0.67f);
*/
using UnityEngine;
public static class EasingFunction
{
public enum Ease
{
Custom = -1,
EaseInQuad = 0,
EaseOutQuad,
EaseInOutQuad,
EaseInCubic,
EaseOutCubic,
EaseInOutCubic,
EaseInQuart,
EaseOutQuart,
EaseInOutQuart,
EaseInQuint,
EaseOutQuint,
EaseInOutQuint,
EaseInSine,
EaseOutSine,
EaseInOutSine,
EaseInExpo,
EaseOutExpo,
EaseInOutExpo,
EaseInCirc,
EaseOutCirc,
EaseInOutCirc,
Linear,
Spring,
EaseInBounce,
EaseOutBounce,
EaseInOutBounce,
EaseInBack,
EaseOutBack,
EaseInOutBack,
EaseInElastic,
EaseOutElastic,
EaseInOutElastic,
}
private const float NATURAL_LOG_OF_2 = 0.693147181f;
//
// Easing functions
//
public static float Linear(float value) => Linear(0, 1, value);
public static float Linear(float start, float end, float value)
=> Mathf.Lerp(start, end, value);
public static float Spring(float value) => Spring(0, 1, value);
public static float Spring(float start, float end, float value)
{
value = Mathf.Clamp01(value);
value = (Mathf.Sin(value * Mathf.PI * (0.2f + 2.5f * value * value * value)) * Mathf.Pow(1f - value, 2.2f) + value) * (1f + (1.2f * (1f - value)));
return start + (end - start) * value;
}
public static float EaseInQuad(float value) => EaseInQuad(0, 1, value);
public static float EaseInQuad(float start, float end, float value)
{
end -= start;
return end * value * value + start;
}
public static float EaseOutQuad(float value) => EaseOutQuad(0, 1, value);
public static float EaseOutQuad(float start, float end, float value)
{
end -= start;
return -end * value * (value - 2) + start;
}
public static float EaseInOutQuad(float value) => EaseInOutQuad(0, 1, value);
public static float EaseInOutQuad(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1) return end * 0.5f * value * value + start;
value--;
return -end * 0.5f * (value * (value - 2) - 1) + start;
}
public static float EaseInCubic(float value) => EaseInCubic(0, 1, value);
public static float EaseInCubic(float start, float end, float value)
{
end -= start;
return end * value * value * value + start;
}
public static float EaseOutCubic(float value) => EaseOutCubic(0, 1, value);
public static float EaseOutCubic(float start, float end, float value)
{
value--;
end -= start;
return end * (value * value * value + 1) + start;
}
public static float EaseInOutCubic(float value) => EaseInOutCubic(0, 1, value);
public static float EaseInOutCubic(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1) return end * 0.5f * value * value * value + start;
value -= 2;
return end * 0.5f * (value * value * value + 2) + start;
}
public static float EaseInQuart(float value) => EaseInQuart(0, 1, value);
public static float EaseInQuart(float start, float end, float value)
{
end -= start;
return end * value * value * value * value + start;
}
public static float EaseOutQuart(float value) => EaseOutQuart(0, 1, value);
public static float EaseOutQuart(float start, float end, float value)
{
value--;
end -= start;
return -end * (value * value * value * value - 1) + start;
}
public static float EaseInOutQuart(float value) => EaseInOutQuart(0, 1, value);
public static float EaseInOutQuart(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1) return end * 0.5f * value * value * value * value + start;
value -= 2;
return -end * 0.5f * (value * value * value * value - 2) + start;
}
public static float EaseInQuint(float value) => EaseInQuint(0, 1, value);
public static float EaseInQuint(float start, float end, float value)
{
end -= start;
return end * value * value * value * value * value + start;
}
public static float EaseOutQuint(float value) => EaseOutQuint(0, 1, value);
public static float EaseOutQuint(float start, float end, float value)
{
value--;
end -= start;
return end * (value * value * value * value * value + 1) + start;
}
public static float EaseInOutQuint(float value) => EaseInOutQuint(0, 1, value);
public static float EaseInOutQuint(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1) return end * 0.5f * value * value * value * value * value + start;
value -= 2;
return end * 0.5f * (value * value * value * value * value + 2) + start;
}
public static float EaseInSine(float value) => EaseInSine(0, 1, value);
public static float EaseInSine(float start, float end, float value)
{
end -= start;
return -end * Mathf.Cos(value * (Mathf.PI * 0.5f)) + end + start;
}
public static float EaseOutSine(float value) => EaseOutSine(0, 1, value);
public static float EaseOutSine(float start, float end, float value)
{
end -= start;
return end * Mathf.Sin(value * (Mathf.PI * 0.5f)) + start;
}
public static float EaseInOutSine(float value) => EaseInOutSine(0, 1, value);
public static float EaseInOutSine(float start, float end, float value)
{
end -= start;
return -end * 0.5f * (Mathf.Cos(Mathf.PI * value) - 1) + start;
}
public static float EaseInExpo(float value) => EaseInExpo(0, 1, value);
public static float EaseInExpo(float start, float end, float value)
{
end -= start;
return end * Mathf.Pow(2, 10 * (value - 1)) + start;
}
public static float EaseOutExpo(float value) => EaseOutExpo(0, 1, value);
public static float EaseOutExpo(float start, float end, float value)
{
end -= start;
return end * (-Mathf.Pow(2, -10 * value) + 1) + start;
}
public static float EaseInOutExpo(float value) => EaseInOutExpo(0, 1, value);
public static float EaseInOutExpo(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1) return end * 0.5f * Mathf.Pow(2, 10 * (value - 1)) + start;
value--;
return end * 0.5f * (-Mathf.Pow(2, -10 * value) + 2) + start;
}
public static float EaseInCirc(float value) => EaseInCirc(0, 1, value);
public static float EaseInCirc(float start, float end, float value)
{
end -= start;
return -end * (Mathf.Sqrt(1 - value * value) - 1) + start;
}
public static float EaseOutCirc(float value) => EaseOutCirc(0, 1, value);
public static float EaseOutCirc(float start, float end, float value)
{
value--;
end -= start;
return end * Mathf.Sqrt(1 - value * value) + start;
}
public static float EaseInOutCirc(float value) => EaseInOutCirc(0, 1, value);
public static float EaseInOutCirc(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1) return -end * 0.5f * (Mathf.Sqrt(1 - value * value) - 1) + start;
value -= 2;
return end * 0.5f * (Mathf.Sqrt(1 - value * value) + 1) + start;
}
public static float EaseInBounce(float value) => EaseInBounce(0, 1, value);
public static float EaseInBounce(float start, float end, float value)
{
end -= start;
float d = 1f;
return end - EaseOutBounce(0, end, d - value) + start;
}
public static float EaseOutBounce(float value) => EaseOutBounce(0, 1, value);
public static float EaseOutBounce(float start, float end, float value)
{
value /= 1f;
end -= start;
if (value < (1 / 2.75f))
return end * (7.5625f * value * value) + start;
else if (value < (2 / 2.75f))
{
value -= (1.5f / 2.75f);
return end * (7.5625f * (value) * value + .75f) + start;
}
else if (value < (2.5 / 2.75))
{
value -= (2.25f / 2.75f);
return end * (7.5625f * (value) * value + .9375f) + start;
}
else
{
value -= (2.625f / 2.75f);
return end * (7.5625f * (value) * value + .984375f) + start;
}
}
public static float EaseInOutBounce(float value) => EaseInOutBounce(0, 1, value);
public static float EaseInOutBounce(float start, float end, float value)
{
end -= start;
float d = 1f;
if (value < d * 0.5f) return EaseInBounce(0, end, value * 2) * 0.5f + start;
else return EaseOutBounce(0, end, value * 2 - d) * 0.5f + end * 0.5f + start;
}
public static float EaseInBack(float value) => EaseInBack(0, 1, value);
public static float EaseInBack(float start, float end, float value)
{
end -= start;
value /= 1;
float s = 1.70158f;
return end * (value) * value * ((s + 1) * value - s) + start;
}
public static float EaseOutBack(float value) => EaseOutBack(0, 1, value);
public static float EaseOutBack(float start, float end, float value)
{
float s = 1.70158f;
end -= start;
value = (value) - 1;
return end * ((value) * value * ((s + 1) * value + s) + 1) + start;
}
public static float EaseInOutBack(float value) => EaseInOutBack(0, 1, value);
public static float EaseInOutBack(float start, float end, float value)
{
float s = 1.70158f;
end -= start;
value /= .5f;
if ((value) < 1)
{
s *= (1.525f);
return end * 0.5f * (value * value * (((s) + 1) * value - s)) + start;
}
value -= 2;
s *= (1.525f);
return end * 0.5f * ((value) * value * (((s) + 1) * value + s) + 2) + start;
}
public static float EaseInElastic(float value) => EaseInElastic(0, 1, value);
public static float EaseInElastic(float start, float end, float value)
{
end -= start;
float d = 1f;
float p = d * .3f;
float s;
float a = 0;
if (value == 0) return start;
if ((value /= d) == 1) return start + end;
if (a == 0f || a < Mathf.Abs(end))
{
a = end;
s = p / 4;
}
else
s = p / (2 * Mathf.PI) * Mathf.Asin(end / a);
return -(a * Mathf.Pow(2, 10 * (value -= 1)) * Mathf.Sin((value * d - s) * (2 * Mathf.PI) / p)) + start;
}
public static float EaseOutElastic(float value) => EaseOutElastic(0, 1, value);
public static float EaseOutElastic(float start, float end, float value)
{
end -= start;
float d = 1f;
float p = d * .3f;
float s;
float a = 0;
if (value == 0) return start;
if ((value /= d) == 1) return start + end;
if (a == 0f || a < Mathf.Abs(end))
{
a = end;
s = p * 0.25f;
}
else
s = p / (2 * Mathf.PI) * Mathf.Asin(end / a);
return (a * Mathf.Pow(2, -10 * value) * Mathf.Sin((value * d - s) * (2 * Mathf.PI) / p) + end + start);
}
public static float EaseInOutElastic(float value) => EaseInOutElastic(0, 1, value);
public static float EaseInOutElastic(float start, float end, float value)
{
end -= start;
float d = 1f;
float p = d * .3f;
float s;
float a = 0;
if (value == 0) return start;
if ((value /= d * 0.5f) == 2) return start + end;
if (a == 0f || a < Mathf.Abs(end))
{
a = end;
s = p / 4;
}
else
s = p / (2 * Mathf.PI) * Mathf.Asin(end / a);
if (value < 1) return -0.5f * (a * Mathf.Pow(2, 10 * (value -= 1)) * Mathf.Sin((value * d - s) * (2 * Mathf.PI) / p)) + start;
return a * Mathf.Pow(2, -10 * (value -= 1)) * Mathf.Sin((value * d - s) * (2 * Mathf.PI) / p) * 0.5f + end + start;
}
//
// These are derived functions that the motor can use to get the speed at a specific time.
//
// The easing functions all work with a normalized time (0 to 1) and the returned value here
// reflects that. Values returned here should be divided by the actual time.
//
// TODO: These functions have not had the testing they deserve. If there is odd behavior around
// dash speeds then this would be the first place I'd look.
public static float LinearD(float value) => LinearD(0, 1, value);
public static float LinearD(float start, float end, float value)
=> end - start;
public static float EaseInQuadD(float value) => EaseInQuadD(0, 1, value);
public static float EaseInQuadD(float start, float end, float value)
=> 2f * (end - start) * value;
public static float EaseOutQuadD(float value) => EaseOutQuadD(0, 1, value);
public static float EaseOutQuadD(float start, float end, float value)
{
end -= start;
return -end * value - end * (value - 2);
}
public static float EaseInOutQuadD(float value) => EaseInOutQuadD(0, 1, value);
public static float EaseInOutQuadD(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1)
return end * value;
return end * (1 - --value);
}
public static float EaseInCubicD(float value) => EaseInCubicD(0, 1, value);
public static float EaseInCubicD(float start, float end, float value)
=> 3f * (end - start) * value * value;
public static float EaseOutCubicD(float value) => EaseOutCubicD(0, 1, value);
public static float EaseOutCubicD(float start, float end, float value)
{
value--;
end -= start;
return 3f * end * value * value;
}
public static float EaseInOutCubicD(float value) => EaseInOutCubicD(0, 1, value);
public static float EaseInOutCubicD(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1)
return (3f / 2f) * end * value * value;
value -= 2;
return (3f / 2f) * end * value * value;
}
public static float EaseInQuartD(float value) => EaseInQuartD(0, 1, value);
public static float EaseInQuartD(float start, float end, float value)
=> 4f * (end - start) * value * value * value;
public static float EaseOutQuartD(float value) => EaseOutQuartD(0, 1, value);
public static float EaseOutQuartD(float start, float end, float value)
{
value--;
end -= start;
return -4f * end * value * value * value;
}
public static float EaseInOutQuartD(float value) => EaseInOutQuartD(0, 1, value);
public static float EaseInOutQuartD(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1)
return 2f * end * value * value * value;
value -= 2;
return -2f * end * value * value * value;
}
public static float EaseInQuintD(float value) => EaseInQuintD(0, 1, value);
public static float EaseInQuintD(float start, float end, float value)
=> 5f * (end - start) * value * value * value * value;
public static float EaseOutQuintD(float value) => EaseOutQuintD(0, 1, value);
public static float EaseOutQuintD(float start, float end, float value)
{
value--;
end -= start;
return 5f * end * value * value * value * value;
}
public static float EaseInOutQuintD(float value) => EaseInOutQuintD(0, 1, value);
public static float EaseInOutQuintD(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1)
return (5f / 2f) * end * value * value * value * value;
value -= 2;
return (5f / 2f) * end * value * value * value * value;
}
public static float EaseInSineD(float value) => EaseInSineD(0, 1, value);
public static float EaseInSineD(float start, float end, float value)
=> (end - start) * 0.5f * Mathf.PI * Mathf.Sin(0.5f * Mathf.PI * value);
public static float EaseOutSineD(float value) => EaseOutSineD(0, 1, value);
public static float EaseOutSineD(float start, float end, float value)
{
end -= start;
return (Mathf.PI * 0.5f) * end * Mathf.Cos(value * (Mathf.PI * 0.5f));
}
public static float EaseInOutSineD(float value) => EaseInOutSineD(0, 1, value);
public static float EaseInOutSineD(float start, float end, float value)
{
end -= start;
return end * 0.5f * Mathf.PI * Mathf.Sin(Mathf.PI * value);
}
public static float EaseInExpoD(float value) => EaseInExpoD(0, 1, value);
public static float EaseInExpoD(float start, float end, float value)
=> (10f * NATURAL_LOG_OF_2 * (end - start) * Mathf.Pow(2f, 10f * (value - 1)));
public static float EaseOutExpoD(float value) => EaseOutExpoD(0, 1, value);
public static float EaseOutExpoD(float start, float end, float value)
{
end -= start;
return 5f * NATURAL_LOG_OF_2 * end * Mathf.Pow(2f, 1f - 10f * value);
}
public static float EaseInOutExpoD(float value) => EaseInOutExpoD(0, 1, value);
public static float EaseInOutExpoD(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1)
return 5f * NATURAL_LOG_OF_2 * end * Mathf.Pow(2f, 10f * (value - 1));
value--;
return (5f * NATURAL_LOG_OF_2 * end) / (Mathf.Pow(2f, 10f * value));
}
public static float EaseInCircD(float value) => EaseInCircD(0, 1, value);
public static float EaseInCircD(float start, float end, float value)
=> ((end - start) * value) / Mathf.Sqrt(1f - value * value);
public static float EaseOutCircD(float value) => EaseOutCircD(0, 1, value);
public static float EaseOutCircD(float start, float end, float value)
{
value--;
end -= start;
return (-end * value) / Mathf.Sqrt(1f - value * value);
}
public static float EaseInOutCircD(float value) => EaseInOutCircD(0, 1, value);
public static float EaseInOutCircD(float start, float end, float value)
{
value /= .5f;
end -= start;
if (value < 1)
return (end * value) / (2f * Mathf.Sqrt(1f - value * value));
value -= 2;
return (-end * value) / (2f * Mathf.Sqrt(1f - value * value));
}
public static float EaseInBounceD(float value) => EaseInBounceD(0, 1, value);
public static float EaseInBounceD(float start, float end, float value)
{
end -= start;
float d = 1f;
return EaseOutBounceD(0, end, d - value);
}
public static float EaseOutBounceD(float value) => EaseOutBounceD(0, 1, value);
public static float EaseOutBounceD(float start, float end, float value)
{
value /= 1f;
end -= start;
if (value < (1 / 2.75f))
return 2f * end * 7.5625f * value;
else if (value < (2 / 2.75f))
value -= (1.5f / 2.75f);
else if (value < (2.5 / 2.75))
value -= (2.25f / 2.75f);
else
value -= (2.625f / 2.75f);
return 2f * end * 7.5625f * value;
}
public static float EaseInOutBounceD(float value) => EaseInOutBounceD(0, 1, value);
public static float EaseInOutBounceD(float start, float end, float value)
{
end -= start;
float d = 1f;
if (value < d * 0.5f)
return EaseInBounceD(0, end, value * 2) * 0.5f;
return EaseOutBounceD(0, end, value * 2 - d) * 0.5f;
}
public static float EaseInBackD(float value) => EaseInBackD(0, 1, value);
public static float EaseInBackD(float start, float end, float value)
{
float s = 1.70158f;
return 3f * (s + 1f) * (end - start) * value * value - 2f * s * (end - start) * value;
}
public static float EaseOutBackD(float value) => EaseOutBackD(0, 1, value);
public static float EaseOutBackD(float start, float end, float value)
{
float s = 1.70158f;
end -= start;
value = (value) - 1;
return end * ((s + 1f) * value * value + 2f * value * ((s + 1f) * value + s));
}
public static float EaseInOutBackD(float value) => EaseInOutBackD(0, 1, value);
public static float EaseInOutBackD(float start, float end, float value)
{
float s = 1.70158f;
end -= start;
value /= .5f;
if ((value) < 1)
{
s *= (1.525f);
return 0.5f * end * (s + 1) * value * value + end * value * ((s + 1f) * value - s);
}
value -= 2;
s *= (1.525f);
return 0.5f * end * ((s + 1) * value * value + 2f * value * ((s + 1f) * value + s));
}
public static float EaseInElasticD(float value) => EaseInElasticD(0, 1, value);
public static float EaseInElasticD(float start, float end, float value)
=> EaseOutElasticD(start, end, 1f - value);
public static float EaseOutElasticD(float value) => EaseOutElasticD(0, 1, value);
public static float EaseOutElasticD(float start, float end, float value)
{
end -= start;
float d = 1f;
float p = d * .3f;
float s;
float a = 0;
if (a == 0f || a < Mathf.Abs(end))
{
a = end;
s = p * 0.25f;
}
else
s = p / (2 * Mathf.PI) * Mathf.Asin(end / a);
return (a * Mathf.PI * d * Mathf.Pow(2f, 1f - 10f * value) *
Mathf.Cos((2f * Mathf.PI * (d * value - s)) / p)) / p - 5f * NATURAL_LOG_OF_2 * a *
Mathf.Pow(2f, 1f - 10f * value) * Mathf.Sin((2f * Mathf.PI * (d * value - s)) / p);
}
public static float EaseInOutElasticD(float value) => EaseInOutElasticD(0, 1, value);
public static float EaseInOutElasticD(float start, float end, float value)
{
end -= start;
float d = 1f;
float p = d * .3f;
float s;
float a = 0;
if (a == 0f || a < Mathf.Abs(end))
{
a = end;
s = p / 4;
}
else
s = p / (2 * Mathf.PI) * Mathf.Asin(end / a);
if (value < 1)
{
value -= 1;
return -5f * NATURAL_LOG_OF_2 * a * Mathf.Pow(2f, 10f * value) * Mathf.Sin(2 * Mathf.PI * (d * value - 2f) / p) -
a * Mathf.PI * d * Mathf.Pow(2f, 10f * value) * Mathf.Cos(2 * Mathf.PI * (d * value - s) / p) / p;
}
value -= 1;
return a * Mathf.PI * d * Mathf.Cos(2f * Mathf.PI * (d * value - s) / p) / (p * Mathf.Pow(2f, 10f * value)) -
5f * NATURAL_LOG_OF_2 * a * Mathf.Sin(2f * Mathf.PI * (d * value - s) / p) / (Mathf.Pow(2f, 10f * value));
}
public static float SpringD(float value) => SpringD(0, 1, value);
public static float SpringD(float start, float end, float value)
{
value = Mathf.Clamp01(value);
end -= start;
// Damn... Thanks http://www.derivative-calculator.net/
// TODO: And it's a little bit wrong
return end * (6f * (1f - value) / 5f + 1f) * (-2.2f * Mathf.Pow(1f - value, 1.2f) *
Mathf.Sin(Mathf.PI * value * (2.5f * value * value * value + 0.2f)) + Mathf.Pow(1f - value, 2.2f) *
(Mathf.PI * (2.5f * value * value * value + 0.2f) + 7.5f * Mathf.PI * value * value * value) *
Mathf.Cos(Mathf.PI * value * (2.5f * value * value * value + 0.2f)) + 1f) -
6f * end * (Mathf.Pow(1 - value, 2.2f) * Mathf.Sin(Mathf.PI * value * (2.5f * value * value * value + 0.2f)) + value
/ 5f);
}
public delegate float Function(float s, float e, float v);
public delegate float Function01(float v);
/// <summary>
/// Returns the function associated to the easingFunction enum. This value returned should be cached as it allocates memory
/// to return.
/// </summary>
/// <param name="easingFunction">The enum associated with the easing function.</param>
/// <returns>The easing function</returns>
public static Function GetEasingFunction(Ease easingFunction)
=> (easingFunction) switch
{
Ease.EaseInQuad => EaseInQuad,
Ease.EaseOutQuad => EaseOutQuad,
Ease.EaseInOutQuad => EaseInOutQuad,
Ease.EaseInCubic => EaseInCubic,
Ease.EaseOutCubic => EaseOutCubic,
Ease.EaseInOutCubic => EaseInOutCubic,
Ease.EaseInQuart => EaseInQuart,
Ease.EaseOutQuart => EaseOutQuart,
Ease.EaseInOutQuart => EaseInOutQuart,
Ease.EaseInQuint => EaseInQuint,
Ease.EaseOutQuint => EaseOutQuint,
Ease.EaseInOutQuint => EaseInOutQuint,
Ease.EaseInSine => EaseInSine,
Ease.EaseOutSine => EaseOutSine,
Ease.EaseInOutSine => EaseInOutSine,
Ease.EaseInExpo => EaseInExpo,
Ease.EaseOutExpo => EaseOutExpo,
Ease.EaseInOutExpo => EaseInOutExpo,
Ease.EaseInCirc => EaseInCirc,
Ease.EaseOutCirc => EaseOutCirc,
Ease.EaseInOutCirc => EaseInOutCirc,
Ease.Linear => Linear,
Ease.Spring => Spring,
Ease.EaseInBounce => EaseInBounce,
Ease.EaseOutBounce => EaseOutBounce,
Ease.EaseInOutBounce => EaseInOutBounce,
Ease.EaseInBack => EaseInBack,
Ease.EaseOutBack => EaseOutBack,
Ease.EaseInOutBack => EaseInOutBack,
Ease.EaseInElastic => EaseInElastic,
Ease.EaseOutElastic => EaseOutElastic,
Ease.EaseInOutElastic => EaseInOutElastic,
_ => null
};
/// <summary>
/// Returns the function associated to the easingFunction enum. This value returned should be cached as it allocates memory
/// to return.
/// </summary>
/// <param name="easingFunction">The enum associated with the easing function.</param>
/// <returns>The easing function</returns>
public static Function01 GetEasingFunction01(Ease easingFunction)
=> (easingFunction) switch
{
Ease.EaseInQuad => EaseInQuad,
Ease.EaseOutQuad => EaseOutQuad,
Ease.EaseInOutQuad => EaseInOutQuad,
Ease.EaseInCubic => EaseInCubic,
Ease.EaseOutCubic => EaseOutCubic,
Ease.EaseInOutCubic => EaseInOutCubic,
Ease.EaseInQuart => EaseInQuart,
Ease.EaseOutQuart => EaseOutQuart,
Ease.EaseInOutQuart => EaseInOutQuart,
Ease.EaseInQuint => EaseInQuint,
Ease.EaseOutQuint => EaseOutQuint,
Ease.EaseInOutQuint => EaseInOutQuint,
Ease.EaseInSine => EaseInSine,
Ease.EaseOutSine => EaseOutSine,
Ease.EaseInOutSine => EaseInOutSine,
Ease.EaseInExpo => EaseInExpo,
Ease.EaseOutExpo => EaseOutExpo,
Ease.EaseInOutExpo => EaseInOutExpo,
Ease.EaseInCirc => EaseInCirc,
Ease.EaseOutCirc => EaseOutCirc,
Ease.EaseInOutCirc => EaseInOutCirc,
Ease.Linear => Linear,
Ease.Spring => Spring,
Ease.EaseInBounce => EaseInBounce,
Ease.EaseOutBounce => EaseOutBounce,
Ease.EaseInOutBounce => EaseInOutBounce,
Ease.EaseInBack => EaseInBack,
Ease.EaseOutBack => EaseOutBack,
Ease.EaseInOutBack => EaseInOutBack,
Ease.EaseInElastic => EaseInElastic,
Ease.EaseOutElastic => EaseOutElastic,
Ease.EaseInOutElastic => EaseInOutElastic,
_ => null
};
/// <summary>
/// Gets the derivative function of the appropriate easing function. If you use an easing function for position then this
/// function can get you the speed at a given time (normalized).
/// </summary>
/// <param name="easingFunction"></param>
/// <returns>The derivative function</returns>
public static Function GetEasingFunctionDerivative(Ease easingFunction)
=> (easingFunction) switch
{
Ease.EaseInQuad => EaseInQuadD,
Ease.EaseOutQuad => EaseOutQuadD,
Ease.EaseInOutQuad => EaseInOutQuadD,
Ease.EaseInCubic => EaseInCubicD,
Ease.EaseOutCubic => EaseOutCubicD,
Ease.EaseInOutCubic => EaseInOutCubicD,
Ease.EaseInQuart => EaseInQuartD,
Ease.EaseOutQuart => EaseOutQuartD,
Ease.EaseInOutQuart => EaseInOutQuartD,
Ease.EaseInQuint => EaseInQuintD,
Ease.EaseOutQuint => EaseOutQuintD,
Ease.EaseInOutQuint => EaseInOutQuintD,
Ease.EaseInSine => EaseInSineD,
Ease.EaseOutSine => EaseOutSineD,
Ease.EaseInOutSine => EaseInOutSineD,
Ease.EaseInExpo => EaseInExpoD,
Ease.EaseOutExpo => EaseOutExpoD,
Ease.EaseInOutExpo => EaseInOutExpoD,
Ease.EaseInCirc => EaseInCircD,
Ease.EaseOutCirc => EaseOutCircD,
Ease.EaseInOutCirc => EaseInOutCircD,
Ease.Linear => LinearD,
Ease.Spring => SpringD,
Ease.EaseInBounce => EaseInBounceD,
Ease.EaseOutBounce => EaseOutBounceD,
Ease.EaseInOutBounce => EaseInOutBounceD,
Ease.EaseInBack => EaseInBackD,
Ease.EaseOutBack => EaseOutBackD,
Ease.EaseInOutBack => EaseInOutBackD,
Ease.EaseInElastic => EaseInElasticD,
Ease.EaseOutElastic => EaseOutElasticD,
Ease.EaseInOutElastic => EaseInOutElasticD,
_ => null
};
/// <summary>
/// Gets the derivative function of the appropriate easing function. If you use an easing function for position then this
/// function can get you the speed at a given time (normalized).
/// </summary>
/// <param name="easingFunction"></param>
/// <returns>The derivative function</returns>
public static Function01 GetEasingFunction01Derivative(Ease easingFunction)
=> (easingFunction) switch
{
Ease.EaseInQuad => EaseInQuadD,
Ease.EaseOutQuad => EaseOutQuadD,
Ease.EaseInOutQuad => EaseInOutQuadD,
Ease.EaseInCubic => EaseInCubicD,
Ease.EaseOutCubic => EaseOutCubicD,
Ease.EaseInOutCubic => EaseInOutCubicD,
Ease.EaseInQuart => EaseInQuartD,
Ease.EaseOutQuart => EaseOutQuartD,
Ease.EaseInOutQuart => EaseInOutQuartD,
Ease.EaseInQuint => EaseInQuintD,
Ease.EaseOutQuint => EaseOutQuintD,
Ease.EaseInOutQuint => EaseInOutQuintD,
Ease.EaseInSine => EaseInSineD,
Ease.EaseOutSine => EaseOutSineD,
Ease.EaseInOutSine => EaseInOutSineD,
Ease.EaseInExpo => EaseInExpoD,
Ease.EaseOutExpo => EaseOutExpoD,
Ease.EaseInOutExpo => EaseInOutExpoD,
Ease.EaseInCirc => EaseInCircD,
Ease.EaseOutCirc => EaseOutCircD,
Ease.EaseInOutCirc => EaseInOutCircD,
Ease.Linear => LinearD,
Ease.Spring => SpringD,
Ease.EaseInBounce => EaseInBounceD,
Ease.EaseOutBounce => EaseOutBounceD,
Ease.EaseInOutBounce => EaseInOutBounceD,
Ease.EaseInBack => EaseInBackD,
Ease.EaseOutBack => EaseOutBackD,
Ease.EaseInOutBack => EaseInOutBackD,
Ease.EaseInElastic => EaseInElasticD,
Ease.EaseOutElastic => EaseOutElasticD,
Ease.EaseInOutElastic => EaseInOutElasticD,
_ => null
};
}
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