Easing Functions for Unity3D

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
    {
        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 start, float end, float value)
    {
        return Mathf.Lerp(start, end, 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 start, float end, float value)
    {
        end -= start;
        return end * value * value + start;
    }

    public static float EaseOutQuad(float start, float end, float value)
    {
        end -= start;
        return -end * value * (value - 2) + start;
    }

    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 start, float end, float value)
    {
        end -= start;
        return end * value * value * value + start;
    }

    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 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 start, float end, float value)
    {
        end -= start;
        return end * value * value * value * value + start;
    }

    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 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 start, float end, float value)
    {
        end -= start;
        return end * value * value * value * value * value + start;
    }

    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 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 start, float end, float value)
    {
        end -= start;
        return -end * Mathf.Cos(value * (Mathf.PI * 0.5f)) + end + start;
    }

    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 start, float end, float value)
    {
        end -= start;
        return -end * 0.5f * (Mathf.Cos(Mathf.PI * value) - 1) + start;
    }

    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 start, float end, float value)
    {
        end -= start;
        return end * (-Mathf.Pow(2, -10 * value) + 1) + start;
    }

    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 start, float end, float value)
    {
        end -= start;
        return -end * (Mathf.Sqrt(1 - value * value) - 1) + start;
    }

    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 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 start, float end, float value)
    {
        end -= start;
        float d = 1f;
        return end - EaseOutBounce(0, end, d - value) + start;
    }

    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 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 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 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 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 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 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 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 start, float end, float value)
    {
        return end - start;
    }

    public static float EaseInQuadD(float start, float end, float value)
    {
        return 2f * (end - start) * value;
    }

    public static float EaseOutQuadD(float start, float end, float value)
    {
        end -= start;
        return -end * value - end * (value - 2);
    }

    public static float EaseInOutQuadD(float start, float end, float value)
    {
        value /= .5f;
        end -= start;

        if (value < 1)
        {
            return end * value;
        }

        value--;

        return end * (1 - value);
    }

    public static float EaseInCubicD(float start, float end, float value)
    {
        return 3f * (end - start) * value * value;
    }

    public static float EaseOutCubicD(float start, float end, float value)
    {
        value--;
        end -= start;
        return 3f * end * value * 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 start, float end, float value)
    {
        return 4f * (end - start) * value * value * 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 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 start, float end, float value)
    {
        return 5f * (end - start) * value * value * value * 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 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 start, float end, float value)
    {
        return (end - start) * 0.5f * Mathf.PI * Mathf.Sin(0.5f * Mathf.PI * 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 start, float end, float value)
    {
        end -= start;
        return end * 0.5f * Mathf.PI * Mathf.Sin(Mathf.PI * value);
    }
    public static float EaseInExpoD(float start, float end, float value)
    {
        return (10f * NATURAL_LOG_OF_2 * (end - start) * Mathf.Pow(2f, 10f * (value - 1)));
    }

    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 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 start, float end, float value)
    {
        return ((end - start) * value) / Mathf.Sqrt(1f - value * 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 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 start, float end, float value)
    {
        end -= start;
        float d = 1f;

        return EaseOutBounceD(0, end, d - 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);
            return 2f * end * 7.5625f * value;
        }
        else if (value < (2.5 / 2.75))
        {
            value -= (2.25f / 2.75f);
            return 2f * end * 7.5625f * value;
        }
        else
        {
            value -= (2.625f / 2.75f);
            return 2f * end * 7.5625f * 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;
        }
        else
        {
            return EaseOutBounceD(0, end, value * 2 - d) * 0.5f;
        }
    }

    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 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 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 start, float end, float value)
    {
        return EaseOutElasticD(start, end, 1f - 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 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 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);

    /// <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)
    {
        if (easingFunction == Ease.EaseInQuad)
        {
            return EaseInQuad;
        }

        if (easingFunction == Ease.EaseOutQuad)
        {
            return EaseOutQuad;
        }

        if (easingFunction == Ease.EaseInOutQuad)
        {
            return EaseInOutQuad;
        }

        if (easingFunction == Ease.EaseInCubic)
        {
            return EaseInCubic;
        }

        if (easingFunction == Ease.EaseOutCubic)
        {
            return EaseOutCubic;
        }

        if (easingFunction == Ease.EaseInOutCubic)
        {
            return EaseInOutCubic;
        }

        if (easingFunction == Ease.EaseInQuart)
        {
            return EaseInQuart;
        }

        if (easingFunction == Ease.EaseOutQuart)
        {
            return EaseOutQuart;
        }

        if (easingFunction == Ease.EaseInOutQuart)
        {
            return EaseInOutQuart;
        }

        if (easingFunction == Ease.EaseInQuint)
        {
            return EaseInQuint;
        }

        if (easingFunction == Ease.EaseOutQuint)
        {
            return EaseOutQuint;
        }

        if (easingFunction == Ease.EaseInOutQuint)
        {
            return EaseInOutQuint;
        }

        if (easingFunction == Ease.EaseInSine)
        {
            return EaseInSine;
        }

        if (easingFunction == Ease.EaseOutSine)
        {
            return EaseOutSine;
        }

        if (easingFunction == Ease.EaseInOutSine)
        {
            return EaseInOutSine;
        }

        if (easingFunction == Ease.EaseInExpo)
        {
            return EaseInExpo;
        }

        if (easingFunction == Ease.EaseOutExpo)
        {
            return EaseOutExpo;
        }

        if (easingFunction == Ease.EaseInOutExpo)
        {
            return EaseInOutExpo;
        }

        if (easingFunction == Ease.EaseInCirc)
        {
            return EaseInCirc;
        }

        if (easingFunction == Ease.EaseOutCirc)
        {
            return EaseOutCirc;
        }

        if (easingFunction == Ease.EaseInOutCirc)
        {
            return EaseInOutCirc;
        }

        if (easingFunction == Ease.Linear)
        {
            return Linear;
        }

        if (easingFunction == Ease.Spring)
        {
            return Spring;
        }

        if (easingFunction == Ease.EaseInBounce)
        {
            return EaseInBounce;
        }

        if (easingFunction == Ease.EaseOutBounce)
        {
            return EaseOutBounce;
        }

        if (easingFunction == Ease.EaseInOutBounce)
        {
            return EaseInOutBounce;
        }

        if (easingFunction == Ease.EaseInBack)
        {
            return EaseInBack;
        }

        if (easingFunction == Ease.EaseOutBack)
        {
            return EaseOutBack;
        }

        if (easingFunction == Ease.EaseInOutBack)
        {
            return EaseInOutBack;
        }

        if (easingFunction == Ease.EaseInElastic)
        {
            return EaseInElastic;
        }

        if (easingFunction == Ease.EaseOutElastic)
        {
            return EaseOutElastic;
        }

        if (easingFunction == Ease.EaseInOutElastic)
        {
            return EaseInOutElastic;
        }

        return 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)
    {
        if (easingFunction == Ease.EaseInQuad)
        {
            return EaseInQuadD;
        }

        if (easingFunction == Ease.EaseOutQuad)
        {
            return EaseOutQuadD;
        }

        if (easingFunction == Ease.EaseInOutQuad)
        {
            return EaseInOutQuadD;
        }

        if (easingFunction == Ease.EaseInCubic)
        {
            return EaseInCubicD;
        }

        if (easingFunction == Ease.EaseOutCubic)
        {
            return EaseOutCubicD;
        }

        if (easingFunction == Ease.EaseInOutCubic)
        {
            return EaseInOutCubicD;
        }

        if (easingFunction == Ease.EaseInQuart)
        {
            return EaseInQuartD;
        }

        if (easingFunction == Ease.EaseOutQuart)
        {
            return EaseOutQuartD;
        }

        if (easingFunction == Ease.EaseInOutQuart)
        {
            return EaseInOutQuartD;
        }

        if (easingFunction == Ease.EaseInQuint)
        {
            return EaseInQuintD;
        }

        if (easingFunction == Ease.EaseOutQuint)
        {
            return EaseOutQuintD;
        }

        if (easingFunction == Ease.EaseInOutQuint)
        {
            return EaseInOutQuintD;
        }

        if (easingFunction == Ease.EaseInSine)
        {
            return EaseInSineD;
        }

        if (easingFunction == Ease.EaseOutSine)
        {
            return EaseOutSineD;
        }

        if (easingFunction == Ease.EaseInOutSine)
        {
            return EaseInOutSineD;
        }

        if (easingFunction == Ease.EaseInExpo)
        {
            return EaseInExpoD;
        }

        if (easingFunction == Ease.EaseOutExpo)
        {
            return EaseOutExpoD;
        }

        if (easingFunction == Ease.EaseInOutExpo)
        {
            return EaseInOutExpoD;
        }

        if (easingFunction == Ease.EaseInCirc)
        {
            return EaseInCircD;
        }

        if (easingFunction == Ease.EaseOutCirc)
        {
            return EaseOutCircD;
        }

        if (easingFunction == Ease.EaseInOutCirc)
        {
            return EaseInOutCircD;
        }

        if (easingFunction == Ease.Linear)
        {
            return LinearD;
        }

        if (easingFunction == Ease.Spring)
        {
            return SpringD;
        }

        if (easingFunction == Ease.EaseInBounce)
        {
            return EaseInBounceD;
        }

        if (easingFunction == Ease.EaseOutBounce)
        {
            return EaseOutBounceD;
        }

        if (easingFunction == Ease.EaseInOutBounce)
        {
            return EaseInOutBounceD;
        }

        if (easingFunction == Ease.EaseInBack)
        {
            return EaseInBackD;
        }

        if (easingFunction == Ease.EaseOutBack)
        {
            return EaseOutBackD;
        }

        if (easingFunction == Ease.EaseInOutBack)
        {
            return EaseInOutBackD;
        }

        if (easingFunction == Ease.EaseInElastic)
        {
            return EaseInElasticD;
        }

        if (easingFunction == Ease.EaseOutElastic)
        {
            return EaseOutElasticD;
        }

        if (easingFunction == Ease.EaseInOutElastic)
        {
            return EaseInOutElasticD;
        }

        return null;
    }
}

You rock!

This is going to be a pretty noob question (just getting started with the mathematics of easing functions) but here it goes:

I'm slightly confused about what value to use for the "value" parameter (so the easing value of the easing function).

For example say I was trying to rotate an object 90 degrees using the EaseOutBounce function, and that I wanted that animation to last 3 seconds — how would I define the easing value?

EasingFunction.Ease ease = EasingFunction.Ease.EaseOutBounce;
EasingFunction.EasingFunc func = GetEasingFunction(ease);

float rotationAmountForThisFrame = func(currentRotation, 90, easingValue);

Thanks for your help!

easingValue is just the normalized value (0...1) between the start and end values. For linear this is very simple, 0.5 easing value of 0 to 10 would be 5. But for other easing functions it can give back a different answer. If I was making a 90 degree rotation over three seconds I would do something like this every frame float rotationAmount = func(0, 90, timeRunning / 3) timeRunning += Time.deltaTime;

…

On Fri, Jul 17, 2020 at 4:51 AM zovig23 ***@***.***> wrote: ***@***.**** commented on this gist. ------------------------------ This is going to be a pretty noob question (just getting started with the mathematics of easing functions) but here it goes: I'm slightly confused about what value to use for the "value" parameter (so the easing value of the easing function). For example say I was trying to rotate an object 90 degrees using the EaseOutBounce function, and that I wanted that animation to last 3 seconds — how would I define the easing value? EasingFunction.Ease ease = EasingFunction.Ease.EaseOutBounce; EasingFunction.EasingFunc func = GetEasingFunction(ease); float rotationAmount = func(0, 10, *easingValue*); Thanks for your help! — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <https://gist.github.com/d789b9eb78216998e95c#gistcomment-3381083>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAW4A365D7K3CZRXGAXWFGLR4A3MZANCNFSM4HZDWX7A> .

Thanks for the help! It worked Sent from a mobile phone

…

On Fri, Jul 17, 2020, 20:07 C.J. Kimberlin ***@***.***> wrote: ***@***.**** commented on this gist. ------------------------------ easingValue is just the normalized value (0...1) between the start and end values. For linear this is very simple, 0.5 easing value of 0 to 10 would be 5. But for other easing functions it can give back a different answer. If I was making a 90 degree rotation over three seconds I would do something like this every frame float rotationAmount = func(0, 90, timeRunning / 3) timeRunning += Time.deltaTime; On Fri, Jul 17, 2020 at 4:51 AM zovig23 ***@***.***> wrote: > ***@***.**** commented on this gist. > ------------------------------ > > This is going to be a pretty noob question (just getting started with the > mathematics of easing functions) but here it goes: > > I'm slightly confused about what value to use for the "value" parameter > (so the easing value of the easing function). > > For example say I was trying to rotate an object 90 degrees using the > EaseOutBounce function, and that I wanted that animation to last 3 seconds > — how would I define the easing value? > > EasingFunction.Ease ease = EasingFunction.Ease.EaseOutBounce; > EasingFunction.EasingFunc func = GetEasingFunction(ease); > > float rotationAmount = func(0, 10, *easingValue*); > > Thanks for your help! > > — > You are receiving this because you authored the thread. > Reply to this email directly, view it on GitHub > <https://gist.github.com/d789b9eb78216998e95c#gistcomment-3381083>, or > unsubscribe > < https://github.com/notifications/unsubscribe-auth/AAW4A365D7K3CZRXGAXWFGLR4A3MZANCNFSM4HZDWX7A > > . > — You are receiving this because you commented. Reply to this email directly, view it on GitHub <https://gist.github.com/d789b9eb78216998e95c#gistcomment-3381622>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AMUOINJOQ3ZCNGQ5HCXQLXLR4COP7ANCNFSM4HZDWX7A> .

With a more dated C# you can do this:

        public static Function GetEasingFunction(Ease easingFunction)
            => (easingFunction) switch
            {
                Ease.EaseInQuad => EaseInQuad,
                Ease.EaseOutQuad => EaseOutQuad,
                Ease.EaseInOutQuad => EaseInOutQuad,
                Ease.EaseInCubic => EaseInCubic,
                . . . 
                . . . 
                . . . 
                Ease.EaseInElastic => EaseInElastic,
                Ease.EaseOutElastic => EaseOutElastic,
                Ease.EaseInOutElastic => EaseInOutElastic,
                _ => null
            };

For both GetEasingFunction() and GetEasingFunctionDerivative() to get ~300 less lines :)
Check my fork

❤️

Hi, is there any source to see these functions on a graph. I just could find some of them but I want to see each of these functions pattern on a graph to visualize.
Thanks.

Hi, is there any source to see these functions on a graph. I just could find some of them but I want to see each of these functions pattern on a graph to visualize.
Thanks.

Sure here https://easings.net/

I also found these which are helpful:
https://greensock.com/ease-visualizer/
https://observablehq.com/@nhogs/easing-graphs-editor
https://github.com/noisecrime/Unity-EasingLibraryVisualisation

Lines 53 to 55 are incomplete.
53 seems to have a spelling mistake and it looks like nothing like this exists "EasingFunction.EaseingFunc"
Could you please give a clearer example of how to get the derivative of the defined easing function?

53 * EasingFunction.EaseingFunc derivativeFunc = GetEasingFunctionDerivative(ease);
54 * 
55 * float derivativeValue = derivativeFunc(0, 10, 0.67f);

rock You!

Hey, what is EasingFunction.EasingFunc?
@androvisuals did you solve this?
Cheers!

Lines 53 to 55 are incomplete. 53 seems to have a spelling mistake and it looks like nothing like this exists "EasingFunction.EaseingFunc" Could you please give a clearer example of how to get the derivative of the defined easing function?

53 * EasingFunction.EaseingFunc derivativeFunc = GetEasingFunctionDerivative(ease);
54 * 
55 * float derivativeValue = derivativeFunc(0, 10, 0.67f);

Hey, what is EasingFunction.EasingFunc? @androvisuals did you solve this? Cheers!

EasingFunction.EaseingFunc is referring to the two delegates EasingFunction.Function and EasingFunction.Function01

Has anybody coded an implementation of cubic-bezier like CSS3 does in order to use custom values?
I mean stuff like: https://matthewlein.com/tools/ceaser

This is in one of my random math utility files. Maybe what you want?

public static float3 BezierCubicCurve(float t, float3 p0, float3 p1, float3 p2, float3 p3)
{
float u = 1 - t;
float tt = t * t;
float uu = u * u;
float uuu = uu * u;
float ttt = tt * t;
float3 p = uuu * p0;
p += 3 * uu * t * p1;
p += 3 * u * tt * p2;
p += ttt * p3;
return p;
}

Hello! So I'm new to Unity and I'm having some trouble using this library and hope you can help me. I have four variables: StartValue, EndValue, Duration, PowerValue (the strength of the curve basically). Say I would like the player to become smarter by going from 10 int to 50 int over 30 seconds in a non-linear fashion and I would like to control this curve on runtime by substituting the power value.

EasingFunction.EaseOutQuad(0f, 50f, 30f);

Is that how this works? You can't really modify the power of the curve x^2, x^3, x^4, x^5, etc. since it's already hardcoded to the function itself right? EaseOutQuad = x^2, EaseOutCubic = x^3. So I guess that would mean I would need to create as basic easing function with a fourth parameter unless I'm missing something that your library has I can use.

EDIT: Oh I see... "value" parameter is basically a percentage of completion. So basically 0 to 1 and everything in between. My other question still stands though, we can't really change the strength of the curvature since it's hardcoded AS the function, right?

This is in one of my random math utility files. Maybe what you want?

public static float3 BezierCubicCurve(float t, float3 p0, float3 p1, float3 p2, float3 p3) { float u = 1 - t; float tt = t * t; float uu = u * u; float uuu = uu * u; float ttt = tt * t; float3 p = uuu * p0; p += 3 * uu * t * p1; p += 3 * u * tt * p2; p += ttt * p3; return p; }

That function returns a float3, I was thinking something that just returns a plain float between 0 and 1 like the functions in this gist, for example the CSS3 spec says that easy-in-out is equivalent to cubic-bezier(0.42, 0, 0.58, 1)

@Ivanca You can pretty simply convert that function to do what you want, there are resources out there that can help. Original code is from https://www.gamedeveloper.com/business/how-to-work-with-bezier-curve-in-games-with-unity

@LizThompson93 Each function is hardcoded but each one in a stronger/different ease. You're right that Quad is basically x^2 and Cubic is x^3 and there's also Quart and Quint. It's basically different function interpolations between 0 to 1. You can always get creative and multiply some of these against each other to create new curves. This isn't to say this covers all the interpolation functions you could think of but they would just need to be created and added.

You're right that it's effectively a percentage of completion. Some of the easing functions support going outside the bounds of 0 and 1 but I don't guarantee it.

Thank man for this amazing work saves a lot of routine time for me :)

Please, take a look at my fork (https://gist.github.com/ManeFunction/9f2d437fca6ccf31e4a48fec0584e21a) I've made some quick improvements:

* implement constants in methods where they should be

* fixed float comparisons to prevent issues and warnings

* replaced if-else to switch-case's within root methods (in the new C# versions they use code jumps instead of if-else trees what is obviously more efficient with such a big if-chains, you can read about it here for ex.: https://stackoverflow.com/questions/395618/is-there-any-significant-difference-between-using-if-else-and-switch-case-in-c)

* fixed a few typos :)

Great work.

I have it forked to works on Godot Engine: https://gist.github.com/nodlag/9e0f975e3bf26a9e80c38d8381fd96b8

@nodlag be aware that at a time of your comment my fork contained cos/sin issue mentioned above, so your's had it as well (549 line)

P.S.: Updated, cleaned and refactored it today with new C# features (like switch expressions) and some personal preferences with a code style.

Just out of interest, how come we are dividing 'value' by 0.5f instead of simply multiplying it by 2f?
I was under the impression that division is always slower than multiplication when it comes to programming.

Just out of interest, how come we are dividing 'value' by 0.5f instead of simply multiplying it by 2f? I was under the impression that division is always slower than multiplication when it comes to programming.

No particular reason

Absolutely fantastic