Interpolate manager

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

// made by Erik Säll
// free to use CC0

public static class InterpolateManager {
    /// <param name="p_time">from 0f to 1f</param>
    public static float Linear(float p_start, float p_target, float p_time)
    {
        return (p_start * (1f - p_time)) + (p_target * p_time);
    }

    public static float Logarithmic(float p_start, float p_target, float p_time, float p_base)
    {
        float scale = p_time * p_base;

        // Logarithmic functions always have the root 1
        // so to start at 1 we do
        // (base * k) + 1 = base
        // which gives us
        // k = (base - 1) / base;

        float k = (p_base - 1) / p_base;
        float t = (scale * k) + 1;

        return Linear(p_start, p_target, Mathf.Log(t, p_base));
    }

    public static float Sqrt(float p_start, float p_target, float p_time)
    {
        return Linear(p_start, p_target, Mathf.Sqrt(p_time));
    }
    public static float Exponential(float p_start, float p_target, float p_time, float p_power)
    {
        return Linear(p_start, p_target, Mathf.Pow(p_time, p_power));
    }

    /// <summary>
    ///
    /// </summary>
    /// <param name="p_time">from 0f to 1f</param>
    public static float Sine(float p_start, float p_target, float p_time)
    {
        float pi = Mathf.PI;
        float t = p_time * pi;

        float sin = (Mathf.Sin((p_time * pi) - (pi / 2)) + 1) / 2;

        return Linear(p_start, p_target, sin);
    }

    /// <summary>Bouncy interpolation which overshoots the target</summary>
    /// <param name="p_time">from 0f to 1f</param>
    /// <param name="p_peak">the placement of the peak between 0f to 1f</param>
    /// <param name="p_magnitude">how much it overshoots the target. 0.5 is 50%</param>
    public static float Overshoot(float p_start, float p_target, float p_time, float p_peak, float p_magnitude)
    {
        float b = Linear(p_start, p_target, p_time);

        if (p_time < p_peak) {
            float t = p_time / p_peak;
            b += Sine(0, p_magnitude, t);
        }
        else {
            float t = (p_time - p_peak) / (1 - p_peak);
            b += Sine(p_magnitude, 0, t);
        }

        return b;
    }
}