hellbound/Assets/Sources/Feel/MMTools/Tools/MMHelpers/MMMaths.cs

using UnityEngine;
using UnityEngine.UI;
using System.Collections;
using System;

namespace MoreMountains.Tools
{	
	/// <summary>
	/// Math helpers
	/// </summary>

	public static class MMMaths
    {
        /// <summary>
        /// Internal method used to compute the spring velocity
        /// </summary>
        /// <param name="currentValue"></param>
        /// <param name="targetValue"></param>
        /// <param name="velocity"></param>
        /// <param name="damping"></param>
        /// <param name="frequency"></param>
        /// <param name="speed"></param>
        /// <param name="deltaTime"></param>
        /// <returns></returns>
        private static float SpringVelocity(float currentValue, float targetValue, float velocity, float damping, float frequency, float speed, float deltaTime)
        {
            frequency = frequency * 2f * Mathf.PI;
            return velocity + (deltaTime * frequency * frequency * (targetValue - currentValue)) + (-2.0f * deltaTime * frequency * damping * velocity);
        }

        /// <summary>
        /// Springs a float towards a target value 
        /// </summary>
        /// <param name="currentValue">the current value to spring, passed as a ref</param>
        /// <param name="targetValue">the target value we're aiming for</param>
        /// <param name="velocity">a velocity value, passed as ref, used to compute the current speed of the springed value</param>
        /// <param name="damping">the damping, between 0.01f and 1f, the higher the daming, the less springy it'll be</param>
        /// <param name="frequency">the frequency, in Hz, so the amount of periods the spring should go over in 1 second</param>
        /// <param name="speed">the speed (between 0 and 1) at which the spring should operate</param>
        /// <param name="deltaTime">the delta time (usually Time.deltaTime or Time.unscaledDeltaTime)</param>
        public static void Spring(ref float currentValue, float targetValue, ref float velocity, float damping, float frequency, float speed, float deltaTime)
        {
            float initialVelocity = velocity;
            velocity = SpringVelocity(currentValue, targetValue, velocity, damping, frequency, speed, deltaTime);
            velocity = MMMaths.Lerp(initialVelocity, velocity, speed, Time.deltaTime);
            currentValue += deltaTime * velocity;
        }

        /// <summary>
        /// Springs a Vector2 towards a target value 
        /// </summary>
        /// <param name="currentValue">the current value to spring, passed as a ref</param>
        /// <param name="targetValue">the target value we're aiming for</param>
        /// <param name="velocity">a velocity value, passed as ref, used to compute the current speed of the springed value</param>
        /// <param name="damping">the damping, between 0.01f and 1f, the higher the daming, the less springy it'll be</param>
        /// <param name="frequency">the frequency, in Hz, so the amount of periods the spring should go over in 1 second</param>
        /// <param name="speed">the speed (between 0 and 1) at which the spring should operate</param>
        /// <param name="deltaTime">the delta time (usually Time.deltaTime or Time.unscaledDeltaTime)</param>
        public static void Spring(ref Vector2 currentValue, Vector2 targetValue, ref Vector2 velocity, float damping, float frequency, float speed, float deltaTime)
        {
            Vector2 initialVelocity = velocity;
            velocity.x = SpringVelocity(currentValue.x, targetValue.x, velocity.x, damping, frequency, speed, deltaTime);
            velocity.y = SpringVelocity(currentValue.y, targetValue.y, velocity.y, damping, frequency, speed, deltaTime);
            velocity.x = MMMaths.Lerp(initialVelocity.x, velocity.x, speed, Time.deltaTime);
            velocity.y = MMMaths.Lerp(initialVelocity.y, velocity.y, speed, Time.deltaTime);
            currentValue += deltaTime * velocity;
        }

        /// <summary>
        /// Springs a Vector3 towards a target value 
        /// </summary>
        /// <param name="currentValue">the current value to spring, passed as a ref</param>
        /// <param name="targetValue">the target value we're aiming for</param>
        /// <param name="velocity">a velocity value, passed as ref, used to compute the current speed of the springed value</param>
        /// <param name="damping">the damping, between 0.01f and 1f, the higher the daming, the less springy it'll be</param>
        /// <param name="frequency">the frequency, in Hz, so the amount of periods the spring should go over in 1 second</param>
        /// <param name="speed">the speed (between 0 and 1) at which the spring should operate</param>
        /// <param name="deltaTime">the delta time (usually Time.deltaTime or Time.unscaledDeltaTime)</param>
        public static void Spring(ref Vector3 currentValue, Vector3 targetValue, ref Vector3 velocity, float damping, float frequency, float speed, float deltaTime)
        {
            Vector3 initialVelocity = velocity;
            velocity.x = SpringVelocity(currentValue.x, targetValue.x, velocity.x, damping, frequency, speed, deltaTime);
            velocity.y = SpringVelocity(currentValue.y, targetValue.y, velocity.y, damping, frequency, speed, deltaTime);
            velocity.z = SpringVelocity(currentValue.z, targetValue.z, velocity.z, damping, frequency, speed, deltaTime);
            velocity.x = MMMaths.Lerp(initialVelocity.x, velocity.x, speed, Time.deltaTime);
            velocity.y = MMMaths.Lerp(initialVelocity.y, velocity.y, speed, Time.deltaTime);
            velocity.z = MMMaths.Lerp(initialVelocity.z, velocity.z, speed, Time.deltaTime);
            currentValue += deltaTime * velocity;
        }

        /// <summary>
        /// Springs a Vector4 towards a target value 
        /// </summary>
        /// <param name="currentValue">the current value to spring, passed as a ref</param>
        /// <param name="targetValue">the target value we're aiming for</param>
        /// <param name="velocity">a velocity value, passed as ref, used to compute the current speed of the springed value</param>
        /// <param name="damping">the damping, between 0.01f and 1f, the higher the daming, the less springy it'll be</param>
        /// <param name="frequency">the frequency, in Hz, so the amount of periods the spring should go over in 1 second</param>
        /// <param name="speed">the speed (between 0 and 1) at which the spring should operate</param>
        /// <param name="deltaTime">the delta time (usually Time.deltaTime or Time.unscaledDeltaTime)</param>
        public static void Spring(ref Vector4 currentValue, Vector4 targetValue, ref Vector4 velocity, float damping, float frequency, float speed, float deltaTime)
        {
            Vector4 initialVelocity = velocity;
            velocity.x = SpringVelocity(currentValue.x, targetValue.x, velocity.x, damping, frequency, speed, deltaTime);
            velocity.y = SpringVelocity(currentValue.y, targetValue.y, velocity.y, damping, frequency, speed, deltaTime);
            velocity.z = SpringVelocity(currentValue.z, targetValue.z, velocity.z, damping, frequency, speed, deltaTime);
            velocity.w = SpringVelocity(currentValue.w, targetValue.w, velocity.w, damping, frequency, speed, deltaTime);
            velocity.x = MMMaths.Lerp(initialVelocity.x, velocity.x, speed, Time.deltaTime);
            velocity.y = MMMaths.Lerp(initialVelocity.y, velocity.y, speed, Time.deltaTime);
            velocity.z = MMMaths.Lerp(initialVelocity.z, velocity.z, speed, Time.deltaTime);
            velocity.w = MMMaths.Lerp(initialVelocity.w, velocity.w, speed, Time.deltaTime);
            currentValue += deltaTime * velocity;
        }

        /// <summary>
        /// internal method used to determine the lerp rate
        /// </summary>
        /// <param name="rate"></param>
        /// <returns></returns>
        private static float LerpRate(float rate, float deltaTime)
        {
            rate = Mathf.Clamp01(rate);
            float invRate = - Mathf.Log(1.0f - rate, 2.0f) * 60f;
            return Mathf.Pow(2.0f, -invRate * deltaTime);
        }

        /// <summary>
        /// Lerps a float towards a target at the specified rate
        /// </summary>
        /// <param name="value"></param>
        /// <param name="target"></param>
        /// <param name="rate"></param>
        /// <returns></returns>
        public static float Lerp(float value, float target, float rate, float deltaTime)
        {
            if (deltaTime == 0f) { return value; }
            return Mathf.Lerp(target, value, LerpRate(rate, deltaTime));
        }

        /// <summary>
        /// Lerps a Vector2 towards a target at the specified rate
        /// </summary>
        /// <param name="value"></param>
        /// <param name="target"></param>
        /// <param name="rate"></param>
        /// <returns></returns>
        public static Vector2 Lerp(Vector2 value, Vector2 target, float rate, float deltaTime)
        {
            if (deltaTime == 0f) { return value; }
            return Vector2.Lerp(target, value, LerpRate(rate, deltaTime));
        }

        /// <summary>
        /// Lerps a Vector3 towards a target at the specified rate
        /// </summary>
        /// <param name="value"></param>
        /// <param name="target"></param>
        /// <param name="rate"></param>
        /// <returns></returns>
        public static Vector3 Lerp(Vector3 value, Vector3 target, float rate, float deltaTime)
        {
            if (deltaTime == 0f) { return value; }
            return Vector3.Lerp(target, value, LerpRate(rate, deltaTime));
        }

        /// <summary>
        /// Lerps a Vector4 towards a target at the specified rate
        /// </summary>
        /// <param name="value"></param>
        /// <param name="target"></param>
        /// <param name="rate"></param>
        /// <returns></returns>
        public static Vector4 Lerp(Vector4 value, Vector4 target, float rate, float deltaTime)
        {
            if (deltaTime == 0f) { return value; }
            return Vector4.Lerp(target, value, LerpRate(rate, deltaTime));
        }

        /// <summary>
        /// Lerps a Quaternion towards a target at the specified rate
        /// </summary>
        /// <param name="value"></param>
        /// <param name="target"></param>
        /// <param name="rate"></param>
        /// <returns></returns>
        public static Quaternion Lerp(Quaternion value, Quaternion target, float rate, float deltaTime)
        {
            if (deltaTime == 0f) { return value; }
            return Quaternion.Lerp(target, value, LerpRate(rate, deltaTime));
        }

        /// <summary>
        /// Lerps a Color towards a target at the specified rate
        /// </summary>
        /// <param name="value"></param>
        /// <param name="target"></param>
        /// <param name="rate"></param>
        /// <returns></returns>
        public static Color Lerp(Color value, Color target, float rate, float deltaTime)
        {
            if (deltaTime == 0f) { return value; }
            return Color.Lerp(target, value, LerpRate(rate, deltaTime));
        }

        /// <summary>
        /// Lerps a Color32 towards a target at the specified rate
        /// </summary>
        /// <param name="value"></param>
        /// <param name="target"></param>
        /// <param name="rate"></param>
        /// <returns></returns>
        public static Color32 Lerp(Color32 value, Color32 target, float rate, float deltaTime)
        {
            if (deltaTime == 0f) { return value; }
            return Color32.Lerp(target, value, LerpRate(rate, deltaTime));
        }

        /// <summary>
        /// Clamps a float between min and max, both bounds being optional and driven by clampMin and clampMax respectively
        /// </summary>
        /// <param name="value"></param>
        /// <param name="min"></param>
        /// <param name="max"></param>
        /// <param name="clampMin"></param>
        /// <param name="clampMax"></param>
        /// <returns></returns>
        public static float Clamp(float value, float min, float max, bool clampMin, bool clampMax)
        {
            float returnValue = value;
            if (clampMin && (returnValue < min))
            {
                returnValue = min;
            }
            if (clampMax && (returnValue > max))
            {
                returnValue = max;
            }
            return returnValue;
        }

        /// <summary>
        /// Rounds a float to the nearest half value : 1, 1.5, 2, 2.5 etc
        /// </summary>
        /// <param name="a"></param>
        /// <returns></returns>
        public static float RoundToNearestHalf(float a)
        {
            return a = a - (a % 0.5f);
        }

        /// <summary>
        /// Takes a Vector3 and turns it into a Vector2
        /// </summary>
        /// <returns>The vector2.</returns>
        /// <param name="target">The Vector3 to turn into a Vector2.</param>
        public static Vector2 Vector3ToVector2 (Vector3 target) 
		{
			return new Vector2(target.x, target.y);
		}

		/// <summary>
		/// Takes a Vector2 and turns it into a Vector3 with a null z value
		/// </summary>
		/// <returns>The vector3.</returns>
		/// <param name="target">The Vector2 to turn into a Vector3.</param>
		public static Vector3 Vector2ToVector3 (Vector2 target) 
		{
			return new Vector3(target.x, target.y, 0);
		}

		/// <summary>
		/// Takes a Vector2 and turns it into a Vector3 with the specified z value 
		/// </summary>
		/// <returns>The vector3.</returns>
		/// <param name="target">The Vector2 to turn into a Vector3.</param>
		/// <param name="newZValue">New Z value.</param>
		public static Vector3 Vector2ToVector3 (Vector2 target, float newZValue) 
		{
			return new Vector3(target.x, target.y, newZValue);
		}

		/// <summary>
		/// Rounds all components of a Vector3.
		/// </summary>
		/// <returns>The vector3.</returns>
		/// <param name="vector">Vector.</param>
		public static Vector3 RoundVector3 (Vector3 vector)
		{
			return new Vector3 (Mathf.Round (vector.x), Mathf.Round (vector.y), Mathf.Round (vector.z));
        }

        /// <summary>
        /// Returns a random Vector2 from 2 defined Vector2.
        /// </summary>
        /// <returns>The random Vector2.</returns>
        /// <param name="min">Minimum.</param>
        /// <param name="max">Maximum.</param>
        public static Vector2 RandomVector2(Vector2 minimum, Vector2 maximum)
        {
            return new Vector2(UnityEngine.Random.Range(minimum.x, maximum.x),
                                             UnityEngine.Random.Range(minimum.y, maximum.y));
        }

        /// <summary>
        /// Returns a random Vector3 from 2 defined Vector3.
        /// </summary>
        /// <returns>The random Vector3.</returns>
        /// <param name="min">Minimum.</param>
        /// <param name="max">Maximum.</param>
        public static Vector3 RandomVector3(Vector3 minimum, Vector3 maximum)
        {
            return new Vector3(UnityEngine.Random.Range(minimum.x, maximum.x),
                                             UnityEngine.Random.Range(minimum.y, maximum.y),
                                             UnityEngine.Random.Range(minimum.z, maximum.z));
        }

        /// <summary>
        /// Returns a random point on the circle of the specified radius
        /// </summary>
        /// <param name="circleRadius"></param>
        /// <returns></returns>
        public static Vector2 RandomPointOnCircle(float circleRadius)
        {
	        return UnityEngine.Random.insideUnitCircle.normalized * circleRadius;
        }

        /// <summary>
        /// Returns a random point on the sphere of the specified radius
        /// </summary>
        /// <param name="sphereRadius"></param>
        /// <returns></returns>
        public static Vector3 RandomPointOnSphere(float sphereRadius)
        {
	        return UnityEngine.Random.onUnitSphere * sphereRadius;
        }

        /// <summary>
        /// Rotates a point around the given pivot.
        /// </summary>
        /// <returns>The new point position.</returns>
        /// <param name="point">The point to rotate.</param>
        /// <param name="pivot">The pivot's position.</param>
        /// <param name="angle">The angle we want to rotate our point.</param>
        public static Vector3 RotatePointAroundPivot(Vector3 point, Vector3 pivot, float angle) 
		{			
			angle = angle*(Mathf.PI/180f);
            float rotatedX = Mathf.Cos(angle) * (point.x - pivot.x) - Mathf.Sin(angle) * (point.y-pivot.y) + pivot.x;
            float rotatedY = Mathf.Sin(angle) * (point.x - pivot.x) + Mathf.Cos(angle) * (point.y - pivot.y) + pivot.y;
			return new Vector3(rotatedX,rotatedY,0);		
				}

		/// <summary>
		/// Rotates a point around the given pivot.
		/// </summary>
		/// <returns>The new point position.</returns>
		/// <param name="point">The point to rotate.</param>
		/// <param name="pivot">The pivot's position.</param>
		/// <param name="angles">The angle as a Vector3.</param>
		public static Vector3 RotatePointAroundPivot(Vector3 point, Vector3 pivot, Vector3 angle) 
		{
			// we get point direction from the point to the pivot
		   	Vector3 direction = point - pivot; 
		   	// we rotate the direction
		   	direction = Quaternion.Euler(angle) * direction; 
		   	// we determine the rotated point's position
		   	point = direction + pivot; 
		   	return point; 
		}

		/// <summary>
		/// Rotates a point around the given pivot.
		/// </summary>
		/// <returns>The new point position.</returns>
		/// <param name="point">The point to rotate.</param>
		/// <param name="pivot">The pivot's position.</param>
		/// <param name="angles">The angle as a Vector3.</param>
		public static Vector3 RotatePointAroundPivot(Vector3 point, Vector3 pivot, Quaternion quaternion) 
		{
			// we get point direction from the point to the pivot
		   	Vector3 direction = point - pivot; 
		   	// we rotate the direction
		   	direction = quaternion * direction; 
		   	// we determine the rotated point's position
		   	point = direction + pivot; 
		   	return point; 
		 }

		/// <summary>
		/// Rotates a vector2 by the angle (in degrees) specified and returns it
		/// </summary>
		/// <returns>The rotated Vector2.</returns>
		/// <param name="vector">The vector to rotate.</param>
		/// <param name="angle">Degrees.</param>
		public static Vector2 RotateVector2(Vector2 vector, float angle) {
			if (angle == 0)
			{
				return vector;
			}
			float sinus = Mathf.Sin(angle * Mathf.Deg2Rad);
			float cosinus = Mathf.Cos(angle * Mathf.Deg2Rad);

			float oldX = vector.x;
			float oldY = vector.y;
			vector.x = (cosinus * oldX) - (sinus * oldY);
			vector.y = (sinus * oldX) + (cosinus * oldY);
			return vector;
		}

		/// <summary>
		/// Computes and returns the angle between two vectors, on a 360° scale
		/// </summary>
		/// <returns>The <see cref="System.Single"/>.</returns>
		/// <param name="vectorA">Vector a.</param>
		/// <param name="vectorB">Vector b.</param>
		public static float AngleBetween(Vector2 vectorA, Vector2 vectorB)
		{
			float angle = Vector2.Angle(vectorA, vectorB);
			Vector3 cross = Vector3.Cross(vectorA, vectorB);

			if (cross.z > 0)
			{
				angle = 360 - angle;
			}

			return angle;
		}

		/// <summary>
		/// Returns the distance between a point and a line.
		/// </summary>
		/// <returns>The between point and line.</returns>
		/// <param name="point">Point.</param>
		/// <param name="lineStart">Line start.</param>
		/// <param name="lineEnd">Line end.</param>
		public static float DistanceBetweenPointAndLine(Vector3 point, Vector3 lineStart, Vector3 lineEnd)
		{
			return Vector3.Magnitude(ProjectPointOnLine(point, lineStart, lineEnd) - point);
		}

		/// <summary>
		/// Projects a point on a line (perpendicularly) and returns the projected point.
		/// </summary>
		/// <returns>The point on line.</returns>
		/// <param name="point">Point.</param>
		/// <param name="lineStart">Line start.</param>
		/// <param name="lineEnd">Line end.</param>
		public static Vector3 ProjectPointOnLine(Vector3 point, Vector3 lineStart, Vector3 lineEnd)
		{
			Vector3 rhs = point - lineStart;
			Vector3 vector2 = lineEnd - lineStart;
			float magnitude = vector2.magnitude;
			Vector3 lhs = vector2;
			if (magnitude > 1E-06f)
			{
				lhs = (Vector3)(lhs / magnitude);
			}
			float num2 = Mathf.Clamp(Vector3.Dot(lhs, rhs), 0f, magnitude);
			return (lineStart + ((Vector3)(lhs * num2)));
		}

		/// <summary>
		/// Returns the sum of all the int passed in parameters
		/// </summary>
		/// <param name="thingsToAdd">Things to add.</param>
		public static int Sum(params int[] thingsToAdd)
		{
			int result=0;
			for (int i = 0; i < thingsToAdd.Length; i++)
			{
				result += thingsToAdd[i];
			}
			return result;
		}

		/// <summary>
		/// Returns the result of rolling a dice of the specified number of sides
		/// </summary>
		/// <returns>The result of the dice roll.</returns>
		/// <param name="numberOfSides">Number of sides of the dice.</param>
		public static int RollADice(int numberOfSides)
		{
			return (UnityEngine.Random.Range(1,numberOfSides+1));
		}

		/// <summary>
		/// Returns a random success based on X% of chance.
		/// Example : I have 20% of chance to do X, Chance(20) > true, yay!
		/// </summary>
		/// <param name="percent">Percent of chance.</param>
		public static bool Chance(int percent)
		{
			return (UnityEngine.Random.Range(0,100) <= percent);
		}

		/// <summary>
		/// Moves from "from" to "to" by the specified amount and returns the corresponding value
		/// </summary>
		/// <param name="from">From.</param>
		/// <param name="to">To.</param>
		/// <param name="amount">Amount.</param>
		public static float Approach(float from, float to, float amount)
		{
			if (from < to)
			{
				from += amount;
				if (from > to)
				{
					return to;
				}
			}
			else
			{
				from -= amount;
				if (from < to)
				{
					return to;
				}
			}
			return from;
		} 


		/// <summary>
		/// Remaps a value x in interval [A,B], to the proportional value in interval [C,D]
		/// </summary>
		/// <param name="x">The value to remap.</param>
		/// <param name="A">the minimum bound of interval [A,B] that contains the x value</param>
		/// <param name="B">the maximum bound of interval [A,B] that contains the x value</param>
		/// <param name="C">the minimum bound of target interval [C,D]</param>
		/// <param name="D">the maximum bound of target interval [C,D]</param>
		public static float Remap(float x, float A, float B, float C, float D)
		{
			float remappedValue = C + (x-A)/(B-A) * (D - C);
			return remappedValue;
		}

        /// <summary>
        /// Clamps the angle in parameters between a minimum and maximum angle (all angles expressed in degrees)
        /// </summary>
        /// <param name="angle"></param>
        /// <param name="minimumAngle"></param>
        /// <param name="maximumAngle"></param>
        /// <returns></returns>
        public static float ClampAngle(float angle, float minimumAngle, float maximumAngle)
        {
            if (angle < -360)
            {
                angle += 360;
            }
            if (angle > 360)
            {
                angle -= 360;
            }
            return Mathf.Clamp(angle, minimumAngle, maximumAngle);
        }

        public static float RoundToDecimal(float value, int numberOfDecimals)
        {
	        if (numberOfDecimals <= 0)
	        {
		        return Mathf.Round(value);   
	        }
	        else
	        {
		        return Mathf.Round(value * 10f * numberOfDecimals) / (10f * numberOfDecimals);    
	        }
        }

        /// <summary>
        /// Rounds the value passed in parameters to the closest value in the parameter array
        /// </summary>
        /// <param name="value"></param>
        /// <param name="possibleValues"></param>
        /// <returns></returns>
        public static float RoundToClosest(float value, float[] possibleValues, bool pickSmallestDistance = false)
		{
			if (possibleValues.Length == 0) 
			{
				return 0f;
			}

			float closestValue = possibleValues[0];

			foreach (float possibleValue in possibleValues)
			{
                float closestDistance = Mathf.Abs(closestValue - value);
                float possibleDistance = Mathf.Abs(possibleValue - value);

                if (closestDistance > possibleDistance)
				{
					closestValue = possibleValue;
				}
                else if (closestDistance == possibleDistance)
                {                    
                    if ((pickSmallestDistance && closestValue > possibleValue) || (!pickSmallestDistance && closestValue < possibleValue))
                    {
                        closestValue = (value < 0) ? closestValue : possibleValue;
                    }
                }
			}
            return closestValue;

        }

        /// <summary>
        /// Returns a vector3 based on the angle in parameters
        /// </summary>
        /// <param name="angle"></param>
        /// <returns></returns>
        public static Vector3 DirectionFromAngle(float angle, float additionalAngle)
        {
            angle += additionalAngle;

            Vector3 direction = Vector3.zero;
            direction.x = Mathf.Sin(angle * Mathf.Deg2Rad);
            direction.y = 0f;
            direction.z = Mathf.Cos(angle * Mathf.Deg2Rad);
            return direction;
        }

        /// <summary>
        /// Returns a vector3 based on the angle in parameters
        /// </summary>
        /// <param name="angle"></param>
        /// <returns></returns>
        public static Vector3 DirectionFromAngle2D(float angle, float additionalAngle)
        {
            angle += additionalAngle;

            Vector3 direction = Vector3.zero;
            direction.x = Mathf.Cos(angle * Mathf.Deg2Rad);
            direction.y = Mathf.Sin(angle * Mathf.Deg2Rad);
            direction.z = 0f;
            return direction;
        }
    }
}