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)
{
float maxDeltaTime = Mathf.Min(1.0f / (frequency * 10.0f), deltaTime);
frequency = frequency * 2f * Mathf.PI;
deltaTime = Mathf.Min(deltaTime, maxDeltaTime);
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>
///
/// </summary>
/// <param name="direction"></param>
/// <returns></returns>
public static Quaternion LookAt2D(Vector2 direction)
{
var angle = Mathf.Atan2(direction.y, direction.x) * Mathf.Rad2Deg;
return Quaternion.AngleAxis(angle, Vector3.forward);
}
/// <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>
/// Computes and returns the direction between two vector3, used to check if a vector is pointing left or right of another one
/// </summary>
/// <returns>The <see cref="System.Single"/>.</returns>
/// <param name="vectorA">Vector a.</param>
/// <param name="vectorB">Vector b.</param>
public static float AngleDirection(Vector3 vectorA, Vector3 vectorB, Vector3 up)
{
Vector3 cross = Vector3.Cross(vectorA, vectorB);
float direction = Vector3.Dot(cross, up);
return direction;
}
/// <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;
}
}
}