/Utilities/Helpers/MathHelper.cs

using System;

using Delta.Utilities.Datatypes;

using NUnit.Framework;



namespace Delta.Utilities.Helpers

{

	/// <summary>

	/// Math helper class. Provides the same functionality as System.Math, but

	/// instead of using doubles for all the functions here are using floats!

	/// </summary>

	public static class MathHelper

	{

		#region Constants

		/// <summary>

		/// Epsilon is a small comparison offset for NearlyEqual checks.

		/// Note: Other frameworks use float.Epsilon (1.192092896e-07f), but we

		/// work great with this value too, so we should keep it this way.

		/// </summary>

		public const float Epsilon = 0.0001f;



		/// <summary>

		/// E constant as a float (2.718282).

		/// </summary>

		public const float E = 2.718282f;



		/// <summary>

		/// Pi constants, same as PI (double), but as a float here (less precise),

		/// please note that we usually use degrees and not radians in the engine!

		/// </summary>

		public const float Pi = 3.14159265359f;



		/// <summary>

		/// Pi times two for getting around a whole circle (360 degrees).

		/// </summary>

		public const float PiDouble = Pi * 2.0f;



		/// <summary>

		/// Pi Half, which represents 90 degrees.

		/// </summary>

		public const float PiHalf = Pi * 0.5f;



		/// <summary>

		/// Pi Quarter, which represents 45 degrees.

		/// </summary>

		public const float PiQuarter = PiHalf * 0.5f;



		/// <summary>

		/// Represents just the fraction of 1/3 or in decimal 0.333333

		/// </summary>

		public const float OneThird = 1.0f / 3.0f;



		/// <summary>

		/// The default value for an invalid index check (-1), very often used to

		/// set invalid and initial values to integer values to make sure that we

		/// initialize them first before using them, e.g. for shader parameters or

		/// for indices in precomputed arrays, but also often used by the .NET

		/// framework, e.g String.IndexOf returns -1 for not found.

		/// </summary>

		public const int InvalidIndex = -1;



		/// <summary>

		/// Sinus value of 45 Degree

		/// </summary>

		public const float Sin45 = 0.707106781f;



		/// <summary>

		/// Half of the short max. value (32768), which is 16392. This is used

		/// for the calculation of ViewProjection2DViaShorts and in the

		/// MaterialManager to setup compressed vertices.

		/// </summary>

		public const short HalfShortMaxValue = short.MaxValue / 2;

		#endregion



		#region NearlyEqual (Static)

		/// <summary>

		/// Compares two floats if they are almost equal, taking an Epsilon offset

		/// (see Math.Epsilon) into account.

		/// </summary>

		/// <param name="value1">first float</param>

		/// <param name="value2">second float</param>

		/// <returns>Bool: True if Nearly Equal</returns>

		public static bool NearlyEqual(this float value1, float value2)

		{

			float difference = Abs(value1 - value2);

			return difference <= Epsilon;

		}

		#endregion



		#region InvertScalar (Static)

		/// <summary>

		/// Invert scalar safely.

		/// </summary>

		/// <param name="value">Value</param>

		/// <returns>1.0f</returns>

		public static float InvertScalar(float value)

		{

			if (Abs(value) < Epsilon)

			{

				return float.MaxValue;

			}

			return 1.0f / value;

		}

		#endregion



		#region Clamp (Static)

		/// <summary>

		/// Clamps the value between [0, 1].

		/// </summary>

		/// <param name="value">Value</param>

		/// <returns>Clamp Value</returns>

		public static int Clamp(int value)

		{

			return Clamp(value, 0, 1);

		}



		/// <summary>

		/// Clamps the value between the given range [minimum, maximum].

		/// </summary>

		/// <param name="max">Max</param>

		/// <param name="min">Min</param>

		/// <param name="value">Value</param>

		/// <returns>value between the given range [minimum, maximum]</returns>

		public static int Clamp(int value, int min, int max)

		{

			return Min(Max(value, min), max);

		}



		/// <summary>

		/// Clamps the value between [0.0, 1.0].

		/// </summary>

		/// <param name="value">Value</param>

		/// <returns>value between [0.0, 1.0]</returns>

		public static float Clamp(float value)

		{

			return Clamp(value, 0.0f, 1.0f);

		}



		/// <summary>

		/// Clamps the value between the given range [minimum, maximum].

		/// </summary>

		/// <param name="max">Max</param>

		/// <param name="min">Min</param>

		/// <param name="value">Value</param>

		/// <returns>value between the given range [minimum, maximum]</returns>

		public static float Clamp(float value, float min, float max)

		{

			return Min(Max(value, min), max);

		}

		#endregion



		#region Wrap (Static)

		/// <summary>

		/// Wrap the value between the given range [minimun, maximum].

		/// </summary>

		/// <param name="max">Max</param>

		/// <param name="min">Min</param>

		/// <param name="value">Value</param>

		/// <returns>value between the given range [minimun, maximum]</returns>

		public static int Wrap(int value, int min, int max)

		{

			int delta = max - min;

			if (value > delta)

			{

				value = value / delta;

				value = value - (int)Math.Floor((double)value);

				value = value * delta;

			}

			return value;

		}



		/// <summary>

		/// Wrap the value between the given range [minimun, maximum].

		/// </summary>

		/// <param name="max">Max</param>

		/// <param name="min">Min</param>

		/// <param name="value">Value</param>

		/// <returns>The wrapped Value</returns>

		public static float Wrap(float value, float min, float max)

		{

			float delta = max - min;

			if (value > delta)

			{

				value = value / delta;

				value = value - (float)Math.Floor(value);

				value = value * delta;

			}

			return value;

		}

		#endregion



		#region Distance (Static)

		/// <summary>

		/// Distance between two float values.

		/// </summary>

		/// <param name="value1">First float value</param>

		/// <param name="value2">Second float value</param>

		/// <returns>Distance between the two values, always positive</returns>

		public static float Distance(float value1, float value2)

		{

			return Abs(value1 - value2);

		}

		#endregion



		#region Min (Static)

		/// <summary>

		/// Returns the smaller of two values.

		/// </summary>

		/// <param name="value1">Value 1</param>

		/// <param name="value2">Value 2</param>

		/// <returns>the smaller of two values</returns>

		public static float Min(float value1, float value2)

		{

			return

				value1 < value2

					? value1

					: value2;

		}



		/// <summary>

		/// Returns the smaller of three values.

		/// </summary>

		/// <param name="value1">Value 1</param>

		/// <param name="value2">Value 2</param>

		/// <param name="value3">Value 3</param>

		/// <returns>Returns the smaller of three values</returns>

		public static float Min(float value1, float value2, float value3)

		{

			return Min(Min(value1, value2), value3);

		}



		/// <summary>

		/// Returns the smaller of two values.

		/// </summary>

		/// <param name="value1">Value 1</param>

		/// <param name="value2">Value 2</param>

		/// <returns>Returns the smaller of two values</returns>

		public static int Min(int value1, int value2)

		{

			return

				value1 < value2

					? value1

					: value2;

		}



		/// <summary>

		/// Returns the smaller of three values.

		/// </summary>

		/// <param name="value1">Value1</param>

		/// <param name="value2">Value2</param>

		/// <param name="value3">Value3</param>

		/// <returns>eturns the smaller of three values</returns>

		public static int Min(int value1, int value2, int value3)

		{

			return Min(Min(value1, value2), value3);

		}

		#endregion



		#region Max (Static)

		/// <summary>

		/// Returns the bigger one of the two values.

		/// </summary>

		/// <param name="value1">Value 1</param>

		/// <param name="value2">Value 2</param>

		/// <returns>Returns the bigger one of the two values</returns>

		public static int Max(int value1, int value2)

		{

			return

				value1 > value2

					? value1

					: value2;

		}



		/// <summary>

		/// Returns the bigger one of the three values.

		/// </summary>

		/// <param name="value1">Value1</param>

		/// <param name="value2">Value2</param>

		/// <param name="value3">Value3</param>

		/// <returns>Returns the bigger one of the three values</returns>

		public static int Max(int value1, int value2, int value3)

		{

			return Max(Max(value1, value2), value3);

		}



		/// <summary>

		/// Returns the bigger one of the two values.

		/// </summary>

		/// <param name="value1">Value1</param>

		/// <param name="value2">Value2</param>

		/// <returns>Returns the bigger one of the two values</returns>

		public static float Max(float value1, float value2)

		{

			return

				value1 > value2

					? value1

					: value2;

		}



		/// <summary>

		/// Returns the bigger one of the three values.

		/// </summary>

		/// <param name="value1">Value1</param>

		/// <param name="value2">Value2</param>

		/// <param name="value3">Value3</param>

		/// <returns>Returns the bigger one of the three values</returns>

		public static float Max(float value1, float value2, float value3)

		{

			return Max(Max(value1, value2), value3);

		}

		#endregion



		#region Lerp (Static)

		/// <summary>

		/// Performs a linear interpolation between two values. 

		/// </summary>

		/// <param name="minValue">Value at "percentage = 0"</param>

		/// <param name="maxValue">Value at "percentage = 1"</param>

		/// <param name="percentage">Percentage in the range [0,1]</param>

		/// <returns>Float</returns>

		public static float Lerp(float minValue, float maxValue, float percentage)

		{

			return minValue + (maxValue - minValue) * percentage;

		}



		/// <summary>

		/// Performs a linear interpolation between two values. 

		/// </summary>

		/// <param name="minValue">Value at "percentage = 0"</param>

		/// <param name="maxValue">Value at "percentage = 1"</param>

		/// <param name="percentage">Percentage in the range [0,1]</param>

		/// <returns>Float</returns>

		public static int Lerp(int minValue, int maxValue, float percentage)

		{

			return minValue + Round((maxValue - minValue) * percentage);

		}



		/// <summary>

		/// Performs a linear interpolation between two values. 

		/// </summary>

		/// <param name="minValue">Value at "percentage = 0"</param>

		/// <param name="maxValue">Value at "percentage = 1"</param>

		/// <param name="percentage">Percentage in the range [0,1]</param>

		/// <returns>Float</returns>

		public static long Lerp(long minValue, long maxValue, float percentage)

		{

			return minValue + Round((maxValue - minValue) * percentage);

		}

		#endregion



		#region Sqrt (Static)

		/// <summary>

		/// Sqrt

		/// </summary>

		/// <returns>Float</returns>

		public static float Sqrt(float value)

		{



			return (float)Math.Sqrt(value);

		}

		#endregion



		#region Round (Static)

		/// <summary>

		/// Rounds a value to a given position after the decimal point

		/// </summary>

		/// <param name="value">Value to round</param>

		/// <param name="decimals">Decimals</param>

		/// <returns>Float</returns>

		public static float Round(float value, int decimals)

		{

			return (float)Math.Round(value, decimals);

		}



		/// <summary>

		/// Rounds a value to an int

		/// </summary>

		/// <param name="value">Value to round</param>

		/// <returns>Float</returns>

		public static int Round(float value)

		{

			return (int)Math.Round(value);

		}

		#endregion



		#region Ceiling (Static)

		/// <summary>

		/// Ceiling

		/// </summary>

		/// <param name="value">Value</param>

		/// <returns>Ceiling</returns>

		public static int Ceiling(float value)

		{

			return (int)Math.Ceiling(value);

		}

		#endregion



		#region Abs (Static)

		/// <summary>

		/// Returns the absolute value of a float

		/// </summary>

		/// <param name="value">Value</param>

		/// <returns>Returns the absolute value of a float</returns>

		public static float Abs(float value)

		{

			return

				value < 0f

					? -value

					: value;

		}

		#endregion



		#region Pow (Static)

		/// <summary>

		/// Pow

		/// </summary>

		/// <param name="power">Power</param>

		/// <param name="value">Value</param>

		/// <returns>Power</returns>

		public static float Pow(float value, float power)

		{

			return (float)Math.Pow(value, power);

		}

		#endregion



		#region DegreeToRadians (Static)

		/// <summary>

		/// Degree to radians

		/// </summary>

		/// <param name="degrees">Degrees</param>

		/// <returns>Degree to radians</returns>

		public static float DegreeToRadians(this float degrees)

		{

			return degrees * (Pi / 180.0f); //same: * 0.01745329f;

		}

		#endregion



		#region RadiansToDegrees (Static)

		/// <summary>

		/// Radians to degrees

		/// </summary>

		/// <param name="radians">Radians</param>

		/// <returns>radians</returns>

		public static float RadiansToDegrees(this float radians)

		{

			return radians * (180.0f / Pi); //same: * 57.29578f;

		}

		#endregion



		#region Sin (Static)

		/// <summary>

		/// Return the sinus of a degreeValue. Note: Most other math libraries use

		/// radians, please provide degrees here (used throughout the engine).

		/// </summary>

		/// <param name="degreeValue">Degree value for the sinus</param>

		/// <returns>Sinus of degreeValue</returns>

		public static float Sin(float degreeValue)

		{

			return (float)Math.Sin(degreeValue * (Pi / 180.0f));

		}

		#endregion



		#region Cos (Static)

		/// <summary>

		/// Cosinus of a degreeValue, please use degree values here (not radians)

		/// </summary>

		/// <param name="degreeValue">Degree Value for the cosinus</param>

		/// <returns>Cosinus of degreeValue</returns>

		public static float Cos(float degreeValue)

		{

			return (float)Math.Cos(degreeValue * (Pi / 180.0f));

		}

		#endregion



		#region Tan (Static)

		/// <summary>

		/// Get the tangent value, again using degrees, not radians.

		/// </summary>

		/// <param name="degreeValue">Degree value for the tagent</param>

		/// <returns>Tangent of degreeValue</returns>

		public static float Tan(float degreeValue)

		{

			return (float)Math.Tan(DegreeToRadians(degreeValue));

		}

		#endregion



		#region Asin (Static)

		/// <summary>

		/// Returns the angle in degrees whose sin value is the specified value.

		/// </summary>

		/// <param name="value">Value for asin</param>

		/// <returns>Asin value in degrees from the value</returns>

		public static float Asin(float value)

		{

			return RadiansToDegrees((float)Math.Asin(value));

		}

		#endregion



		#region Acos (Static)

		/// <summary>

		/// Returns the angle in degrees whose cos value is the specified value.

		/// </summary>

		/// <param name="value">Value for acos</param>

		/// <returns>Acos value in degrees from the value</returns>

		public static float Acos(float value)

		{

			return RadiansToDegrees((float)Math.Acos(value));

		}

		#endregion



		#region Atan (Static)

		/// <summary>

		/// Returns the angle in degrees whose tangent is the specified number.

		/// Use Atan(x, y) if you do not want to calculate the quotient yourself.

		/// </summary>

		/// <param name="tangent">Tangent</param>

		/// <returns>Atan value in degrees from the tangent value</returns>

		public static float Atan(float tangent)

		{

			return RadiansToDegrees((float)Math.Atan(tangent));

		}



		/// <summary>

		/// Returns the angle in degrees whose tangent is the quotient of two

		/// specified numbers. For more help see System.Math.Atan2 (which works in

		/// radians however).

		/// </summary>

		/// <param name="x">X value for atan2</param>

		/// <param name="y">Y value for atan2</param>

		/// <returns>Atan value in degrees from the x and y values</returns>

		public static float Atan(float x, float y)

		{

			return RadiansToDegrees((float)Math.Atan2(x, y));

		}

		#endregion



		#region GetNextPowerOfTwo (Static)

		/// <summary>

		/// Get the nearest power of two value that must be bigger or equal to

		/// value. Used for making sure textures are power of two. E.g.

		/// GetNextPowerOfTwo(128) is 128, GetNextPowerOfTwo(129) is 256, etc.

		/// </summary>

		/// <param name="value">Value</param>

		/// <returns>the nearest power of two value</returns>

		public static int GetNextPowerOfTwo(this float value)

		{

			int logValue = (int)Math.Ceiling(Math.Log(value, 2));

			return (int)Math.Pow(2, logValue);

		}

		#endregion



		#region IsPowerOfTwo (Static)

		/// <summary>

		/// Is power of two

		/// </summary>

		/// <param name="value">Value</param>

		/// <returns>Is power of two</returns>

		public static bool IsPowerOfTwo(this float value)

		{

			return GetNextPowerOfTwo(value) == value;

		}

		#endregion



		#region GetNearestMultiple (Static)

		/// <summary>

		/// Get the nearest multiple of 'multipleValue' from the value.

		/// </summary>

		/// <param name="multipleValue">Multiple Value</param>

		/// <param name="value">Value</param>

		/// <returns>the nearest multiple of 'multipleValue' from the 

		/// value</returns>

		public static int GetNearestMultiple(this int value, int multipleValue)

		{

			int min =

				((int)(value / (float)multipleValue)) * multipleValue;

			int max =

				((int)(value / (float)multipleValue) + 1) * multipleValue;



			return max - value < value - min

			       	? max

			       	: min;

		}

		#endregion



		#region Sign (Static)

		/// <summary>

		/// System.Math.Sign method, that crashes on the iPad if the value is not

		/// valid (e.g. NaN). This method will always return -1, 0 or 1.

		/// </summary>

		/// <param name="value">Value</param>

		/// <returns>-1, 0 or 1</returns>

		public static float Sign(float value)

		{

			//2010-05-28: dummy fix for iPad

			if (value == float.NaN)

			{

				return 0;

			}



			if (value < 0)

			{

				return -1;

			}

			else if (value > 0)

			{

				return 1;

			}

			else

			{

				return 0;

			}

		}

		#endregion



		#region ComputePercentageValue (Static)

		/// <summary>

		/// Computes the percentage value in the range [0 = 0%, 1 = 100%] based on

		/// the given value related to the given value range.

		/// </summary>

		/// <param name="value">

		/// The value we want to calculate the percentage for.

		/// </param>

		/// <param name="minValue">The minimum allowed value.</param>

		/// <param name="maxValue">The maximum allowed value.</param>

		/// <returns>

		/// The percentage value in the range [0 = 0%, 1 = 100%] based on the given

		/// value related to the given value range.

		/// </returns>

		public static float ComputePercentageValue(float value, float minValue,

			float maxValue)

		{

			// Validation

			float realMinValue =

				maxValue > minValue

					? minValue

					: maxValue;

			float realMaxValue =

				minValue > maxValue

					? minValue

					: maxValue;

			

			// Absolute difference between max and min value (should not be 0)

			float diff = realMaxValue - realMinValue;

			if (diff <= 0.0f)

			{

				return 0.0f;

			}



			// Clamp value to always get a result between 0 and 1.

			float clampedValue = Clamp(value, realMinValue, realMaxValue);



			// Difference from min to desired value in 0-1 range!

			return (clampedValue - realMinValue) / diff;

		}

		#endregion



		#region ComputeValue (Static)

		/// <summary>

		/// Returns the exact value based on the given percentage related to the

		/// given value range.

		/// </summary>

		/// <param name="percentageValue">Percentage value in the range of [0 = 0%,

		/// 1 = 100%].</param>

		/// <param name="minValue">The minimum allowed value.</param>

		/// <param name="maxValue">The maximum allowed value.</param>

		/// <returns>Float</returns>

		public static float ComputeValue(float percentageValue, float minValue,

			float maxValue)

		{

			// Validation

			float realMinValue = (maxValue > minValue)

			                     	? minValue

			                     	: maxValue;

			float realMaxValue = (minValue > maxValue)

			                     	? minValue

			                     	: maxValue;

			// clamp value

			float clampedPercentageValue = Clamp(percentageValue);



			// absolute difference between max and min value

			float diff = Abs(realMaxValue - realMinValue) * clampedPercentageValue;

			// return how many percent "diffFromMinToValue" is when diff = 100%

			return realMinValue + diff;

		}

		#endregion



		#region LineToLineIntersection (Static)

		/// <summary>

		/// Check if two lines intersect and return the position if occurred.

		/// </summary>

		/// <param name="a">The start point of line one.</param>

		/// <param name="b">The end point of line one.</param>

		/// <param name="c">The start point of line two.</param>

		/// <param name="d">The end point of line two.</param>

		/// <param name="resultX">If they intersect the X value is stored here.

		/// </param>

		/// <param name="resultY">If they intersect the Y value is stored here.

		/// </param>

		/// <returns>True if they intersect, otherwise false.</returns>

		public static bool LineToLineIntersection(Point a, Point b, Point c,

			Point d, out float resultX, out float resultY)

		{

			resultX = 0f;

			resultY = 0f;



			float denominator =

				((d.Y - c.Y) * (b.X - a.X)) - ((d.X - c.X) * (b.Y - a.Y));



			float ua = (((d.X - c.X) * (a.Y - c.Y)) - ((d.Y - c.Y) * (a.X - c.X))) /

			           denominator;

			float ub = (((b.X - a.X) * (a.Y - c.Y)) - ((b.Y - a.Y) * (a.X - c.X))) /

			           denominator;



			if (ua >= 0f && ua <= 1f && ub >= 0f &&

			    ub <= 1f)

			{

				resultX = a.X + (ua * (b.X - a.X));

				resultY = a.Y + (ua * (b.Y - a.Y));

				return true;

			}



			return false;

		}



		/// <summary>

		/// Check if two lines intersect and return the position if occurred.

		/// </summary>

		/// <param name="a">The start point of line one.</param>

		/// <param name="b">The end point of line one.</param>

		/// <param name="c">The start point of line two.</param>

		/// <param name="d">The end point of line two.</param>

		/// <returns>True if they intersect, otherwise false.</returns>

		public static bool LineToLineIntersection(Point a, Point b, Point c,

			Point d)

		{

			float denominator =

				((d.Y - c.Y) * (b.X - a.X)) - ((d.X - c.X) * (b.Y - a.Y));



			float ua = (((d.X - c.X) * (a.Y - c.Y)) - ((d.Y - c.Y) * (a.X - c.X))) /

			           denominator;

			float ub = (((b.X - a.X) * (a.Y - c.Y)) - ((b.Y - a.Y) * (a.X - c.X))) /

			           denominator;



			return ua >= 0f && ua <= 1f && ub >= 0f && ub <= 1f;

		}

		#endregion



		/// <summary>

		/// Tests

		/// </summary>

		internal class MathHelperTests

		{

			#region NearlyEqual (Static)

			/// <summary>

			/// Nearly equal

			/// </summary>

			[Test]

			public static void NearlyEqual()

			{

				Assert.True(0.0f.NearlyEqual(0.0f));

				Assert.True(0.000001f.NearlyEqual(0.000002f));

				Assert.False(1.0f.NearlyEqual(2.0f));

				Assert.True(1.0f.NearlyEqual(1.0f + (Epsilon * 0.9f)));

			}

			#endregion



			#region Clamp (Static)

			/// <summary>

			/// Clamp

			/// </summary>

			[Test]

			public static void Clamp()

			{

				// Int's

				Assert.Equal(1, MathHelper.Clamp(1, 0, 10));

				Assert.Equal(0, MathHelper.Clamp(-1, 0, 10));

				Assert.Equal(10, MathHelper.Clamp(111, 0, 10));

				Assert.Equal(0, MathHelper.Clamp(2598, 0, 0));



				// Float's

				Assert.Equal(0.1f, MathHelper.Clamp(0.1f, 0.0f, 1.0f));

				Assert.Equal(0.59f, MathHelper.Clamp(0.64f, 0.53f, 0.59f));

				Assert.Equal(0.64f, MathHelper.Clamp(0.53f, 0.64f, 0.69f));



				//Assert.Equal(new Point(-1, -1),

				//	MathHelper.Clamp(new Point(-2, -3.5f), new Point(-1, -1),

				//		new Point(0, 0)));

			}

			#endregion



			#region Min (Static)

			/// <summary>

			/// Minimum

			/// </summary>

			[Test]

			public static void Min()

			{

				Assert.Equal(10, MathHelper.Min(10, 20));

				Assert.Equal(43, MathHelper.Min(134, 43));

				Assert.Equal(-20, MathHelper.Min(-10, -20));

				Assert.Equal(-20, MathHelper.Min(-5, -10, -20));

			}

			#endregion



			#region Max (Static)

			/// <summary>

			/// Maximum

			/// </summary>

			[Test]

			public static void Max()

			{

				Assert.Equal(20, MathHelper.Max(10, 20));

				Assert.Equal(134, MathHelper.Max(134, 43));

				Assert.Equal(-10, MathHelper.Max(-10, -20));

				Assert.Equal(-5, MathHelper.Max(-5, -10, -20));

			}

			#endregion



			#region Sqrt (Static)

			/// <summary>

			/// Sqrt

			/// </summary>

			[Test]

			public static void Sqrt()

			{

				Assert.Equal(0, MathHelper.Sqrt(0));

				Assert.Equal(2, MathHelper.Sqrt(4));

				Assert.Equal(9, MathHelper.Sqrt(81));

				Assert.NotEqual(1, MathHelper.Sqrt(2));

			}

			#endregion



			#region Round (Static)

			/// <summary>

			/// Round

			/// </summary>

			[Test]

			public static void Round()

			{

				Assert.Equal(1, MathHelper.Round(1.25f));

				Assert.Equal(10, MathHelper.Round(9.68f));

				Assert.Equal(1.23f, MathHelper.Round(1.2345f, 2));

			}

			#endregion



			#region Abs (Static)

			/// <summary>

			/// Absolute

			/// </summary>

			[Test]

			public static void Abs()

			{

				Assert.Equal(13, MathHelper.Abs(13));

				Assert.Equal(13, MathHelper.Abs(-13));

				Assert.Equal(13.52f, MathHelper.Abs(-13.52f));

			}

			#endregion



			#region Pow (Static)

			/// <summary>

			/// Pow

			/// </summary>

			[Test]

			public static void Pow()

			{

				Assert.Equal(25, MathHelper.Pow(5, 2));

			}

			#endregion



			#region GetNearestMultiple (Static)

			/// <summary>

			/// Test GetNearestMultiple

			/// </summary>

			[Test]

			public static void GetNearestMultiple()

			{

				int result = 130.GetNearestMultiple(32);

				Assert.Equal(128, result);

				result = 157.GetNearestMultiple(32);

				Assert.Equal(160, result);



				result = 17.GetNearestMultiple(4);

				Assert.Equal(16, result);

				result = 19.GetNearestMultiple(4);

				Assert.Equal(20, result);

			}

			#endregion



			#region Ceiling

			/// <summary>

			/// Ceiling

			/// </summary>

			[Test]

			public void Ceiling()

			{

				Assert.Equal(MathHelper.Ceiling(0.0f), 0);

				Assert.Equal(MathHelper.Ceiling(4.0f), 4);

				Assert.Equal(MathHelper.Ceiling(-2.0f), -2);

				Assert.Equal(MathHelper.Ceiling(2.3f), 3);

				Assert.Equal(MathHelper.Ceiling(7.8f), 8);

			}

			#endregion



			#region DegreeToRadians

			/// <summary>

			/// Degree to radians

			/// </summary>

			[Test]

			public void DegreeToRadians()

			{

				Assert.Equal(0, MathHelper.DegreeToRadians(0));

				Assert.True(Pi.NearlyEqual(MathHelper.DegreeToRadians(180)),

					"180 degrees is converted to radians nearly pi");

				Assert.True(PiHalf.NearlyEqual(MathHelper.DegreeToRadians(90)),

					"90 degrees is converted to radians nearly HalfPi");

				Assert.True(PiDouble.NearlyEqual(MathHelper.DegreeToRadians(360)),

					"360 degrees is converted to radians nearly PiDouble");

				Assert.NotEqual(0, MathHelper.DegreeToRadians(-1));

			}

			#endregion



			#region RadiansToDegrees

			/// <summary>

			/// Radians to degrees

			/// </summary>

			[Test]

			public void RadiansToDegrees()

			{

				Assert.Equal(0, MathHelper.RadiansToDegrees(0));

				Assert.True(MathHelper.NearlyEqual(180,

					Pi.RadiansToDegrees()),

					"Pi in radians is converted to degrees nearly 180 degree");

				Assert.True(MathHelper.NearlyEqual(90,

					PiHalf.RadiansToDegrees()),

					"HalfPi in radians is converted to degrees nearly 90 degree");

				Assert.True(MathHelper.NearlyEqual(360,

					PiDouble.RadiansToDegrees()),

					"PiDouble in radians is converted to degrees nearly 360 degree");

				Assert.NotEqual(0, MathHelper.RadiansToDegrees(-1));

			}

			#endregion



			#region Lerp

			/// <summary>

			/// Lerp

			/// </summary>

			[Test]

			public void Lerp()

			{

				Assert.Equal(3, MathHelper.Lerp(5, 3, 1));

			}

			#endregion



			#region TestIntTruncate

			/// <summary>

			/// Test int truncate

			/// </summary>

			[Test]

			public void TestIntTruncate()

			{

				Assert.Equal(17, (int)17.7f);

				Assert.Equal(17, (int)(17.2f + 0.5f));

			}

			#endregion



			#region Sin

			/// <summary>

			/// Sin

			/// </summary>

			[Test]

			public void Sin()

			{

				Assert.Equal(0, MathHelper.Sin(0));

				Assert.Equal(1, MathHelper.Sin(90));

				Assert.True(MathHelper.NearlyEqual(0, MathHelper.Sin(180)),

					"the sin of 180 is nearly zero");

				Assert.True(MathHelper.NearlyEqual(0, MathHelper.Sin(360)),

					"the sin of 360 is nearly zero");

				Assert.NotEqual(0, MathHelper.Sin(32));

			}

			#endregion



			#region Cos

			/// <summary>

			/// Sin

			/// </summary>

			[Test]

			public void Cos()

			{

				Assert.Equal(1, MathHelper.Cos(0));

				Assert.True(MathHelper.NearlyEqual(0, MathHelper.Cos(90)),

					"the cos of 90 is nearly zero");

				Assert.True(MathHelper.NearlyEqual(-1, MathHelper.Cos(180)),

					"the cos of 180 is nearly minus one");

				Assert.True(MathHelper.NearlyEqual(1, MathHelper.Cos(360)),

					"the cos of 360 is nearly one");

				Assert.NotEqual(0, MathHelper.Cos(32));

			}

			#endregion



			#region Tan

			/// <summary>

			/// Tan

			/// </summary>

			[Test]

			public void Tan()

			{

				Assert.Equal(0, MathHelper.Tan(0));

				Assert.True(MathHelper.NearlyEqual(0, MathHelper.Tan(180)),

					"the tan of 180 is nearly zero");

				Assert.True(1.732051f.NearlyEqual(MathHelper.Tan(60)),

					"the tan of 60 is nearly 1.732051f");

				Assert.True(MathHelper.NearlyEqual(1, MathHelper.Tan(45)),

					"the tan of 45 is nearly one");

				Assert.True(MathHelper.NearlyEqual(-1, MathHelper.Tan(135)),

					"the tan of 135 is nearly minus one");

				Assert.NotEqual(0, MathHelper.Tan(32));

			}

			#endregion



			#region Asin

			/// <summary>

			/// Asin

			/// </summary>

			[Test]

			public void Asin()

			{

				Assert.Equal(0, MathHelper.Asin(0));

				Assert.True(MathHelper.NearlyEqual(90, MathHelper.Asin(1)),

					"The Asin of 1 is nearly 90");

				Assert.True(MathHelper.NearlyEqual(30, MathHelper.Asin(0.5f)),

					"The Asin of 0.5 is nearly 30");

				Assert.NotEqual(0, MathHelper.Asin(0.2f));

			}

			#endregion



			#region Acos

			/// <summary>

			/// Acos

			/// </summary>

			[Test]

			public void Acos()

			{

				Assert.True(MathHelper.NearlyEqual(90, MathHelper.Acos(0)),

					"The Acos of zero is nearly 90");

				Assert.True(MathHelper.NearlyEqual(0, MathHelper.Acos(1)),

					"The Acos of one is nearly zero");

				Assert.True(MathHelper.NearlyEqual(60, MathHelper.Acos(0.5f)),

					"The Acos of 0.5 is nearly 60");

				Assert.NotEqual(0, MathHelper.Acos(0.2f));

			}

			#endregion



			#region Atan

			/// <summary>

			/// Atan

			/// </summary>

			[Test]

			public void Atan()

			{

				Assert.Equal(0, MathHelper.Atan(0));

				Assert.True(MathHelper.NearlyEqual(60, MathHelper.Atan(1.732051f)),

					"The Atan of 1.732051f is nearly 60");

				Assert.NotEqual(0, MathHelper.Atan(0.2f));

				Assert.Equal(0, MathHelper.Atan(0, 0));

				Assert.Equal(0, MathHelper.Atan(0, 1));

				Assert.True(MathHelper.NearlyEqual(90, MathHelper.Atan(1, 0)),

					"The Atan of the tangent(of one and zero) is nearly 90");

				Assert.True(MathHelper.NearlyEqual(45, MathHelper.Atan(1, 1)),

					"The Atan of the tangent(of one and one) is nearly 45");

				Assert.True(MathHelper.NearlyEqual(-90, MathHelper.Atan(-1, 0)),

					"The Atan of the tangent(of minus one and zero) is nearly minus 90");

				//  Math.Atan(0, -1));

				// Always works:

				Assert.Equal("180", MathHelper.Atan(0, -1).ToString());

				// Only works if Math.Epsilon for NearlyEqual is not smaller than

				// 0.0001

				Assert.True(MathHelper.NearlyEqual(180, MathHelper.Atan(0, -1)),

					"The Atan of the tangent(of zero and minus one) is nearly 180");

			}

			#endregion



			#region GetNextPowerOfTwo

			/// <summary>

			/// Get next power of two

			/// </summary>

			[Test]

			public void GetNextPowerOfTwo()

			{

				Assert.Equal(128, MathHelper.GetNextPowerOfTwo(128));

				Assert.Equal(256, MathHelper.GetNextPowerOfTwo(129));

				Assert.Equal(1024, MathHelper.GetNextPowerOfTwo(529));

				Assert.Equal(2048, MathHelper.GetNextPowerOfTwo(1111));

				Assert.Equal(0, MathHelper.GetNextPowerOfTwo(-1));

			}

			#endregion



			#region IsPowerOfTwo

			/// <summary>

			/// IsPowerOfTwo

			/// </summary>

			[Test]

			public void IsPowerOfTwo()

			{

				Assert.True(MathHelper.IsPowerOfTwo(128));

				Assert.False(MathHelper.IsPowerOfTwo(129));

				Assert.False(MathHelper.IsPowerOfTwo(529));

				Assert.False(MathHelper.IsPowerOfTwo(1111));

				Assert.True(MathHelper.IsPowerOfTwo(1024));

				Assert.False(MathHelper.IsPowerOfTwo(-1));

				Assert.True(MathHelper.IsPowerOfTwo(4));

			}

			#endregion



			#region ComputeValue

			/// <summary>

			/// Compute value

			/// </summary>

			[Test]

			public void ComputeValue()

			{

				Assert.Equal(MathHelper.ComputeValue(0.5f, 10, 20), 15.0f);



				Assert.Equal(MathHelper.ComputeValue(0.5f, 0, 10), 5.0f);



				Assert.Equal(MathHelper.ComputeValue(0.5f, -10, 0), -5.0f);



				Assert.Equal(MathHelper.ComputeValue(0.5f, -10, 10), 0.0f);

			}

			#endregion



			#region ComputePercentageValue

			/// <summary>

			/// Compute percentage value

			/// </summary>

			[Test]

			public void ComputePercentageValue()

			{

				Assert.Equal(MathHelper.ComputePercentageValue(5, 0, 10), 0.5f);



				Assert.Equal(MathHelper.ComputePercentageValue(0, -10, 10), 0.5f);



				Assert.Equal(MathHelper.ComputePercentageValue(0, -360, 360), 0.5f);



				Assert.Equal(MathHelper.ComputePercentageValue(-50, -100, -50), 1.0f);



				Assert.Equal(MathHelper.ComputePercentageValue(-100, -100, -50), 0.0f);



				Assert.Equal(MathHelper.ComputePercentageValue(0, 1000, -1000), 0.5f);

			}

			#endregion

		}

	}

}