#region License
#endregion
#region Using Statements
using System;
#endregion
namespace Microsoft.Xna.Framework
{
/// <summary>
/// Contains commonly used precalculated values and mathematical operations.
/// </summary>
public static class MathHelper
{
#region Public Constants
/// <summary>
/// Represents the mathematical constant e(2.71828175).
/// </summary>
public const float E = (float) Math.E;
/// <summary>
/// Represents the log base ten of e(0.4342945).
/// </summary>
public const float Log10E = 0.4342945f;
/// <summary>
/// Represents the log base two of e(1.442695).
/// </summary>
public const float Log2E = 1.442695f;
/// <summary>
/// Represents the value of pi(3.14159274).
/// </summary>
public const float Pi = (float) Math.PI;
/// <summary>
/// Represents the value of pi divided by two(1.57079637).
/// </summary>
public const float PiOver2 = (float) (Math.PI / 2.0);
/// <summary>
/// Represents the value of pi divided by four(0.7853982).
/// </summary>
public const float PiOver4 = (float) (Math.PI / 4.0);
/// <summary>
/// Represents the value of pi times two(6.28318548).
/// </summary>
public const float TwoPi = (float) (Math.PI * 2.0);
#endregion
#region Internal Static Readonly Fields
internal static readonly float MachineEpsilonFloat = GetMachineEpsilonFloat();
#endregion
#region Public Static Methods
/// <summary>
/// Returns the Cartesian coordinate for one axis of a point that is defined by a
/// given triangle and two normalized barycentric (areal) coordinates.
/// </summary>
/// <param name="value1">
/// The coordinate on one axis of vertex 1 of the defining triangle.
/// </param>
/// <param name="value2">
/// The coordinate on the same axis of vertex 2 of the defining triangle.
/// </param>
/// <param name="value3">
/// The coordinate on the same axis of vertex 3 of the defining triangle.
/// </param>
/// <param name="amount1">
/// The normalized barycentric (areal) coordinate b2, equal to the weighting factor
/// for vertex 2, the coordinate of which is specified in value2.
/// </param>
/// <param name="amount2">
/// The normalized barycentric (areal) coordinate b3, equal to the weighting factor
/// for vertex 3, the coordinate of which is specified in value3.
/// </param>
/// <returns>
/// Cartesian coordinate of the specified point with respect to the axis being used.
/// </returns>
public static float Barycentric(
float value1,
float value2,
float value3,
float amount1,
float amount2
) {
return value1 + (value2 - value1) * amount1 + (value3 - value1) * amount2;
}
/// <summary>
/// Performs a Catmull-Rom interpolation using the specified positions.
/// </summary>
/// <param name="value1">The first position in the interpolation.</param>
/// <param name="value2">The second position in the interpolation.</param>
/// <param name="value3">The third position in the interpolation.</param>
/// <param name="value4">The fourth position in the interpolation.</param>
/// <param name="amount">Weighting factor.</param>
/// <returns>A position that is the result of the Catmull-Rom interpolation.</returns>
public static float CatmullRom(
float value1,
float value2,
float value3,
float value4,
float amount
) {
double amountSquared = amount * amount;
double amountCubed = amountSquared * amount;
return (float) (
0.5 *
(
((2.0 * value2 + (value3 - value1) * amount) +
((2.0 * value1 - 5.0 * value2 + 4.0 * value3 - value4) * amountSquared) +
(3.0 * value2 - value1 - 3.0 * value3 + value4) * amountCubed)
)
);
}
/// <summary>
/// Restricts a value to be within a specified range.
/// </summary>
/// <param name="value">The value to clamp.</param>
/// <param name="min">
/// The minimum value. If <c>value</c> is less than <c>min</c>, <c>min</c>
/// will be returned.
/// </param>
/// <param name="max">
/// The maximum value. If <c>value</c> is greater than <c>max</c>, <c>max</c>
/// will be returned.
/// </param>
/// <returns>The clamped value.</returns>
public static float Clamp(float value, float min, float max)
{
value = (value > max) ? max : value;
value = (value < min) ? min : value;
return value;
}
/// <summary>
/// Calculates the absolute value of the difference of two values.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <returns>Distance between the two values.</returns>
public static float Distance(float value1, float value2)
{
return Math.Abs(value1 - value2);
}
/// <summary>
/// Performs a Hermite spline interpolation.
/// </summary>
/// <param name="value1">Source position.</param>
/// <param name="tangent1">Source tangent.</param>
/// <param name="value2">Source position.</param>
/// <param name="tangent2">Source tangent.</param>
/// <param name="amount">Weighting factor.</param>
/// <returns>The result of the Hermite spline interpolation.</returns>
public static float Hermite(
float value1,
float tangent1,
float value2,
float tangent2,
float amount
) {
double v1 = value1, v2 = value2, t1 = tangent1, t2 = tangent2, s = amount;
double result;
double sCubed = s * s * s;
double sSquared = s * s;
if (WithinEpsilon(amount, 0f))
{
result = value1;
}
else if (WithinEpsilon(amount, 1f))
{
result = value2;
}
else
{
result = (
((2 * v1 - 2 * v2 + t2 + t1) * sCubed) +
((3 * v2 - 3 * v1 - 2 * t1 - t2) * sSquared) +
(t1 * s) +
v1
);
}
return (float) result;
}
/// <summary>
/// Linearly interpolates between two values.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <param name="amount">
/// Value between 0 and 1 indicating the weight of value2.
/// </param>
/// <returns>Interpolated value.</returns>
/// <remarks>
/// This method performs the linear interpolation based on the following formula.
/// <c>value1 + (value2 - value1) * amount</c>
/// Passing amount a value of 0 will cause value1 to be returned, a value of 1 will
/// cause value2 to be returned.
/// </remarks>
public static float Lerp(float value1, float value2, float amount)
{
return value1 + (value2 - value1) * amount;
}
/// <summary>
/// Returns the greater of two values.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <returns>The greater value.</returns>
public static float Max(float value1, float value2)
{
return value1 > value2 ? value1 : value2;
}
/// <summary>
/// Returns the lesser of two values.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <returns>The lesser value.</returns>
public static float Min(float value1, float value2)
{
return value1 < value2 ? value1 : value2;
}
/// <summary>
/// Interpolates between two values using a cubic equation.
/// </summary>
/// <param name="value1">Source value.</param>
/// <param name="value2">Source value.</param>
/// <param name="amount">Weighting value.</param>
/// <returns>Interpolated value.</returns>
public static float SmoothStep(float value1, float value2, float amount)
{
float result = MathHelper.Clamp(amount, 0f, 1f);
result = MathHelper.Hermite(value1, 0f, value2, 0f, result);
return result;
}
/// <summary>
/// Converts radians to degrees.
/// </summary>
/// <param name="radians">The angle in radians.</param>
/// <returns>The angle in degrees.</returns>
/// <remarks>
/// This method uses double precision internally, though it returns single float.
/// Factor = 180 / pi
/// </remarks>
public static float ToDegrees(float radians)
{
return (float) (radians * 57.295779513082320876798154814105);
}
/// <summary>
/// Converts degrees to radians.
/// </summary>
/// <param name="degrees">The angle in degrees.</param>
/// <returns>The angle in radians.</returns>
/// <remarks>
/// This method uses double precision internally, though it returns single float.
/// Factor = pi / 180
/// </remarks>
public static float ToRadians(float degrees)
{
return (float) (degrees * 0.017453292519943295769236907684886);
}
/// <summary>
/// Reduces a given angle to a value between pi and -pi.
/// </summary>
/// <param name="angle">The angle to reduce, in radians.</param>
/// <returns>The new angle, in radians.</returns>
public static float WrapAngle(float angle)
{
angle = (float) Math.IEEERemainder((double) angle, 6.2831854820251465);
if (angle <= -3.14159274f)
{
angle += 6.28318548f;
}
else
{
if (angle > 3.14159274f)
{
angle -= 6.28318548f;
}
}
return angle;
}
#endregion
#region Internal Static Methods
/// <summary>
/// Restricts a value to be within a specified range.
/// </summary>
/// <param name="value">The value to clamp.</param>
/// <param name="min">
/// The minimum value. If <c>value</c> is less than <c>min</c>, <c>min</c>
/// will be returned.
/// </param>
/// <param name="max">
/// The maximum value. If <c>value</c> is greater than <c>max</c>, <c>max</c>
/// will be returned.
/// </param>
/// <returns>The clamped value.</returns>
internal static int Clamp(int value, int min, int max)
{
value = (value > max) ? max : value;
value = (value < min) ? min : value;
return value;
}
internal static bool WithinEpsilon(float floatA, float floatB)
{
return Math.Abs(floatA - floatB) < MachineEpsilonFloat;
}
internal static int ClosestMSAAPower(int value)
{
if (value == 1)
{
return 0;
}
int result = value - 1;
result |= result >> 1;
result |= result >> 2;
result |= result >> 4;
result |= result >> 8;
result |= result >> 16;
result += 1;
if (result == value)
{
return result;
}
return result >> 1;
}
#endregion
#region Private Static Methods
/// <summary>
/// Find the current machine's Epsilon for the float data type.
/// (That is, the largest float, e, where e == 0.0f is true.)
/// </summary>
private static float GetMachineEpsilonFloat()
{
float machineEpsilon = 1.0f;
float comparison;
do
{
machineEpsilon *= 0.5f;
comparison = 1.0f + machineEpsilon;
}
while (comparison > 1.0f);
return machineEpsilon;
}
#endregion
}
}
