419 lines
12 KiB
C#
419 lines
12 KiB
C#
#region License
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/* MoonWorks - Game Development Framework
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* Copyright 2021 Evan Hemsley
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*/
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/* Derived from code by Ethan Lee (Copyright 2009-2021).
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* Released under the Microsoft Public License.
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* See fna.LICENSE for details.
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* Derived from code by the Mono.Xna Team (Copyright 2006).
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* Released under the MIT License. See monoxna.LICENSE for details.
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*/
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#endregion
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namespace MoonWorks.Math
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{
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/// <summary>
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/// Contains commonly used precalculated values and mathematical operations.
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/// </summary>
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public static class MathHelper
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{
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#region Public Constants
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/// <summary>
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/// Represents the mathematical constant e(2.71828175).
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/// </summary>
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public const float E = (float) System.Math.E;
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/// <summary>
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/// Represents the log base ten of e(0.4342945).
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/// </summary>
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public const float Log10E = 0.4342945f;
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/// <summary>
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/// Represents the log base two of e(1.442695).
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/// </summary>
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public const float Log2E = 1.442695f;
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/// <summary>
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/// Represents the value of pi(3.14159274).
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/// </summary>
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public const float Pi = (float) System.Math.PI;
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/// <summary>
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/// Represents the value of pi divided by two(1.57079637).
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/// </summary>
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public const float PiOver2 = (float) (System.Math.PI / 2.0);
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/// <summary>
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/// Represents the value of pi divided by four(0.7853982).
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/// </summary>
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public const float PiOver4 = (float) (System.Math.PI / 4.0);
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/// <summary>
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/// Represents the value of pi times two(6.28318548).
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/// </summary>
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public const float TwoPi = (float) (System.Math.PI * 2.0);
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#endregion
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#region Internal Static Readonly Fields
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internal static readonly float MachineEpsilonFloat = GetMachineEpsilonFloat();
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#endregion
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#region Public Static Methods
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/// <summary>
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/// Returns the Cartesian coordinate for one axis of a point that is defined by a
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/// given triangle and two normalized barycentric (areal) coordinates.
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/// </summary>
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/// <param name="value1">
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/// The coordinate on one axis of vertex 1 of the defining triangle.
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/// </param>
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/// <param name="value2">
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/// The coordinate on the same axis of vertex 2 of the defining triangle.
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/// </param>
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/// <param name="value3">
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/// The coordinate on the same axis of vertex 3 of the defining triangle.
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/// </param>
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/// <param name="amount1">
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/// The normalized barycentric (areal) coordinate b2, equal to the weighting factor
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/// for vertex 2, the coordinate of which is specified in value2.
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/// </param>
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/// <param name="amount2">
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/// The normalized barycentric (areal) coordinate b3, equal to the weighting factor
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/// for vertex 3, the coordinate of which is specified in value3.
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/// </param>
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/// <returns>
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/// Cartesian coordinate of the specified point with respect to the axis being used.
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/// </returns>
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public static float Barycentric(
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float value1,
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float value2,
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float value3,
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float amount1,
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float amount2
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)
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{
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return value1 + (value2 - value1) * amount1 + (value3 - value1) * amount2;
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}
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/// <summary>
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/// Performs a Catmull-Rom interpolation using the specified positions.
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/// </summary>
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/// <param name="value1">The first position in the interpolation.</param>
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/// <param name="value2">The second position in the interpolation.</param>
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/// <param name="value3">The third position in the interpolation.</param>
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/// <param name="value4">The fourth position in the interpolation.</param>
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/// <param name="amount">Weighting factor.</param>
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/// <returns>A position that is the result of the Catmull-Rom interpolation.</returns>
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public static float CatmullRom(
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float value1,
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float value2,
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float value3,
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float value4,
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float amount
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)
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{
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/* Using formula from http://www.mvps.org/directx/articles/catmull/
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* Internally using doubles not to lose precision.
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*/
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double amountSquared = amount * amount;
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double amountCubed = amountSquared * amount;
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return (float) (
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0.5 *
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(
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((2.0 * value2 + (value3 - value1) * amount) +
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((2.0 * value1 - 5.0 * value2 + 4.0 * value3 - value4) * amountSquared) +
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(3.0 * value2 - value1 - 3.0 * value3 + value4) * amountCubed)
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)
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);
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}
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/// <summary>
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/// Restricts a value to be within a specified range.
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/// </summary>
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/// <param name="value">The value to clamp.</param>
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/// <param name="min">
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/// The minimum value. If <c>value</c> is less than <c>min</c>, <c>min</c>
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/// will be returned.
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/// </param>
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/// <param name="max">
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/// The maximum value. If <c>value</c> is greater than <c>max</c>, <c>max</c>
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/// will be returned.
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/// </param>
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/// <returns>The clamped value.</returns>
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public static float Clamp(float value, float min, float max)
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{
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// First we check to see if we're greater than the max.
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value = (value > max) ? max : value;
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// Then we check to see if we're less than the min.
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value = (value < min) ? min : value;
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// There's no check to see if min > max.
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return value;
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}
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/// <summary>
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/// Calculates the absolute value of the difference of two values.
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/// </summary>
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/// <param name="value1">Source value.</param>
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/// <param name="value2">Source value.</param>
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/// <returns>Distance between the two values.</returns>
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public static float Distance(float value1, float value2)
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{
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return System.Math.Abs(value1 - value2);
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}
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/// <summary>
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/// Performs a Hermite spline interpolation.
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/// </summary>
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/// <param name="value1">Source position.</param>
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/// <param name="tangent1">Source tangent.</param>
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/// <param name="value2">Source position.</param>
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/// <param name="tangent2">Source tangent.</param>
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/// <param name="amount">Weighting factor.</param>
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/// <returns>The result of the Hermite spline interpolation.</returns>
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public static float Hermite(
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float value1,
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float tangent1,
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float value2,
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float tangent2,
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float amount
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)
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{
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/* All transformed to double not to lose precision
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* Otherwise, for high numbers of param:amount the result is NaN instead
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* of Infinity.
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*/
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double v1 = value1, v2 = value2, t1 = tangent1, t2 = tangent2, s = amount;
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double result;
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double sCubed = s * s * s;
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double sSquared = s * s;
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if (WithinEpsilon(amount, 0f))
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{
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result = value1;
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}
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else if (WithinEpsilon(amount, 1f))
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{
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result = value2;
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}
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else
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{
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result = (
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((2 * v1 - 2 * v2 + t2 + t1) * sCubed) +
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((3 * v2 - 3 * v1 - 2 * t1 - t2) * sSquared) +
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(t1 * s) +
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v1
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);
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}
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return (float) result;
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}
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/// <summary>
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/// Linearly interpolates between two values.
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/// </summary>
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/// <param name="value1">Source value.</param>
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/// <param name="value2">Source value.</param>
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/// <param name="amount">
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/// Value between 0 and 1 indicating the weight of value2.
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/// </param>
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/// <returns>Interpolated value.</returns>
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/// <remarks>
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/// This method performs the linear interpolation based on the following formula.
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/// <c>value1 + (value2 - value1) * amount</c>
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/// Passing amount a value of 0 will cause value1 to be returned, a value of 1 will
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/// cause value2 to be returned.
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/// </remarks>
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public static float Lerp(float value1, float value2, float amount)
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{
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return value1 + (value2 - value1) * amount;
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}
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/// <summary>
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/// Returns the greater of two values.
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/// </summary>
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/// <param name="value1">Source value.</param>
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/// <param name="value2">Source value.</param>
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/// <returns>The greater value.</returns>
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public static float Max(float value1, float value2)
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{
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return value1 > value2 ? value1 : value2;
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}
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/// <summary>
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/// Returns the lesser of two values.
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/// </summary>
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/// <param name="value1">Source value.</param>
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/// <param name="value2">Source value.</param>
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/// <returns>The lesser value.</returns>
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public static float Min(float value1, float value2)
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{
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return value1 < value2 ? value1 : value2;
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}
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/// <summary>
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/// Interpolates between two values using a cubic equation.
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/// </summary>
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/// <param name="value1">Source value.</param>
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/// <param name="value2">Source value.</param>
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/// <param name="amount">Weighting value.</param>
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/// <returns>Interpolated value.</returns>
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public static float SmoothStep(float value1, float value2, float amount)
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{
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/* It is expected that 0 < amount < 1.
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* If amount < 0, return value1.
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* If amount > 1, return value2.
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*/
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float result = MathHelper.Clamp(amount, 0f, 1f);
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result = MathHelper.Hermite(value1, 0f, value2, 0f, result);
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return result;
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}
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/// <summary>
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/// Converts radians to degrees.
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/// </summary>
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/// <param name="radians">The angle in radians.</param>
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/// <returns>The angle in degrees.</returns>
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/// <remarks>
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/// This method uses double precision internally, though it returns single float.
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/// Factor = 180 / pi
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/// </remarks>
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public static float ToDegrees(float radians)
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{
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return (float) (radians * 57.295779513082320876798154814105);
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}
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/// <summary>
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/// Converts degrees to radians.
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/// </summary>
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/// <param name="degrees">The angle in degrees.</param>
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/// <returns>The angle in radians.</returns>
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/// <remarks>
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/// This method uses double precision internally, though it returns single float.
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/// Factor = pi / 180
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/// </remarks>
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public static float ToRadians(float degrees)
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{
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return (float) (degrees * 0.017453292519943295769236907684886);
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}
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/// <summary>
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/// Reduces a given angle to a value between pi and -pi.
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/// </summary>
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/// <param name="angle">The angle to reduce, in radians.</param>
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/// <returns>The new angle, in radians.</returns>
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public static float WrapAngle(float angle)
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{
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if ((angle > -Pi) && (angle <= Pi))
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{
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return angle;
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}
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angle %= TwoPi;
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if (angle <= -Pi)
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{
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return angle + TwoPi;
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}
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if (angle > Pi)
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{
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return angle - TwoPi;
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}
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return angle;
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}
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#endregion
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#region Internal Static Methods
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// FIXME: This could be an extension! ClampIntEXT? -flibit
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/// <summary>
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/// Restricts a value to be within a specified range.
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/// </summary>
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/// <param name="value">The value to clamp.</param>
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/// <param name="min">
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/// The minimum value. If <c>value</c> is less than <c>min</c>, <c>min</c>
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/// will be returned.
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/// </param>
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/// <param name="max">
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/// The maximum value. If <c>value</c> is greater than <c>max</c>, <c>max</c>
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/// will be returned.
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/// </param>
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/// <returns>The clamped value.</returns>
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internal static int Clamp(int value, int min, int max)
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{
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value = (value > max) ? max : value;
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value = (value < min) ? min : value;
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return value;
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}
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internal static bool WithinEpsilon(float floatA, float floatB)
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{
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return System.Math.Abs(floatA - floatB) < MachineEpsilonFloat;
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}
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internal static int ClosestMSAAPower(int value)
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{
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/* Checking for the highest power of two _after_ than the given int:
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* http://graphics.stanford.edu/~seander/bithacks.html#RoundUpPowerOf2
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* Take result, divide by 2, get the highest power of two _before_!
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* -flibit
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*/
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if (value == 1)
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{
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// ... Except for 1, which is invalid for MSAA -flibit
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return 0;
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}
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int result = value - 1;
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result |= result >> 1;
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result |= result >> 2;
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result |= result >> 4;
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result |= result >> 8;
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result |= result >> 16;
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result += 1;
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if (result == value)
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{
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return result;
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}
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return result >> 1;
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}
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#endregion
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#region Private Static Methods
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/// <summary>
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/// Find the current machine's Epsilon for the float data type.
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/// (That is, the largest float, e, where e == 0.0f is true.)
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/// </summary>
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private static float GetMachineEpsilonFloat()
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{
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float machineEpsilon = 1.0f;
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float comparison;
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/* Keep halving the working value of machineEpsilon until we get a number that
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* when added to 1.0f will still evaluate as equal to 1.0f.
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*/
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do
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{
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machineEpsilon *= 0.5f;
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comparison = 1.0f + machineEpsilon;
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}
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while (comparison > 1.0f);
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return machineEpsilon;
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}
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#endregion
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}
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}
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