321 lines
14 KiB
C#
321 lines
14 KiB
C#
// MIT License - Copyright (C) The Mono.Xna Team
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// This file is subject to the terms and conditions defined in
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// file 'LICENSE.txt', which is part of this source code package.
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using System;
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namespace Microsoft.Xna.Framework
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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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/// <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)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)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)(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)(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)(Math.PI * 2.0);
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/// <summary>
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/// Returns the Cartesian coordinate for one axis of a point that is defined by a given triangle and two normalized barycentric (areal) coordinates.
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/// </summary>
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/// <param name="value1">The coordinate on one axis of vertex 1 of the defining triangle.</param>
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/// <param name="value2">The coordinate on the same axis of vertex 2 of the defining triangle.</param>
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/// <param name="value3">The coordinate on the same axis of vertex 3 of the defining triangle.</param>
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/// <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>
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/// <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>
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/// <returns>Cartesian coordinate of the specified point with respect to the axis being used.</returns>
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public static float Barycentric(float value1, float value2, float value3, float amount1, float amount2)
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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(float value1, float value2, float value3, float value4, float amount)
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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 precission
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double amountSquared = amount * amount;
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double amountCubed = amountSquared * amount;
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return (float)(0.5 * (2.0 * value2 +
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(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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/// <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">The minimum value. If <c>value</c> is less than <c>min</c>, <c>min</c> will be returned.</param>
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/// <param name="max">The maximum value. If <c>value</c> is greater than <c>max</c>, <c>max</c> will be returned.</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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/// 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">The minimum value. If <c>value</c> is less than <c>min</c>, <c>min</c> will be returned.</param>
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/// <param name="max">The maximum value. If <c>value</c> is greater than <c>max</c>, <c>max</c> will be returned.</param>
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/// <returns>The clamped value.</returns>
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public 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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/// <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 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(float value1, float tangent1, float value2, float tangent2, float amount)
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{
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// All transformed to double not to lose precission
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// Otherwise, for high numbers of param:amount the result is NaN instead of Infinity
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double v1 = value1, v2 = value2, t1 = tangent1, t2 = tangent2, s = amount, result;
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double sCubed = s * s * s;
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double sSquared = s * s;
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if (amount == 0f)
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result = value1;
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else if (amount == 1f)
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result = value2;
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else
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result = (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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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">Destination value.</param>
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/// <param name="amount">Value between 0 and 1 indicating the weight of value2.</param>
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/// <returns>Interpolated value.</returns>
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/// <remarks>This method performs the linear interpolation based on the following formula:
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/// <code>value1 + (value2 - value1) * amount</code>.
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/// Passing amount a value of 0 will cause value1 to be returned, a value of 1 will cause value2 to be returned.
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/// See <see cref="MathHelper.LerpPrecise"/> for a less efficient version with more precision around edge cases.
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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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/// Linearly interpolates between two values.
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/// This method is a less efficient, more precise version of <see cref="MathHelper.Lerp"/>.
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/// See remarks for more info.
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/// </summary>
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/// <param name="value1">Source value.</param>
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/// <param name="value2">Destination value.</param>
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/// <param name="amount">Value between 0 and 1 indicating the weight of value2.</param>
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/// <returns>Interpolated value.</returns>
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/// <remarks>This method performs the linear interpolation based on the following formula:
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/// <code>((1 - amount) * value1) + (value2 * amount)</code>.
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/// Passing amount a value of 0 will cause value1 to be returned, a value of 1 will cause value2 to be returned.
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/// This method does not have the floating point precision issue that <see cref="MathHelper.Lerp"/> has.
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/// i.e. If there is a big gap between value1 and value2 in magnitude (e.g. value1=10000000000000000, value2=1),
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/// right at the edge of the interpolation range (amount=1), <see cref="MathHelper.Lerp"/> will return 0 (whereas it should return 1).
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/// This also holds for value1=10^17, value2=10; value1=10^18,value2=10^2... so on.
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/// For an in depth explanation of the issue, see below references:
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/// Relevant Wikipedia Article: https://en.wikipedia.org/wiki/Linear_interpolation#Programming_language_support
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/// Relevant StackOverflow Answer: http://stackoverflow.com/questions/4353525/floating-point-linear-interpolation#answer-23716956
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/// </remarks>
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public static float LerpPrecise(float value1, float value2, float amount)
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{
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return ((1 - amount) * value1) + (value2 * 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 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 int Max(int value1, int 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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/// 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 int Min(int value1, int 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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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 precission internally,
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/// 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 precission internally,
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/// 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 π and -π.
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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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return angle;
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angle %= TwoPi;
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if (angle <= -Pi)
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return angle + TwoPi;
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if (angle > Pi)
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return angle - TwoPi;
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return angle;
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}
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/// <summary>
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/// Determines if value is powered by two.
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/// </summary>
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/// <param name="value">A value.</param>
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/// <returns><c>true</c> if <c>value</c> is powered by two; otherwise <c>false</c>.</returns>
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public static bool IsPowerOfTwo(int value)
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{
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return (value > 0) && ((value & (value - 1)) == 0);
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}
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}
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}
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