#region License
/*
MIT License
Copyright © 2006 The Mono.Xna Team

All rights reserved.

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#endregion License

using System;

namespace Otter {
    /// <summary>
    /// Contains commonly used precalculated values and mathematical operations.
    /// </summary>
    public static class MathHelper {
        /// <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);

        /// <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) {
            // Using formula from http://www.mvps.org/directx/articles/catmull/
            // Internally using doubles not to lose precission
            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) {
            // First we check to see if we're greater than the max
            value = (value > max) ? max : value;

            // Then we check to see if we're less than the min.
            value = (value < min) ? min : value;

            // There's no check to see if min > max.
            return value;
        }

        /// <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 int Clamp(int value, int min, int 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) {
            // All transformed to double not to lose precission
            // Otherwise, for high numbers of param:amount the result is NaN instead of Infinity
            double v1 = value1, v2 = value2, t1 = tangent1, t2 = tangent2, s = amount, result;
            double sCubed = s * s * s;
            double sSquared = s * s;

            if (amount == 0f)
                result = value1;
            else if (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 Math.Max(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 Math.Min(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) {
            // It is expected that 0 < amount < 1
            // If amount < 0, return value1
            // If amount > 1, return value2
            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 precission 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 precission 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 π and -π.
        /// </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;
        }

        /// <summary>
        /// Determines if value is powered by two.
        /// </summary>
        /// <param name="value">A value.</param>
        /// <returns><c>true</c> if <c>value</c> is powered by two; otherwise <c>false</c>.</returns>
        public static bool IsPowerOfTwo(int value) {
            return (value > 0) && ((value & (value - 1)) == 0);
        }
    }
}