source: code/trunk/src/util/Math.h @ 2997

/*
 *   ORXONOX - the hottest 3D action shooter ever to exist
 *                    > www.orxonox.net <
 *
 *
 *   License notice:
 *
 *   This program is free software; you can redistribute it and/or
 *   modify it under the terms of the GNU General Public License
 *   as published by the Free Software Foundation; either version 2
 *   of the License, or (at your option) any later version.
 *
 *   This program is distributed in the hope that it will be useful,
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *   GNU General Public License for more details.
 *
 *   You should have received a copy of the GNU General Public License
 *   along with this program; if not, write to the Free Software
 *   Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 *
 *   Author:
 *      Fabian 'x3n' Landau
 *   Co-authors:
 *      ...
 *
 */

/**
    @file
    @brief Declaration and implementation of several math-functions, typedefs of some Ogre::Math classes to the orxonox namespace.
*/

#ifndef _Util_Math_H__
#define _Util_Math_H__

#include "UtilPrereqs.h"

#include <ostream>
#include <string>
#include <cmath>
#include <boost/static_assert.hpp>

#include <OgreMath.h>
#include <OgreVector2.h>
#include <OgreVector3.h>
#include <OgreVector4.h>
#include <OgreMatrix3.h>
#include <OgreMatrix4.h>
#include <OgreQuaternion.h>
#include <OgreColourValue.h>

// Certain headers might define min and max macros
#if defined(max) || defined(min) || defined(sgn) || defined(clamp) || defined(square) || defined(mod)
#  error An inline math function was overridden by a macro
#endif

namespace orxonox
{
    using Ogre::Radian;
    using Ogre::Degree;
    using Ogre::Vector2;
    using Ogre::Vector3;
    using Ogre::Vector4;
    using Ogre::Matrix3;
    using Ogre::Matrix4;
    using Ogre::Quaternion;
    using Ogre::ColourValue;

    // Also define our own transform space enum
    namespace TransformSpace
    {
        /**
        @brief
            Enumeration denoting the spaces which a transform can be relative to.
        */
        enum Enum
        {
            //! Transform is relative to the local space
            Local,
            //! Transform is relative to the space of the parent node
            Parent,
            //! Transform is relative to world space
            World
        };
    }

    _UtilExport std::ostream& operator<<(std::ostream& out, const orxonox::Radian& radian);
    _UtilExport std::istream& operator>>(std::istream& in, orxonox::Radian& radian);
    _UtilExport std::ostream& operator<<(std::ostream& out, const orxonox::Degree& degree);
    _UtilExport std::istream& operator>>(std::istream& in, orxonox::Degree& degree);

    _UtilExport float getAngle(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& otherposition);
    _UtilExport orxonox::Vector2 get2DViewdirection(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& myorthonormal, const orxonox::Vector3& otherposition);
    _UtilExport orxonox::Vector2 get2DViewcoordinates(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& myorthonormal, const orxonox::Vector3& otherposition);
    _UtilExport orxonox::Vector3 getPredictedPosition(const orxonox::Vector3& myposition, float projectilespeed, const orxonox::Vector3& targetposition, const orxonox::Vector3& targetvelocity);

    /**
        @brief Returns the sign of the given value.
        @param x The value
        @return 1 if the value is positive or zero, -1 if the value is negative
    */
    template <typename T>
    inline T sgn(T x)
    {
        return (x >= 0) ? 1 : -1;
    }

    /**
        @brief Returns the smaller of two values.
    */
    template <typename T>
    inline T min(T a, T b)
    {
        return (a <= b) ? a : b;
    }

    /**
        @brief Returns the greater of two values.
    */
    template <typename T>
    inline T max(T a, T b)
    {
        return (a >= b) ? a : b;
    }

    /**
        @brief Keeps a value between a lower and an upper limit.
        @param x The value
        @param min The lower limit
        @param max The upper limit
    */
    template <typename T>
    inline T clamp(T x, T min, T max)
    {
        if (x < min)
            return min;

        if (x > max)
            return max;

        return x;
    }

    /**
        @brief Returns the square value (x^2).
    */
    template <typename T>
    inline T square(T x)
    {
        return x*x;
    }

    /**
        @brief Returns the cube value (x^3).
    */
    template <typename T>
    inline T cube(T x)
    {
        return x*x*x;
    }

    /**
        @brief Rounds the value.
    */
    template <typename T>
    inline int round(T x)
    {
        return (int)(x + 0.5);
    }

    /**
        @brief The modulo operation, enhanced to work properly with negative values.
        @param x The value
        @param max The operand
    */
    template <typename T>
    inline int mod(T x, int max)
    {
        if (x >= 0)
            return (x % max);
        else
            return ((x % max) + max);
    }

    template <typename T>
    inline T zeroise()
    {
        // Default, raise a compiler error without including large boost header cascade.
        T temp();
        *********temp; // If you reach this code, you abused zeroise()!
        return temp;
    }

    template <> inline char                 zeroise<char>()                 { return 0; }
    template <> inline unsigned char        zeroise<unsigned char>()        { return 0; }
    template <> inline short                zeroise<short>()                { return 0; }
    template <> inline unsigned short       zeroise<unsigned short>()       { return 0; }
    template <> inline int                  zeroise<int>()                  { return 0; }
    template <> inline unsigned int         zeroise<unsigned int>()         { return 0; }
    template <> inline long                 zeroise<long>()                 { return 0; }
    template <> inline unsigned long        zeroise<unsigned long>()        { return 0; }
    template <> inline long long            zeroise<long long>()            { return 0; }
    template <> inline unsigned long long   zeroise<unsigned long long>()   { return 0; }
    template <> inline float                zeroise<float>()                { return 0; }
    template <> inline double               zeroise<double>()               { return 0; }
    template <> inline long double          zeroise<long double>()          { return 0; }
    template <> inline bool                 zeroise<bool>()                 { return 0; }
    template <> inline void*                zeroise<void*>()                { return 0; }
    template <> inline std::string          zeroise<std::string>()          { return ""; }
    template <> inline orxonox::Radian      zeroise<orxonox::Radian>()      { return orxonox::Radian(0.0f); }
    template <> inline orxonox::Degree      zeroise<orxonox::Degree>()      { return orxonox::Degree(0.0f); }
    template <> inline orxonox::Vector2     zeroise<orxonox::Vector2>()     { return orxonox::Vector2    (0, 0)      ; }
    template <> inline orxonox::Vector3     zeroise<orxonox::Vector3>()     { return orxonox::Vector3    (0, 0, 0)   ; }
    template <> inline orxonox::Vector4     zeroise<orxonox::Vector4>()     { return orxonox::Vector4    (0, 0, 0, 0); }
    template <> inline orxonox::ColourValue zeroise<orxonox::ColourValue>() { return orxonox::ColourValue(0, 0, 0, 0); }
    template <> inline orxonox::Quaternion  zeroise<orxonox::Quaternion>()  { return orxonox::Quaternion (0, 0, 0, 0); }

    /**
        @brief Interpolates between two values for a time between 0 and 1.
        @param time The time is a value between 0 and 1 - the function returns start if time is 0 and end if time is 1 and interpolates if time is between 0 and 1.
        @param start The value at time = 0
        @param end The value at time = 1
        @return The interpolation at a given time
    */
    template <typename T>
    T interpolate(float time, const T& start, const T& end)
    {
        return time * (end - start) + start;
    }

    /**
        @brief Interpolates smoothly between two values for a time between 0 and 1. The function starts slowly, increases faster and stops slowly again.
        @param time The time is a value between 0 and 1 - the function returns start if time is 0 and end if time is 1 and interpolates if time is between 0 and 1.
        @param start The value at time = 0
        @param end The value at time = 1
        @return The smoothed interpolation at a given time
    */
    template <typename T>
    T interpolateSmooth(float time, const T& start, const T& end)
    {
        return (-2 * (end - start) * cube(time)) + (3 * (end - start) * square(time)) + start;
    }

    /**
        @brief Returns a random number between 0 and almost 1: 0 <= rnd < 1.
    */
    inline float rnd()
    {
        return rand() / (RAND_MAX + 1.0);
    }

    /**
        @brief Returns a random number between 0 and almost max: 0 <= rnd < max.
        @param max The maximum
    */
    inline float rnd(float max)
    {
        return rnd() * max;
    }

    /**
        @brief Returns a random number between min and almost max: min <= rnd < max.
        @param min The minimum
        @param max The maximum
    */
    inline float rnd(float min, float max)
    {
        return rnd(max - min) + min;
    }

    /**
        @brief Returns randomly 1 or -1 with equal probability.
    */
    inline float rndsgn()
    {
        return ((rand() & 0x2) - 1); // rand() & 0x2 is either 2 or 0
    }

    _UtilExport unsigned long getUniqueNumber();

    class IntVector2
    {
    public:
      IntVector2() : x(0), y(0) { }
      IntVector2(int _x, int _y) : x(_x), y(_y) { }
      int x;
      int y;
    };

    class IntVector3
    {
    public:
      IntVector3() : x(0), y(0), z(0) { }
      IntVector3(int _x, int _y, int _z) : x(_x), y(_y), z(_z) { }
      int x;
      int y;
      int z;
    };
}

#endif /* _Util_Math_H__ */