source: code/trunk/src/libraries/util/Math.h @ 11997

/*
 *   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:
 *      Wolfgang Roenninger
 *
 */

/**
    @defgroup Math Mathematical functions
    @ingroup Util
*/

/**
    @file
    @ingroup Math
    @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 <string>
#include <cmath>
#include <cstdlib>
#include <random>
#include <type_traits>

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

// Certain headers might define unwanted macros...
#undef max
#undef min
#undef sgn
#undef clamp
#undef sqrt
#undef square
#undef mod
#undef rnd

namespace orxonox
{
    /** Often used numerical constants because C++ doesn't define any.
    @note
        The values here are decimal representations of the approximate floating
        point value as it is stored according to the IEEE 754 standard.
    */
    namespace math
    {
        constexpr float twoPi   = 6.283185482025146484375f;     ///< PI * 2
        constexpr float pi      = 3.1415927410125732421875f;    ///< PI
        constexpr float pi_2    = 1.57079637050628662109375f;   ///< PI / 2
        constexpr float pi_4    = 0.785398185253143310546875f;  ///< PI / 4
        constexpr float e       = 2.718281269073486328125f;     ///< e
        constexpr float sqrt2   = 1.41421353816986083984375f;   ///< sqrt(2)
        constexpr float sqrt2_2 = 0.707106769084930419921875f;  ///< sqrt(2) / 2
    }

#if OGRE_VERSION < 0x010603
    _UtilExport std::ostream& operator<<(std::ostream& out, const orxonox::Radian& radian);
    _UtilExport std::ostream& operator<<(std::ostream& out, const orxonox::Degree& degree);
#endif
    _UtilExport std::istream& operator>>(std::istream& in, orxonox::Radian& radian);
    _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::Vector2 get3DProjection(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& myorthonormal, const orxonox::Vector3& otherposition, const float mapangle, const float detectionlimit);
    _UtilExport bool isObjectHigherThanShipOnMap(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& myorthonormal, const orxonox::Vector3& otherposition, const float mapangle);
    _UtilExport int determineMap3DZOrder(const orxonox::Vector3& myposition, const orxonox::Vector3& mydirection, const orxonox::Vector3& myorthonormal, const orxonox::Vector3& otherposition, const float detectionlimit);
    _UtilExport orxonox::Vector3 getTransformedVector(const orxonox::Vector3& distance, const orxonox::Vector3& mydirection, const orxonox::Vector3& myorthonormal, const orxonox::Vector3& myside);
    _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>
    constexpr inline T sgn(T x)
    {
        return (x >= 0) ? (T)1 : (T)-1;
    }

    /**
        @brief Keeps a value between a lower and an upper limit. Values beyond these limits are limited to either @a min or @a max.
        @param x The value
        @param min The lower limit
        @param max The upper limit
    */
    template <typename T>
    constexpr inline T clamp(T x, T min, T max)
    {
        return x < min ? min : (x > max ? max : x);
    }

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

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

    /**
        @brief The modulo operation, enhanced to work properly with negative values.
        @param x The value
        @param max The operand

        The built in modulo operator % yields a strange behavior with negative values.
        This function corrects this - the result is guaranteed to lie always between
        zero and (max-1).

        Example:
        @code
        int var = 11 % 10;      //  1
        int var = -1 % 10;      // -1

        int var = mod(11, 10);  //  1
        int var = mod(-1, 10);  //  9
        @endcode
    */
    template <typename T>
    inline int mod(T x, int max)
    {
        if (x >= 0)
            return (x % max);
        else
        {
            T temp = x % max;
            return (temp < 0) ? (temp + max) : temp;
        }
    }

    /**
        @brief Returns a "zero" value for the given type.
        @note This is the default template of the zeroise() function. The template is spezialized for each supported type.

        The exact return value of the function depends on the type. For @c int this is 0,
        for @c float it's 0.0f. For a @c std::string the function returns "" and for
        @c Vector3 you get <tt>Vector3(0, 0, 0)</tt>.
    */
    template <typename T> /* for normal classes */ typename std::enable_if<!std::is_enum<T>::value, T>::type
    inline /*T*/ zeroise()
    {
        // If you reach this code, you abused zeroise()!
        static_assert(sizeof(T) != sizeof(T), "No template specialization available for T");
    }
    /// Implementation for enum classes: uses the underlying type to create a zero value.
    template <typename T> /* for enum classes */ typename std::enable_if<std::is_enum<T>::value, T>::type
    inline /*T*/ zeroise()
    {
        return static_cast<T>(zeroise<typename std::underlying_type<T>::type>());
    }

    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 nullptr; }
    template <> inline std::string          zeroise<std::string>()          { return std::string(); }
    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 Provides zero value symbols that can be returned as reference
        @see zeroise()
    */
    template <typename T>
    struct NilValue
    {
        inline operator const T&() const
        {
            return value;
        }
        static T value;
    };
    template <typename T>
    T NilValue<T>::value = zeroise<T>();

    /**
        @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 @a start if @a time is 0, @a end if @a time is 1, and interpolates if @a time is between 0 and 1.
        @param start The value at @a time = 0
        @param end The value at @a time = 1
        @return The interpolated value at a given time
    */
    template <typename T>
    inline T interpolate(float time, const T& start, const T& end)
    {
        return static_cast<T>(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 @a start if @a time is 0, @a end if @a time is 1, and interpolates if @a time is between 0 and 1.
        @param start The value at @a time = 0
        @param end The value at @a time = 1
        @return The interpolated value at a given time
    */
    template <typename T>
    inline T interpolateSmooth(float time, const T& start, const T& end)
    {
        return static_cast<T>((-2 * (end - start) * cube(time)) + (3 * (end - start) * square(time)) + start);
    }

    namespace detail
    {
        /**
        Random number generator used for the functions below. Marked extern to only have one global instance.
        */
        _UtilExport extern std::mt19937 rngen;
    }

    /**
    @brief Seeds the random number generator used for the functions below.
    */
    inline void rndseed(unsigned int seed)
    {
        detail::rngen.seed(seed);
    }

    /**
    @brief Returns a random number between @a min and almost @a max: <tt>min <= rnd < max</tt>.
    @param min The minimum
    @param max The maximum
    */
    inline float rnd(float min, float max)
    {
        std::uniform_real_distribution<float> dist(min, max);
        return dist(detail::rngen);
    }

    /**
        @brief Returns a random number between 0 and almost 1: <tt>0 <= rnd < 1</tt>.
    */
    inline float rnd()
    {
        return rnd(0, 1);
    }

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

    /**
        @brief Returns randomly 1 or -1 with equal probability.
    */
    inline float rndsgn()
    {
        std::uniform_int_distribution<> dist;
        return static_cast<float>((dist(detail::rngen) & 0x2) - 1); // dist(...) & 0x2 is either 2 or 0
    }

    _UtilExport unsigned long getUniqueNumber();
}

#endif /* _Util_Math_H__ */