OgreMath.h

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/*
-----------------------------------------------------------------------------
This source file is part of OGRE
    (Object-oriented Graphics Rendering Engine)
For the latest info, see http://www.ogre3d.org/

Copyright (c) 2000-2013 Torus Knot Software Ltd

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.
-----------------------------------------------------------------------------
*/
#ifndef __Math_H__
#define __Math_H__

#include "OgrePrerequisites.h"

namespace Ogre
{
    class Radian
    {
        Real mRad;

    public:
        explicit Radian ( Real r=0 ) : mRad(r) {}
        Radian ( const Degree& d );
        Radian& operator = ( const Real& f ) { mRad = f; return *this; }
        Radian& operator = ( const Radian& r ) { mRad = r.mRad; return *this; }
        Radian& operator = ( const Degree& d );

        Real valueDegrees() const; // see bottom of this file
        Real valueRadians() const { return mRad; }
        Real valueAngleUnits() const;

        const Radian& operator + () const { return *this; }
        Radian operator + ( const Radian& r ) const { return Radian ( mRad + r.mRad ); }
        Radian operator + ( const Degree& d ) const;
        Radian& operator += ( const Radian& r ) { mRad += r.mRad; return *this; }
        Radian& operator += ( const Degree& d );
        Radian operator - () const { return Radian(-mRad); }
        Radian operator - ( const Radian& r ) const { return Radian ( mRad - r.mRad ); }
        Radian operator - ( const Degree& d ) const;
        Radian& operator -= ( const Radian& r ) { mRad -= r.mRad; return *this; }
        Radian& operator -= ( const Degree& d );
        Radian operator * ( Real f ) const { return Radian ( mRad * f ); }
        Radian operator * ( const Radian& f ) const { return Radian ( mRad * f.mRad ); }
        Radian& operator *= ( Real f ) { mRad *= f; return *this; }
        Radian operator / ( Real f ) const { return Radian ( mRad / f ); }
        Radian& operator /= ( Real f ) { mRad /= f; return *this; }

        bool operator <  ( const Radian& r ) const { return mRad <  r.mRad; }
        bool operator <= ( const Radian& r ) const { return mRad <= r.mRad; }
        bool operator == ( const Radian& r ) const { return mRad == r.mRad; }
        bool operator != ( const Radian& r ) const { return mRad != r.mRad; }
        bool operator >= ( const Radian& r ) const { return mRad >= r.mRad; }
        bool operator >  ( const Radian& r ) const { return mRad >  r.mRad; }

        inline _OgreExport friend std::ostream& operator <<
            ( std::ostream& o, const Radian& v )
        {
            o << "Radian(" << v.valueRadians() << ")";
            return o;
        }
    };

    class Degree
    {
        Real mDeg; // if you get an error here - make sure to define/typedef 'Real' first

    public:
        explicit Degree ( Real d=0 ) : mDeg(d) {}
        Degree ( const Radian& r ) : mDeg(r.valueDegrees()) {}
        Degree& operator = ( const Real& f ) { mDeg = f; return *this; }
        Degree& operator = ( const Degree& d ) { mDeg = d.mDeg; return *this; }
        Degree& operator = ( const Radian& r ) { mDeg = r.valueDegrees(); return *this; }

        Real valueDegrees() const { return mDeg; }
        Real valueRadians() const; // see bottom of this file
        Real valueAngleUnits() const;

        const Degree& operator + () const { return *this; }
        Degree operator + ( const Degree& d ) const { return Degree ( mDeg + d.mDeg ); }
        Degree operator + ( const Radian& r ) const { return Degree ( mDeg + r.valueDegrees() ); }
        Degree& operator += ( const Degree& d ) { mDeg += d.mDeg; return *this; }
        Degree& operator += ( const Radian& r ) { mDeg += r.valueDegrees(); return *this; }
        Degree operator - () const { return Degree(-mDeg); }
        Degree operator - ( const Degree& d ) const { return Degree ( mDeg - d.mDeg ); }
        Degree operator - ( const Radian& r ) const { return Degree ( mDeg - r.valueDegrees() ); }
        Degree& operator -= ( const Degree& d ) { mDeg -= d.mDeg; return *this; }
        Degree& operator -= ( const Radian& r ) { mDeg -= r.valueDegrees(); return *this; }
        Degree operator * ( Real f ) const { return Degree ( mDeg * f ); }
        Degree operator * ( const Degree& f ) const { return Degree ( mDeg * f.mDeg ); }
        Degree& operator *= ( Real f ) { mDeg *= f; return *this; }
        Degree operator / ( Real f ) const { return Degree ( mDeg / f ); }
        Degree& operator /= ( Real f ) { mDeg /= f; return *this; }

        bool operator <  ( const Degree& d ) const { return mDeg <  d.mDeg; }
        bool operator <= ( const Degree& d ) const { return mDeg <= d.mDeg; }
        bool operator == ( const Degree& d ) const { return mDeg == d.mDeg; }
        bool operator != ( const Degree& d ) const { return mDeg != d.mDeg; }
        bool operator >= ( const Degree& d ) const { return mDeg >= d.mDeg; }
        bool operator >  ( const Degree& d ) const { return mDeg >  d.mDeg; }

        inline _OgreExport friend std::ostream& operator <<
            ( std::ostream& o, const Degree& v )
        {
            o << "Degree(" << v.valueDegrees() << ")";
            return o;
        }
    };

    class Angle
    {
        Real mAngle;
    public:
        explicit Angle ( Real angle ) : mAngle(angle) {}
        operator Radian() const;
        operator Degree() const;
    };

    // these functions could not be defined within the class definition of class
    // Radian because they required class Degree to be defined
    inline Radian::Radian ( const Degree& d ) : mRad(d.valueRadians()) {
    }
    inline Radian& Radian::operator = ( const Degree& d ) {
        mRad = d.valueRadians(); return *this;
    }
    inline Radian Radian::operator + ( const Degree& d ) const {
        return Radian ( mRad + d.valueRadians() );
    }
    inline Radian& Radian::operator += ( const Degree& d ) {
        mRad += d.valueRadians();
        return *this;
    }
    inline Radian Radian::operator - ( const Degree& d ) const {
        return Radian ( mRad - d.valueRadians() );
    }
    inline Radian& Radian::operator -= ( const Degree& d ) {
        mRad -= d.valueRadians();
        return *this;
    }

    class _OgreExport Math 
    {
   public:
       enum AngleUnit
       {
           AU_DEGREE,
           AU_RADIAN
       };

    protected:
       // angle units used by the api
       static AngleUnit msAngleUnit;

        static int mTrigTableSize;

        static Real mTrigTableFactor;
        static Real* mSinTable;
        static Real* mTanTable;

        void buildTrigTables();

        static Real SinTable (Real fValue);
        static Real TanTable (Real fValue);
    public:
        Math(unsigned int trigTableSize = 4096);

        ~Math();

        static inline int IAbs (int iValue) { return ( iValue >= 0 ? iValue : -iValue ); }
        static inline int ICeil (float fValue) { return int(ceil(fValue)); }
        static inline int IFloor (float fValue) { return int(floor(fValue)); }
        static int ISign (int iValue);

        static inline Real Abs (Real fValue) { return Real(fabs(fValue)); }

        static inline Degree Abs (const Degree& dValue) { return Degree(fabs(dValue.valueDegrees())); }

        static inline Radian Abs (const Radian& rValue) { return Radian(fabs(rValue.valueRadians())); }

        static Radian ACos (Real fValue);

        static Radian ASin (Real fValue);

        static inline Radian ATan (Real fValue) { return Radian(atan(fValue)); }

        static inline Radian ATan2 (Real fY, Real fX) { return Radian(atan2(fY,fX)); }

        static inline Real Ceil (Real fValue) { return Real(ceil(fValue)); }
        static inline bool isNaN(Real f)
        {
            // std::isnan() is C99, not supported by all compilers
            // However NaN always fails this next test, no other number does.
            return f != f;
        }

        static inline Real Cos (const Radian& fValue, bool useTables = false) {
            return (!useTables) ? Real(cos(fValue.valueRadians())) : SinTable(fValue.valueRadians() + HALF_PI);
        }
        static inline Real Cos (Real fValue, bool useTables = false) {
            return (!useTables) ? Real(cos(fValue)) : SinTable(fValue + HALF_PI);
        }

        static inline Real Exp (Real fValue) { return Real(exp(fValue)); }

        static inline Real Floor (Real fValue) { return Real(floor(fValue)); }

        static inline Real Log (Real fValue) { return Real(log(fValue)); }

        static const Real LOG2;

        static inline Real Log2 (Real fValue) { return Real(log(fValue)/LOG2); }

        static inline Real LogN (Real base, Real fValue) { return Real(log(fValue)/log(base)); }

        static inline Real Pow (Real fBase, Real fExponent) { return Real(pow(fBase,fExponent)); }

        static Real Sign (Real fValue);
        static inline Radian Sign ( const Radian& rValue )
        {
            return Radian(Sign(rValue.valueRadians()));
        }
        static inline Degree Sign ( const Degree& dValue )
        {
            return Degree(Sign(dValue.valueDegrees()));
        }

        static inline Real Sin (const Radian& fValue, bool useTables = false) {
            return (!useTables) ? Real(sin(fValue.valueRadians())) : SinTable(fValue.valueRadians());
        }
        static inline Real Sin (Real fValue, bool useTables = false) {
            return (!useTables) ? Real(sin(fValue)) : SinTable(fValue);
        }

        static inline Real Sqr (Real fValue) { return fValue*fValue; }

        static inline Real Sqrt (Real fValue) { return Real(sqrt(fValue)); }

        static inline Radian Sqrt (const Radian& fValue) { return Radian(sqrt(fValue.valueRadians())); }

        static inline Degree Sqrt (const Degree& fValue) { return Degree(sqrt(fValue.valueDegrees())); }

        static Real InvSqrt (Real fValue);

        static Real UnitRandom ();

        static Real RangeRandom (Real fLow, Real fHigh);

        static Real SymmetricRandom ();

        static inline Real Tan (const Radian& fValue, bool useTables = false) {
            return (!useTables) ? Real(tan(fValue.valueRadians())) : TanTable(fValue.valueRadians());
        }
        static inline Real Tan (Real fValue, bool useTables = false) {
            return (!useTables) ? Real(tan(fValue)) : TanTable(fValue);
        }

        static inline Real DegreesToRadians(Real degrees) { return degrees * fDeg2Rad; }
        static inline Real RadiansToDegrees(Real radians) { return radians * fRad2Deg; }

       static void setAngleUnit(AngleUnit unit);
       static AngleUnit getAngleUnit(void);

       static Real AngleUnitsToRadians(Real units);
       static Real RadiansToAngleUnits(Real radians);
       static Real AngleUnitsToDegrees(Real units);
       static Real DegreesToAngleUnits(Real degrees);

        static bool pointInTri2D(const Vector2& p, const Vector2& a, 
            const Vector2& b, const Vector2& c);

        static bool pointInTri3D(const Vector3& p, const Vector3& a, 
            const Vector3& b, const Vector3& c, const Vector3& normal);
        static std::pair<bool, Real> intersects(const Ray& ray, const Plane& plane);

        static std::pair<bool, Real> intersects(const Ray& ray, const Sphere& sphere, 
            bool discardInside = true);
        
        static std::pair<bool, Real> intersects(const Ray& ray, const AxisAlignedBox& box);

        static bool intersects(const Ray& ray, const AxisAlignedBox& box,
            Real* d1, Real* d2);

        static std::pair<bool, Real> intersects(const Ray& ray, const Vector3& a,
            const Vector3& b, const Vector3& c, const Vector3& normal,
            bool positiveSide = true, bool negativeSide = true);

        static std::pair<bool, Real> intersects(const Ray& ray, const Vector3& a,
            const Vector3& b, const Vector3& c,
            bool positiveSide = true, bool negativeSide = true);

        static bool intersects(const Sphere& sphere, const AxisAlignedBox& box);

        static bool intersects(const Plane& plane, const AxisAlignedBox& box);

        static std::pair<bool, Real> intersects(
            const Ray& ray, const vector<Plane>::type& planeList, 
            bool normalIsOutside);
        static std::pair<bool, Real> intersects(
            const Ray& ray, const list<Plane>::type& planeList, 
            bool normalIsOutside);

        static bool intersects(const Sphere& sphere, const Plane& plane);

        static bool RealEqual(Real a, Real b,
            Real tolerance = std::numeric_limits<Real>::epsilon());

        static Vector3 calculateTangentSpaceVector(
            const Vector3& position1, const Vector3& position2, const Vector3& position3,
            Real u1, Real v1, Real u2, Real v2, Real u3, Real v3);

        static Matrix4 buildReflectionMatrix(const Plane& p);
        static Vector4 calculateFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3);
        static Vector3 calculateBasicFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3);
        static Vector4 calculateFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3);
        static Vector3 calculateBasicFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3);

        static Real gaussianDistribution(Real x, Real offset = 0.0f, Real scale = 1.0f);

        template <typename T>
        static T Clamp(T val, T minval, T maxval)
        {
            assert (minval <= maxval && "Invalid clamp range");
            return std::max(std::min(val, maxval), minval);
        }

        static Matrix4 makeViewMatrix(const Vector3& position, const Quaternion& orientation, 
            const Matrix4* reflectMatrix = 0);

        static Real boundingRadiusFromAABB(const AxisAlignedBox& aabb);



        static const Real POS_INFINITY;
        static const Real NEG_INFINITY;
        static const Real PI;
        static const Real TWO_PI;
        static const Real HALF_PI;
        static const Real fDeg2Rad;
        static const Real fRad2Deg;

    };

    // these functions must be defined down here, because they rely on the
    // angle unit conversion functions in class Math:

    inline Real Radian::valueDegrees() const
    {
        return Math::RadiansToDegrees ( mRad );
    }

    inline Real Radian::valueAngleUnits() const
    {
        return Math::RadiansToAngleUnits ( mRad );
    }

    inline Real Degree::valueRadians() const
    {
        return Math::DegreesToRadians ( mDeg );
    }

    inline Real Degree::valueAngleUnits() const
    {
        return Math::DegreesToAngleUnits ( mDeg );
    }

    inline Angle::operator Radian() const
    {
        return Radian(Math::AngleUnitsToRadians(mAngle));
    }

    inline Angle::operator Degree() const
    {
        return Degree(Math::AngleUnitsToDegrees(mAngle));
    }

    inline Radian operator * ( Real a, const Radian& b )
    {
        return Radian ( a * b.valueRadians() );
    }

    inline Radian operator / ( Real a, const Radian& b )
    {
        return Radian ( a / b.valueRadians() );
    }

    inline Degree operator * ( Real a, const Degree& b )
    {
        return Degree ( a * b.valueDegrees() );
    }

    inline Degree operator / ( Real a, const Degree& b )
    {
        return Degree ( a / b.valueDegrees() );
    }
}
#endif