source: downloads/OgreMain/include/OgreMath.h @ 3

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

Copyright (c) 2000-2006 Torus Knot Software Ltd
Also see acknowledgements in Readme.html

This program is free software; you can redistribute it and/or modify it under
the terms of the GNU Lesser 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 Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with
this program; if not, write to the Free Software Foundation, Inc., 59 Temple
Place - Suite 330, Boston, MA 02111-1307, USA, or go to
http://www.gnu.org/copyleft/lesser.txt.

You may alternatively use this source under the terms of a specific version of
the OGRE Unrestricted License provided you have obtained such a license from
Torus Knot Software Ltd.
-----------------------------------------------------------------------------
*/
#ifndef __Math_H__
#define __Math_H__

#include "OgrePrerequisites.h"

namespace Ogre
{
    /** Wrapper class which indicates a given angle value is in Radians.
    @remarks
        Radian values are interchangeable with Degree values, and conversions
        will be done automatically between them.
    */
        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; }
        };

    /** Wrapper class which indicates a given angle value is in Degrees.
    @remarks
        Degree values are interchangeable with Radian values, and conversions
        will be done automatically between them.
    */
        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; }
        };

    /** Wrapper class which identifies a value as the currently default angle 
        type, as defined by Math::setAngleUnit.
    @remarks
        Angle values will be automatically converted between radians and degrees,
        as appropriate.
    */
        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 to provide access to common mathematical functions.
        @remarks
            Most of the maths functions are aliased versions of the C runtime
            library functions. They are aliased here to provide future
            optimisation opportunities, either from faster RTLs or custom
            math approximations.
        @note
            <br>This is based on MgcMath.h from
            <a href="http://www.geometrictools.com/">Wild Magic</a>.
    */
    class _OgreExport Math 
    {
   public:
       /** The angular units used by the API. This functionality is now deprecated in favor
               of discreet angular unit types ( see Degree and Radian above ). The only place
                   this functionality is actually still used is when parsing files. Search for
                   usage of the Angle class for those instances
       */
       enum AngleUnit
       {
           AU_DEGREE,
           AU_RADIAN
       };

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

        /// Size of the trig tables as determined by constructor.
        static int mTrigTableSize;

        /// Radian -> index factor value ( mTrigTableSize / 2 * PI )
        static Real mTrigTableFactor;
        static Real* mSinTable;
        static Real* mTanTable;

        /** Private function to build trig tables.
        */
        void buildTrigTables();

                static Real SinTable (Real fValue);
                static Real TanTable (Real fValue);
    public:
        /** Default constructor.
            @param
                trigTableSize Optional parameter to set the size of the
                tables used to implement Sin, Cos, Tan
        */
        Math(unsigned int trigTableSize = 4096);

        /** Default destructor.
        */
        ~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)); }

        /** Cosine function.
            @param
                fValue Angle in radians
            @param
                useTables If true, uses lookup tables rather than
                calculation - faster but less accurate.
        */
        static inline Real Cos (const Radian& fValue, bool useTables = false) {
                        return (!useTables) ? Real(cos(fValue.valueRadians())) : SinTable(fValue.valueRadians() + HALF_PI);
                }
        /** Cosine function.
            @param
                fValue Angle in radians
            @param
                useTables If true, uses lookup tables rather than
                calculation - faster but less accurate.
        */
        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 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()));
                }

        /** Sine function.
            @param
                fValue Angle in radians
            @param
                useTables If true, uses lookup tables rather than
                calculation - faster but less accurate.
        */
        static inline Real Sin (const Radian& fValue, bool useTables = false) {
                        return (!useTables) ? Real(sin(fValue.valueRadians())) : SinTable(fValue.valueRadians());
                }
        /** Sine function.
            @param
                fValue Angle in radians
            @param
                useTables If true, uses lookup tables rather than
                calculation - faster but less accurate.
        */
        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())); }

        /** Inverse square root i.e. 1 / Sqrt(x), good for vector
            normalisation.
        */
                static Real InvSqrt(Real fValue);

        static Real UnitRandom ();  // in [0,1]

        static Real RangeRandom (Real fLow, Real fHigh);  // in [fLow,fHigh]

        static Real SymmetricRandom ();  // in [-1,1]

        /** Tangent function.
            @param
                fValue Angle in radians
            @param
                useTables If true, uses lookup tables rather than
                calculation - faster but less accurate.
        */
                static inline Real Tan (const Radian& fValue, bool useTables = false) {
                        return (!useTables) ? Real(tan(fValue.valueRadians())) : TanTable(fValue.valueRadians());
                }
        /** Tangent function.
            @param
                fValue Angle in radians
            @param
                useTables If true, uses lookup tables rather than
                calculation - faster but less accurate.
        */
                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; }

       /** These functions used to set the assumed angle units (radians or degrees) 
            expected when using the Angle type.
       @par
            You can set this directly after creating a new Root, and also before/after resource creation,
            depending on whether you want the change to affect resource files.
       */
       static void setAngleUnit(AngleUnit unit);
       /** Get the unit being used for angles. */
       static AngleUnit getAngleUnit(void);

       /** Convert from the current AngleUnit to radians. */
       static Real AngleUnitsToRadians(Real units);
       /** Convert from radians to the current AngleUnit . */
       static Real RadiansToAngleUnits(Real radians);
       /** Convert from the current AngleUnit to degrees. */
       static Real AngleUnitsToDegrees(Real units);
       /** Convert from degrees to the current AngleUnit. */
       static Real DegreesToAngleUnits(Real degrees);

       /** Checks whether a given point is inside a triangle, in a
            2-dimensional (Cartesian) space.
            @remarks
                The vertices of the triangle must be given in either
                trigonometrical (anticlockwise) or inverse trigonometrical
                (clockwise) order.
            @param
                p The point.
            @param
                a The triangle's first vertex.
            @param
                b The triangle's second vertex.
            @param
                c The triangle's third vertex.
            @returns
                If the point resides in the triangle, <b>true</b> is
                returned.
            @par
                If the point is outside the triangle, <b>false</b> is
                returned.
        */
        static bool pointInTri2D(const Vector2& p, const Vector2& a, 
                        const Vector2& b, const Vector2& c);

       /** Checks whether a given 3D point is inside a triangle.
       @remarks
            The vertices of the triangle must be given in either
            trigonometrical (anticlockwise) or inverse trigonometrical
            (clockwise) order, and the point must be guaranteed to be in the
                        same plane as the triangle
        @param
            p The point.
        @param
            a The triangle's first vertex.
        @param
            b The triangle's second vertex.
        @param
            c The triangle's third vertex.
                @param 
                        normal The triangle plane's normal (passed in rather than calculated
                                on demand since the callermay already have it)
        @returns
            If the point resides in the triangle, <b>true</b> is
            returned.
        @par
            If the point is outside the triangle, <b>false</b> is
            returned.
        */
        static bool pointInTri3D(const Vector3& p, const Vector3& a, 
                        const Vector3& b, const Vector3& c, const Vector3& normal);
        /** Ray / plane intersection, returns boolean result and distance. */
        static std::pair<bool, Real> intersects(const Ray& ray, const Plane& plane);

        /** Ray / sphere intersection, returns boolean result and distance. */
        static std::pair<bool, Real> intersects(const Ray& ray, const Sphere& sphere, 
            bool discardInside = true);
        
        /** Ray / box intersection, returns boolean result and distance. */
        static std::pair<bool, Real> intersects(const Ray& ray, const AxisAlignedBox& box);

        /** Ray / box intersection, returns boolean result and two intersection distance.
        @param
            ray The ray.
        @param
            box The box.
        @param
            d1 A real pointer to retrieve the near intersection distance
                from the ray origin, maybe <b>null</b> which means don't care
                about the near intersection distance.
        @param
            d2 A real pointer to retrieve the far intersection distance
                from the ray origin, maybe <b>null</b> which means don't care
                about the far intersection distance.
        @returns
            If the ray is intersects the box, <b>true</b> is returned, and
            the near intersection distance is return by <i>d1</i>, the
            far intersection distance is return by <i>d2</i>. Guarantee
            <b>0</b> <= <i>d1</i> <= <i>d2</i>.
        @par
            If the ray isn't intersects the box, <b>false</b> is returned, and
            <i>d1</i> and <i>d2</i> is unmodified.
        */
        static bool intersects(const Ray& ray, const AxisAlignedBox& box,
            Real* d1, Real* d2);

        /** Ray / triangle intersection, returns boolean result and distance.
        @param
            ray The ray.
        @param
            a The triangle's first vertex.
        @param
            b The triangle's second vertex.
        @param
            c The triangle's third vertex.
                @param 
                        normal The triangle plane's normal (passed in rather than calculated
                                on demand since the callermay already have it), doesn't need
                normalised since we don't care.
        @param
            positiveSide Intersect with "positive side" of the triangle
        @param
            negativeSide Intersect with "negative side" of the triangle
        @returns
            If the ray is intersects the triangle, a pair of <b>true</b> and the
            distance between intersection point and ray origin returned.
        @par
            If the ray isn't intersects the triangle, a pair of <b>false</b> and
            <b>0</b> returned.
        */
        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);

        /** Ray / triangle intersection, returns boolean result and distance.
        @param
            ray The ray.
        @param
            a The triangle's first vertex.
        @param
            b The triangle's second vertex.
        @param
            c The triangle's third vertex.
        @param
            positiveSide Intersect with "positive side" of the triangle
        @param
            negativeSide Intersect with "negative side" of the triangle
        @returns
            If the ray is intersects the triangle, a pair of <b>true</b> and the
            distance between intersection point and ray origin returned.
        @par
            If the ray isn't intersects the triangle, a pair of <b>false</b> and
            <b>0</b> returned.
        */
        static std::pair<bool, Real> intersects(const Ray& ray, const Vector3& a,
            const Vector3& b, const Vector3& c,
            bool positiveSide = true, bool negativeSide = true);

        /** Sphere / box intersection test. */
        static bool intersects(const Sphere& sphere, const AxisAlignedBox& box);

        /** Plane / box intersection test. */
        static bool intersects(const Plane& plane, const AxisAlignedBox& box);

        /** Ray / convex plane list intersection test. 
        @param ray The ray to test with
        @param plaeList List of planes which form a convex volume
        @param normalIsOutside Does the normal point outside the volume
        */
        static std::pair<bool, Real> intersects(
            const Ray& ray, const std::vector<Plane>& planeList, 
            bool normalIsOutside);
        /** Ray / convex plane list intersection test. 
        @param ray The ray to test with
        @param plaeList List of planes which form a convex volume
        @param normalIsOutside Does the normal point outside the volume
        */
        static std::pair<bool, Real> intersects(
            const Ray& ray, const std::list<Plane>& planeList, 
            bool normalIsOutside);

        /** Sphere / plane intersection test. 
        @remarks NB just do a plane.getDistance(sphere.getCenter()) for more detail!
        */
        static bool intersects(const Sphere& sphere, const Plane& plane);

        /** Compare 2 reals, using tolerance for inaccuracies.
        */
        static bool RealEqual(Real a, Real b,
            Real tolerance = std::numeric_limits<Real>::epsilon());

        /** Calculates the tangent space vector for a given set of positions / texture coords. */
        static Vector3 calculateTangentSpaceVector(
            const Vector3& position1, const Vector3& position2, const Vector3& position3,
            Real u1, Real v1, Real u2, Real v2, Real u3, Real v3);

        /** Build a reflection matrix for the passed in plane. */
        static Matrix4 buildReflectionMatrix(const Plane& p);
        /** Calculate a face normal, including the w component which is the offset from the origin. */
        static Vector4 calculateFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3);
        /** Calculate a face normal, no w-information. */
        static Vector3 calculateBasicFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3);
        /** Calculate a face normal without normalize, including the w component which is the offset from the origin. */
        static Vector4 calculateFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3);
        /** Calculate a face normal without normalize, no w-information. */
        static Vector3 calculateBasicFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3);

                /** Generates a value based on the gaussian (normal) distribution function
                        with the given offset and scale parameters.
                */
                static Real gaussianDistribution(Real x, Real offset = 0.0f, Real scale = 1.0f);

        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