OgreMath.h

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00001 /*
00002 -----------------------------------------------------------------------------
00003 This source file is part of OGRE
00004     (Object-oriented Graphics Rendering Engine)
00005 For the latest info, see http://www.ogre3d.org/
00006 
00007 Copyright (c) 2000-2006 Torus Knot Software Ltd
00008 Also see acknowledgements in Readme.html
00009 
00010 This program is free software; you can redistribute it and/or modify it under
00011 the terms of the GNU Lesser General Public License as published by the Free Software
00012 Foundation; either version 2 of the License, or (at your option) any later
00013 version.
00014 
00015 This program is distributed in the hope that it will be useful, but WITHOUT
00016 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
00017 FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
00018 
00019 You should have received a copy of the GNU Lesser General Public License along with
00020 this program; if not, write to the Free Software Foundation, Inc., 59 Temple
00021 Place - Suite 330, Boston, MA 02111-1307, USA, or go to
00022 http://www.gnu.org/copyleft/lesser.txt.
00023 
00024 You may alternatively use this source under the terms of a specific version of
00025 the OGRE Unrestricted License provided you have obtained such a license from
00026 Torus Knot Software Ltd.
00027 -----------------------------------------------------------------------------
00028 */
00029 #ifndef __Math_H__
00030 #define __Math_H__
00031 
00032 #include "OgrePrerequisites.h"
00033 
00034 namespace Ogre
00035 {
00041     class Radian
00042     {
00043         Real mRad;
00044 
00045     public:
00046         explicit Radian ( Real r=0 ) : mRad(r) {}
00047         Radian ( const Degree& d );
00048         Radian& operator = ( const Real& f ) { mRad = f; return *this; }
00049         Radian& operator = ( const Radian& r ) { mRad = r.mRad; return *this; }
00050         Radian& operator = ( const Degree& d );
00051 
00052         Real valueDegrees() const; // see bottom of this file
00053         Real valueRadians() const { return mRad; }
00054         Real valueAngleUnits() const;
00055 
00056         const Radian& operator + () const { return *this; }
00057         Radian operator + ( const Radian& r ) const { return Radian ( mRad + r.mRad ); }
00058         Radian operator + ( const Degree& d ) const;
00059         Radian& operator += ( const Radian& r ) { mRad += r.mRad; return *this; }
00060         Radian& operator += ( const Degree& d );
00061         Radian operator - () const { return Radian(-mRad); }
00062         Radian operator - ( const Radian& r ) const { return Radian ( mRad - r.mRad ); }
00063         Radian operator - ( const Degree& d ) const;
00064         Radian& operator -= ( const Radian& r ) { mRad -= r.mRad; return *this; }
00065         Radian& operator -= ( const Degree& d );
00066         Radian operator * ( Real f ) const { return Radian ( mRad * f ); }
00067         Radian operator * ( const Radian& f ) const { return Radian ( mRad * f.mRad ); }
00068         Radian& operator *= ( Real f ) { mRad *= f; return *this; }
00069         Radian operator / ( Real f ) const { return Radian ( mRad / f ); }
00070         Radian& operator /= ( Real f ) { mRad /= f; return *this; }
00071 
00072         bool operator <  ( const Radian& r ) const { return mRad <  r.mRad; }
00073         bool operator <= ( const Radian& r ) const { return mRad <= r.mRad; }
00074         bool operator == ( const Radian& r ) const { return mRad == r.mRad; }
00075         bool operator != ( const Radian& r ) const { return mRad != r.mRad; }
00076         bool operator >= ( const Radian& r ) const { return mRad >= r.mRad; }
00077         bool operator >  ( const Radian& r ) const { return mRad >  r.mRad; }
00078     };
00079 
00085     class Degree
00086     {
00087         Real mDeg; // if you get an error here - make sure to define/typedef 'Real' first
00088 
00089     public:
00090         explicit Degree ( Real d=0 ) : mDeg(d) {}
00091         Degree ( const Radian& r ) : mDeg(r.valueDegrees()) {}
00092         Degree& operator = ( const Real& f ) { mDeg = f; return *this; }
00093         Degree& operator = ( const Degree& d ) { mDeg = d.mDeg; return *this; }
00094         Degree& operator = ( const Radian& r ) { mDeg = r.valueDegrees(); return *this; }
00095 
00096         Real valueDegrees() const { return mDeg; }
00097         Real valueRadians() const; // see bottom of this file
00098         Real valueAngleUnits() const;
00099 
00100         const Degree& operator + () const { return *this; }
00101         Degree operator + ( const Degree& d ) const { return Degree ( mDeg + d.mDeg ); }
00102         Degree operator + ( const Radian& r ) const { return Degree ( mDeg + r.valueDegrees() ); }
00103         Degree& operator += ( const Degree& d ) { mDeg += d.mDeg; return *this; }
00104         Degree& operator += ( const Radian& r ) { mDeg += r.valueDegrees(); return *this; }
00105         Degree operator - () const { return Degree(-mDeg); }
00106         Degree operator - ( const Degree& d ) const { return Degree ( mDeg - d.mDeg ); }
00107         Degree operator - ( const Radian& r ) const { return Degree ( mDeg - r.valueDegrees() ); }
00108         Degree& operator -= ( const Degree& d ) { mDeg -= d.mDeg; return *this; }
00109         Degree& operator -= ( const Radian& r ) { mDeg -= r.valueDegrees(); return *this; }
00110         Degree operator * ( Real f ) const { return Degree ( mDeg * f ); }
00111         Degree operator * ( const Degree& f ) const { return Degree ( mDeg * f.mDeg ); }
00112         Degree& operator *= ( Real f ) { mDeg *= f; return *this; }
00113         Degree operator / ( Real f ) const { return Degree ( mDeg / f ); }
00114         Degree& operator /= ( Real f ) { mDeg /= f; return *this; }
00115 
00116         bool operator <  ( const Degree& d ) const { return mDeg <  d.mDeg; }
00117         bool operator <= ( const Degree& d ) const { return mDeg <= d.mDeg; }
00118         bool operator == ( const Degree& d ) const { return mDeg == d.mDeg; }
00119         bool operator != ( const Degree& d ) const { return mDeg != d.mDeg; }
00120         bool operator >= ( const Degree& d ) const { return mDeg >= d.mDeg; }
00121         bool operator >  ( const Degree& d ) const { return mDeg >  d.mDeg; }
00122     };
00123 
00130     class Angle
00131     {
00132         Real mAngle;
00133     public:
00134         explicit Angle ( Real angle ) : mAngle(angle) {}
00135         operator Radian() const;
00136         operator Degree() const;
00137     };
00138 
00139     // these functions could not be defined within the class definition of class
00140     // Radian because they required class Degree to be defined
00141     inline Radian::Radian ( const Degree& d ) : mRad(d.valueRadians()) {
00142     }
00143     inline Radian& Radian::operator = ( const Degree& d ) {
00144         mRad = d.valueRadians(); return *this;
00145     }
00146     inline Radian Radian::operator + ( const Degree& d ) const {
00147         return Radian ( mRad + d.valueRadians() );
00148     }
00149     inline Radian& Radian::operator += ( const Degree& d ) {
00150         mRad += d.valueRadians();
00151         return *this;
00152     }
00153     inline Radian Radian::operator - ( const Degree& d ) const {
00154         return Radian ( mRad - d.valueRadians() );
00155     }
00156     inline Radian& Radian::operator -= ( const Degree& d ) {
00157         mRad -= d.valueRadians();
00158         return *this;
00159     }
00160 
00171     class _OgreExport Math 
00172     {
00173    public:
00179        enum AngleUnit
00180        {
00181            AU_DEGREE,
00182            AU_RADIAN
00183        };
00184 
00185     protected:
00186        // angle units used by the api
00187        static AngleUnit msAngleUnit;
00188 
00190         static int mTrigTableSize;
00191 
00193         static Real mTrigTableFactor;
00194         static Real* mSinTable;
00195         static Real* mTanTable;
00196 
00199         void buildTrigTables();
00200 
00201         static Real SinTable (Real fValue);
00202         static Real TanTable (Real fValue);
00203     public:
00209         Math(unsigned int trigTableSize = 4096);
00210 
00213         ~Math();
00214 
00215         static inline int IAbs (int iValue) { return ( iValue >= 0 ? iValue : -iValue ); }
00216         static inline int ICeil (float fValue) { return int(ceil(fValue)); }
00217         static inline int IFloor (float fValue) { return int(floor(fValue)); }
00218         static int ISign (int iValue);
00219 
00220         static inline Real Abs (Real fValue) { return Real(fabs(fValue)); }
00221         static inline Degree Abs (const Degree& dValue) { return Degree(fabs(dValue.valueDegrees())); }
00222         static inline Radian Abs (const Radian& rValue) { return Radian(fabs(rValue.valueRadians())); }
00223         static Radian ACos (Real fValue);
00224         static Radian ASin (Real fValue);
00225         static inline Radian ATan (Real fValue) { return Radian(atan(fValue)); }
00226         static inline Radian ATan2 (Real fY, Real fX) { return Radian(atan2(fY,fX)); }
00227         static inline Real Ceil (Real fValue) { return Real(ceil(fValue)); }
00228 
00236         static inline Real Cos (const Radian& fValue, bool useTables = false) {
00237             return (!useTables) ? Real(cos(fValue.valueRadians())) : SinTable(fValue.valueRadians() + HALF_PI);
00238         }
00246         static inline Real Cos (Real fValue, bool useTables = false) {
00247             return (!useTables) ? Real(cos(fValue)) : SinTable(fValue + HALF_PI);
00248         }
00249 
00250         static inline Real Exp (Real fValue) { return Real(exp(fValue)); }
00251 
00252         static inline Real Floor (Real fValue) { return Real(floor(fValue)); }
00253 
00254         static inline Real Log (Real fValue) { return Real(log(fValue)); }
00255 
00256         static inline Real Pow (Real fBase, Real fExponent) { return Real(pow(fBase,fExponent)); }
00257 
00258         static Real Sign (Real fValue);
00259         static inline Radian Sign ( const Radian& rValue )
00260         {
00261             return Radian(Sign(rValue.valueRadians()));
00262         }
00263         static inline Degree Sign ( const Degree& dValue )
00264         {
00265             return Degree(Sign(dValue.valueDegrees()));
00266         }
00267 
00275         static inline Real Sin (const Radian& fValue, bool useTables = false) {
00276             return (!useTables) ? Real(sin(fValue.valueRadians())) : SinTable(fValue.valueRadians());
00277         }
00285         static inline Real Sin (Real fValue, bool useTables = false) {
00286             return (!useTables) ? Real(sin(fValue)) : SinTable(fValue);
00287         }
00288 
00289         static inline Real Sqr (Real fValue) { return fValue*fValue; }
00290 
00291         static inline Real Sqrt (Real fValue) { return Real(sqrt(fValue)); }
00292 
00293         static inline Radian Sqrt (const Radian& fValue) { return Radian(sqrt(fValue.valueRadians())); }
00294 
00295         static inline Degree Sqrt (const Degree& fValue) { return Degree(sqrt(fValue.valueDegrees())); }
00296 
00300         static Real InvSqrt(Real fValue);
00301 
00302         static Real UnitRandom ();  // in [0,1]
00303 
00304         static Real RangeRandom (Real fLow, Real fHigh);  // in [fLow,fHigh]
00305 
00306         static Real SymmetricRandom ();  // in [-1,1]
00307 
00315         static inline Real Tan (const Radian& fValue, bool useTables = false) {
00316             return (!useTables) ? Real(tan(fValue.valueRadians())) : TanTable(fValue.valueRadians());
00317         }
00325         static inline Real Tan (Real fValue, bool useTables = false) {
00326             return (!useTables) ? Real(tan(fValue)) : TanTable(fValue);
00327         }
00328 
00329         static inline Real DegreesToRadians(Real degrees) { return degrees * fDeg2Rad; }
00330         static inline Real RadiansToDegrees(Real radians) { return radians * fRad2Deg; }
00331 
00338        static void setAngleUnit(AngleUnit unit);
00340        static AngleUnit getAngleUnit(void);
00341 
00343        static Real AngleUnitsToRadians(Real units);
00345        static Real RadiansToAngleUnits(Real radians);
00347        static Real AngleUnitsToDegrees(Real units);
00349        static Real DegreesToAngleUnits(Real degrees);
00350 
00372         static bool pointInTri2D(const Vector2& p, const Vector2& a, 
00373             const Vector2& b, const Vector2& c);
00374 
00399         static bool pointInTri3D(const Vector3& p, const Vector3& a, 
00400             const Vector3& b, const Vector3& c, const Vector3& normal);
00402         static std::pair<bool, Real> intersects(const Ray& ray, const Plane& plane);
00403 
00405         static std::pair<bool, Real> intersects(const Ray& ray, const Sphere& sphere, 
00406             bool discardInside = true);
00407         
00409         static std::pair<bool, Real> intersects(const Ray& ray, const AxisAlignedBox& box);
00410 
00433         static bool intersects(const Ray& ray, const AxisAlignedBox& box,
00434             Real* d1, Real* d2);
00435 
00460         static std::pair<bool, Real> intersects(const Ray& ray, const Vector3& a,
00461             const Vector3& b, const Vector3& c, const Vector3& normal,
00462             bool positiveSide = true, bool negativeSide = true);
00463 
00484         static std::pair<bool, Real> intersects(const Ray& ray, const Vector3& a,
00485             const Vector3& b, const Vector3& c,
00486             bool positiveSide = true, bool negativeSide = true);
00487 
00489         static bool intersects(const Sphere& sphere, const AxisAlignedBox& box);
00490 
00492         static bool intersects(const Plane& plane, const AxisAlignedBox& box);
00493 
00499         static std::pair<bool, Real> intersects(
00500             const Ray& ray, const std::vector<Plane>& planeList, 
00501             bool normalIsOutside);
00507         static std::pair<bool, Real> intersects(
00508             const Ray& ray, const std::list<Plane>& planeList, 
00509             bool normalIsOutside);
00510 
00514         static bool intersects(const Sphere& sphere, const Plane& plane);
00515 
00518         static bool RealEqual(Real a, Real b,
00519             Real tolerance = std::numeric_limits<Real>::epsilon());
00520 
00522         static Vector3 calculateTangentSpaceVector(
00523             const Vector3& position1, const Vector3& position2, const Vector3& position3,
00524             Real u1, Real v1, Real u2, Real v2, Real u3, Real v3);
00525 
00527         static Matrix4 buildReflectionMatrix(const Plane& p);
00529         static Vector4 calculateFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3);
00531         static Vector3 calculateBasicFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3);
00533         static Vector4 calculateFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3);
00535         static Vector3 calculateBasicFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3);
00536 
00540         static Real gaussianDistribution(Real x, Real offset = 0.0f, Real scale = 1.0f);
00541 
00542         static const Real POS_INFINITY;
00543         static const Real NEG_INFINITY;
00544         static const Real PI;
00545         static const Real TWO_PI;
00546         static const Real HALF_PI;
00547         static const Real fDeg2Rad;
00548         static const Real fRad2Deg;
00549 
00550     };
00551 
00552     // these functions must be defined down here, because they rely on the
00553     // angle unit conversion functions in class Math:
00554 
00555     inline Real Radian::valueDegrees() const
00556     {
00557         return Math::RadiansToDegrees ( mRad );
00558     }
00559 
00560     inline Real Radian::valueAngleUnits() const
00561     {
00562         return Math::RadiansToAngleUnits ( mRad );
00563     }
00564 
00565     inline Real Degree::valueRadians() const
00566     {
00567         return Math::DegreesToRadians ( mDeg );
00568     }
00569 
00570     inline Real Degree::valueAngleUnits() const
00571     {
00572         return Math::DegreesToAngleUnits ( mDeg );
00573     }
00574 
00575     inline Angle::operator Radian() const
00576     {
00577         return Radian(Math::AngleUnitsToRadians(mAngle));
00578     }
00579 
00580     inline Angle::operator Degree() const
00581     {
00582         return Degree(Math::AngleUnitsToDegrees(mAngle));
00583     }
00584 
00585     inline Radian operator * ( Real a, const Radian& b )
00586     {
00587         return Radian ( a * b.valueRadians() );
00588     }
00589 
00590     inline Radian operator / ( Real a, const Radian& b )
00591     {
00592         return Radian ( a / b.valueRadians() );
00593     }
00594 
00595     inline Degree operator * ( Real a, const Degree& b )
00596     {
00597         return Degree ( a * b.valueDegrees() );
00598     }
00599 
00600     inline Degree operator / ( Real a, const Degree& b )
00601     {
00602         return Degree ( a / b.valueDegrees() );
00603     }
00604 
00605 }
00606 #endif

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Last modified Mon Jun 16 12:48:52 2008