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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) 2000-2005 The OGRE Team
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 */
00025 #ifndef __Math_H__
00026 #define __Math_H__
00027 
00028 #include "OgrePrerequisites.h"
00029 
00030 namespace Ogre
00031 {
00037     class Radian
00038     {
00039         Real mRad;
00040 
00041     public:
00042         explicit Radian ( Real r=0 ) : mRad(r) {}
00043         Radian ( const Degree& d );
00044         Radian& operator = ( const Real& f ) { mRad = f; return *this; }
00045         Radian& operator = ( const Radian& r ) { mRad = r.mRad; return *this; }
00046         Radian& operator = ( const Degree& d );
00047 
00048         Real valueDegrees() const; // see bottom of this file
00049         Real valueRadians() const { return mRad; }
00050         Real valueAngleUnits() const;
00051 
00052         const Radian& operator + () const { return *this; }
00053         Radian operator + ( const Radian& r ) const { return Radian ( mRad + r.mRad ); }
00054         Radian operator + ( const Degree& d ) const;
00055         Radian& operator += ( const Radian& r ) { mRad += r.mRad; return *this; }
00056         Radian& operator += ( const Degree& d );
00057         Radian operator - () const { return Radian(-mRad); }
00058         Radian operator - ( const Radian& r ) const { return Radian ( mRad - r.mRad ); }
00059         Radian operator - ( const Degree& d ) const;
00060         Radian& operator -= ( const Radian& r ) { mRad -= r.mRad; return *this; }
00061         Radian& operator -= ( const Degree& d );
00062         Radian operator * ( Real f ) const { return Radian ( mRad * f ); }
00063         Radian operator * ( const Radian& f ) const { return Radian ( mRad * f.mRad ); }
00064         Radian& operator *= ( Real f ) { mRad *= f; return *this; }
00065         Radian operator / ( Real f ) const { return Radian ( mRad / f ); }
00066         Radian& operator /= ( Real f ) { mRad /= f; return *this; }
00067 
00068         bool operator <  ( const Radian& r ) const { return mRad <  r.mRad; }
00069         bool operator <= ( const Radian& r ) const { return mRad <= r.mRad; }
00070         bool operator == ( const Radian& r ) const { return mRad == r.mRad; }
00071         bool operator != ( const Radian& r ) const { return mRad != r.mRad; }
00072         bool operator >= ( const Radian& r ) const { return mRad >= r.mRad; }
00073         bool operator >  ( const Radian& r ) const { return mRad >  r.mRad; }
00074     };
00075 
00081     class Degree
00082     {
00083         Real mDeg; // if you get an error here - make sure to define/typedef 'Real' first
00084 
00085     public:
00086         explicit Degree ( Real d=0 ) : mDeg(d) {}
00087         Degree ( const Radian& r ) : mDeg(r.valueDegrees()) {}
00088         Degree& operator = ( const Real& f ) { mDeg = f; return *this; }
00089         Degree& operator = ( const Degree& d ) { mDeg = d.mDeg; return *this; }
00090         Degree& operator = ( const Radian& r ) { mDeg = r.valueDegrees(); return *this; }
00091 
00092         Real valueDegrees() const { return mDeg; }
00093         Real valueRadians() const; // see bottom of this file
00094         Real valueAngleUnits() const;
00095 
00096         const Degree& operator + () const { return *this; }
00097         Degree operator + ( const Degree& d ) const { return Degree ( mDeg + d.mDeg ); }
00098         Degree operator + ( const Radian& r ) const { return Degree ( mDeg + r.valueDegrees() ); }
00099         Degree& operator += ( const Degree& d ) { mDeg += d.mDeg; return *this; }
00100         Degree& operator += ( const Radian& r ) { mDeg += r.valueDegrees(); return *this; }
00101         Degree operator - () const { return Degree(-mDeg); }
00102         Degree operator - ( const Degree& d ) const { return Degree ( mDeg - d.mDeg ); }
00103         Degree operator - ( const Radian& r ) const { return Degree ( mDeg - r.valueDegrees() ); }
00104         Degree& operator -= ( const Degree& d ) { mDeg -= d.mDeg; return *this; }
00105         Degree& operator -= ( const Radian& r ) { mDeg -= r.valueDegrees(); return *this; }
00106         Degree operator * ( Real f ) const { return Degree ( mDeg * f ); }
00107         Degree operator * ( const Degree& f ) const { return Degree ( mDeg * f.mDeg ); }
00108         Degree& operator *= ( Real f ) { mDeg *= f; return *this; }
00109         Degree operator / ( Real f ) const { return Degree ( mDeg / f ); }
00110         Degree& operator /= ( Real f ) { mDeg /= f; return *this; }
00111 
00112         bool operator <  ( const Degree& d ) const { return mDeg <  d.mDeg; }
00113         bool operator <= ( const Degree& d ) const { return mDeg <= d.mDeg; }
00114         bool operator == ( const Degree& d ) const { return mDeg == d.mDeg; }
00115         bool operator != ( const Degree& d ) const { return mDeg != d.mDeg; }
00116         bool operator >= ( const Degree& d ) const { return mDeg >= d.mDeg; }
00117         bool operator >  ( const Degree& d ) const { return mDeg >  d.mDeg; }
00118     };
00119 
00126     class Angle
00127     {
00128         Real mAngle;
00129     public:
00130         explicit Angle ( Real angle ) : mAngle(angle) {}
00131         operator Radian() const;
00132         operator Degree() const;
00133     };
00134 
00135     // these functions could not be defined within the class definition of class
00136     // Radian because they required class Degree to be defined
00137     inline Radian::Radian ( const Degree& d ) : mRad(d.valueRadians()) {
00138     }
00139     inline Radian& Radian::operator = ( const Degree& d ) {
00140         mRad = d.valueRadians(); return *this;
00141     }
00142     inline Radian Radian::operator + ( const Degree& d ) const {
00143         return Radian ( mRad + d.valueRadians() );
00144     }
00145     inline Radian& Radian::operator += ( const Degree& d ) {
00146         mRad += d.valueRadians();
00147         return *this;
00148     }
00149     inline Radian Radian::operator - ( const Degree& d ) const {
00150         return Radian ( mRad - d.valueRadians() );
00151     }
00152     inline Radian& Radian::operator -= ( const Degree& d ) {
00153         mRad -= d.valueRadians();
00154         return *this;
00155     }
00156 
00167     class _OgreExport Math 
00168     {
00169    public:
00175        enum AngleUnit
00176        {
00177            AU_DEGREE,
00178            AU_RADIAN
00179        };
00180 
00181     protected:
00182        // angle units used by the api
00183        static AngleUnit msAngleUnit;
00184 
00186         static int mTrigTableSize;
00187 
00189         static Real mTrigTableFactor;
00190         static Real* mSinTable;
00191         static Real* mTanTable;
00192 
00195         void buildTrigTables();
00196 
00197         static Real SinTable (Real fValue);
00198         static Real TanTable (Real fValue);
00199     public:
00205         Math(unsigned int trigTableSize = 4096);
00206 
00209         ~Math();
00210 
00211         static inline int IAbs (int iValue) { return ( iValue >= 0 ? iValue : -iValue ); }
00212         static inline int ICeil (float fValue) { return int(ceil(fValue)); }
00213         static inline int IFloor (float fValue) { return int(floor(fValue)); }
00214         static int ISign (int iValue);
00215 
00216         static inline Real Abs (Real fValue) { return Real(fabs(fValue)); }
00217         static inline Degree Abs (const Degree& dValue) { return Degree(fabs(dValue.valueDegrees())); }
00218         static inline Radian Abs (const Radian& rValue) { return Radian(fabs(rValue.valueRadians())); }
00219         static Radian ACos (Real fValue);
00220         static Radian ASin (Real fValue);
00221         static inline Radian ATan (Real fValue) { return Radian(atan(fValue)); }
00222         static inline Radian ATan2 (Real fY, Real fX) { return Radian(atan2(fY,fX)); }
00223         static inline Real Ceil (Real fValue) { return Real(ceil(fValue)); }
00224 
00232         static inline Real Cos (const Radian& fValue, bool useTables = false) {
00233             return (!useTables) ? Real(cos(fValue.valueRadians())) : SinTable(fValue.valueRadians() + HALF_PI);
00234         }
00242         static inline Real Cos (Real fValue, bool useTables = false) {
00243             return (!useTables) ? Real(cos(fValue)) : SinTable(fValue + HALF_PI);
00244         }
00245 
00246         static inline Real Exp (Real fValue) { return Real(exp(fValue)); }
00247 
00248         static inline Real Floor (Real fValue) { return Real(floor(fValue)); }
00249 
00250         static inline Real Log (Real fValue) { return Real(log(fValue)); }
00251 
00252         static inline Real Pow (Real fBase, Real fExponent) { return Real(pow(fBase,fExponent)); }
00253 
00254         static Real Sign (Real fValue);
00255         static inline Radian Sign ( const Radian& rValue )
00256         {
00257             return Radian(Sign(rValue.valueRadians()));
00258         }
00259         static inline Degree Sign ( const Degree& dValue )
00260         {
00261             return Degree(Sign(dValue.valueDegrees()));
00262         }
00263 
00271         static inline Real Sin (const Radian& fValue, bool useTables = false) {
00272             return (!useTables) ? Real(sin(fValue.valueRadians())) : SinTable(fValue.valueRadians());
00273         }
00281         static inline Real Sin (Real fValue, bool useTables = false) {
00282             return (!useTables) ? Real(sin(fValue)) : SinTable(fValue);
00283         }
00284 
00285         static inline Real Sqr (Real fValue) { return fValue*fValue; }
00286 
00287         static inline Real Sqrt (Real fValue) { return Real(sqrt(fValue)); }
00288 
00289         static inline Radian Sqrt (const Radian& fValue) { return Radian(sqrt(fValue.valueRadians())); }
00290 
00291         static inline Degree Sqrt (const Degree& fValue) { return Degree(sqrt(fValue.valueDegrees())); }
00292 
00296         static Real InvSqrt(Real fValue);
00297 
00298         static Real UnitRandom ();  // in [0,1]
00299 
00300         static Real RangeRandom (Real fLow, Real fHigh);  // in [fLow,fHigh]
00301 
00302         static Real SymmetricRandom ();  // in [-1,1]
00303 
00311         static inline Real Tan (const Radian& fValue, bool useTables = false) {
00312             return (!useTables) ? Real(tan(fValue.valueRadians())) : TanTable(fValue.valueRadians());
00313         }
00321         static inline Real Tan (Real fValue, bool useTables = false) {
00322             return (!useTables) ? Real(tan(fValue)) : TanTable(fValue);
00323         }
00324 
00325         static inline Real DegreesToRadians(Real degrees) { return degrees * fDeg2Rad; }
00326         static inline Real RadiansToDegrees(Real radians) { return radians * fRad2Deg; }
00327 
00334        static void setAngleUnit(AngleUnit unit);
00336        static AngleUnit getAngleUnit(void);
00337 
00339        static Real AngleUnitsToRadians(Real units);
00341        static Real RadiansToAngleUnits(Real radians);
00343        static Real AngleUnitsToDegrees(Real units);
00345        static Real DegreesToAngleUnits(Real degrees);
00346 
00368         static bool pointInTri2D(const Vector2& p, const Vector2& a, 
00369             const Vector2& b, const Vector2& c);
00370 
00395         static bool pointInTri3D(const Vector3& p, const Vector3& a, 
00396             const Vector3& b, const Vector3& c, const Vector3& normal);
00398         static std::pair<bool, Real> intersects(const Ray& ray, const Plane& plane);
00399 
00401         static std::pair<bool, Real> intersects(const Ray& ray, const Sphere& sphere, 
00402             bool discardInside = true);
00403         
00405         static std::pair<bool, Real> intersects(const Ray& ray, const AxisAlignedBox& box);
00406 
00429         static bool intersects(const Ray& ray, const AxisAlignedBox& box,
00430             Real* d1, Real* d2);
00431 
00456         static std::pair<bool, Real> intersects(const Ray& ray, const Vector3& a,
00457             const Vector3& b, const Vector3& c, const Vector3& normal,
00458             bool positiveSide = true, bool negativeSide = true);
00459 
00480         static std::pair<bool, Real> intersects(const Ray& ray, const Vector3& a,
00481             const Vector3& b, const Vector3& c,
00482             bool positiveSide = true, bool negativeSide = true);
00483 
00485         static bool intersects(const Sphere& sphere, const AxisAlignedBox& box);
00486 
00488         static bool intersects(const Plane& plane, const AxisAlignedBox& box);
00489 
00495         static std::pair<bool, Real> intersects(
00496             const Ray& ray, const std::vector<Plane>& planeList, 
00497             bool normalIsOutside);
00503         static std::pair<bool, Real> intersects(
00504             const Ray& ray, const std::list<Plane>& planeList, 
00505             bool normalIsOutside);
00506 
00510         static bool intersects(const Sphere& sphere, const Plane& plane);
00511 
00514         static bool RealEqual(Real a, Real b,
00515             Real tolerance = std::numeric_limits<Real>::epsilon());
00516 
00518         static Vector3 calculateTangentSpaceVector(
00519             const Vector3& position1, const Vector3& position2, const Vector3& position3,
00520             Real u1, Real v1, Real u2, Real v2, Real u3, Real v3);
00521 
00523         static Matrix4 buildReflectionMatrix(const Plane& p);
00525         static Vector4 calculateFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3);
00527         static Vector3 calculateBasicFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3);
00529         static Vector4 calculateFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3);
00531         static Vector3 calculateBasicFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3);
00532 
00536         static Real gaussianDistribution(Real x, Real offset = 0.0f, Real scale = 1.0f);
00537 
00538         static const Real POS_INFINITY;
00539         static const Real NEG_INFINITY;
00540         static const Real PI;
00541         static const Real TWO_PI;
00542         static const Real HALF_PI;
00543         static const Real fDeg2Rad;
00544         static const Real fRad2Deg;
00545 
00546     };
00547 
00548     // these functions must be defined down here, because they rely on the
00549     // angle unit conversion functions in class Math:
00550 
00551     inline Real Radian::valueDegrees() const
00552     {
00553         return Math::RadiansToDegrees ( mRad );
00554     }
00555 
00556     inline Real Radian::valueAngleUnits() const
00557     {
00558         return Math::RadiansToAngleUnits ( mRad );
00559     }
00560 
00561     inline Real Degree::valueRadians() const
00562     {
00563         return Math::DegreesToRadians ( mDeg );
00564     }
00565 
00566     inline Real Degree::valueAngleUnits() const
00567     {
00568         return Math::DegreesToAngleUnits ( mDeg );
00569     }
00570 
00571     inline Angle::operator Radian() const
00572     {
00573         return Radian(Math::AngleUnitsToRadians(mAngle));
00574     }
00575 
00576     inline Angle::operator Degree() const
00577     {
00578         return Degree(Math::AngleUnitsToDegrees(mAngle));
00579     }
00580 
00581     inline Radian operator * ( Real a, const Radian& b )
00582     {
00583         return Radian ( a * b.valueRadians() );
00584     }
00585 
00586     inline Radian operator / ( Real a, const Radian& b )
00587     {
00588         return Radian ( a / b.valueRadians() );
00589     }
00590 
00591     inline Degree operator * ( Real a, const Degree& b )
00592     {
00593         return Degree ( a * b.valueDegrees() );
00594     }
00595 
00596     inline Degree operator / ( Real a, const Degree& b )
00597     {
00598         return Degree ( a / b.valueDegrees() );
00599     }
00600 
00601 }
00602 #endif

Copyright © 2000-2005 by The OGRE Team
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Last modified Sun Jan 21 10:01:37 2007