446 lines
16 KiB
C
446 lines
16 KiB
C
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/*
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-----------------------------------------------------------------------------
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This source file is part of OGRE
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(Object-oriented Graphics Rendering Engine)
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For the latest info, see http://www.ogre3d.org/
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Copyright (c) 2000-2009 Torus Knot Software Ltd
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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THE SOFTWARE.
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-----------------------------------------------------------------------------
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*/
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#ifndef __Math_H__
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#define __Math_H__
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#include "OgrePrerequisites.h"
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namespace Ogre
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{
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/** \addtogroup Core
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* @{
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*/
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/** \addtogroup Math
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* @{
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*/
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/** Wrapper class which indicates a given angle value is in Radians.
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@remarks
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Radian values are interchangeable with Degree values, and conversions
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will be done automatically between them.
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*/
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class Radian
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{
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Real mRad;
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public:
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explicit Radian ( Real r=0 ) : mRad(r) {}
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Radian ( const Degree& d );
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Radian& operator = ( const Real& f ) { mRad = f; return *this; }
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Radian& operator = ( const Radian& r ) { mRad = r.mRad; return *this; }
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Radian& operator = ( const Degree& d );
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Real valueDegrees() const; // see bottom of this file
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Real valueRadians() const { return mRad; }
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Real valueAngleUnits() const;
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const Radian& operator + () const { return *this; }
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Radian operator + ( const Radian& r ) const { return Radian ( mRad + r.mRad ); }
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Radian operator + ( const Degree& d ) const;
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Radian& operator += ( const Radian& r ) { mRad += r.mRad; return *this; }
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Radian& operator += ( const Degree& d );
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Radian operator - () const { return Radian(-mRad); }
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Radian operator - ( const Radian& r ) const { return Radian ( mRad - r.mRad ); }
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Radian operator - ( const Degree& d ) const;
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Radian& operator -= ( const Radian& r ) { mRad -= r.mRad; return *this; }
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Radian& operator -= ( const Degree& d );
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Radian operator * ( Real f ) const { return Radian ( mRad * f ); }
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Radian operator * ( const Radian& f ) const { return Radian ( mRad * f.mRad ); }
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Radian& operator *= ( Real f ) { mRad *= f; return *this; }
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Radian operator / ( Real f ) const { return Radian ( mRad / f ); }
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Radian& operator /= ( Real f ) { mRad /= f; return *this; }
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bool operator < ( const Radian& r ) const { return mRad < r.mRad; }
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bool operator <= ( const Radian& r ) const { return mRad <= r.mRad; }
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bool operator == ( const Radian& r ) const { return mRad == r.mRad; }
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bool operator != ( const Radian& r ) const { return mRad != r.mRad; }
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bool operator >= ( const Radian& r ) const { return mRad >= r.mRad; }
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bool operator > ( const Radian& r ) const { return mRad > r.mRad; }
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};
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/** Wrapper class which indicates a given angle value is in Degrees.
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@remarks
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Degree values are interchangeable with Radian values, and conversions
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will be done automatically between them.
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*/
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class Degree
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{
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Real mDeg; // if you get an error here - make sure to define/typedef 'Real' first
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public:
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explicit Degree ( Real d=0 ) : mDeg(d) {}
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Degree ( const Radian& r ) : mDeg(r.valueDegrees()) {}
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Degree& operator = ( const Real& f ) { mDeg = f; return *this; }
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Degree& operator = ( const Degree& d ) { mDeg = d.mDeg; return *this; }
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Degree& operator = ( const Radian& r ) { mDeg = r.valueDegrees(); return *this; }
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Real valueDegrees() const { return mDeg; }
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Real valueRadians() const; // see bottom of this file
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Real valueAngleUnits() const;
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const Degree& operator + () const { return *this; }
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Degree operator + ( const Degree& d ) const { return Degree ( mDeg + d.mDeg ); }
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Degree operator + ( const Radian& r ) const { return Degree ( mDeg + r.valueDegrees() ); }
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Degree& operator += ( const Degree& d ) { mDeg += d.mDeg; return *this; }
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Degree& operator += ( const Radian& r ) { mDeg += r.valueDegrees(); return *this; }
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Degree operator - () const { return Degree(-mDeg); }
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Degree operator - ( const Degree& d ) const { return Degree ( mDeg - d.mDeg ); }
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Degree operator - ( const Radian& r ) const { return Degree ( mDeg - r.valueDegrees() ); }
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Degree& operator -= ( const Degree& d ) { mDeg -= d.mDeg; return *this; }
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Degree& operator -= ( const Radian& r ) { mDeg -= r.valueDegrees(); return *this; }
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Degree operator * ( Real f ) const { return Degree ( mDeg * f ); }
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Degree operator * ( const Degree& f ) const { return Degree ( mDeg * f.mDeg ); }
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Degree& operator *= ( Real f ) { mDeg *= f; return *this; }
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Degree operator / ( Real f ) const { return Degree ( mDeg / f ); }
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Degree& operator /= ( Real f ) { mDeg /= f; return *this; }
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bool operator < ( const Degree& d ) const { return mDeg < d.mDeg; }
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bool operator <= ( const Degree& d ) const { return mDeg <= d.mDeg; }
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bool operator == ( const Degree& d ) const { return mDeg == d.mDeg; }
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bool operator != ( const Degree& d ) const { return mDeg != d.mDeg; }
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bool operator >= ( const Degree& d ) const { return mDeg >= d.mDeg; }
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bool operator > ( const Degree& d ) const { return mDeg > d.mDeg; }
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};
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/** Wrapper class which identifies a value as the currently default angle
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type, as defined by Math::setAngleUnit.
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@remarks
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Angle values will be automatically converted between radians and degrees,
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as appropriate.
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*/
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class Angle
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{
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Real mAngle;
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public:
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explicit Angle ( Real angle ) : mAngle(angle) {}
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operator Radian() const;
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operator Degree() const;
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};
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// these functions could not be defined within the class definition of class
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// Radian because they required class Degree to be defined
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inline Radian::Radian ( const Degree& d ) : mRad(d.valueRadians()) {
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}
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inline Radian& Radian::operator = ( const Degree& d ) {
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mRad = d.valueRadians(); return *this;
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}
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inline Radian Radian::operator + ( const Degree& d ) const {
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return Radian ( mRad + d.valueRadians() );
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}
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inline Radian& Radian::operator += ( const Degree& d ) {
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mRad += d.valueRadians();
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return *this;
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}
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inline Radian Radian::operator - ( const Degree& d ) const {
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return Radian ( mRad - d.valueRadians() );
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}
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inline Radian& Radian::operator -= ( const Degree& d ) {
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mRad -= d.valueRadians();
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return *this;
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}
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/** Class to provide access to common mathematical functions.
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@remarks
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Most of the maths functions are aliased versions of the C runtime
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library functions. They are aliased here to provide future
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optimisation opportunities, either from faster RTLs or custom
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math approximations.
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@note
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<br>This is based on MgcMath.h from
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<a href="http://www.geometrictools.com/">Wild Magic</a>.
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*/
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class Math
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{
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public:
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/** The angular units used by the API. This functionality is now deprecated in favor
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of discreet angular unit types ( see Degree and Radian above ). The only place
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this functionality is actually still used is when parsing files. Search for
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usage of the Angle class for those instances
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*/
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enum AngleUnit
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{
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AU_DEGREE,
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AU_RADIAN
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};
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protected:
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// angle units used by the api
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static AngleUnit msAngleUnit;
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/// Size of the trig tables as determined by constructor.
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static int mTrigTableSize;
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/// Radian -> index factor value ( mTrigTableSize / 2 * PI )
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static Real mTrigTableFactor;
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static Real* mSinTable;
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static Real* mTanTable;
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/** Private function to build trig tables.
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*/
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void buildTrigTables();
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static Real SinTable (Real fValue);
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static Real TanTable (Real fValue);
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public:
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/** Default constructor.
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@param
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trigTableSize Optional parameter to set the size of the
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tables used to implement Sin, Cos, Tan
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*/
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Math(unsigned int trigTableSize = 4096);
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/** Default destructor.
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*/
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~Math();
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static inline int IAbs (int iValue) { return ( iValue >= 0 ? iValue : -iValue ); }
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static inline int ICeil (float fValue) { return int(ceil(fValue)); }
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static inline int IFloor (float fValue) { return int(floor(fValue)); }
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static int ISign (int iValue);
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static inline Real Abs (Real fValue) { return Real(fabs(fValue)); }
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static inline Degree Abs (const Degree& dValue) { return Degree(fabs(dValue.valueDegrees())); }
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static inline Radian Abs (const Radian& rValue) { return Radian(fabs(rValue.valueRadians())); }
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static Radian ACos (Real fValue);
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static Radian ASin (Real fValue);
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static inline Radian ATan (Real fValue) { return Radian(atan(fValue)); }
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static inline Radian ATan2 (Real fY, Real fX) { return Radian(atan2(fY,fX)); }
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static inline Real Ceil (Real fValue) { return Real(ceil(fValue)); }
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static inline bool isNaN(Real f)
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{
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// std::isnan() is C99, not supported by all compilers
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// However NaN always fails this next test, no other number does.
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return f != f;
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}
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/** Cosine function.
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@param
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fValue Angle in radians
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@param
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useTables If true, uses lookup tables rather than
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calculation - faster but less accurate.
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*/
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static inline Real Cos (const Radian& fValue, bool useTables = false) {
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return (!useTables) ? Real(cos(fValue.valueRadians())) : SinTable(fValue.valueRadians() + HALF_PI);
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}
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/** Cosine function.
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@param
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fValue Angle in radians
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@param
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useTables If true, uses lookup tables rather than
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calculation - faster but less accurate.
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*/
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static inline Real Cos (Real fValue, bool useTables = false) {
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return (!useTables) ? Real(cos(fValue)) : SinTable(fValue + HALF_PI);
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}
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static inline Real Exp (Real fValue) { return Real(exp(fValue)); }
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static inline Real Floor (Real fValue) { return Real(floor(fValue)); }
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static inline Real Log (Real fValue) { return Real(log(fValue)); }
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/// Stored value of log(2) for frequent use
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static const Real LOG2;
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static inline Real Log2 (Real fValue) { return Real(log(fValue)/LOG2); }
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static inline Real LogN (Real base, Real fValue) { return Real(log(fValue)/log(base)); }
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static inline Real Pow (Real fBase, Real fExponent) { return Real(pow(fBase,fExponent)); }
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static Real Sign (Real fValue);
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static inline Radian Sign ( const Radian& rValue )
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{
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return Radian(Sign(rValue.valueRadians()));
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}
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static inline Degree Sign ( const Degree& dValue )
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{
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return Degree(Sign(dValue.valueDegrees()));
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}
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/** Sine function.
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@param
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fValue Angle in radians
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@param
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useTables If true, uses lookup tables rather than
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calculation - faster but less accurate.
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*/
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static inline Real Sin (const Radian& fValue, bool useTables = false) {
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return (!useTables) ? Real(sin(fValue.valueRadians())) : SinTable(fValue.valueRadians());
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}
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/** Sine function.
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@param
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fValue Angle in radians
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@param
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useTables If true, uses lookup tables rather than
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calculation - faster but less accurate.
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*/
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static inline Real Sin (Real fValue, bool useTables = false) {
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return (!useTables) ? Real(sin(fValue)) : SinTable(fValue);
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}
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static inline Real Sqr (Real fValue) { return fValue*fValue; }
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static inline Real Sqrt (Real fValue) { return Real(sqrt(fValue)); }
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static inline Radian Sqrt (const Radian& fValue) { return Radian(sqrt(fValue.valueRadians())); }
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static inline Degree Sqrt (const Degree& fValue) { return Degree(sqrt(fValue.valueDegrees())); }
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/** Inverse square root i.e. 1 / Sqrt(x), good for vector
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normalisation.
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*/
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static Real InvSqrt(Real fValue);
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static Real UnitRandom (); // in [0,1]
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static Real RangeRandom (Real fLow, Real fHigh); // in [fLow,fHigh]
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static Real SymmetricRandom (); // in [-1,1]
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/** Tangent function.
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@param
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fValue Angle in radians
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@param
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useTables If true, uses lookup tables rather than
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calculation - faster but less accurate.
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*/
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static inline Real Tan (const Radian& fValue, bool useTables = false) {
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return (!useTables) ? Real(tan(fValue.valueRadians())) : TanTable(fValue.valueRadians());
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}
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/** Tangent function.
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@param
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fValue Angle in radians
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@param
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useTables If true, uses lookup tables rather than
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calculation - faster but less accurate.
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*/
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static inline Real Tan (Real fValue, bool useTables = false) {
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return (!useTables) ? Real(tan(fValue)) : TanTable(fValue);
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}
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static inline Real DegreesToRadians(Real degrees) { return degrees * fDeg2Rad; }
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static inline Real RadiansToDegrees(Real radians) { return radians * fRad2Deg; }
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/** These functions used to set the assumed angle units (radians or degrees)
|
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|
expected when using the Angle type.
|
||
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|
@par
|
||
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|
You can set this directly after creating a new Root, and also before/after resource creation,
|
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|
depending on whether you want the change to affect resource files.
|
||
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|
*/
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static void setAngleUnit(AngleUnit unit);
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/** Get the unit being used for angles. */
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static AngleUnit getAngleUnit(void);
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/** Convert from the current AngleUnit to radians. */
|
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static Real AngleUnitsToRadians(Real units);
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||
|
|
/** 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);
|
||
|
|
|
||
|
|
/** Compare 2 reals, using tolerance for inaccuracies.
|
||
|
|
*/
|
||
|
|
static bool RealEqual(Real a, Real b,
|
||
|
|
Real tolerance = std::numeric_limits<Real>::epsilon());
|
||
|
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|
||
|
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|
||
|
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|
||
|
|
|
||
|
|
static const Real POS_INFINITY;
|
||
|
|
static const Real NEG_INFINITY;
|
||
|
|
static const Real OGRE_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
|