/*	Math.h: the vrtoad::Math classes	Author: Alan Fischer	Email: siralanf_at_lightningtoads_dot_com	Date: 9/21/03	Note: These are untemplated because VC6 fails to optimized templates effectivly.*/#ifndef VRTOAD_MATH_H#define VRTOAD_MATH_H#if defined(WIN32) && defined(_MSC_VER)#	define inline __forceinline#	pragma warning(disable:4244)#endif#ifdef __BORLANDC__#include <cstdlib>#include <cmath>using std::srand;using std::rand;using std::sqrt;using std::acos;using std::asin;using std::cos;using std::sin;using std::atan2;using std::exp;using std::log;using std::fabs;using std::itoa;using std::putenv;using std::ultoa;using std::swab;#define _itoa itoa#define _ultoa ultoa#define _putenv putenv#define _swab swab#else#include <math.h>#include <stdlib.h>#endif#include <vector>#ifdef VRTOAD_MATH_DOUBLE#	define cos cos#	define sin sin#	define sqrt sqrt#	define vrReal double#else#ifndef __BORLANDC__#	define cos cosf#	define sin sinf#	if 1#		define sqrt sqrtf#	else#		define sqrt fastsqrt#	endif#endif#	define vrReal float#endifnamespace vrtoad{//Constantsconst vrReal vrEpsilon=		(vrReal)0.001;const vrReal vrInfinity=	(vrReal)100000000;const vrReal vrSqrt2=		(vrReal)1.41421356237309504880168;const vrReal vrPi=			(vrReal)3.14159265358979323846264;template<class T> inline T Max(const T &t1,const T &t2){	return ((t1>t2)?t1:t2);}template<class T> inline T Min(const T &t1,const T &t2){	return ((t1<t2)?t1:t2);}template<class T> inline T abs(const T &t1){	return ((t1>0)?t1:-t1);}template<class T> inline T square(const T &t1){	return t1*t1;}template<class T> inline T linearInterpolate(const T &t1,const T &t2,vrReal time){	return t1*(1-time)+t2*time;}template<class T1,class T2,class T3> inline T3 clamp(const T1 low,const T2 high,const T3 value){        if(value<low)                return low;        if(value>high)                return high;        return value;}template<class T> inline bool finite(const T &t){	return t==t;}//These two methods aren't templated, because otherwise if you call toRad(90), it will treat it as an integer, which is BADinline vrReal toRad(vrReal deg){	return vrReal(deg*(vrReal)(vrPi/180.0));}inline vrReal toDeg(vrReal rad){	return vrReal(rad*(vrReal)(180.0/vrPi));}#define setBit(v,b) (v|=b)#define clearBit(v,b) (v&=~b)#define isBitSet(v,b) (v&b)inline void setRandomSeed(unsigned int seed){	srand(seed);}//For some reason it appears that the random number functions sometime return numbers equal to upperinline float randomFloat(float lower,float upper){	float r=(float)rand()/(float)RAND_MAX*(upper-lower)+lower;	if(r>=upper){r=lower;}	return r;}inline int randomInt(int lower,int upper){	int r=(int)((float)rand()/(float)RAND_MAX*(float)(upper-lower))+lower;	if(r>=upper){r=lower;}	return r;}float fastsqrt(float n);//Vector2class Vector2{public:	vrReal x,y;	inline Vector2():x(0),y(0){}	inline Vector2(vrReal x1,vrReal y1):x(x1),y(y1){}	inline vrReal *getData(){return (vrReal*)&x;}	inline const vrReal *getData() const{return (vrReal*)&x;}	inline bool operator==(const Vector2 &vec) const{		return (vec.x==x && vec.y==y);	}	inline bool operator!=(const Vector2 &vec) const{		return (vec.x!=x || vec.y!=y);	}	inline Vector2 operator+(const Vector2 &vec) const{		return Vector2(x+vec.x,y+vec.y);	}	inline void operator+=(const Vector2 &vec){		x+=vec.x;		y+=vec.y;	}	inline Vector2 operator-(const Vector2 &vec) const{		return Vector2(x-vec.x,y-vec.y);	}	inline void operator-=(const Vector2 &vec){		x-=vec.x;		y-=vec.y;	}	inline Vector2 operator*(vrReal f) const{		return Vector2(x*f,y*f);	}	inline void operator*=(vrReal f){		x*=f;		y*=f;	}	inline Vector2 operator*(const Vector2 &vec) const{		return Vector2(x*vec.x,y*vec.y);	}	inline void operator*=(const Vector2 &vec){		x*=vec.x;		y*=vec.y;	}	inline Vector2 operator/(vrReal f) const{		f=1/f;		return Vector2(x*f,y*f);	}	inline void operator/=(vrReal f){		f=1/f;		x*=f;		y*=f;	}	inline Vector2 operator/(const Vector2 &vec) const{		return Vector2(x/vec.x,y/vec.y);	}	inline void operator/=(const Vector2 &vec){		x/=vec.x;		y/=vec.y;	}	inline Vector2 operator-() const{		return Vector2(-x,-y);	}	inline vrReal &operator[](int i){		return *(&x+i);	}	inline vrReal operator[](int i) const{		return *(&x+i);	}	//TODO: Remove these on the vectors.  They're not "well defined" operations	inline bool operator>(const Vector2 &vec) const{		return (x>vec.x && y>vec.y);	}	inline bool operator<(const Vector2 &vec) const{		return (x<vec.x && y<vec.y);	}	inline bool operator>=(const Vector2 &vec) const{		return (x>=vec.x && y>=vec.y);	}	inline bool operator<=(const Vector2 &vec) const{		return (x<=vec.x && y<=vec.y);	}};inline Vector2 operator*(vrReal scalar,const Vector2 &vector){	return Vector2(vector.x*scalar,vector.y*scalar);}inline vrReal lengthSquared(const Vector2 &vec){	return vec.x*vec.x+vec.y*vec.y;}inline vrReal length(const Vector2 &vec){	return (vrReal)sqrt((vrReal)(vec.x*vec.x+vec.y*vec.y));}// TODO: return void?inline Vector2 normalize(Vector2 &vec){	vrReal l=1/length(vec);	vec.x*=l;	vec.y*=l;	return vec;}inline Vector2 normalize(const Vector2 &vec){	vrReal l=1/length(vec);	Vector2 vec2;	vec2.x=vec.x*l;	vec2.y=vec.y*l;	return vec2;}//Vector3class Vector3{public:	vrReal x,y,z;	inline Vector3():x(0),y(0),z(0){}	inline Vector3(vrReal x1,vrReal y1,vrReal z1):x(x1),y(y1),z(z1){}	inline Vector3(const Vector2 &vec,vrReal z1){		x=vec.x;y=vec.y;z=z1;	}	inline vrReal *getData(){return (vrReal*)&x;}	inline const vrReal *getData() const{return (vrReal*)&x;}	inline bool operator==(const Vector3 &vec) const{		return (vec.x==x && vec.y==y && vec.z==z);	}	inline bool operator!=(const Vector3 &vec) const{		return (vec.x!=x || vec.y!=y || vec.z!=z);	}	inline Vector3 operator+(const Vector3 &vec) const{		return Vector3(x+vec.x,y+vec.y,z+vec.z);	}	inline void operator+=(const Vector3 &vec){		x+=vec.x;		y+=vec.y;		z+=vec.z;	}	inline Vector3 operator-(const Vector3 &vec) const{		return Vector3(x-vec.x,y-vec.y,z-vec.z);	}	inline void operator-=(const Vector3 &vec){		x-=vec.x;		y-=vec.y;		z-=vec.z;	}	inline Vector3 operator*(vrReal f) const{		return Vector3(x*f,y*f,z*f);	}	inline void operator*=(vrReal f){		x*=f;		y*=f;		z*=f;	}	inline Vector3 operator*(const Vector3 &vec) const{		return Vector3(x*vec.x,y*vec.y,z*vec.z);	}	inline void operator*=(const Vector3 &vec){		x*=vec.x;		y*=vec.y;		z*=vec.z;	}	inline Vector3 operator/(vrReal f) const{		f=1/f;		return Vector3(x*f,y*f,z*f);	}	inline void operator/=(vrReal f){		f=1/f;		x*=f;		y*=f;		z*=f;	}	inline Vector3 operator/(const Vector3 &vec) const{		return Vector3(x/vec.x,y/vec.y,z/vec.z);	}	inline void operator/=(const Vector3 &vec){		x/=vec.x;		y/=vec.y;		z/=vec.z;	}	inline Vector3 operator-() const{		return Vector3(-x,-y,-z);	}	inline vrReal &operator[](int i){		return *(&x+i);	}	inline vrReal operator[](int i) const{		return *(&x+i);	}	inline bool operator>(const Vector3 &vec) const{		return (x>vec.x && y>vec.y && z>vec.z);	}	inline bool operator<(const Vector3 &vec) const{		return (x<vec.x && y<vec.y && z<vec.z);	}	inline bool operator>=(const Vector3 &vec) const{		return (x>=vec.x && y>=vec.y && z>=vec.z);	}	inline bool operator<=(const Vector3 &vec) const{		return (x<=vec.x && y<=vec.y && z<=vec.z);	}};const Vector3 vrRight(1,0,0);const Vector3 vrForward(0,1,0);const Vector3 vrUp(0,0,1);inline vrReal lengthSquared(const Vector3 &vec){	return vec.x*vec.x+vec.y*vec.y+vec.z*vec.z;}inline vrReal length(const Vector3 &vec){	return (vrReal)sqrt((vrReal)(vec.x*vec.x+vec.y*vec.y+vec.z*vec.z));}// TODO: return void?inline Vector3 normalize(Vector3 &vec){	vrReal l=1/length(vec);	vec.x*=l;	vec.y*=l;	vec.z*=l;	return vec;}inline Vector3 normalize(const Vector3 &vec){	vrReal l=1/length(vec);	Vector3 vec2;	vec2.x=vec.x*l;	vec2.y=vec.y*l;	vec2.z=vec.z*l;	return vec2;}// To keep code clean, use this for an XYZ Euler angle, instead of a Vectortypedef Vector3 EulerAngle;inline EulerAngle toRad(const EulerAngle &deg){	return EulerAngle(toRad(deg.x),toRad(deg.y),toRad(deg.z));}inline EulerAngle toDeg(const EulerAngle &deg){	return EulerAngle(toDeg(deg.x),toDeg(deg.y),toDeg(deg.z));}inline Vector3 cross(const Vector3 &vec1,const Vector3 &vec2){	return Vector3(vec1.y*vec2.z-vec1.z*vec2.y,vec1.z*vec2.x-vec1.x*vec2.z,vec1.x*vec2.y-vec1.y*vec2.x);}inline Vector3 operator*(vrReal scalar,const Vector3 &vector){	return Vector3(vector.x*scalar,vector.y*scalar,vector.z*scalar);}inline vrReal dot(const Vector3 &vec1,const Vector3 &vec2){	return vec1.x*vec2.x+vec1.y*vec2.y+vec1.z*vec2.z;}inline Vector3 reflectVector(const Vector3 &vec,const Vector3 &norm){	return norm*(2*dot(vec,norm))-vec;}void setVectorsFromEulerAngles(const EulerAngle &angles,Vector3 &forward,Vector3 &up,Vector3 &right);vrReal getXYAngle(const Vector3 &vec1,const Vector3 &vec2);inline vrReal angleBetween(const Vector3 &vec1,const Vector3 &vec2){	return acos(dot(vec1,vec2));}//Vector4class Vector4{public:	vrReal x,y,z,w;	inline Vector4():x(0),y(0),z(0),w(0){}	inline Vector4(vrReal x1,vrReal y1,vrReal z1,vrReal w1):x(x1),y(y1),z(z1),w(w1){}	inline Vector4(const Vector3 &vec,vrReal w1){		x=vec.x;y=vec.y;z=vec.z;w=w1;	}	inline vrReal *getData(){return (vrReal*)&x;}	inline const vrReal *getData() const{return (vrReal*)&x;}	inline bool operator==(const Vector4 &vec) const{		return (vec.x==x && vec.y==y && vec.z==z && vec.w==w);	}	inline bool operator!=(const Vector4 &vec) const{		return (vec.x!=x || vec.y!=y || vec.z!=z || vec.w!=w);	}	inline Vector4 operator+(const Vector4 &vec) const{		return Vector4(x+vec.x,y+vec.y,z+vec.z,w+vec.w);	}	inline void operator+=(const Vector4 &vec){		x+=vec.x;		y+=vec.y;		z+=vec.z;		w+=vec.w;	}	inline Vector4 operator-(const Vector4 &vec) const{		return Vector4(x-vec.x,y-vec.y,z-vec.z,w-vec.w);	}	inline void operator-=(const Vector4 &vec){		x-=vec.x;		y-=vec.y;		z-=vec.z;		w-=vec.w;	}	inline Vector4 operator*(vrReal f) const{		return Vector4(x*f,y*f,z*f,w*f);	}	inline void operator*=(vrReal f){		x*=f;		y*=f;		z*=f;		w*=f;	}	inline Vector4 operator*(const Vector4 &vec) const{		return Vector4(x*vec.x,y*vec.y,z*vec.z,w*vec.w);	}	inline void operator*=(const Vector4 &vec){		x*=vec.x;		y*=vec.y;		z*=vec.z;		w*=vec.w;	}	inline Vector4 operator/(vrReal f) const{		f=1/f;		return Vector4(x*f,y*f,z*f,w*f);	}	inline void operator/=(vrReal f){		f=1/f;		x*=f;		y*=f;		z*=f;		w*=f;	}	inline void operator/=(const Vector4 &vec){		x/=vec.x;		y/=vec.y;		z/=vec.z;		w/=vec.w;	}	inline Vector4 operator-() const{		return Vector4(-x,-y,-z,-w);	}	inline vrReal &operator[](int i){		return *(&x+i);	}	inline vrReal operator[](int i) const{