text: 
  #ifndef GEOM_H
  #define GEOM_H
  
  #include <math.h>
  
  class Vector;
  class Line;
  class Plane;
  class Matrix;
  class Transform;
  
  const float PI=3.14159265359f;		//180 degrees
  const float TWOPI=PI*2.0f;			//360 degrees
  const float HALFPI=PI*.5f;			//90  degrees
  const float QUARTERPI=PI*.25f;		//45  degrees
  const float EPSILON=.000001f;		//small value
  const float INFINITY=10000000.0f;	//big value
  
  class Vector{
  public:
  	float x,y,z;
  
  	Vector():x(0),y(0),z(0){
  	}
  	Vector( float x,float y,float z ):x(x),y(y),z(z){
  	}
  	operator float*(){
  		return &x;
  	}
  	operator const float *(){
  		return &x;
  	}
  	float &operator[]( int n ){
  		return (&x)[n]; 
  	}
  	float operator[]( int n )const{
  		return (&x)[n]; 
  	}
  	Vector operator-()const{
  		return Vector( -x,-y,-z ); 
  	}
  	Vector operator*( float scale )const{
  		return Vector( x*scale,y*scale,z*scale );
  	}
  	Vector operator*( const Vector &q )const{
  		return Vector( x*q.x,y*q.y,z*q.z );
  	}
  	Vector operator/( float scale )const{
  		return Vector( x/scale,y/scale,z/scale );
  	}
  	Vector operator/( const Vector &q )const{
  		return Vector( x/q.x,y/q.y,z/q.z );
  	}
  	Vector operator+( const Vector &q )const{
  		return Vector( x+q.x,y+q.y,z+q.z );
  	}
  	Vector operator-( const Vector &q )const{
  		return Vector( x-q.x,y-q.y,z-q.z );
  	}
  	Vector &operator*=( float scale ){
  		x*=scale;y*=scale;z*=scale;return *this;
  	}
  	Vector &operator*=( const Vector &q ){
  		x*=q.x;y*=q.y;z*=q.z;return *this;
  	}
  	Vector &operator/=( float scale ){
  		x/=scale;y/=scale;z/=scale;return *this;
  	}
  	Vector &operator/=( const Vector &q ){
  		x/=q.x;y/=q.y;z/=q.z;return *this;
  	}
  	Vector &operator+=( const Vector &q ){
  		x+=q.x;y+=q.y;z+=q.z;return *this;
  	}
  	Vector &operator-=( const Vector &q ){
  		x-=q.x;y-=q.y;z-=q.z;return *this;
  	}
  	bool operator<( const Vector &q )const{
  		if( fabs(x-q.x)>EPSILON ) return x<q.x ? true : false;
  		if( fabs(y-q.y)>EPSILON ) return y<q.y ? true : false;
  		return fabs(z-q.z)>EPSILON && z<q.z;
  	}
  	bool operator==( const Vector &q )const{
  		return fabs(x-q.x)<=EPSILON && fabs(y-q.y)<=EPSILON && fabs(z-q.z)<=EPSILON;
  	}
  	bool operator!=( const Vector &q )const{
  		return fabs(x-q.x)>EPSILON || fabs(y-q.y)>EPSILON || fabs(z-q.z)>EPSILON;
  	}
  	float dot( const Vector &q )const{
  		return x*q.x+y*q.y+z*q.z;
  	}
  	Vector cross( const Vector &q )const{
  		return Vector( y*q.z-z*q.y,z*q.x-x*q.z,x*q.y-y*q.x );
  	}
  	float length()const{
  		return sqrtf(x*x+y*y+z*z);
  	}
  	float distance( const Vector &q )const{
  		float dx=x-q.x,dy=y-q.y,dz=z-q.z;return sqrtf(dx*dx+dy*dy+dz*dz);
  	}
  	float distanceSqr(const Vector &q)const {
  		float dx=x-q.x,dy=y-q.y,dz=z-q.z;return (dx*dx+dy*dy+dz*dz);
  	}
  	Vector normalized()const{
  		float l=length();
  	//	if (abs(l)<EPSILON) return Vector( x,y,z );
  		return Vector( x/l,y/l,z/l );
  	}
  	void normalize(){
  		float l=length();
  		//if (abs(l)<EPSILON) return;
  		x/=l;y/=l;z/=l;
  	}
  	float yaw()const{
  		return -atan2f( x,z );
  	}
  	float pitch()const{
  		return -atan2f( y,sqrtf( x*x+z*z ) );
  	}
  	void clear(){
  		x=y=z=0;
  	}
  };
  
  class Line{
  public:
  	Vector o,d;
  	Line(){
  	}
  	Line( const Vector &o,const Vector &d ):o(o),d(d){
  	}
  	Line operator+( const Vector &q )const{
  		return Line( o+q,d );
  	}
  	Line operator-( const Vector &q )const{
  		return Line( o-q,d );
  	}
  	Vector operator*( float q )const{
  		return o+d*q;
  	}
  	Vector nearest( const Vector &q )const{
  		return o+d*(d.dot(q-o)/d.dot(d));
  	}
  };
  
  class Plane{
  public:
  	Vector n;
  	float d;
  
  	Plane():d(0){
  	}
  	//normal/offset form
  	Plane( const Vector &n,float d ):n(n),d(d){
  	}
  	//point/normal form
  	Plane( const Vector &p,const Vector &n ):n(n),d(-n.dot(p)){
  	}
  	//create plane from tri
  	Plane( const Vector &v0,const Vector &v1,const Vector &v2 ){
  		n=(v1-v0).cross(v2-v0).normalized();d=-n.dot(v0);
  	}
  	Plane operator-()const{
  		return Plane( -n,-d );
  	}
  	float t_intersect( const Line &q )const{
  		return -distance(q.o)/n.dot(q.d);
  	}
  	Vector intersect( const Line &q )const{
  		return q*t_intersect(q);
  	}
  	Line intersect( const Plane &q )const{
  		Vector lv=n.cross( q.n ).normalized();
  		return Line( q.intersect( Line( nearest( n*-d ),n.cross(lv) ) ),lv );
  	}
  	Vector nearest( const Vector &q )const{
  		return q-n*distance(q);
  	}
  	void negate(){
  		n=-n;d=-d;
  	}
  	float distance( const Vector &q )const{
  		return n.dot(q)+d;
  	}
  };
  
  struct Quat{
  	float w;
  	Vector v;
  	Quat():w(1){
  	}
  	Quat( float w,const Vector &v ):w(w),v(v){
  	}
  	Quat operator-()const{
  		return Quat( w,-v );
  	}
  	Quat operator+( const Quat &q )const{
  		return Quat( w+q.w,v+q.v );
  	}
  	Quat operator-( const Quat &q )const{
  		return Quat( w-q.w,v-q.v );
  	}
  	Quat operator*( const Quat &q )const{
  		return Quat( w*q.w-v.dot(q.v),q.v.cross(v)+q.v*w+v*q.w );
  	}
  	Vector operator*( const Vector &q )const{
  		return (*this * Quat(0,q) * -*this).v;
  	}
  	Quat operator*( float q )const{
  		return Quat( w*q,v*q );
  	}
  	Quat operator/( float q )const{
  		return Quat( w/q,v/q );
  	}
  	float dot( const Quat &q )const{
  		return v.x*q.v.x+v.y*q.v.y+v.z*q.v.z+w*q.w;
  	}
  	float length()const{
  		return sqrtf( w*w+v.x*v.x+v.y*v.y+v.z*v.z );
  	}
  	void normalize(){
  		float l=length();
  		//if (l<EPSILON) return;
  		*this=*this/l;
  	}
  	Quat normalized()const{
  		float l=length();
  		//if (l<EPSILON) return *this;
  		return *this/l;
  	}
  	Quat slerpTo( const Quat &q,float a )const{
  		Quat t=q;
  		float d=dot(q),b=1-a;
  		if( d<0 ){ t.w=-t.w;t.v=-t.v;d=-d; }
  		if( d<1-EPSILON ){
  			float om=acosf( d );
  			float si=sinf( om );
  			a=sinf( a*om )/si;
  			b=sinf( b*om )/si;
  		}
  		return *this*b + t*a;
  	}
  	Vector i()const{
  		float xz=v.x*v.z,wy=w*v.y;
  		float xy=v.x*v.y,wz=w*v.z;
  		float yy=v.y*v.y,zz=v.z*v.z;
  		return Vector( 1-2*(yy+zz),2*(xy-wz),2*(xz+wy) );
  	}
  	Vector j()const{
  		float yz=v.y*v.z,wx=w*v.x;
  		float xy=v.x*v.y,wz=w*v.z;
  		float xx=v.x*v.x,zz=v.z*v.z;
  		return Vector( 2*(xy+wz),1-2*(xx+zz),2*(yz-wx) );
  	}
  	Vector k()const{
  		float xz=v.x*v.z,wy=w*v.y;
  		float yz=v.y*v.z,wx=w*v.x;
  		float xx=v.x*v.x,yy=v.y*v.y;
  		return Vector( 2*(xz-wy),2*(yz+wx),1-2*(xx+yy) );
  	}
  };
  
  class Matrix{
  	static Matrix tmps[64];
  	static Matrix &alloc_tmp(){ static int tmp=0;return tmps[tmp++&63];	}
  	friend class Transform;
  public:
  	Vector i,j,k;
  
  	Matrix():i(Vector(1,0,0)),j(Vector(0,1,0)),k(Vector(0,0,1)){
  	}
  	Matrix( const Vector &i,const Vector &j,const Vector &k ):i(i),j(j),k(k){
  	}
  	Matrix( const Quat &q ){
  		float xx=q.v.x*q.v.x,yy=q.v.y*q.v.y,zz=q.v.z*q.v.z;
  		float xy=q.v.x*q.v.y,xz=q.v.x*q.v.z,yz=q.v.y*q.v.z;
  		float wx=q.w*q.v.x,wy=q.w*q.v.y,wz=q.w*q.v.z;
  		i=Vector( 1-2*(yy+zz),2*(xy-wz),2*(xz+wy) ),
  		j=Vector( 2*(xy+wz),1-2*(xx+zz),2*(yz-wx) ),
  		k=Vector( 2*(xz-wy),2*(yz+wx),1-2*(xx+yy) );
  	}
  	Matrix( float angle,const Vector &axis ){
  		const Vector &u=axis;
  		float c=cosf(angle),s=sinf(angle);
  		float x2=axis.x*axis.x,y2=axis.y*axis.y,z2=axis.z*axis.z;
  		i=Vector( x2+c*(1-x2),u.x*u.y*(1-c)-u.z*s,u.z*u.x*(1-c)+u.y*s );
  		j=Vector( u.x*u.y*(1-c)+u.z*s,y2+c*(1-y2),u.y*u.z*(1-c)-u.x*s );
  		k=Vector( u.z*u.x*(1-c)-u.y*s,u.y*u.z*(1-c)+u.x*s,z2+c*(1-z2) );
  	}
  	Vector &operator[]( int n ){
  		return (&i)[n]; 
  	}
  	const Vector &operator[]( int n )const{
  		return (&i)[n];
  	}
  	Matrix &operator~()const{
  		Matrix &m=alloc_tmp();
  		m.i.x=i.x;m.i.y=j.x;m.i.z=k.x;
  		m.j.x=i.y;m.j.y=j.y;m.j.z=k.y;
  		m.k.x=i.z;m.k.y=j.z;m.k.z=k.z;
  		return m;
  	}
  	float determinant()const{
  		return i.x*(j.y*k.z-j.z*k.y )-i.y*(j.x*k.z-j.z*k.x )+i.z*(j.x*k.y-j.y*k.x );
  	}
  	Matrix &operator-()const{
  		Matrix &m=alloc_tmp();
  		float t=1.0f/determinant();
  		m.i.x= t*(j.y*k.z-j.z*k.y);m.i.y=-t*(i.y*k.z-i.z*k.y);m.i.z= t*(i.y*j.z-i.z*j.y);
  		m.j.x=-t*(j.x*k.z-j.z*k.x);m.j.y= t*(i.x*k.z-i.z*k.x);m.j.z=-t*(i.x*j.z-i.z*j.x);
  		m.k.x= t*(j.x*k.y-j.y*k.x);m.k.y=-t*(i.x*k.y-i.y*k.x);m.k.z= t*(i.x*j.y-i.y*j.x);
  		return m;
  	}
  	Matrix &cofactor()const{
  		Matrix &m=alloc_tmp();
  		m.i.x= (j.y*k.z-j.z*k.y);m.i.y=-(j.x*k.z-j.z*k.x);m.i.z= (j.x*k.y-j.y*k.x);
  		m.j.x=-(i.y*k.z-i.z*k.y);m.j.y= (i.x*k.z-i.z*k.x);m.j.z=-(i.x*k.y-i.y*k.x);
  		m.k.x= (i.y*j.z-i.z*j.y);m.k.y=-(i.x*j.z-i.z*j.x);m.k.z= (i.x*j.y-i.y*j.x);
  		return m;
  	}
  	bool operator==( const Matrix &q )const{
  		return i==q.i && j==q.j && k==q.k;
  	}
  	bool operator!=( const Matrix &q )const{
  		return i!=q.i || j!=q.j || k!=q.k;
  	}
  	Vector operator*( const Vector &q )const{
  		return Vector( i.x*q.x+j.x*q.y+k.x*q.z,i.y*q.x+j.y*q.y+k.y*q.z,i.z*q.x+j.z*q.y+k.z*q.z );
  	}
  	Matrix &operator*( const Matrix &q )const{
  		Matrix &m=alloc_tmp();
  		m.i.x=i.x*q.i.x+j.x*q.i.y+k.x*q.i.z;m.i.y=i.y*q.i.x+j.y*q.i.y+k.y*q.i.z;m.i.z=i.z*q.i.x+j.z*q.i.y+k.z*q.i.z;
  		m.j.x=i.x*q.j.x+j.x*q.j.y+k.x*q.j.z;m.j.y=i.y*q.j.x+j.y*q.j.y+k.y*q.j.z;m.j.z=i.z*q.j.x+j.z*q.j.y+k.z*q.j.z;
  		m.k.x=i.x*q.k.x+j.x*q.k.y+k.x*q.k.z;m.k.y=i.y*q.k.x+j.y*q.k.y+k.y*q.k.z;m.k.z=i.z*q.k.x+j.z*q.k.y+k.z*q.k.z;
  		return m;
  	}
  	void orthogonalize(){
  		k.normalize();
  		i=j.cross( k ).normalized();
  		j=k.cross( i );
  	}
  	Matrix &orthogonalized()const{
  		Matrix &m=alloc_tmp();
  		m=*this;m.orthogonalize();
  		return m;
  	}
  };
  
  class Box{
  public:
  	Vector a,b;
  	Box():a( Vector(INFINITY,INFINITY,INFINITY) ),b( Vector(-INFINITY,-INFINITY,-INFINITY) ){
  	}
  	Box( const Vector &q ):a(q),b(q){
  	}
  	Box( const Vector &a,const Vector &b ):a(a),b(b){
  	}
  	Box( const Line &l ):a(l.o),b(l.o){
  		update( l.o+l.d );
  	}
  	void clear(){
  		a.x=a.y=a.z=INFINITY;
  		b.x=b.y=b.z=-INFINITY;
  	}
  	bool empty()const{
  		return b.x<a.x || b.y<a.y || b.z<a.z;
  	}
  	Vector centre()const{
  		return Vector( (a.x+b.x)*.5f,(a.y+b.y)*.5f,(a.z+b.z)*.5f );
  	}
  	Vector corner( int n )const{
  		return Vector( ((n&1)?b:a).x,((n&2)?b:a).y,((n&4)?b:a).z );
  	}
  	void update( const Vector &q ){
  		if( q.x<a.x ) a.x=q.x;if( q.y<a.y ) a.y=q.y;if( q.z<a.z ) a.z=q.z;
  		if( q.x>b.x ) b.x=q.x;if( q.y>b.y ) b.y=q.y;if( q.z>b.z ) b.z=q.z;
  	}
  	void update( const Box &q ){
  		if( q.a.x<a.x ) a.x=q.a.x;if( q.a.y<a.y ) a.y=q.a.y;if( q.a.z<a.z ) a.z=q.a.z;
  		if( q.b.x>b.x ) b.x=q.b.x;if( q.b.y>b.y ) b.y=q.b.y;if( q.b.z>b.z ) b.z=q.b.z;
  	}
  	bool overlaps( const Box &q )const{
  		return
  		(b.x<q.b.x?b.x:q.b.x)>=(a.x>q.a.x?a.x:q.a.x) &&
  		(b.y<q.b.y?b.y:q.b.y)>=(a.y>q.a.y?a.y:q.a.y) &&
  		(b.z<q.b.z?b.z:q.b.z)>=(a.z>q.a.z?a.z:q.a.z);
  	}
  	void expand( float n ){
  		a.x-=n;a.y-=n;a.z-=n;b.x+=n;b.y+=n;b.z+=n;
  	}
  	float width()const{
  		return b.x-a.x;
  	}
  	float height()const{
  		return b.y-a.y;
  	}
  	float depth()const{
  		return b.z-a.z;
  	}
  	bool contains( const Vector &q ){
  		return q.x>=a.x && q.x<=b.x && q.y>=a.y && q.y<=b.y && q.z>=a.z && q.z<=b.z;
  	}
  };
  
  class Transform{
  	static Transform tmps[64];
  	static Transform &alloc_tmp(){ static int tmp=0;return tmps[tmp++&63]; }
  public:
  	Matrix m;
  	Vector v;
  
  	Transform(){
  	}
  	Transform( const Matrix &m ):m(m){
  	}
  	Transform( const Vector &v ):v(v){
  	}
  	Transform( const Matrix &m,const Vector &v ):m(m),v(v){
  	}
  	Transform &operator-()const{
  		Transform &t=alloc_tmp();
  		t.m=-m;t.v=t.m*-v;
  		return t;
  	}
  	Transform &operator~()const{
  		Transform &t=alloc_tmp();
  		t.m=~m;t.v=t.m*-v;
  		return t;
  	}
  	Vector operator*( const Vector &q )const{
  		return m*q+v;
  	}
  	Line operator*( const Line &q )const{
  		Vector t=(*this)*q.o;
  		return Line( t,(*this)*(q.o+q.d)-t );
  	}
  	Box operator*( const Box &q )const{
  		Box t( (*this*q.corner(0) ) );
  		for( int k=1;k<8;++k ) t.update( *this*q.corner(k) );
  		return t;
  	}
  	Transform &operator*( const Transform &q )const{
  		Transform &t=alloc_tmp();
  		t.m=m*q.m;t.v=m*q.v+v;
  		return t;
  	}
  	bool operator==( const Transform &q )const{
  		return m==q.m && v==q.v;
  	}
  	bool operator!=( const Transform &q )const{
  		return !operator==( q );
  	}
  };
  
  inline float transformRadius( float r,const Matrix &t ){
  	static const float sq_3=sqrtf(1.0f/3.0f);
  	return (t * Vector( sq_3,sq_3,sq_3 )).length()*r;
  }
  
  inline Matrix pitchMatrix( float q ){
  	return Matrix( Vector(1,0,0),Vector(0,cosf(q),sinf(q)),Vector(0,-sinf(q),cosf(q)) );
  }
  
  inline Matrix yawMatrix( float q ){
  	return Matrix( Vector(cosf(q),0,sinf(q)),Vector(0,1,0),Vector(-sinf(q),0,cosf(q)) );
  }
  
  inline Matrix rollMatrix( float q ){
  	return Matrix( Vector(cosf(q),sinf(q),0),Vector(-sinf(q),cosf(q),0),Vector(0,0,1) );
  }
  
  inline float matrixPitch( const Matrix &m ){
  	return m.k.pitch();
  //	return asinf( -m.k.y );
  }
  
  inline float matrixYaw( const Matrix &m ){
  	return m.k.yaw();
  	//return atan2f( -m.k.x,m.k.z );
  }
  
  inline float matrixRoll( const Matrix &m ){
  	return atan2f( m.i.y,m.j.y );
  	//Matrix t=pitchMatrix( -matrixPitch(m) )*yawMatrix( -matrixYaw(m) )*m;
  	//return atan2f( t.i.y,t.i.x );
  }
  
  inline Matrix scaleMatrix( float x,float y,float z ){
  	return Matrix( Vector( x,0,0 ),Vector( 0,y,0 ),Vector( 0,0,z ) );
  }
  
  inline Matrix scaleMatrix( const Vector &scale ){
  	return Matrix( Vector( scale.x,0,0 ),Vector( 0,scale.y,0 ),Vector( 0,0,scale.z ) );
  }
  
  inline Quat pitchQuat( float p ){
  	return Quat( cosf(p/-2),Vector( sinf(p/-2),0,0 ) );
  }
  
  inline Quat yawQuat( float y ){
  	return Quat( cosf(y/2),Vector( 0,sinf(y/2),0 ) );
  }
  
  inline Quat rollQuat( float r ){
  	return Quat( cosf(r/-2),Vector( 0,0,sinf(r/-2) ) );
  }
  
  //inline Quat rotationQuat( float p,float y,float r ){
  //	return yawQuat(y)*pitchQuat(p)*rollQuat(r);
  //}
  
  Quat rotationQuat( float p,float y,float r );
  
  inline Matrix rotationMatrix( float p,float y,float r ){
  	return yawMatrix(y)*pitchMatrix(p)*rollMatrix(r);
  }
  
  inline Matrix rotationMatrix( const Vector &rot ){
  	return yawMatrix(rot.y)*pitchMatrix(rot.x)*rollMatrix(rot.z);
  }
  
  inline float quatPitch( const Quat &q ){
  	return q.k().pitch();
  }
  
  inline float quatYaw( const Quat &q ){
  	return q.k().yaw();
  }
  
  inline float quatRoll( const Quat &q ){
  //	Vector i=q.i(),j=q.j();
  //	return atan2f( i.y,j.y );
  	return matrixRoll( q );
  }
  
  inline Quat matrixQuat( const Matrix &p ){
  	Matrix m=p;
  	m.orthogonalize();
  	float t=m.i.x+m.j.y+m.k.z,w,x,y,z;
  	if( t>EPSILON ){
  		t=sqrtf( t+1 )*2;
  		x=(m.k.y-m.j.z)/t;
  		y=(m.i.z-m.k.x)/t;
  		z=(m.j.x-m.i.y)/t;
  		w=t/4;
  	}else if( m.i.x>m.j.y && m.i.x>m.k.z ){
  		t=sqrtf( m.i.x-m.j.y-m.k.z+1 )*2;
  		x=t/4;
  		y=(m.j.x+m.i.y)/t;
  		z=(m.i.z+m.k.x)/t;
  		w=(m.k.y-m.j.z)/t;
  	}else if( m.j.y>m.k.z ){
  		t=sqrtf( m.j.y-m.k.z-m.i.x+1 )*2;
  		x=(m.j.x+m.i.y)/t;
  		y=t/4;
  		z=(m.k.y+m.j.z)/t;
  		w=(m.i.z-m.k.x)/t;
  	}else{
  		t=sqrtf( m.k.z-m.j.y-m.i.x+1 )*2;
  		x=(m.i.z+m.k.x)/t;
  		y=(m.k.y+m.j.z)/t;
  		z=t/4;
  		w=(m.j.x-m.i.y)/t;
  	}
  	return Quat( w,Vector( x,y,z ) );
  }
  
  #endif