math_vector.h

/*
===========================================================================
Copyright (C) 1999-2005 Id Software, Inc.

This file is part of Quake III Arena source code.

Quake III Arena source code is free software; you can redistribute it
and/or modify it under the terms of the GNU General Public License as
published by the Free Software Foundation; either version 2 of the License,
or (at your option) any later version.

Quake III Arena source code is distributed in the hope that it will be
useful, but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with Foobar; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
===========================================================================
*/
#ifndef __MATH_VECTOR_H__
#define __MATH_VECTOR_H__

#if defined(_WIN32)
#pragma warning(disable : 4244)
#endif

#include <math.h>
#include <assert.h>

//#define DotProduct(a,b)			((a)[0]*(b)[0]+(a)[1]*(b)[1]+(a)[2]*(b)[2])
//#define VectorSubtract(a,b,c)	((c)[0]=(a)[0]-(b)[0],(c)[1]=(a)[1]-(b)[1],(c)[2]=(a)[2]-(b)[2])
//#define VectorAdd(a,b,c)		((c)[0]=(a)[0]+(b)[0],(c)[1]=(a)[1]+(b)[1],(c)[2]=(a)[2]+(b)[2])
//#define VectorCopy(a,b)			((b)[0]=(a)[0],(b)[1]=(a)[1],(b)[2]=(a)[2])
//#define VectorCopy(a,b)			((b).x=(a).x,(b).y=(a).y,(b).z=(a).z])

//#define	VectorScale(v, s, o)	((o)[0]=(v)[0]*(s),(o)[1]=(v)[1]*(s),(o)[2]=(v)[2]*(s))
#define	__VectorMA(v, s, b, o)	((o)[0]=(v)[0]+(b)[0]*(s),(o)[1]=(v)[1]+(b)[1]*(s),(o)[2]=(v)[2]+(b)[2]*(s))
//#define CrossProduct(a,b,c)		((c)[0]=(a)[1]*(b)[2]-(a)[2]*(b)[1],(c)[1]=(a)[2]*(b)[0]-(a)[0]*(b)[2],(c)[2]=(a)[0]*(b)[1]-(a)[1]*(b)[0])

#define DotProduct4(x,y)		((x)[0]*(y)[0]+(x)[1]*(y)[1]+(x)[2]*(y)[2]+(x)[3]*(y)[3])
#define VectorSubtract4(a,b,c)	((c)[0]=(a)[0]-(b)[0],(c)[1]=(a)[1]-(b)[1],(c)[2]=(a)[2]-(b)[2],(c)[3]=(a)[3]-(b)[3])
#define VectorAdd4(a,b,c)		((c)[0]=(a)[0]+(b)[0],(c)[1]=(a)[1]+(b)[1],(c)[2]=(a)[2]+(b)[2],(c)[3]=(a)[3]+(b)[3])
#define VectorCopy4(a,b)		((b)[0]=(a)[0],(b)[1]=(a)[1],(b)[2]=(a)[2],(b)[3]=(a)[3])
#define	VectorScale4(v, s, o)	((o)[0]=(v)[0]*(s),(o)[1]=(v)[1]*(s),(o)[2]=(v)[2]*(s),(o)[3]=(v)[3]*(s))
#define	VectorMA4(v, s, b, o)	((o)[0]=(v)[0]+(b)[0]*(s),(o)[1]=(v)[1]+(b)[1]*(s),(o)[2]=(v)[2]+(b)[2]*(s),(o)[3]=(v)[3]+(b)[3]*(s))


//#define VectorClear(a)			((a)[0]=(a)[1]=(a)[2]=0)
#define VectorNegate(a,b)		((b)[0]=-(a)[0],(b)[1]=-(a)[1],(b)[2]=-(a)[2])
//#define VectorSet(v, x, y, z)	((v)[0]=(x), (v)[1]=(y), (v)[2]=(z))
#define Vector4Copy(a,b)		((b)[0]=(a)[0],(b)[1]=(a)[1],(b)[2]=(a)[2],(b)[3]=(a)[3])

#define	SnapVector(v) {v[0]=(int)v[0];v[1]=(int)v[1];v[2]=(int)v[2];}


//#include "util_heap.h"

#ifndef EQUAL_EPSILON
#define EQUAL_EPSILON	0.001
#endif

float Q_fabs( float f );

#ifndef ID_INLINE
#ifdef _WIN32
#define ID_INLINE __inline 
#else
#define ID_INLINE inline
#endif
#endif

// if this is defined, vec3 will take four elements, which may allow
// easier SIMD optimizations
//#define	FAT_VEC3
//#ifdef __ppc__
//#pragma align(16)
//#endif

class angles_t;
#ifdef __ppc__
// Vanilla PPC code, but since PPC has a reciprocal square root estimate instruction, 
// runs *much* faster than calling sqrt(). We'll use two Newton-Raphson 
// refinement steps to get bunch more precision in the 1/sqrt() value for very little cost. 
// We'll then multiply 1/sqrt times the original value to get the sqrt. 
// This is about 12.4 times faster than sqrt() and according to my testing (not exhaustive) 
// it returns fairly accurate results (error below 1.0e-5 up to 100000.0 in 0.1 increments). 

static inline float idSqrt(float x) {
    const float half = 0.5;
    const float one = 1.0;
    float B, y0, y1;

    // This'll NaN if it hits frsqrte. Handle both +0.0 and -0.0
    if (fabs(x) == 0.0)
        return x;
    B = x;
    
#ifdef __GNUC__
    asm("frsqrte %0,%1" : "=f" (y0) : "f" (B));
#else
    y0 = __frsqrte(B);
#endif
    /* First refinement step */
    
    y1 = y0 + half*y0*(one - B*y0*y0);
    
    /* Second refinement step -- copy the output of the last step to the input of this step */
    
    y0 = y1;
    y1 = y0 + half*y0*(one - B*y0*y0);
    
    /* Get sqrt(x) from x * 1/sqrt(x) */
    return x * y1;
}
#else
static inline double idSqrt(double x) {
    return sqrt(x);
}
#endif


//class idVec3_t  : public idHeap<idVec3_t> {
class idVec3_t {
public:	
#ifndef	FAT_VEC3
	    float x,y,z;
#else
	    float x,y,z,dist;
#endif

#ifndef	FAT_VEC3
					idVec3_t() {};
#else
					idVec3_t() {dist = 0.0f;};
#endif
					idVec3_t( const float x, const float y, const float z );

					operator float *();

	float			operator[]( const int index ) const;
	float			&operator[]( const int index );

	void 			set( const float x, const float y, const float z );

	idVec3_t			operator-() const;

	idVec3_t			&operator=( const idVec3_t &a );

	float			operator*( const idVec3_t &a ) const;
	idVec3_t			operator*( const float a ) const;
	friend idVec3_t	operator*( float a, idVec3_t b );

	idVec3_t			operator+( const idVec3_t &a ) const;
	idVec3_t			operator-( const idVec3_t &a ) const;
	
	idVec3_t			&operator+=( const idVec3_t &a );
	idVec3_t			&operator-=( const idVec3_t &a );
	idVec3_t			&operator*=( const float a );

	int				operator==(	const idVec3_t &a ) const;
	int				operator!=(	const idVec3_t &a ) const;

	idVec3_t			Cross( const idVec3_t &a ) const;
	idVec3_t			&Cross( const idVec3_t &a, const idVec3_t &b );

	float			Length( void ) const;
	float			Normalize( void );

	void			Zero( void );
	void			Snap( void );
	void			SnapTowards( const idVec3_t &to );

	float			toYaw( void );
	float			toPitch( void );
	angles_t		toAngles( void );
	friend idVec3_t	LerpVector( const idVec3_t &w1, const idVec3_t &w2, const float t );

	char			*string( void );
};

extern idVec3_t vec_zero;

ID_INLINE idVec3_t::idVec3_t( const float x, const float y, const float z ) {
	this->x = x;
	this->y = y;
	this->z = z;
#ifdef	FAT_VEC3
	this->dist = 0.0f;
#endif
}

ID_INLINE float idVec3_t::operator[]( const int index ) const {
	return ( &x )[ index ];
}

ID_INLINE float &idVec3_t::operator[]( const int index ) {
	return ( &x )[ index ];
}

ID_INLINE idVec3_t::operator float *( void ) {
	return &x;
}

ID_INLINE idVec3_t idVec3_t::operator-() const {
	return idVec3_t( -x, -y, -z );
}
	
ID_INLINE idVec3_t &idVec3_t::operator=( const idVec3_t &a ) { 
	x = a.x;
	y = a.y;
	z = a.z;
	
	return *this;
}

ID_INLINE void idVec3_t::set( const float x, const float y, const float z ) {
	this->x = x;
	this->y = y;
	this->z = z;
}

ID_INLINE idVec3_t idVec3_t::operator-( const idVec3_t &a ) const {
	return idVec3_t( x - a.x, y - a.y, z - a.z );
}

ID_INLINE float idVec3_t::operator*( const idVec3_t &a ) const {
	return x * a.x + y * a.y + z * a.z;
}

ID_INLINE idVec3_t idVec3_t::operator*( const float a ) const {
	return idVec3_t( x * a, y * a, z * a );
}

ID_INLINE idVec3_t operator*( const float a, const idVec3_t b ) {
	return idVec3_t( b.x * a, b.y * a, b.z * a );
}

ID_INLINE idVec3_t idVec3_t::operator+( const idVec3_t &a ) const {
	return idVec3_t( x + a.x, y + a.y, z + a.z );
}

ID_INLINE idVec3_t &idVec3_t::operator+=( const idVec3_t &a ) {
	x += a.x;
	y += a.y;
	z += a.z;

	return *this;
}

ID_INLINE idVec3_t &idVec3_t::operator-=( const idVec3_t &a ) {
	x -= a.x;
	y -= a.y;
	z -= a.z;

	return *this;
}

ID_INLINE idVec3_t &idVec3_t::operator*=( const float a ) {
	x *= a;
	y *= a;
	z *= a;

	return *this;
}

ID_INLINE int idVec3_t::operator==( const idVec3_t &a ) const {
	if ( Q_fabs( x - a.x ) > EQUAL_EPSILON ) {
		return false;
	}
			
	if ( Q_fabs( y - a.y ) > EQUAL_EPSILON ) {
		return false;
	}

	if ( Q_fabs( z - a.z ) > EQUAL_EPSILON ) {
		return false;
	}

	return true;
}

ID_INLINE int idVec3_t::operator!=( const idVec3_t &a ) const {
	if ( Q_fabs( x - a.x ) > EQUAL_EPSILON ) {
		return true;
	}
			
	if ( Q_fabs( y - a.y ) > EQUAL_EPSILON ) {
		return true;
	}

	if ( Q_fabs( z - a.z ) > EQUAL_EPSILON ) {
		return true;
	}

	return false;
}

ID_INLINE idVec3_t idVec3_t::Cross( const idVec3_t &a ) const {
	return idVec3_t( y * a.z - z * a.y, z * a.x - x * a.z, x * a.y - y * a.x );
}

ID_INLINE idVec3_t &idVec3_t::Cross( const idVec3_t &a, const idVec3_t &b ) {
	x = a.y * b.z - a.z * b.y;
	y = a.z * b.x - a.x * b.z;
	z = a.x * b.y - a.y * b.x;

	return *this;
}

ID_INLINE float idVec3_t::Length( void ) const {
	float length;
	
	length = x * x + y * y + z * z;
	return ( float )idSqrt( length );
}

ID_INLINE float idVec3_t::Normalize( void ) {
	float length;
	float ilength;

	length = this->Length();
	if ( length ) {
		ilength = 1.0f / length;
		x *= ilength;
		y *= ilength;
		z *= ilength;
	}
		
	return length;
}

ID_INLINE void idVec3_t::Zero( void ) {
	x = 0.0f;
	y = 0.0f;
	z = 0.0f;
}

ID_INLINE void idVec3_t::Snap( void ) {
	x = float( int( x ) );
	y = float( int( y ) );
	z = float( int( z ) );
}

/*
======================
SnapTowards

Round a vector to integers for more efficient network
transmission, but make sure that it rounds towards a given point
rather than blindly truncating.  This prevents it from truncating 
into a wall.
======================
*/
ID_INLINE void idVec3_t::SnapTowards( const idVec3_t &to ) {
	if ( to.x <= x ) {
		x = float( int( x ) );
	} else {
		x = float( int( x ) + 1 );
	}

	if ( to.y <= y ) {
		y = float( int( y ) );
	} else {
		y = float( int( y ) + 1 );
	}

	if ( to.z <= z ) {
		z = float( int( z ) );
	} else {
		z = float( int( z ) + 1 );
	}
}

//===============================================================

class Bounds {
public:
	idVec3_t	b[2];

			Bounds();
			Bounds( const idVec3_t &mins, const idVec3_t &maxs );

	void	Clear();
	void	Zero();
	float	Radius();		// radius from origin, not from center
	idVec3_t	Center();
	void	AddPoint( const idVec3_t &v );
	void	AddBounds( const Bounds &bb );
	bool	IsCleared();
	bool	ContainsPoint( const idVec3_t &p );
	bool	IntersectsBounds( const Bounds &b2 );	// touching is NOT intersecting
};

extern Bounds	boundsZero;

ID_INLINE Bounds::Bounds(){
}

ID_INLINE bool Bounds::IsCleared() {
	return b[0][0] > b[1][0];
}

ID_INLINE bool Bounds::ContainsPoint( const idVec3_t &p ) {
	if ( p[0] < b[0][0] || p[1] < b[0][1] || p[2] < b[0][2]
		|| p[0] > b[1][0] || p[1] > b[1][1] || p[2] > b[1][2] ) {
		return false;
	}
	return true;
}

ID_INLINE bool Bounds::IntersectsBounds( const Bounds &b2 ) {
	if ( b2.b[1][0] < b[0][0] || b2.b[1][1] < b[0][1] || b2.b[1][2] < b[0][2]
		|| b2.b[0][0] > b[1][0] || b2.b[0][1] > b[1][1] || b2.b[0][2] > b[1][2] ) {
		return false;
	}
	return true;
}

ID_INLINE Bounds::Bounds( const idVec3_t &mins, const idVec3_t &maxs ) {
	b[0] = mins;
	b[1] = maxs;
}

ID_INLINE idVec3_t Bounds::Center() {
	return idVec3_t( ( b[1][0] + b[0][0] ) * 0.5f, ( b[1][1] + b[0][1] ) * 0.5f, ( b[1][2] + b[0][2] ) * 0.5f );
}

ID_INLINE void Bounds::Clear() {
	b[0][0] = b[0][1] = b[0][2] = 99999;
	b[1][0] = b[1][1] = b[1][2] = -99999;
}

ID_INLINE void Bounds::Zero() {
	b[0][0] = b[0][1] = b[0][2] =
	b[1][0] = b[1][1] = b[1][2] = 0;
}

ID_INLINE void Bounds::AddPoint( const idVec3_t &v ) {
	if ( v[0] < b[0][0]) {
		b[0][0] = v[0];
	}
	if ( v[0] > b[1][0]) {
		b[1][0] = v[0];
	}
	if ( v[1] < b[0][1] ) {
		b[0][1] = v[1];
	}
	if ( v[1] > b[1][1]) {
		b[1][1] = v[1];
	}
	if ( v[2] < b[0][2] ) {
		b[0][2] = v[2];
	}
	if ( v[2] > b[1][2]) {
		b[1][2] = v[2];
	}
}


ID_INLINE void Bounds::AddBounds( const Bounds &bb ) {
	if ( bb.b[0][0] < b[0][0]) {
		b[0][0] = bb.b[0][0];
	}
	if ( bb.b[0][1] < b[0][1]) {
		b[0][1] = bb.b[0][1];
	}
	if ( bb.b[0][2] < b[0][2]) {
		b[0][2] = bb.b[0][2];
	}

	if ( bb.b[1][0] > b[1][0]) {
		b[1][0] = bb.b[1][0];
	}
	if ( bb.b[1][1] > b[1][1]) {
		b[1][1] = bb.b[1][1];
	}
	if ( bb.b[1][2] > b[1][2]) {
		b[1][2] = bb.b[1][2];
	}
}

ID_INLINE float Bounds::Radius( ) {
	int		i;
	float	total;
	float	a, aa;

	total = 0;
	for (i=0 ; i<3 ; i++) {
		a = (float)fabs( b[0][i] );
		aa = (float)fabs( b[1][i] );
		if ( aa > a ) {
			a = aa;
		}
		total += a * a;
	}

	return (float)idSqrt( total );
}

//===============================================================


class idVec2_t {
public:
	float			x;
	float			y;

					operator float *();
	float			operator[]( int index ) const;
	float			&operator[]( int index );
};

ID_INLINE float idVec2_t::operator[]( int index ) const {
	return ( &x )[ index ];
}

ID_INLINE float& idVec2_t::operator[]( int index ) {
	return ( &x )[ index ];
}

ID_INLINE idVec2_t::operator float *( void ) {
	return &x;
}

class vec4_t : public idVec3_t {
public:
#ifndef	FAT_VEC3
	float			dist;
#endif
	vec4_t();
	~vec4_t() {};
	
	vec4_t( float x, float y, float z, float dist );
	float			operator[]( int index ) const;
	float			&operator[]( int index );
};

ID_INLINE vec4_t::vec4_t() {}
ID_INLINE vec4_t::vec4_t( float x, float y, float z, float dist ) {
	this->x = x;
	this->y = y;
	this->z = z;
	this->dist = dist;
}

ID_INLINE float vec4_t::operator[]( int index ) const {
	return ( &x )[ index ];
}

ID_INLINE float& vec4_t::operator[]( int index ) {
	return ( &x )[ index ];
}


class idVec5_t : public idVec3_t {
public:
	float			s;
	float			t;
	float			operator[]( int index ) const;
	float			&operator[]( int index );
};


ID_INLINE float idVec5_t::operator[]( int index ) const {
	return ( &x )[ index ];
}

ID_INLINE float& idVec5_t::operator[]( int index ) {
	return ( &x )[ index ];
}

#endif /* !__MATH_VECTOR_H__ */