MathLib.h

/////////////////////////////////////////
//
//   OpenLieroX
//
//   Auxiliary Software class library
//
//   based on the work of JasonB
//   enhanced by Dark Charlie and Albert Zeyer
//
//   code under LGPL
//
/////////////////////////////////////////


// Mathematics Library
// Created 20/12/01
// Jason Boettcher
// Albert Zeyer


#ifndef __MATHLIB_H__
#define __MATHLIB_H__

#include <cmath>

#include "CVec.h"
#include "CodeAttributes.h"


// Constants
#define PI		3.14159265358979323846


const float	D2R(1.745329e-2f); // degrees to radians
const float	R2D(5.729578e+1f); // radians to degrees

#define DEG2RAD(a)  ((a) * D2R)
#define RAD2DEG(a)  ((a) * R2D)

// Routines
int		Round(float x);

/*#ifdef _MSC_VER
float	cos(float _v)  {return cosf(_v); }
float	sin(float _v)  {return sinf(_v); }
float	tan(float _v)  {return tanf(_v); }
float	atan(float _v)  {return atanf(_v); }
float	sqrt(float _v)  {return sqrtf(_v); }
#endif*/


float	CalculateDistance(CVec p1, CVec p2);
float	NormalizeVector(CVec *vec);
void	GetVecsFromAngle(float yaw,CVec *forward, CVec *right);
CVec	GetVecFromAngle(float yaw);
float	VectorAngle(CVec vec1, CVec vec2);
float	VectorLength(CVec vec);
float   fastSQRT(float x);

#define SIGN(x) (((x) > 0)?1:(((x) < 0)?-1:0))
#define SQR(x) ((x)*(x))

#undef MIN
#undef MAX

template <typename T> T MIN(T a, T b) { return a < b ? a : b; }
template <typename T> T MAX(T a, T b) { return a > b ? a : b; }
INLINE unsigned long MIN(unsigned long a, unsigned int b) { return a < b ? a : b; }
template <typename T> T CLAMP(const T& num, const T& lower_bound, const T& upper_bound) {
	return num < lower_bound ? lower_bound : (num > upper_bound ? upper_bound : num); }
template <typename T> int CLAMP_DIRECT(T& num, const T& lower_bound, const T& upper_bound) {
	if(num < lower_bound) {
		num = lower_bound;
		return -1;
	} else if(num > upper_bound) {
	 	num = upper_bound;
	 	return 1;
	} else return 0;
}
template <typename T> void REDUCE_CONST(T& v, const T& red_const) {
	if(v > 0) v = MAX((T)0, v - red_const); else if(v < 0) v = MIN((T)0, v + red_const); }
template <typename T> void RESET_SMALL(T& v, const T& limit) {
	if((v > 0 && v < limit) || (v < 0 && v > -limit)) v = 0; }

template <typename T1, typename T2> void MOD(T1& a, const T2& b) { a %= b; if(a < 0) a += b; }
template <typename T> void FMOD(T& a, const T& b) { a -= b * floor(a / b); if(a < 0) a += b; }


template<typename _T>
class SquareMatrix {
public:
	VectorD2<_T> v1, v2;
	SquareMatrix(VectorD2<_T> _v1 = VectorD2<_T>(0,0), VectorD2<_T> _v2 = VectorD2<_T>(0,0)) {
		v1 = _v1; v2 = _v2;
	}

	static SquareMatrix Identity() {
		 return SquareMatrix(VectorD2<_T>(1,0), VectorD2<_T>(0,1));
	}

	static SquareMatrix RotateMatrix(float angle) {
		SquareMatrix m;
		m.v1.x = cosf(angle);
		m.v1.y = sinf(angle);
		m.v2.x = -m.v1.y;
		m.v2.y = m.v1.x;
		return m;
	}

	CVec operator()(const VectorD2<_T>& v) const {
		return CVec(v.x*v1.x + v.y*v2.x, v.x*v1.y + v.y*v2.y);
	}
	SquareMatrix operator*(const SquareMatrix& m) const {
		return SquareMatrix((*this)(m.v1), (*this)(m.v2));
	}
	SquareMatrix operator*(const float m) const {
		return SquareMatrix(v1*m, v2*m);
	}
	SquareMatrix operator*(const int m) const {
		return SquareMatrix(v1*m, v2*m);
	}
	SquareMatrix operator/(const float m) const {
		return SquareMatrix(v1/m, v2/m);
	}
	SquareMatrix operator/(const int m) const {
		return SquareMatrix(v1/m, v2/m);
	}
	_T det() const {
		return v1.x*v2.y - v1.y*v2.x;
	}
	SquareMatrix inverse() const {
		_T tdet = det();
		if(tdet == 0)
			return SquareMatrix();
		else
			return SquareMatrix(VectorD2<_T>(v2.y,-v1.y),VectorD2<_T>(-v2.x,v1.x))/tdet;
	}

	// v1 is the upper-left, v2 the right-bottom
	bool isInDefinedArea(const VectorD2<_T>& p) const {
		return v1.x <= p.x && p.x <= v2.x && v1.y <= p.y && p.y <= v2.y;
	}

	VectorD2<_T> getCenter() const {
		return (v1 + v2) / 2;
	}

	SquareMatrix getInsersectionWithArea(const SquareMatrix& a) const {
		return SquareMatrix(
			VectorD2<_T>( MAX(a.v1.x, v1.x), MAX(a.v1.y, v1.y) ),
			VectorD2<_T>( MIN(a.v2.x, v2.x), MIN(a.v2.y, v2.y) )
			);
	}

};


class Parabola  {
public:
	float a, b, c; // a*x^2 + b*x + c
public:
	Parabola() : a(0), b(0), c(0) {}
	Parabola(float pa, float pb, float pc) : a(pa), b(pb), c(pc) {}
	Parabola(const Parabola& p) { a = p.a; b = p.b; c = p.c; }
	Parabola(CVec p1, CVec p2, CVec p3);
	Parabola(CVec p1, float angleP1, CVec p2);

	INLINE bool operator==(const Parabola& p) const {
		return (a == p.a && b == p.b && c == p.c);
	}

	float getLength(CVec p1, CVec p2);
	float getLength(float pa, float pb);
	bool isPointAtParabola(CVec p1)  {
		return (p1.y == (a * p1.x * p1.x ) + (b * p1.x) + c);
	}
};


// Random number generator with save()/restore() methods that will save and restore generator's state
// This generator should produce the same numbers on any CPU architecture, if initialized with the same seed.
// Ripped from Gnu Math library
// I don't want to use Mersenne Twister 'cuz it has a state of 624 ints which should be copied with Save()/Restore()

class SyncedRandom
{
public:

	SyncedRandom( unsigned long s = getRandomSeed() )
	{
		if (!s)
			s = 1UL; /* default seed is 1 */

  		z1 = LCG (s);
		if (z1 < 2UL)
			z1 += 2UL;
		z2 = LCG (z1);
		if (z2 < 8UL)
			z2 += 8UL;
		z3 = LCG (z2);
		if (z3 < 16UL)
			z3 += 16UL;
		z4 = LCG (z3);
		if (z4 < 128UL)
			z4 += 128UL;

		/* Calling RNG ten times to satify recurrence condition */
		getInt(); getInt(); getInt(); getInt();	getInt();
		getInt(); getInt(); getInt(); getInt();	getInt();
	};
	
	// Returns unsigned int in a range 0 : UINT_MAX
	unsigned long getInt()
	{
		unsigned long b1, b2, b3, b4;

		b1 = ((((z1 << 6UL) & MASK) ^ z1) >> 13UL);
		z1 = ((((z1 & 4294967294UL) << 18UL) & MASK) ^ b1);

		b2 = ((((z2 << 2UL) & MASK) ^ z2) >> 27UL);
		z2 = ((((z2 & 4294967288UL) << 2UL) & MASK) ^ b2);

		b3 = ((((z3 << 13UL) & MASK) ^ z3) >> 21UL);
		z3 = ((((z3 & 4294967280UL) << 7UL) & MASK) ^ b3);

		b4 = ((((z4 << 3UL) & MASK) ^ z4) >> 12UL);
		z4 = ((((z4 & 4294967168UL) << 13UL) & MASK) ^ b4);

		return (z1 ^ z2 ^ z3 ^ z4);
	};
	
	// Returns float in range 0 : 1 (1 non-inclusive)
	float getFloat()
	{
		return getInt() / 4294967296.0f;
	};
	
	void save()
	{
		save_z1 = z1;
		save_z2 = z2;
		save_z3 = z3;
		save_z4 = z4;
	};

	void restore()
	{
		z1 = save_z1;
		z2 = save_z2;
		z3 = save_z3;
		z4 = save_z4;
	};
	
	// Returns random seed based on time() and SDL_GetTicks() functions
	static unsigned long getRandomSeed();

private:

	static const unsigned long MASK = 0xffffffffUL;
	unsigned long LCG(unsigned long n) { return ((69069UL * n) & MASK); };
	
	unsigned long z1, z2, z3, z4;

	unsigned long save_z1, save_z2, save_z3, save_z4;
};


#endif  //  __MATHLIB_H__