/******************************************************************************

	This source file is part of Viewizard Game Engine
	For the latest info, see http://www.viewizard.com/

	File name: Math.cpp

	Copyright (c) 2001-2007 Michael Kurinnoy, Viewizard
	All Rights Reserved.

	File Version: 3.0

******************************************************************************

	AstroMenace game source code available under "dual licensing" model.
	The licensing options available are:

	* Commercial Licensing. This is the appropriate option if you are
	  creating proprietary applications and you are not prepared to
	  distribute and share the source code of your application.
	  Contact us for pricing at viewizard@viewizard.com

	* Open Source Licensing. This is the appropriate option if you want
	  to share the source code of your application with everyone you
	  distribute it to, and you also want to give them the right to share
	  who uses it. You should have received a copy of the GNU General Public
	  License version 3 with this source codes.
	  If not, see <http://www.gnu.org/licenses/>.

******************************************************************************/


#include "Math.h"



//------------------------------------------------------------------------------------
// Cosine Tab
//------------------------------------------------------------------------------------
double Cos[360] = {1.000000,0.999848,0.999391,0.998630,0.997564,0.996195,0.994522,
	0.992546,0.990268,0.987688,0.984808,0.981627,0.978148,0.974370,
	0.970296,0.965926,0.961262,0.956305,0.951057,0.945519,0.939693,
	0.933580,0.927184,0.920505,0.913545,0.906308,0.898794,0.891007,
	0.882948,0.874620,0.866025,0.857167,0.848048,0.838671,0.829038,
	0.819152,0.809017,0.798636,0.788011,0.777146,0.766044,0.754710,
	0.743145,0.731354,0.719340,0.707107,0.694658,0.681998,0.669131,
	0.656059,0.642788,0.629320,0.615661,0.601815,0.587785,0.573576,
	0.559193,0.544639,0.529919,0.515038,0.500000,0.484810,0.469472,
	0.453990,0.438371,0.422618,0.406737,0.390731,0.374607,0.358368,
	0.342020,0.325568,0.309017,0.292372,0.275637,0.258819,0.241922,
	0.224951,0.207912,0.190809,0.173648,0.156434,0.139173,0.121869,
	0.104528,0.087156,0.069756,0.052336,0.034899,0.017452,0.000000,
	-0.017452,-0.034899,-0.052336,-0.069756,-0.087156,-0.104528,
	-0.121869,-0.139173,-0.156434,-0.173648,-0.190809,-0.207912,
	-0.224951,-0.241922,-0.258819,-0.275637,-0.292372,-0.309017,
	-0.325568,-0.342020,-0.358368,-0.374607,-0.390731,-0.406737,
	-0.422618,-0.438371,-0.453990,-0.469472,-0.484810,-0.500000,
	-0.515038,-0.529919,-0.544639,-0.559193,-0.573576,-0.587785,
	-0.601815,-0.615661,-0.629320,-0.642788,-0.656059,-0.669131,
	-0.681998,-0.694658,-0.707107,-0.719340,-0.731354,-0.743145,
	-0.754710,-0.766044,-0.777146,-0.788011,-0.798636,-0.809017,
	-0.819152,-0.829038,-0.838671,-0.848048,-0.857167,-0.866025,
	-0.874620,-0.882948,-0.891007,-0.898794,-0.906308,-0.913545,
	-0.920505,-0.927184,-0.933580,-0.939693,-0.945519,-0.951057,
	-0.956305,-0.961262,-0.965926,-0.970296,-0.974370,-0.978148,
	-0.981627,-0.984808,-0.987688,-0.990268,-0.992546,-0.994522,
	-0.996195,-0.997564,-0.998630,-0.999391,-0.999848,-1.000000,
	-0.999848,-0.999391,-0.998630,-0.997564,-0.996195,-0.994522,
	-0.992546,-0.990268,-0.987688,-0.984808,-0.981627,-0.978148,
	-0.974370,-0.970296,-0.965926,-0.961262,-0.956305,-0.951057,
	-0.945519,-0.939693,-0.933580,-0.927184,-0.920505,-0.913545,
	-0.906308,-0.898794,-0.891007,-0.882948,-0.874620,-0.866025,
	-0.857167,-0.848048,-0.838671,-0.829038,-0.819152,-0.809017,
	-0.798636,-0.788011,-0.777146,-0.766044,-0.754710,-0.743145,
	-0.731354,-0.719340,-0.707107,-0.694658,-0.681998,-0.669131,
	-0.656059,-0.642788,-0.629320,-0.615661,-0.601815,-0.587785,
	-0.573576,-0.559193,-0.544639,-0.529919,-0.515038,-0.500000,
	-0.484810,-0.469472,-0.453990,-0.438371,-0.422618,-0.406737,
	-0.390731,-0.374607,-0.358368,-0.342020,-0.325568,-0.309017,
	-0.292372,-0.275637,-0.258819,-0.241922,-0.224951,-0.207912,
	-0.190809,-0.173648,-0.156434,-0.139173,-0.121869,-0.104528,
	-0.087156,-0.069756,-0.052336,-0.034899,-0.017452,-0.000000,
	0.017452,0.034899,0.052336,0.069756,0.087156,0.104528,0.121869,
	0.139173,0.156434,0.173648,0.190809,0.207912,0.224951,0.241922,
	0.258819,0.275637,0.292372,0.309017,0.325568,0.342020,
	0.358368,0.374607,0.390731,0.406737,0.422618,0.438371,0.453990,
	0.469472,0.484810,0.500000,0.515038,0.529919,0.544639,0.559193,
	0.573576,0.587785,0.601815,0.615661,0.629320,0.642788,0.656059,
	0.669131,0.681998,0.694658,0.707107,0.719340,0.731354,0.743145,
	0.754710,0.766044,0.777146,0.788011,0.798636,0.809017,0.819152,
	0.829038,0.838671,0.848048,0.857167,0.866025,0.874620,0.882948,
	0.891007,0.898794,0.906308,0.913545,0.920505,0.927184,0.933580,
	0.939693,0.945519,0.951057,0.956305,0.961262,0.965926,0.970296,
	0.974370,0.978148,0.981627,0.984808,0.987688,0.990268,0.992546,
	0.994522,0.996195,0.997564,0.998630,0.999391,0.999848};

//------------------------------------------------------------------------------------
// Get Cosine
//------------------------------------------------------------------------------------
double vw_dcos(int Angle)
{
	return Cos[Angle];
}









//------------------------------------------------------------------------------------
// Sine Tab
//------------------------------------------------------------------------------------
double Sin[360] = {0.000000,0.017452,0.034899,0.052336,0.069756,0.087156,
	0.104528,0.121869,0.139173,0.156434,0.173648,0.190809,0.207912,
	0.224951,0.241922,0.258819,0.275637,0.292372,0.309017,0.325568,
	0.342020,0.358368,0.374607,0.390731,0.406737,0.422618,0.438371,
	0.453990,0.469472,0.484810,0.500000,0.515038,0.529919,0.544639,
	0.559193,0.573576,0.587785,0.601815,0.615661,0.629320,0.642788,
	0.656059,0.669131,0.681998,0.694658,0.707107,0.719340,0.731354,
	0.743145,0.754710,0.766044,0.777146,0.788011,0.798636,0.809017,
	0.819152,0.829038,0.838671,0.848048,0.857167,0.866025,0.874620,
	0.882948,0.891007,0.898794,0.906308,0.913545,0.920505,0.927184,
	0.933580,0.939693,0.945519,0.951057,0.956305,0.961262,0.965926,
	0.970296,0.974370,0.978148,0.981627,0.984808,0.987688,0.990268,
	0.992546,0.994522,0.996195,0.997564,0.998630,0.999391,0.999848,
	1.000000,0.999848,0.999391,0.998630,0.997564,0.996195,0.994522,
	0.992546,0.990268,0.987688,0.984808,0.981627,0.978148,0.974370,
	0.970296,0.965926,0.961262,0.956305,0.951057,0.945519,0.939693,
	0.933580,0.927184,0.920505,0.913545,0.906308,0.898794,0.891007,
	0.882948,0.874620,0.866025,0.857167,0.848048,0.838671,0.829038,
	0.819152,0.809017,0.798636,0.788011,0.777146,0.766044,0.754710,
	0.743145,0.731354,0.719340,0.707107,0.694658,0.681998,0.669131,
	0.656059,0.642788,0.629320,0.615661,0.601815,0.587785,0.573576,
	0.559193,0.544639,0.529919,0.515038,0.500000,0.484810,0.469472,
	0.453990,0.438371,0.422618,0.406737,0.390731,0.374607,0.358368,
	0.342020,0.325568,0.309017,0.292372,0.275637,0.258819,0.241922,
	0.224951,0.207912,0.190809,0.173648,0.156434,0.139173,0.121869,
	0.104528,0.087156,0.069756,0.052336,0.034899,0.017452,0.000000,
	-0.017452,-0.034899,-0.052336,-0.069756,-0.087156,-0.104528,
	-0.121869,-0.139173,-0.156434,-0.173648,-0.190809,-0.207912,
	-0.224951,-0.241922,-0.258819,-0.275637,-0.292372,-0.309017,
	-0.325568,-0.342020,-0.358368,-0.374607,-0.390731,-0.406737,
	-0.422618,-0.438371,-0.453990,-0.469472,-0.484810,-0.500000,
	-0.515038,-0.529919,-0.544639,-0.559193,-0.573576,-0.587785,
	-0.601815,-0.615661,-0.629320,-0.642788,-0.656059,-0.669131,
	-0.681998,-0.694658,-0.707107,-0.719340,-0.731354,-0.743145,
	-0.754710,-0.766044,-0.777146,-0.788011,-0.798636,-0.809017,
	-0.819152,-0.829038,-0.838671,-0.848048,-0.857167,-0.866025,
	-0.874620,-0.882948,-0.891007,-0.898794,-0.906308,-0.913545,
	-0.920505,-0.927184,-0.933580,-0.939693,-0.945519,-0.951057,
	-0.956305,-0.961262,-0.965926,-0.970296,-0.974370,-0.978148,
	-0.981627,-0.984808,-0.987688,-0.990268,-0.992546,-0.994522,
	-0.996195,-0.997564,-0.998630,-0.999391,-0.999848,-1.000000,
	-0.999848,-0.999391,-0.998630,-0.997564,-0.996195,-0.994522,
	-0.992546,-0.990268,-0.987688,-0.984808,-0.981627,-0.978148,
	-0.974370,-0.970296,-0.965926,-0.961262,-0.956305,-0.951057,
	-0.945519,-0.939693,-0.933580,-0.927184,-0.920505,-0.913545,
	-0.906308,-0.898794,-0.891007,-0.882948,-0.874620,-0.866025,
	-0.857167,-0.848048,-0.838671,-0.829038,-0.819152,-0.809017,
	-0.798636,-0.788011,-0.777146,-0.766044,-0.754710,-0.743145,
	-0.731354,-0.719340,-0.707107,-0.694658,-0.681998,-0.669131,
	-0.656059,-0.642788,-0.629320,-0.615661,-0.601815,-0.587785,
	-0.573576,-0.559193,-0.544639,-0.529919,-0.515038,-0.500000,
	-0.484810,-0.469472,-0.453990,-0.438371,-0.422618,-0.406737,
	-0.390731,-0.374607,-0.358368,-0.342020,-0.325568,-0.309017,
	-0.292372,-0.275637,-0.258819,-0.241922,-0.224951,-0.207912,
	-0.190809,-0.173648,-0.156434,-0.139173,-0.121869,-0.104528,
	-0.087156,-0.069756,-0.052336,-0.034899,-0.017452};

//------------------------------------------------------------------------------------
// Get Sine
//------------------------------------------------------------------------------------
double vw_dsin(int Angle)
{
	return Sin[Angle];
}








//------------------------------------------------------------------------------------
// Fast string comparison
//------------------------------------------------------------------------------------
int vw_strcmp(const char *a, const char *b)
{
	while(*a == *b)
	{
		if(*a == '\0')return 0;
		a++;
		b++;
	}
	return 1;
}






//------------------------------------------------------------------------------------
// Fast root (without sqrtf)
//------------------------------------------------------------------------------------
#define ONE_AS_INTEGER ((DWORD)(0x3F800000))
#ifdef WIN32 // для MSVC используем
float __fastcall ulrsqrt(float x)
#else
float ulrsqrt(const float & x)
#endif
{
	DWORD   tmp = ((ONE_AS_INTEGER << 1) + ONE_AS_INTEGER - *(DWORD*)&x) >> 1;
	float y = *((float*)&tmp);

	// первый способ
	y = (3.0f - x * (y * y)) * y * 0.5f;
	return y;
	// второй способ
	// return (y * (1.47f - 0.47f * x * y * y));
}
float vw_sqrtf(float x)
{
	return x*ulrsqrt(x);
	// второй способ, с делением, более точный
	// return 1.0f/ulrsqrt(x);
	// самый-самый точный способ :)
	//return sqrtf(x);
}





//------------------------------------------------------------------------------------
// Randomize float
//------------------------------------------------------------------------------------
#include "MersenneTwister.h"
// делаем при старте, т.к. инится все... иначе будут тормоза
MTRand mtrand1;

float vw_Rand()
{
	float Result = (float)mtrand1.rand(RAND_MAX);
	if (Result < 0.0f) Result = 0.0f;
	if (Result > RAND_MAX) Result = RAND_MAX;
	return Result;
}

float vw_RandNum(float Max)
{
	float Result = (float)mtrand1.rand(RAND_MAX);
	if (Result < 0.0f) Result = 0.0f;
	if (Result > Max) Result = Max;
	return Result;
}

int vw_iRandNum(int Max)
{
	int Result = mtrand1.randInt(Max);
	if (Result < 0) Result = 0;
	if (Result > Max) Result = Max;
	return Result;
}













//------------------------------------------------------------------------------------
// Fast normalization...
//------------------------------------------------------------------------------------

#define ONE_AS_INTEGER ((DWORD)(0x3F800000))

#ifdef WIN32 // для MSVC используем __fastcall
float __fastcall InvSqrt(const float & x)
#else
float InvSqrt(const float & x)
#endif
{
	DWORD   tmp = ((ONE_AS_INTEGER << 1) + ONE_AS_INTEGER - *(DWORD*)&x) >> 1;
	float y = *(float*)&tmp;
	return y * (1.47f - 0.47f * x * y * y);
}
void Normalise(VECTOR3D *v)
{
	float L_squared, one_over_L;
	L_squared = (v->x * v->x) + (v->y * v->y) + (v->z * v->z);
	one_over_L = InvSqrt(L_squared);
	v->x = v->x * one_over_L;
	v->y = v->y * one_over_L;
	v->z = v->z * one_over_L;
}


//------------------------------------------------------------------------------------
// Точная нормализация
//------------------------------------------------------------------------------------
void NormaliseHi(VECTOR3D *v)
{
	float Length;
	Length = sqrtf((v->x * v->x) + (v->y * v->y) + (v->z * v->z));
	if (Length < 0.001f) return; // если все координаты очень маленькие
	v->x = v->x / Length;
	v->y = v->y / Length;
	v->z = v->z / Length;
}




//------------------------------------------------------------------------------------
// 3D Vector
//------------------------------------------------------------------------------------
float VECTOR3D::Length()
{
	return vw_sqrtf(x * x + y * y + z * z);
}

void VECTOR3D::Normalize()
{
	Normalise(this);
}

void VECTOR3D::NormalizeHi()
{
	NormaliseHi(this);
}

void VECTOR3D::Multiply( VECTOR3D A)
{
	float tV[3];
	tV[0] = y * A.z - z * A.y;
	tV[1] = z * A.x - x * A.z;
	tV[2] = x * A.y - y * A.x;
	x = tV[0];
	y = tV[1];
	z = tV[2];
}











//------------------------------------------------------------------------------------
// Get max
//------------------------------------------------------------------------------------
float Max3(float a1,float a2,float a3)
{
	if ((a1>=a2)&(a1>=a3)){return a1;}
	if ((a2>=a1)&(a2>=a3)){return a2;}
	if ((a3>=a1)&(a3>=a2)){return a3;}
	return a1;
}







//------------------------------------------------------------------------------------
// Get min
//------------------------------------------------------------------------------------
float Min3(float a1,float a2,float a3)
{
	if ((a1<=a2)&(a1<=a3)){return a1;}
	if ((a2<=a1)&(a2<=a3)){return a2;}
	if ((a3<=a1)&(a3<=a2)){return a3;}
	return a1;
}









//-----------------------------------------------------------------------------
// Get Plane ABCD value, via 3 points on plane
//-----------------------------------------------------------------------------
void GetPlaneABCD(float *A, float *B, float *C, float *D, VECTOR3D Point1, VECTOR3D Point2, VECTOR3D Point3)
{
	*A = (Point2.y-Point1.y)*(Point3.z-Point1.z)-(Point2.z-Point1.z)*(Point3.y-Point1.y);
	*B = (Point2.z-Point1.z)*(Point3.x-Point1.x)-(Point2.x-Point1.x)*(Point3.z-Point1.z);
	*C = (Point2.x-Point1.x)*(Point3.y-Point1.y)-(Point2.y-Point1.y)*(Point3.x-Point1.x);
	*D = -Point1.x*(Point2.y-Point1.y)*(Point3.z-Point1.z)
			-Point1.y*(Point2.z-Point1.z)*(Point3.x-Point1.x)
			-Point1.z*(Point2.x-Point1.x)*(Point3.y-Point1.y)
			+Point1.z*(Point2.y-Point1.y)*(Point3.x-Point1.x)
			+Point1.y*(Point2.x-Point1.x)*(Point3.z-Point1.z)
			+Point1.x*(Point2.z-Point1.z)*(Point3.y-Point1.y);
}









//------------------------------------------------------------------------------------
// Rotate point on Angle regard to point(0,0,0)
//------------------------------------------------------------------------------------
const float p180 = 0.0174532925f;
void RotatePoint(VECTOR3D *Point, VECTOR3D Angle)
{
	float xTMP = Point->x;
	float yTMP = Point->y;
	float zTMP = Point->z;

		// X
		if (Angle.x != 0)
		{
			float a = Angle.x*p180;
			float c = cosf(a);
			float s = sinf(a);
			Point->y = yTMP*c + zTMP*s;
			Point->z = -yTMP*s + zTMP*c;
			xTMP = Point->x;
			yTMP = Point->y;
			zTMP = Point->z;
		}

		// Y
		if (Angle.y != 0)
		{
			float a = -Angle.y*p180;
			float c = cosf(a);
			float s = sinf(a);
			Point->x = xTMP*c + zTMP*s;
			Point->z = -xTMP*s + zTMP*c;
			xTMP = Point->x;
			yTMP = Point->y;
			zTMP = Point->z;
		}

		// Z
		if (Angle.z != 0)
		{
			float a = Angle.z*p180;
			float c = cosf(a);
			float s = sinf(a);
			Point->x = xTMP*c + yTMP*s;
			Point->y = -xTMP*s + yTMP*c;
		}
}


//------------------------------------------------------------------------------------
// обратный поворот точки (обратная последовательность поворота по осям)
//------------------------------------------------------------------------------------
void RotatePointInv(VECTOR3D *Point, VECTOR3D Angle)
{
	float xTMP = Point->x;
	float yTMP = Point->y;
	float zTMP = Point->z;

		// Z
		if (Angle.z != 0)
		{
			float a = Angle.z*p180;
			float c = cosf(a);
			float s = sinf(a);
			Point->x = xTMP*c + yTMP*s;
			Point->y = -xTMP*s + yTMP*c;
			xTMP = Point->x;
			yTMP = Point->y;
			zTMP = Point->z;
		}

		// Y
		if (Angle.y != 0)
		{
			float a = -Angle.y*p180;
			float c = cosf(a);
			float s = sinf(a);
			Point->x = xTMP*c + zTMP*s;
			Point->z = -xTMP*s + zTMP*c;
			xTMP = Point->x;
			yTMP = Point->y;
			zTMP = Point->z;
		}

		// X
		if (Angle.x != 0)
		{
			float a = Angle.x*p180;
			float c = cosf(a);
			float s = sinf(a);
			Point->y = yTMP*c + zTMP*s;
			Point->z = -yTMP*s + zTMP*c;
		}
}