text: ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
  /**
   *	Contains code for 3D vectors.
   *	\file		IcePoint.h
   *	\author		Pierre Terdiman
   *	\date		April, 4, 2000
   */
  ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
  
  ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
  // Include Guard
  #ifndef __ICEPOINT_H__
  #define __ICEPOINT_H__
  
  	// Forward declarations
  	class HPoint;
  	class Plane;
  	class Matrix3x3;
  	class Matrix4x4;
  
  	#define CROSS2D(a, b)	(a.x*b.y - b.x*a.y)
  
  	const float EPSILON2 = 1.0e-20f;
  
  	class ICEMATHS_API Point
  	{
  		public:
  
  		//! Empty constructor
  		inline_					Point()														{}
  		//! Constructor from a single float
  //		inline_					Point(float val) : x(val), y(val), z(val)					{}
  // Removed since it introduced the nasty "Point T = *Matrix4x4.GetTrans();" bug.......
  		//! Constructor from floats
  		inline_					Point(float _x, float _y, float _z) : x(_x), y(_y), z(_z)	{}
  		//! Constructor from array
  		inline_					Point(const float f[3]) : x(f[_X]), y(f[_Y]), z(f[_Z])		{}
  		//! Copy constructor
  		inline_					Point(const Point& p) : x(p.x), y(p.y), z(p.z)				{}
  		//! Destructor
  		inline_					~Point()													{}
  
  		//! Clears the vector
  		inline_	Point&			Zero()									{ x =			y =			z = 0.0f;			return *this;	}
  
  		//! + infinity
  		inline_	Point&			SetPlusInfinity()						{ x =			y =			z = MAX_FLOAT;		return *this;	}
  		//! - infinity
  		inline_	Point&			SetMinusInfinity()						{ x =			y =			z = MIN_FLOAT;		return *this;	}
  
  		//! Sets positive unit random vector
  				Point&			PositiveUnitRandomVector();
  		//! Sets unit random vector
  				Point&			UnitRandomVector();
  
  		//! Assignment from values
  		inline_	Point&			Set(float _x, float _y, float _z)		{ x  = _x;		y  = _y;	z  = _z;			return *this;	}
  		//! Assignment from array
  		inline_	Point&			Set(const float f[3])					{ x  = f[_X];	y  = f[_Y];	z  = f[_Z];			return *this;	}
  		//! Assignment from another point
  		inline_	Point&			Set(const Point& src)					{ x  = src.x;	y  = src.y;	z  = src.z;			return *this;	}
  
  		//! Adds a vector
  		inline_	Point&			Add(const Point& p)						{ x += p.x;		y += p.y;	z += p.z;			return *this;	}
  		//! Adds a vector
  		inline_	Point&			Add(float _x, float _y, float _z)		{ x += _x;		y += _y;	z += _z;			return *this;	}
  		//! Adds a vector
  		inline_	Point&			Add(const float f[3])					{ x += f[_X];	y += f[_Y];	z += f[_Z];			return *this;	}
  		//! Adds vectors
  		inline_	Point&			Add(const Point& p, const Point& q)		{ x = p.x+q.x;	y = p.y+q.y;	z = p.z+q.z;	return *this;	}
  
  		//! Subtracts a vector
  		inline_	Point&			Sub(const Point& p)						{ x -= p.x;		y -= p.y;	z -= p.z;			return *this;	}
  		//! Subtracts a vector
  		inline_	Point&			Sub(float _x, float _y, float _z)		{ x -= _x;		y -= _y;	z -= _z;			return *this;	}
  		//! Subtracts a vector
  		inline_	Point&			Sub(const float f[3])					{ x -= f[_X];	y -= f[_Y];	z -= f[_Z];			return *this;	}
  		//! Subtracts vectors
  		inline_	Point&			Sub(const Point& p, const Point& q)		{ x = p.x-q.x;	y = p.y-q.y;	z = p.z-q.z;	return *this;	}
  
  		//! this = -this
  		inline_	Point&			Neg()									{ x = -x;		y = -y;			z = -z;			return *this;	}
  		//! this = -a
  		inline_	Point&			Neg(const Point& a)						{ x = -a.x;		y = -a.y;		z = -a.z;		return *this;	}
  
  		//! Multiplies by a scalar
  		inline_	Point&			Mult(float s)							{ x *= s;		y *= s;		z *= s;				return *this;	}
  
  		//! this = a * scalar
  		inline_	Point&			Mult(const Point& a, float scalar)
  								{
  									x = a.x * scalar;
  									y = a.y * scalar;
  									z = a.z * scalar;
  									return *this;
  								}
  
  		//! this = a + b * scalar
  		inline_	Point&			Mac(const Point& a, const Point& b, float scalar)
  								{
  									x = a.x + b.x * scalar;
  									y = a.y + b.y * scalar;
  									z = a.z + b.z * scalar;
  									return *this;
  								}
  
  		//! this = this + a * scalar
  		inline_	Point&			Mac(const Point& a, float scalar)
  								{
  									x += a.x * scalar;
  									y += a.y * scalar;
  									z += a.z * scalar;
  									return *this;
  								}
  
  		//! this = a - b * scalar
  		inline_	Point&			Msc(const Point& a, const Point& b, float scalar)
  								{
  									x = a.x - b.x * scalar;
  									y = a.y - b.y * scalar;
  									z = a.z - b.z * scalar;
  									return *this;
  								}
  
  		//! this = this - a * scalar
  		inline_	Point&			Msc(const Point& a, float scalar)
  								{
  									x -= a.x * scalar;
  									y -= a.y * scalar;
  									z -= a.z * scalar;
  									return *this;
  								}
  
  		//! this = a + b * scalarb + c * scalarc
  		inline_	Point&			Mac2(const Point& a, const Point& b, float scalarb, const Point& c, float scalarc)
  								{
  									x = a.x + b.x * scalarb + c.x * scalarc;
  									y = a.y + b.y * scalarb + c.y * scalarc;
  									z = a.z + b.z * scalarb + c.z * scalarc;
  									return *this;
  								}
  
  		//! this = a - b * scalarb - c * scalarc
  		inline_	Point&			Msc2(const Point& a, const Point& b, float scalarb, const Point& c, float scalarc)
  								{
  									x = a.x - b.x * scalarb - c.x * scalarc;
  									y = a.y - b.y * scalarb - c.y * scalarc;
  									z = a.z - b.z * scalarb - c.z * scalarc;
  									return *this;
  								}
  
  		//! this = mat * a
  		inline_	Point&			Mult(const Matrix3x3& mat, const Point& a);
  
  		//! this = mat1 * a1 + mat2 * a2
  		inline_	Point&			Mult2(const Matrix3x3& mat1, const Point& a1, const Matrix3x3& mat2, const Point& a2);
  
  		//! this = this + mat * a
  		inline_	Point&			Mac(const Matrix3x3& mat, const Point& a);
  
  		//! this = transpose(mat) * a
  		inline_	Point&			TransMult(const Matrix3x3& mat, const Point& a);
  
  		//! Linear interpolate between two vectors: this = a + t * (b - a)
  		inline_	Point&			Lerp(const Point& a, const Point& b, float t)
  								{
  									x = a.x + t * (b.x - a.x);
  									y = a.y + t * (b.y - a.y);
  									z = a.z + t * (b.z - a.z);
  									return *this;
  								}
  
  		//! Hermite interpolate between p1 and p2. p0 and p3 are used for finding gradient at p1 and p2.
  		//! this =	p0 * (2t^2 - t^3 - t)/2
  		//!			+ p1 * (3t^3 - 5t^2 + 2)/2
  		//!			+ p2 * (4t^2 - 3t^3 + t)/2
  		//!			+ p3 * (t^3 - t^2)/2
  		inline_	Point&			Herp(const Point& p0, const Point& p1, const Point& p2, const Point& p3, float t)
  								{
  									float t2 = t * t;
  									float t3 = t2 * t;
  									float kp0 = (2.0f * t2 - t3 - t) * 0.5f;
  									float kp1 = (3.0f * t3 - 5.0f * t2 + 2.0f) * 0.5f;
  									float kp2 = (4.0f * t2 - 3.0f * t3 + t) * 0.5f;
  									float kp3 = (t3 - t2) * 0.5f;
  									x = p0.x * kp0 + p1.x * kp1 + p2.x * kp2 + p3.x * kp3;
  									y = p0.y * kp0 + p1.y * kp1 + p2.y * kp2 + p3.y * kp3;
  									z = p0.z * kp0 + p1.z * kp1 + p2.z * kp2 + p3.z * kp3;
  									return *this;
  								}
  
  		//! this = rotpos * r + linpos
  		inline_	Point&			Transform(const Point& r, const Matrix3x3& rotpos, const Point& linpos);
  
  		//! this = trans(rotpos) * (r - linpos)
  		inline_	Point&			InvTransform(const Point& r, const Matrix3x3& rotpos, const Point& linpos);
  
  		//! Returns MIN(x, y, z);
  		inline_	float			Min()				const		{ return MIN(x, MIN(y, z));												}
  		//! Returns MAX(x, y, z);
  		inline_	float			Max()				const		{ return MAX(x, MAX(y, z));												}
  		//! Sets each element to be componentwise minimum
  		inline_	Point&			Min(const Point& p)				{ x = MIN(x, p.x); y = MIN(y, p.y); z = MIN(z, p.z);	return *this;	}
  		//! Sets each element to be componentwise maximum
  		inline_	Point&			Max(const Point& p)				{ x = MAX(x, p.x); y = MAX(y, p.y); z = MAX(z, p.z);	return *this;	}
  
  		//! Clamps each element
  		inline_	Point&			Clamp(float min, float max)
  								{
  									if(x<min)	x=min;	if(x>max)	x=max;
  									if(y<min)	y=min;	if(y>max)	y=max;
  									if(z<min)	z=min;	if(z>max)	z=max;
  									return *this;
  								}
  
  		//! Computes square magnitude
  		inline_	float			SquareMagnitude()	const		{ return x*x + y*y + z*z;												}
  		//! Computes magnitude
  		inline_	float			Magnitude()			const		{ return sqrtf(x*x + y*y + z*z);										}
  		//! Computes volume
  		inline_	float			Volume()			const		{ return x * y * z;														}
  
  		//! Checks the point is near zero
  		inline_	bool			ApproxZero()		const		{ return SquareMagnitude() < EPSILON2;									}
  
  		//! Tests for exact zero vector
  		inline_	BOOL			IsZero()			const
  								{
  									if(IR(x) || IR(y) || IR(z))	return FALSE;
  									return TRUE;
  								}
  
  		//! Checks point validity
  		inline_	BOOL			IsValid()			const
  								{
  									if(!IsValidFloat(x))	return FALSE;
  									if(!IsValidFloat(y))	return FALSE;
  									if(!IsValidFloat(z))	return FALSE;
  									return TRUE;
  								}
  
  		//! Slighty moves the point
  				void			Tweak(udword coord_mask, udword tweak_mask)
  								{
  									if(coord_mask&1)	{ udword Dummy = IR(x);	Dummy^=tweak_mask;	x = FR(Dummy); }
  									if(coord_mask&2)	{ udword Dummy = IR(y);	Dummy^=tweak_mask;	y = FR(Dummy); }
  									if(coord_mask&4)	{ udword Dummy = IR(z);	Dummy^=tweak_mask;	z = FR(Dummy); }
  								}
  
  		#define TWEAKMASK		0x3fffff
  		#define TWEAKNOTMASK	~TWEAKMASK
  		//! Slighty moves the point out
  		inline_	void			TweakBigger()
  								{
  									udword	Dummy = (IR(x)&TWEAKNOTMASK);	if(!IS_NEGATIVE_FLOAT(x))	Dummy+=TWEAKMASK+1;	x = FR(Dummy);
  											Dummy = (IR(y)&TWEAKNOTMASK);	if(!IS_NEGATIVE_FLOAT(y))	Dummy+=TWEAKMASK+1;	y = FR(Dummy);
  											Dummy = (IR(z)&TWEAKNOTMASK);	if(!IS_NEGATIVE_FLOAT(z))	Dummy+=TWEAKMASK+1;	z = FR(Dummy);
  								}
  
  		//! Slighty moves the point in
  		inline_	void			TweakSmaller()
  								{
  									udword	Dummy = (IR(x)&TWEAKNOTMASK);	if(IS_NEGATIVE_FLOAT(x))	Dummy+=TWEAKMASK+1;	x = FR(Dummy);
  											Dummy = (IR(y)&TWEAKNOTMASK);	if(IS_NEGATIVE_FLOAT(y))	Dummy+=TWEAKMASK+1;	y = FR(Dummy);
  											Dummy = (IR(z)&TWEAKNOTMASK);	if(IS_NEGATIVE_FLOAT(z))	Dummy+=TWEAKMASK+1;	z = FR(Dummy);
  								}
  
  		//! Normalizes the vector
  		inline_	Point&			Normalize()
  								{
  									float M = x*x + y*y + z*z;
  									if(M)
  									{
  										M = 1.0f / sqrtf(M);
  										x *= M;
  										y *= M;
  										z *= M;
  									}
  									return *this;
  								}
  
  		//! Sets vector length
  		inline_	Point&			SetLength(float length)
  								{
  									float NewLength = length / Magnitude();
  									x *= NewLength;
  									y *= NewLength;
  									z *= NewLength;
  									return *this;
  								}
  
  		//! Clamps vector length
  		inline_	Point&			ClampLength(float limit_length)
  								{
  									if(limit_length>=0.0f)	// Magnitude must be positive
  									{
  										float CurrentSquareLength = SquareMagnitude();
  
  										if(CurrentSquareLength > limit_length * limit_length)
  										{
  											float Coeff = limit_length / sqrtf(CurrentSquareLength);
  											x *= Coeff;
  											y *= Coeff;
  											z *= Coeff;
  										}
  									}
  									return *this;
  								}
  
  		//! Computes distance to another point
  		inline_	float			Distance(const Point& b)			const
  								{
  									return sqrtf((x - b.x)*(x - b.x) + (y - b.y)*(y - b.y) + (z - b.z)*(z - b.z));
  								}
  
  		//! Computes square distance to another point
  		inline_	float			SquareDistance(const Point& b)		const
  								{
  									return ((x - b.x)*(x - b.x) + (y - b.y)*(y - b.y) + (z - b.z)*(z - b.z));
  								}
  
  		//! Dot product dp = this|a
  		inline_	float			Dot(const Point& p)					const		{	return p.x * x + p.y * y + p.z * z;				}
  
  		//! Cross product this = a x b
  		inline_	Point&			Cross(const Point& a, const Point& 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;
  								}
  
  		//! Vector code ( bitmask = sign(z) | sign(y) | sign(x) )
  		inline_	udword			VectorCode()						const
  								{
  									return (IR(x)>>31) | ((IR(y)&SIGN_BITMASK)>>30) | ((IR(z)&SIGN_BITMASK)>>29);
  								}
  
  		//! Returns largest axis
  		inline_	PointComponent	LargestAxis()						const
  								{
  									const float* Vals = &x;
  									PointComponent m = _X;
  									if(Vals[_Y] > Vals[m]) m = _Y;
  									if(Vals[_Z] > Vals[m]) m = _Z;
  									return m;
  								}
  
  		//! Returns closest axis
  		inline_	PointComponent	ClosestAxis()						const
  								{
  									const float* Vals = &x;
  									PointComponent m = _X;
  									if(AIR(Vals[_Y]) > AIR(Vals[m])) m = _Y;
  									if(AIR(Vals[_Z]) > AIR(Vals[m])) m = _Z;
  									return m;
  								}
  
  		//! Returns smallest axis
  		inline_	PointComponent	SmallestAxis()						const
  								{
  									const float* Vals = &x;
  									PointComponent m = _X;
  									if(Vals[_Y] < Vals[m]) m = _Y;
  									if(Vals[_Z] < Vals[m]) m = _Z;
  									return m;
  								}
  
  		//! Refracts the point
  				Point&			Refract(const Point& eye, const Point& n, float refractindex, Point& refracted);
  
  		//! Projects the point onto a plane
  				Point&			ProjectToPlane(const Plane& p);
  
  		//! Projects the point onto the screen
  				void			ProjectToScreen(float halfrenderwidth, float halfrenderheight, const Matrix4x4& mat, HPoint& projected) const;
  
  		//! Unfolds the point onto a plane according to edge(a,b)
  				Point&			Unfold(Plane& p, Point& a, Point& b);
  
  		//! Hash function from Ville Miettinen
  		inline_	udword			GetHashValue()						const
  								{
  									const udword* h = (const udword*)(this);
  									udword f = (h[0]+h[1]*11-(h[2]*17)) & 0x7fffffff;	// avoid problems with +-0
  									return (f>>22)^(f>>12)^(f);
  								}
  
  		//! Stuff magic values in the point, marking it as explicitely not used.
  				void			SetNotUsed();
  		//! Checks the point is marked as not used
  				BOOL			IsNotUsed()							const;
  
  		// Arithmetic operators
  
  		//! Unary operator for Point Negate = - Point
  		inline_	Point			operator-()							const		{ return Point(-x, -y, -z);							}
  
  		//! Operator for Point Plus = Point + Point.
  		inline_	Point			operator+(const Point& p)			const		{ return Point(x + p.x, y + p.y, z + p.z);			}
  		//! Operator for Point Minus = Point - Point.
  		inline_	Point			operator-(const Point& p)			const		{ return Point(x - p.x, y - p.y, z - p.z);			}
  
  		//! Operator for Point Mul   = Point * Point.
  		inline_	Point			operator*(const Point& p)			const		{ return Point(x * p.x, y * p.y, z * p.z);			}
  		//! Operator for Point Scale = Point * float.
  		inline_	Point			operator*(float s)					const		{ return Point(x * s,   y * s,   z * s );			}
  		//! Operator for Point Scale = float * Point.
  		inline_ friend	Point	operator*(float s, const Point& p)				{ return Point(s * p.x, s * p.y, s * p.z);			}
  
  		//! Operator for Point Div   = Point / Point.
  		inline_	Point			operator/(const Point& p)			const		{ return Point(x / p.x, y / p.y, z / p.z);			}
  		//! Operator for Point Scale = Point / float.
  		inline_	Point			operator/(float s)					const		{ s = 1.0f / s; return Point(x * s, y * s, z * s);	}
  		//! Operator for Point Scale = float / Point.
  		inline_	friend	Point	operator/(float s, const Point& p)				{ return Point(s / p.x, s / p.y, s / p.z);			}
  
  		//! Operator for float DotProd = Point | Point.
  		inline_	float			operator|(const Point& p)			const		{ return x*p.x + y*p.y + z*p.z;						}
  		//! Operator for Point VecProd = Point ^ Point.
  		inline_	Point			operator^(const Point& p)			const
  								{
  									return Point(
  									y * p.z - z * p.y,
  									z * p.x - x * p.z,
  									x * p.y - y * p.x );
  								}
  
  		//! Operator for Point += Point.
  		inline_	Point&			operator+=(const Point& p)						{ x += p.x; y += p.y; z += p.z;	return *this;		}
  		//! Operator for Point += float.
  		inline_	Point&			operator+=(float s)								{ x += s;   y += s;   z += s;	return *this;		}
  
  		//! Operator for Point -= Point.
  		inline_	Point&			operator-=(const Point& p)						{ x -= p.x; y -= p.y; z -= p.z;	return *this;		}
  		//! Operator for Point -= float.
  		inline_	Point&			operator-=(float s)								{ x -= s;   y -= s;   z -= s;	return *this;		}
  
  		//! Operator for Point *= Point.
  		inline_	Point&			operator*=(const Point& p)						{ x *= p.x; y *= p.y; z *= p.z;	return *this;		}
  		//! Operator for Point *= float.
  		inline_	Point&			operator*=(float s)								{ x *= s; y *= s; z *= s;		return *this;		}
  
  		//! Operator for Point /= Point.
  		inline_	Point&			operator/=(const Point& p)						{ x /= p.x; y /= p.y; z /= p.z;	return *this;		}
  		//! Operator for Point /= float.
  		inline_	Point&			operator/=(float s)								{ s = 1.0f/s; x *= s; y *= s; z *= s; return *this; }
  
  		// Logical operators
  
  		//! Operator for "if(Point==Point)"
  		inline_	bool			operator==(const Point& p)			const		{ return ( (IR(x)==IR(p.x))&&(IR(y)==IR(p.y))&&(IR(z)==IR(p.z)));	}
  		//! Operator for "if(Point!=Point)"
  		inline_	bool			operator!=(const Point& p)			const		{ return ( (IR(x)!=IR(p.x))||(IR(y)!=IR(p.y))||(IR(z)!=IR(p.z)));	}
  
  		// Arithmetic operators
  
  		//! Operator for Point Mul = Point * Matrix3x3.
  		inline_	Point			operator*(const Matrix3x3& mat)		const
  								{
  									class ShadowMatrix3x3{ public: float m[3][3]; };	// To allow inlining
  									const ShadowMatrix3x3* Mat = (const ShadowMatrix3x3*)&mat;
  
  									return Point(
  									x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0],
  									x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1],
  									x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] );
  								}
  
  		//! Operator for Point Mul = Point * Matrix4x4.
  		inline_	Point			operator*(const Matrix4x4& mat)		const
  								{
  									class ShadowMatrix4x4{ public: float m[4][4]; };	// To allow inlining
  									const ShadowMatrix4x4* Mat = (const ShadowMatrix4x4*)&mat;
  
  									return Point(
  									x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0] + Mat->m[3][0],
  									x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1] + Mat->m[3][1],
  									x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] + Mat->m[3][2]);
  								}
  
  		//! Operator for Point *= Matrix3x3.
  		inline_	Point&			operator*=(const Matrix3x3& mat)
  								{
  									class ShadowMatrix3x3{ public: float m[3][3]; };	// To allow inlining
  									const ShadowMatrix3x3* Mat = (const ShadowMatrix3x3*)&mat;
  
  									float xp = x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0];
  									float yp = x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1];
  									float zp = x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2];
  
  									x = xp;	y = yp;	z = zp;
  
  									return *this;
  								}
  
  		//! Operator for Point *= Matrix4x4.
  		inline_	Point&			operator*=(const Matrix4x4& mat)
  								{
  									class ShadowMatrix4x4{ public: float m[4][4]; };	// To allow inlining
  									const ShadowMatrix4x4* Mat = (const ShadowMatrix4x4*)&mat;
  
  									float xp = x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0] + Mat->m[3][0];
  									float yp = x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1] + Mat->m[3][1];
  									float zp = x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] + Mat->m[3][2];
  
  									x = xp;	y = yp;	z = zp;
  
  									return *this;
  								}
  
  		// Cast operators
  
  		//! Cast a Point to a HPoint. w is set to zero.
  								operator	HPoint()				const;
  
  		inline_					operator	const	float*() const	{ return &x; }
  		inline_					operator			float*()		{ return &x; }
  
  		public:
  				float			x, y, z;
  	};
  
  	FUNCTION ICEMATHS_API void Normalize1(Point& a);
  	FUNCTION ICEMATHS_API void Normalize2(Point& a);
  
  #endif //__ICEPOINT_H__
  