icepoint.h

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///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/**
 *	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 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);