1 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
2 /**
3  *	Contains code for 3D vectors.
4  *	\file		IcePoint.h
5  *	\author		Pierre Terdiman
6  *	\date		April, 4, 2000
7  */
8 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
9 
10 ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
11 // Include Guard
12 #ifndef __ICEPOINT_H__
13 #define __ICEPOINT_H__
14 
15 	// Forward declarations
16 	class HPoint;
17 	class Plane;
18 	class Matrix3x3;
19 	class Matrix4x4;
20 
21 	#define CROSS2D(a, b)	(a.x*b.y - b.x*a.y)
22 
23 	const float EPSILON2 = 1.0e-20f;
24 
25 	class ICEMATHS_API Point
26 	{
27 		public:
28 
29 		//! Empty constructor
Point()30 		inline_					Point()														{}
31 		//! Constructor from a single float
32 //		inline_					Point(float val) : x(val), y(val), z(val)					{}
33 // Removed since it introduced the nasty "Point T = *Matrix4x4.GetTrans();" bug.......
34 		//! Constructor from floats
35 		template<typename toffsetfloat>
Point(toffsetfloat xx,toffsetfloat yy,toffsetfloat zz)36 		inline_					Point(toffsetfloat xx, toffsetfloat yy, toffsetfloat zz) : x((float)xx), y((float)yy), z((float)zz)	{}
37 		//! Constructor from array
Point(const float f[3])38 		inline_					Point(const float f[3]) : x(f[X]), y(f[Y]), z(f[Z])		{}
39 		//! Copy constructor
Point(const Point & p)40 		inline_					Point(const Point& p) : x(p.x), y(p.y), z(p.z)				{}
41 		//! Destructor
~Point()42 		inline_					~Point()													{}
43 
44 		//! Clears the vector
Zero()45 		inline_	Point&			Zero()									{ x =			y =			z = 0.0f;			return *this;	}
46 
47 		//! + infinity
SetPlusInfinity()48 		inline_	Point&			SetPlusInfinity()						{ x =			y =			z = MAX_FLOAT;		return *this;	}
49 		//! - infinity
SetMinusInfinity()50 		inline_	Point&			SetMinusInfinity()						{ x =			y =			z = MIN_FLOAT;		return *this;	}
51 
52 		//! Sets positive unit random vector
53 				Point&			PositiveUnitRandomVector();
54 		//! Sets unit random vector
55 				Point&			UnitRandomVector();
56 
57 		//! Assignment from values
58 		template<typename toffsetfloat>
Set(toffsetfloat xx,toffsetfloat yy,toffsetfloat zz)59 		inline_	Point&			Set(toffsetfloat xx, toffsetfloat yy, toffsetfloat zz)	{ x  = (float)xx;	y  = (float)yy;	z  = (float)zz;	return *this;	}
60 		//! Assignment from array
Set(const float f[3])61 		inline_	Point&			Set(const float f[3])					{ x  = f[X];	y  = f[Y];	z  = f[Z];			return *this;	}
62 		//! Assignment from another point
Set(const Point & src)63 		inline_	Point&			Set(const Point& src)					{ x  = src.x;	y  = src.y;	z  = src.z;			return *this;	}
64 
65 		//! Adds a vector
Add(const Point & p)66 		inline_	Point&			Add(const Point& p)						{ x += p.x;		y += p.y;	z += p.z;			return *this;	}
67 		//! Adds a vector
Add(float xx,float yy,float zz)68 		inline_	Point&			Add(float xx, float yy, float zz)		{ x += xx;		y += yy;	z += zz;			return *this;	}
69 		//! Adds a vector
Add(const float f[3])70 		inline_	Point&			Add(const float f[3])					{ x += f[X];	y += f[Y];	z += f[Z];			return *this;	}
71 		//! Adds vectors
Add(const Point & p,const Point & q)72 		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;	}
73 
74 		//! Subtracts a vector
Sub(const Point & p)75 		inline_	Point&			Sub(const Point& p)						{ x -= p.x;		y -= p.y;	z -= p.z;			return *this;	}
76 		//! Subtracts a vector
Sub(float xx,float yy,float zz)77 		inline_	Point&			Sub(float xx, float yy, float zz)		{ x -= xx;		y -= yy;	z -= zz;			return *this;	}
78 		//! Subtracts a vector
Sub(const float f[3])79 		inline_	Point&			Sub(const float f[3])					{ x -= f[X];	y -= f[Y];	z -= f[Z];			return *this;	}
80 		//! Subtracts vectors
Sub(const Point & p,const Point & q)81 		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;	}
82 
83 		//! this = -this
Neg()84 		inline_	Point&			Neg()									{ x = -x;		y = -y;			z = -z;			return *this;	}
85 		//! this = -a
Neg(const Point & a)86 		inline_	Point&			Neg(const Point& a)						{ x = -a.x;		y = -a.y;		z = -a.z;		return *this;	}
87 
88 		//! Multiplies by a scalar
Mult(float s)89 		inline_	Point&			Mult(float s)							{ x *= s;		y *= s;		z *= s;				return *this;	}
90 
91 		//! this = a * scalar
Mult(const Point & a,float scalar)92 		inline_	Point&			Mult(const Point& a, float scalar)
93 								{
94 									x = a.x * scalar;
95 									y = a.y * scalar;
96 									z = a.z * scalar;
97 									return *this;
98 								}
99 
100 		//! this = a + b * scalar
Mac(const Point & a,const Point & b,float scalar)101 		inline_	Point&			Mac(const Point& a, const Point& b, float scalar)
102 								{
103 									x = a.x + b.x * scalar;
104 									y = a.y + b.y * scalar;
105 									z = a.z + b.z * scalar;
106 									return *this;
107 								}
108 
109 		//! this = this + a * scalar
Mac(const Point & a,float scalar)110 		inline_	Point&			Mac(const Point& a, float scalar)
111 								{
112 									x += a.x * scalar;
113 									y += a.y * scalar;
114 									z += a.z * scalar;
115 									return *this;
116 								}
117 
118 		//! this = a - b * scalar
Msc(const Point & a,const Point & b,float scalar)119 		inline_	Point&			Msc(const Point& a, const Point& b, float scalar)
120 								{
121 									x = a.x - b.x * scalar;
122 									y = a.y - b.y * scalar;
123 									z = a.z - b.z * scalar;
124 									return *this;
125 								}
126 
127 		//! this = this - a * scalar
Msc(const Point & a,float scalar)128 		inline_	Point&			Msc(const Point& a, float scalar)
129 								{
130 									x -= a.x * scalar;
131 									y -= a.y * scalar;
132 									z -= a.z * scalar;
133 									return *this;
134 								}
135 
136 		//! this = a + b * scalarb + c * scalarc
Mac2(const Point & a,const Point & b,float scalarb,const Point & c,float scalarc)137 		inline_	Point&			Mac2(const Point& a, const Point& b, float scalarb, const Point& c, float scalarc)
138 								{
139 									x = a.x + b.x * scalarb + c.x * scalarc;
140 									y = a.y + b.y * scalarb + c.y * scalarc;
141 									z = a.z + b.z * scalarb + c.z * scalarc;
142 									return *this;
143 								}
144 
145 		//! this = a - b * scalarb - c * scalarc
Msc2(const Point & a,const Point & b,float scalarb,const Point & c,float scalarc)146 		inline_	Point&			Msc2(const Point& a, const Point& b, float scalarb, const Point& c, float scalarc)
147 								{
148 									x = a.x - b.x * scalarb - c.x * scalarc;
149 									y = a.y - b.y * scalarb - c.y * scalarc;
150 									z = a.z - b.z * scalarb - c.z * scalarc;
151 									return *this;
152 								}
153 
154 		//! this = mat * a
155 		inline_	Point&			Mult(const Matrix3x3& mat, const Point& a);
156 
157 		//! this = mat1 * a1 + mat2 * a2
158 		inline_	Point&			Mult2(const Matrix3x3& mat1, const Point& a1, const Matrix3x3& mat2, const Point& a2);
159 
160 		//! this = this + mat * a
161 		inline_	Point&			Mac(const Matrix3x3& mat, const Point& a);
162 
163 		//! this = transpose(mat) * a
164 		inline_	Point&			TransMult(const Matrix3x3& mat, const Point& a);
165 
166 		//! Linear interpolate between two vectors: this = a + t * (b - a)
Lerp(const Point & a,const Point & b,float t)167 		inline_	Point&			Lerp(const Point& a, const Point& b, float t)
168 								{
169 									x = a.x + t * (b.x - a.x);
170 									y = a.y + t * (b.y - a.y);
171 									z = a.z + t * (b.z - a.z);
172 									return *this;
173 								}
174 
175 		//! Hermite interpolate between p1 and p2. p0 and p3 are used for finding gradient at p1 and p2.
176 		//! this =	p0 * (2t^2 - t^3 - t)/2
177 		//!			+ p1 * (3t^3 - 5t^2 + 2)/2
178 		//!			+ p2 * (4t^2 - 3t^3 + t)/2
179 		//!			+ p3 * (t^3 - t^2)/2
Herp(const Point & p0,const Point & p1,const Point & p2,const Point & p3,float t)180 		inline_	Point&			Herp(const Point& p0, const Point& p1, const Point& p2, const Point& p3, float t)
181 								{
182 									float t2 = t * t;
183 									float t3 = t2 * t;
184 									float kp0 = (2.0f * t2 - t3 - t) * 0.5f;
185 									float kp1 = (3.0f * t3 - 5.0f * t2 + 2.0f) * 0.5f;
186 									float kp2 = (4.0f * t2 - 3.0f * t3 + t) * 0.5f;
187 									float kp3 = (t3 - t2) * 0.5f;
188 									x = p0.x * kp0 + p1.x * kp1 + p2.x * kp2 + p3.x * kp3;
189 									y = p0.y * kp0 + p1.y * kp1 + p2.y * kp2 + p3.y * kp3;
190 									z = p0.z * kp0 + p1.z * kp1 + p2.z * kp2 + p3.z * kp3;
191 									return *this;
192 								}
193 
194 		//! this = rotpos * r + linpos
195 		inline_	Point&			Transform(const Point& r, const Matrix3x3& rotpos, const Point& linpos);
196 
197 		//! this = trans(rotpos) * (r - linpos)
198 		inline_	Point&			InvTransform(const Point& r, const Matrix3x3& rotpos, const Point& linpos);
199 
200 		//! Returns MIN(x, y, z);
Min()201 		inline_	float			Min()				const		{ return MIN(x, MIN(y, z));												}
202 		//! Returns MAX(x, y, z);
Max()203 		inline_	float			Max()				const		{ return MAX(x, MAX(y, z));												}
204 		//! Sets each element to be componentwise minimum
Min(const Point & p)205 		inline_	Point&			Min(const Point& p)				{ x = MIN(x, p.x); y = MIN(y, p.y); z = MIN(z, p.z);	return *this;	}
206 		//! Sets each element to be componentwise maximum
Max(const Point & p)207 		inline_	Point&			Max(const Point& p)				{ x = MAX(x, p.x); y = MAX(y, p.y); z = MAX(z, p.z);	return *this;	}
208 
209 		//! Clamps each element
Clamp(float min,float max)210 		inline_	Point&			Clamp(float min, float max)
211 								{
212 									if(x<min)	x=min;	if(x>max)	x=max;
213 									if(y<min)	y=min;	if(y>max)	y=max;
214 									if(z<min)	z=min;	if(z>max)	z=max;
215 									return *this;
216 								}
217 
218 		//! Computes square magnitude
SquareMagnitude()219 		inline_	float			SquareMagnitude()	const		{ return x*x + y*y + z*z;												}
220 		//! Computes magnitude
Magnitude()221 		inline_	float			Magnitude()			const		{ return sqrtf(x*x + y*y + z*z);										}
222 		//! Computes volume
Volume()223 		inline_	float			Volume()			const		{ return x * y * z;														}
224 
225 		//! Checks the point is near zero
ApproxZero()226 		inline_	bool			ApproxZero()		const		{ return SquareMagnitude() < EPSILON2;									}
227 
228 		//! Tests for exact zero vector
IsZero()229 		inline_	BOOL			IsZero()			const
230 								{
231 									if(IR(x) || IR(y) || IR(z))	return FALSE;
232 									return TRUE;
233 								}
234 
235 		//! Checks point validity
IsValid()236 		inline_	BOOL			IsValid()			const
237 								{
238 									if(!IsValidFloat(x))	return FALSE;
239 									if(!IsValidFloat(y))	return FALSE;
240 									if(!IsValidFloat(z))	return FALSE;
241 									return TRUE;
242 								}
243 
244 		//! Slighty moves the point
Tweak(udword coord_mask,udword tweak_mask)245 				void			Tweak(udword coord_mask, udword tweak_mask)
246 								{
247 									if(coord_mask&1)	{ udword Dummy = IR(x);	Dummy^=tweak_mask;	x = FR(Dummy); }
248 									if(coord_mask&2)	{ udword Dummy = IR(y);	Dummy^=tweak_mask;	y = FR(Dummy); }
249 									if(coord_mask&4)	{ udword Dummy = IR(z);	Dummy^=tweak_mask;	z = FR(Dummy); }
250 								}
251 
252 		#define TWEAKMASK		0x3fffff
253 		#define TWEAKNOTMASK	~TWEAKMASK
254 		//! Slighty moves the point out
TweakBigger()255 		inline_	void			TweakBigger()
256 								{
257 									udword	Dummy = (IR(x)&TWEAKNOTMASK);	if(!IS_NEGATIVE_FLOAT(x))	Dummy+=TWEAKMASK+1;	x = FR(Dummy);
258 											Dummy = (IR(y)&TWEAKNOTMASK);	if(!IS_NEGATIVE_FLOAT(y))	Dummy+=TWEAKMASK+1;	y = FR(Dummy);
259 											Dummy = (IR(z)&TWEAKNOTMASK);	if(!IS_NEGATIVE_FLOAT(z))	Dummy+=TWEAKMASK+1;	z = FR(Dummy);
260 								}
261 
262 		//! Slighty moves the point in
TweakSmaller()263 		inline_	void			TweakSmaller()
264 								{
265 									udword	Dummy = (IR(x)&TWEAKNOTMASK);	if(IS_NEGATIVE_FLOAT(x))	Dummy+=TWEAKMASK+1;	x = FR(Dummy);
266 											Dummy = (IR(y)&TWEAKNOTMASK);	if(IS_NEGATIVE_FLOAT(y))	Dummy+=TWEAKMASK+1;	y = FR(Dummy);
267 											Dummy = (IR(z)&TWEAKNOTMASK);	if(IS_NEGATIVE_FLOAT(z))	Dummy+=TWEAKMASK+1;	z = FR(Dummy);
268 								}
269 
270 		//! Normalizes the vector
Normalize()271 		inline_	Point&			Normalize()
272 								{
273 									float M = x*x + y*y + z*z;
274 									if(M)
275 									{
276 										M = 1.0f / sqrtf(M);
277 										x *= M;
278 										y *= M;
279 										z *= M;
280 									}
281 									return *this;
282 								}
283 
284 		//! Sets vector length
SetLength(float length)285 		inline_	Point&			SetLength(float length)
286 								{
287 									float NewLength = length / Magnitude();
288 									x *= NewLength;
289 									y *= NewLength;
290 									z *= NewLength;
291 									return *this;
292 								}
293 
294 		//! Clamps vector length
ClampLength(float limit_length)295 		inline_	Point&			ClampLength(float limit_length)
296 								{
297 									if(limit_length>=0.0f)	// Magnitude must be positive
298 									{
299 										float CurrentSquareLength = SquareMagnitude();
300 
301 										if(CurrentSquareLength > limit_length * limit_length)
302 										{
303 											float Coeff = limit_length / sqrtf(CurrentSquareLength);
304 											x *= Coeff;
305 											y *= Coeff;
306 											z *= Coeff;
307 										}
308 									}
309 									return *this;
310 								}
311 
312 		//! Computes distance to another point
Distance(const Point & b)313 		inline_	float			Distance(const Point& b)			const
314 								{
315 									return sqrtf((x - b.x)*(x - b.x) + (y - b.y)*(y - b.y) + (z - b.z)*(z - b.z));
316 								}
317 
318 		//! Computes square distance to another point
SquareDistance(const Point & b)319 		inline_	float			SquareDistance(const Point& b)		const
320 								{
321 									return ((x - b.x)*(x - b.x) + (y - b.y)*(y - b.y) + (z - b.z)*(z - b.z));
322 								}
323 
324 		//! Dot product dp = this|a
Dot(const Point & p)325 		inline_	float			Dot(const Point& p)					const		{	return p.x * x + p.y * y + p.z * z;				}
326 
327 		//! Cross product this = a x b
Cross(const Point & a,const Point & b)328 		inline_	Point&			Cross(const Point& a, const Point& b)
329 								{
330 									x = a.y * b.z - a.z * b.y;
331 									y = a.z * b.x - a.x * b.z;
332 									z = a.x * b.y - a.y * b.x;
333 									return *this;
334 								}
335 
336 		//! Vector code ( bitmask = sign(z) | sign(y) | sign(x) )
VectorCode()337 		inline_	udword			VectorCode()						const
338 								{
339 									return (IR(x)>>31) | ((IR(y)&SIGN_BITMASK)>>30) | ((IR(z)&SIGN_BITMASK)>>29);
340 								}
341 
342 		//! Returns largest axis
LargestAxis()343 		inline_	PointComponent	LargestAxis()						const
344 								{
345 									const float* Vals = &x;
346 									PointComponent m = X;
347 									if(Vals[Y] > Vals[m]) m = Y;
348 									if(Vals[Z] > Vals[m]) m = Z;
349 									return m;
350 								}
351 
352 		//! Returns closest axis
ClosestAxis()353 		inline_	PointComponent	ClosestAxis()						const
354 								{
355 									const float* Vals = &x;
356 									PointComponent m = X;
357 									if(AIR(Vals[Y]) > AIR(Vals[m])) m = Y;
358 									if(AIR(Vals[Z]) > AIR(Vals[m])) m = Z;
359 									return m;
360 								}
361 
362 		//! Returns smallest axis
SmallestAxis()363 		inline_	PointComponent	SmallestAxis()						const
364 								{
365 									const float* Vals = &x;
366 									PointComponent m = X;
367 									if(Vals[Y] < Vals[m]) m = Y;
368 									if(Vals[Z] < Vals[m]) m = Z;
369 									return m;
370 								}
371 
372 		//! Refracts the point
373 				Point&			Refract(const Point& eye, const Point& n, float refractindex, Point& refracted);
374 
375 		//! Projects the point onto a plane
376 				Point&			ProjectToPlane(const Plane& p);
377 
378 		//! Projects the point onto the screen
379 				void			ProjectToScreen(float halfrenderwidth, float halfrenderheight, const Matrix4x4& mat, HPoint& projected) const;
380 
381 		//! Unfolds the point onto a plane according to edge(a,b)
382 				Point&			Unfold(Plane& p, Point& a, Point& b);
383 
384 		//! Hash function from Ville Miettinen
GetHashValue()385 		inline_	udword			GetHashValue()						const
386 								{
387 									const udword* h = (const udword*)(this);
388 									udword f = (h[0]+h[1]*11-(h[2]*17)) & 0x7fffffff;	// avoid problems with +-0
389 									return (f>>22)^(f>>12)^(f);
390 								}
391 
392 		//! Stuff magic values in the point, marking it as explicitely not used.
393 				void			SetNotUsed();
394 		//! Checks the point is marked as not used
395 				BOOL			IsNotUsed()							const;
396 
397 		// Arithmetic operators
398 
399 		//! Unary operator for Point Negate = - Point
400 		inline_	Point			operator-()							const		{ return Point(-x, -y, -z);							}
401 
402 		//! Operator for Point Plus = Point + Point.
403 		inline_	Point			operator+(const Point& p)			const		{ return Point(x + p.x, y + p.y, z + p.z);			}
404 		//! Operator for Point Minus = Point - Point.
405 		inline_	Point			operator-(const Point& p)			const		{ return Point(x - p.x, y - p.y, z - p.z);			}
406 
407 		//! Operator for Point Mul   = Point * Point.
408 		inline_	Point			operator*(const Point& p)			const		{ return Point(x * p.x, y * p.y, z * p.z);			}
409 		//! Operator for Point Scale = Point * float.
410 		inline_	Point			operator*(float s)					const		{ return Point(x * s,   y * s,   z * s );			}
411 		//! Operator for Point Scale = float * Point.
412 		inline_ friend	Point	operator*(float s, const Point& p)				{ return Point(s * p.x, s * p.y, s * p.z);			}
413 
414 		//! Operator for Point Div   = Point / Point.
415 		inline_	Point			operator/(const Point& p)			const		{ return Point(x / p.x, y / p.y, z / p.z);			}
416 		//! Operator for Point Scale = Point / float.
417 		inline_	Point			operator/(float s)					const		{ s = 1.0f / s; return Point(x * s, y * s, z * s);	}
418 		//! Operator for Point Scale = float / Point.
419 		inline_	friend	Point	operator/(float s, const Point& p)				{ return Point(s / p.x, s / p.y, s / p.z);			}
420 
421 		//! Operator for float DotProd = Point | Point.
422 		inline_	float			operator|(const Point& p)			const		{ return x*p.x + y*p.y + z*p.z;						}
423 		//! Operator for Point VecProd = Point ^ Point.
424 		inline_	Point			operator^(const Point& p)			const
425 								{
426 									return Point(
427 									y * p.z - z * p.y,
428 									z * p.x - x * p.z,
429 									x * p.y - y * p.x );
430 								}
431 
432 		//! Operator for Point += Point.
433 		inline_	Point&			operator+=(const Point& p)						{ x += p.x; y += p.y; z += p.z;	return *this;		}
434 		//! Operator for Point += float.
435 		inline_	Point&			operator+=(float s)								{ x += s;   y += s;   z += s;	return *this;		}
436 
437 		//! Operator for Point -= Point.
438 		inline_	Point&			operator-=(const Point& p)						{ x -= p.x; y -= p.y; z -= p.z;	return *this;		}
439 		//! Operator for Point -= float.
440 		inline_	Point&			operator-=(float s)								{ x -= s;   y -= s;   z -= s;	return *this;		}
441 
442 		//! Operator for Point *= Point.
443 		inline_	Point&			operator*=(const Point& p)						{ x *= p.x; y *= p.y; z *= p.z;	return *this;		}
444 		//! Operator for Point *= float.
445 		inline_	Point&			operator*=(float s)								{ x *= s; y *= s; z *= s;		return *this;		}
446 
447 		//! Operator for Point /= Point.
448 		inline_	Point&			operator/=(const Point& p)						{ x /= p.x; y /= p.y; z /= p.z;	return *this;		}
449 		//! Operator for Point /= float.
450 		inline_	Point&			operator/=(float s)								{ s = 1.0f/s; x *= s; y *= s; z *= s; return *this; }
451 
452 		// Logical operators
453 
454 		//! Operator for "if(Point==Point)"
455 		inline_	bool			operator==(const Point& p)			const		{ return ( (IR(x)==IR(p.x))&&(IR(y)==IR(p.y))&&(IR(z)==IR(p.z)));	}
456 		//! Operator for "if(Point!=Point)"
457 		inline_	bool			operator!=(const Point& p)			const		{ return ( (IR(x)!=IR(p.x))||(IR(y)!=IR(p.y))||(IR(z)!=IR(p.z)));	}
458 
459 		// Arithmetic operators
460 
461 		//! Operator for Point Mul = Point * Matrix3x3.
462 		inline_	Point			operator*(const Matrix3x3& mat)		const
463 								{
464 									class ShadowMatrix3x3{ public: float m[3][3]; };	// To allow inlining
465 									const ShadowMatrix3x3* Mat = (const ShadowMatrix3x3*)&mat;
466 
467 									return Point(
468 									x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0],
469 									x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1],
470 									x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] );
471 								}
472 
473 		//! Operator for Point Mul = Point * Matrix4x4.
474 		inline_	Point			operator*(const Matrix4x4& mat)		const
475 								{
476 									class ShadowMatrix4x4{ public: float m[4][4]; };	// To allow inlining
477 									const ShadowMatrix4x4* Mat = (const ShadowMatrix4x4*)&mat;
478 
479 									return Point(
480 									x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0] + Mat->m[3][0],
481 									x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1] + Mat->m[3][1],
482 									x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] + Mat->m[3][2]);
483 								}
484 
485 		//! Operator for Point *= Matrix3x3.
486 		inline_	Point&			operator*=(const Matrix3x3& mat)
487 								{
488 									class ShadowMatrix3x3{ public: float m[3][3]; };	// To allow inlining
489 									const ShadowMatrix3x3* Mat = (const ShadowMatrix3x3*)&mat;
490 
491 									float xp = x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0];
492 									float yp = x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1];
493 									float zp = x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2];
494 
495 									x = xp;	y = yp;	z = zp;
496 
497 									return *this;
498 								}
499 
500 		//! Operator for Point *= Matrix4x4.
501 		inline_	Point&			operator*=(const Matrix4x4& mat)
502 								{
503 									class ShadowMatrix4x4{ public: float m[4][4]; };	// To allow inlining
504 									const ShadowMatrix4x4* Mat = (const ShadowMatrix4x4*)&mat;
505 
506 									float xp = x * Mat->m[0][0] + y * Mat->m[1][0] + z * Mat->m[2][0] + Mat->m[3][0];
507 									float yp = x * Mat->m[0][1] + y * Mat->m[1][1] + z * Mat->m[2][1] + Mat->m[3][1];
508 									float zp = x * Mat->m[0][2] + y * Mat->m[1][2] + z * Mat->m[2][2] + Mat->m[3][2];
509 
510 									x = xp;	y = yp;	z = zp;
511 
512 									return *this;
513 								}
514 
515 		// Cast operators
516 
517 		//! Cast a Point to a HPoint. w is set to zero.
518 								operator	HPoint()				const;
519 
520 		inline_					operator	const	float*() const	{ return &x; }
521 		inline_					operator			float*()		{ return &x; }
522 
523 		public:
524 				float			x, y, z;
525 	};
526 
527 	FUNCTION ICEMATHS_API void Normalize1(Point& a);
528 	FUNCTION ICEMATHS_API void Normalize2(Point& a);
529 
530 #endif //__ICEPOINT_H__
531