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OgreVector3.h @ 7187

Last change on this file since 7187 was 5789, checked in by rgrieder, 15 years ago
Stripped sandbox further down to get a light version that excludes almost all core features. Also, the Ogre dependency has been removed and a little ogremath library been added.
Property svn:eol-style set to `native`
File size: 24.7 KB

Line
1	/*
2	-----------------------------------------------------------------------------
3	This source file is part of OGRE
4	(Object-oriented Graphics Rendering Engine)
5	For the latest info, see http://www.ogre3d.org/
6
7	Copyright (c) 2000-2006 Torus Knot Software Ltd
8	Also see acknowledgements in Readme.html
9
10	This program is free software; you can redistribute it and/or modify it under
11	the terms of the GNU Lesser General Public License as published by the Free Software
12	Foundation; either version 2 of the License, or (at your option) any later
13	version.
14
15	This program is distributed in the hope that it will be useful, but WITHOUT
16	ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17	FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
18
19	You should have received a copy of the GNU Lesser General Public License along with
20	this program; if not, write to the Free Software Foundation, Inc., 59 Temple
21	Place - Suite 330, Boston, MA 02111-1307, USA, or go to
22	http://www.gnu.org/copyleft/lesser.txt.
23
24	You may alternatively use this source under the terms of a specific version of
25	the OGRE Unrestricted License provided you have obtained such a license from
26	Torus Knot Software Ltd.
27	-----------------------------------------------------------------------------
28	*/
29	#ifndef __Vector3_H__
30	#define __Vector3_H__
31
32	#include "OgrePrerequisites.h"
33	#include "OgreMath.h"
34	#include "OgreQuaternion.h"
35	#include <ostream>
36
37	namespace Ogre
38	{
39
40	/** Standard 3-dimensional vector.
41	@remarks
42	A direction in 3D space represented as distances along the 3
43	orthogonal axes (x, y, z). Note that positions, directions and
44	scaling factors can be represented by a vector, depending on how
45	you interpret the values.
46	*/
47	class _OgreExport Vector3
48	{
49	public:
50	Real x, y, z;
51
52	public:
53	inline Vector3()
54	{
55	}
56
57	inline Vector3( const Real fX, const Real fY, const Real fZ )
58	: x( fX ), y( fY ), z( fZ )
59	{
60	}
61
62	inline explicit Vector3( const Real afCoordinate[3] )
63	: x( afCoordinate[0] ),
64	y( afCoordinate[1] ),
65	z( afCoordinate[2] )
66	{
67	}
68
69	inline explicit Vector3( const int afCoordinate[3] )
70	{
71	x = (Real)afCoordinate[0];
72	y = (Real)afCoordinate[1];
73	z = (Real)afCoordinate[2];
74	}
75
76	inline explicit Vector3( Real* const r )
77	: x( r[0] ), y( r[1] ), z( r[2] )
78	{
79	}
80
81	inline explicit Vector3( const Real scaler )
82	: x( scaler )
83	, y( scaler )
84	, z( scaler )
85	{
86	}
87
88
89	inline Real operator [] ( const size_t i ) const
90	{
91	assert( i < 3 );
92
93	return *(&x+i);
94	}
95
96	inline Real& operator [] ( const size_t i )
97	{
98	assert( i < 3 );
99
100	return *(&x+i);
101	}
102	/// Pointer accessor for direct copying
103	inline Real* ptr()
104	{
105	return &x;
106	}
107	/// Pointer accessor for direct copying
108	inline const Real* ptr() const
109	{
110	return &x;
111	}
112
113	/** Assigns the value of the other vector.
114	@param
115	rkVector The other vector
116	*/
117	inline Vector3& operator = ( const Vector3& rkVector )
118	{
119	x = rkVector.x;
120	y = rkVector.y;
121	z = rkVector.z;
122
123	return *this;
124	}
125
126	inline Vector3& operator = ( const Real fScaler )
127	{
128	x = fScaler;
129	y = fScaler;
130	z = fScaler;
131
132	return *this;
133	}
134
135	inline bool operator == ( const Vector3& rkVector ) const
136	{
137	return ( x == rkVector.x && y == rkVector.y && z == rkVector.z );
138	}
139
140	inline bool operator != ( const Vector3& rkVector ) const
141	{
142	return ( x != rkVector.x \|\| y != rkVector.y \|\| z != rkVector.z );
143	}
144
145	// arithmetic operations
146	inline Vector3 operator + ( const Vector3& rkVector ) const
147	{
148	return Vector3(
149	x + rkVector.x,
150	y + rkVector.y,
151	z + rkVector.z);
152	}
153
154	inline Vector3 operator - ( const Vector3& rkVector ) const
155	{
156	return Vector3(
157	x - rkVector.x,
158	y - rkVector.y,
159	z - rkVector.z);
160	}
161
162	inline Vector3 operator * ( const Real fScalar ) const
163	{
164	return Vector3(
165	x * fScalar,
166	y * fScalar,
167	z * fScalar);
168	}
169
170	inline Vector3 operator * ( const Vector3& rhs) const
171	{
172	return Vector3(
173	x * rhs.x,
174	y * rhs.y,
175	z * rhs.z);
176	}
177
178	inline Vector3 operator / ( const Real fScalar ) const
179	{
180	assert( fScalar != 0.0 );
181
182	Real fInv = 1.0 / fScalar;
183
184	return Vector3(
185	x * fInv,
186	y * fInv,
187	z * fInv);
188	}
189
190	inline Vector3 operator / ( const Vector3& rhs) const
191	{
192	return Vector3(
193	x / rhs.x,
194	y / rhs.y,
195	z / rhs.z);
196	}
197
198	inline const Vector3& operator + () const
199	{
200	return *this;
201	}
202
203	inline Vector3 operator - () const
204	{
205	return Vector3(-x, -y, -z);
206	}
207
208	// overloaded operators to help Vector3
209	inline friend Vector3 operator * ( const Real fScalar, const Vector3& rkVector )
210	{
211	return Vector3(
212	fScalar * rkVector.x,
213	fScalar * rkVector.y,
214	fScalar * rkVector.z);
215	}
216
217	inline friend Vector3 operator / ( const Real fScalar, const Vector3& rkVector )
218	{
219	return Vector3(
220	fScalar / rkVector.x,
221	fScalar / rkVector.y,
222	fScalar / rkVector.z);
223	}
224
225	inline friend Vector3 operator + (const Vector3& lhs, const Real rhs)
226	{
227	return Vector3(
228	lhs.x + rhs,
229	lhs.y + rhs,
230	lhs.z + rhs);
231	}
232
233	inline friend Vector3 operator + (const Real lhs, const Vector3& rhs)
234	{
235	return Vector3(
236	lhs + rhs.x,
237	lhs + rhs.y,
238	lhs + rhs.z);
239	}
240
241	inline friend Vector3 operator - (const Vector3& lhs, const Real rhs)
242	{
243	return Vector3(
244	lhs.x - rhs,
245	lhs.y - rhs,
246	lhs.z - rhs);
247	}
248
249	inline friend Vector3 operator - (const Real lhs, const Vector3& rhs)
250	{
251	return Vector3(
252	lhs - rhs.x,
253	lhs - rhs.y,
254	lhs - rhs.z);
255	}
256
257	// arithmetic updates
258	inline Vector3& operator += ( const Vector3& rkVector )
259	{
260	x += rkVector.x;
261	y += rkVector.y;
262	z += rkVector.z;
263
264	return *this;
265	}
266
267	inline Vector3& operator += ( const Real fScalar )
268	{
269	x += fScalar;
270	y += fScalar;
271	z += fScalar;
272	return *this;
273	}
274
275	inline Vector3& operator -= ( const Vector3& rkVector )
276	{
277	x -= rkVector.x;
278	y -= rkVector.y;
279	z -= rkVector.z;
280
281	return *this;
282	}
283
284	inline Vector3& operator -= ( const Real fScalar )
285	{
286	x -= fScalar;
287	y -= fScalar;
288	z -= fScalar;
289	return *this;
290	}
291
292	inline Vector3& operator *= ( const Real fScalar )
293	{
294	x *= fScalar;
295	y *= fScalar;
296	z *= fScalar;
297	return *this;
298	}
299
300	inline Vector3& operator *= ( const Vector3& rkVector )
301	{
302	x *= rkVector.x;
303	y *= rkVector.y;
304	z *= rkVector.z;
305
306	return *this;
307	}
308
309	inline Vector3& operator /= ( const Real fScalar )
310	{
311	assert( fScalar != 0.0 );
312
313	Real fInv = 1.0 / fScalar;
314
315	x *= fInv;
316	y *= fInv;
317	z *= fInv;
318
319	return *this;
320	}
321
322	inline Vector3& operator /= ( const Vector3& rkVector )
323	{
324	x /= rkVector.x;
325	y /= rkVector.y;
326	z /= rkVector.z;
327
328	return *this;
329	}
330
331
332	/** Returns the length (magnitude) of the vector.
333	@warning
334	This operation requires a square root and is expensive in
335	terms of CPU operations. If you don't need to know the exact
336	length (e.g. for just comparing lengths) use squaredLength()
337	instead.
338	*/
339	inline Real length () const
340	{
341	return Math::Sqrt( x * x + y * y + z * z );
342	}
343
344	/** Returns the square of the length(magnitude) of the vector.
345	@remarks
346	This method is for efficiency - calculating the actual
347	length of a vector requires a square root, which is expensive
348	in terms of the operations required. This method returns the
349	square of the length of the vector, i.e. the same as the
350	length but before the square root is taken. Use this if you
351	want to find the longest / shortest vector without incurring
352	the square root.
353	*/
354	inline Real squaredLength () const
355	{
356	return x * x + y * y + z * z;
357	}
358
359	/** Returns the distance to another vector.
360	@warning
361	This operation requires a square root and is expensive in
362	terms of CPU operations. If you don't need to know the exact
363	distance (e.g. for just comparing distances) use squaredDistance()
364	instead.
365	*/
366	inline Real distance(const Vector3& rhs) const
367	{
368	return (*this - rhs).length();
369	}
370
371	/** Returns the square of the distance to another vector.
372	@remarks
373	This method is for efficiency - calculating the actual
374	distance to another vector requires a square root, which is
375	expensive in terms of the operations required. This method
376	returns the square of the distance to another vector, i.e.
377	the same as the distance but before the square root is taken.
378	Use this if you want to find the longest / shortest distance
379	without incurring the square root.
380	*/
381	inline Real squaredDistance(const Vector3& rhs) const
382	{
383	return (*this - rhs).squaredLength();
384	}
385
386	/** Calculates the dot (scalar) product of this vector with another.
387	@remarks
388	The dot product can be used to calculate the angle between 2
389	vectors. If both are unit vectors, the dot product is the
390	cosine of the angle; otherwise the dot product must be
391	divided by the product of the lengths of both vectors to get
392	the cosine of the angle. This result can further be used to
393	calculate the distance of a point from a plane.
394	@param
395	vec Vector with which to calculate the dot product (together
396	with this one).
397	@returns
398	A float representing the dot product value.
399	*/
400	inline Real dotProduct(const Vector3& vec) const
401	{
402	return x * vec.x + y * vec.y + z * vec.z;
403	}
404
405	/** Calculates the absolute dot (scalar) product of this vector with another.
406	@remarks
407	This function work similar dotProduct, except it use absolute value
408	of each component of the vector to computing.
409	@param
410	vec Vector with which to calculate the absolute dot product (together
411	with this one).
412	@returns
413	A Real representing the absolute dot product value.
414	*/
415	inline Real absDotProduct(const Vector3& vec) const
416	{
417	return Math::Abs(x * vec.x) + Math::Abs(y * vec.y) + Math::Abs(z * vec.z);
418	}
419
420	/** Normalises the vector.
421	@remarks
422	This method normalises the vector such that it's
423	length / magnitude is 1. The result is called a unit vector.
424	@note
425	This function will not crash for zero-sized vectors, but there
426	will be no changes made to their components.
427	@returns The previous length of the vector.
428	*/
429	inline Real normalise()
430	{
431	Real fLength = Math::Sqrt( x * x + y * y + z * z );
432
433	// Will also work for zero-sized vectors, but will change nothing
434	if ( fLength > 1e-08 )
435	{
436	Real fInvLength = 1.0 / fLength;
437	x *= fInvLength;
438	y *= fInvLength;
439	z *= fInvLength;
440	}
441
442	return fLength;
443	}
444
445	/** Calculates the cross-product of 2 vectors, i.e. the vector that
446	lies perpendicular to them both.
447	@remarks
448	The cross-product is normally used to calculate the normal
449	vector of a plane, by calculating the cross-product of 2
450	non-equivalent vectors which lie on the plane (e.g. 2 edges
451	of a triangle).
452	@param
453	vec Vector which, together with this one, will be used to
454	calculate the cross-product.
455	@returns
456	A vector which is the result of the cross-product. This
457	vector will <b>NOT</b> be normalised, to maximise efficiency
458	- call Vector3::normalise on the result if you wish this to
459	be done. As for which side the resultant vector will be on, the
460	returned vector will be on the side from which the arc from 'this'
461	to rkVector is anticlockwise, e.g. UNIT_Y.crossProduct(UNIT_Z)
462	= UNIT_X, whilst UNIT_Z.crossProduct(UNIT_Y) = -UNIT_X.
463	This is because OGRE uses a right-handed coordinate system.
464	@par
465	For a clearer explanation, look a the left and the bottom edges
466	of your monitor's screen. Assume that the first vector is the
467	left edge and the second vector is the bottom edge, both of
468	them starting from the lower-left corner of the screen. The
469	resulting vector is going to be perpendicular to both of them
470	and will go <i>inside</i> the screen, towards the cathode tube
471	(assuming you're using a CRT monitor, of course).
472	*/
473	inline Vector3 crossProduct( const Vector3& rkVector ) const
474	{
475	return Vector3(
476	y * rkVector.z - z * rkVector.y,
477	z * rkVector.x - x * rkVector.z,
478	x * rkVector.y - y * rkVector.x);
479	}
480
481	/** Returns a vector at a point half way between this and the passed
482	in vector.
483	*/
484	inline Vector3 midPoint( const Vector3& vec ) const
485	{
486	return Vector3(
487	( x + vec.x ) * 0.5,
488	( y + vec.y ) * 0.5,
489	( z + vec.z ) * 0.5 );
490	}
491
492	/** Returns true if the vector's scalar components are all greater
493	that the ones of the vector it is compared against.
494	*/
495	inline bool operator < ( const Vector3& rhs ) const
496	{
497	if( x < rhs.x && y < rhs.y && z < rhs.z )
498	return true;
499	return false;
500	}
501
502	/** Returns true if the vector's scalar components are all smaller
503	that the ones of the vector it is compared against.
504	*/
505	inline bool operator > ( const Vector3& rhs ) const
506	{
507	if( x > rhs.x && y > rhs.y && z > rhs.z )
508	return true;
509	return false;
510	}
511
512	/** Sets this vector's components to the minimum of its own and the
513	ones of the passed in vector.
514	@remarks
515	'Minimum' in this case means the combination of the lowest
516	value of x, y and z from both vectors. Lowest is taken just
517	numerically, not magnitude, so -1 < 0.
518	*/
519	inline void makeFloor( const Vector3& cmp )
520	{
521	if( cmp.x < x ) x = cmp.x;
522	if( cmp.y < y ) y = cmp.y;
523	if( cmp.z < z ) z = cmp.z;
524	}
525
526	/** Sets this vector's components to the maximum of its own and the
527	ones of the passed in vector.
528	@remarks
529	'Maximum' in this case means the combination of the highest
530	value of x, y and z from both vectors. Highest is taken just
531	numerically, not magnitude, so 1 > -3.
532	*/
533	inline void makeCeil( const Vector3& cmp )
534	{
535	if( cmp.x > x ) x = cmp.x;
536	if( cmp.y > y ) y = cmp.y;
537	if( cmp.z > z ) z = cmp.z;
538	}
539
540	/** Generates a vector perpendicular to this vector (eg an 'up' vector).
541	@remarks
542	This method will return a vector which is perpendicular to this
543	vector. There are an infinite number of possibilities but this
544	method will guarantee to generate one of them. If you need more
545	control you should use the Quaternion class.
546	*/
547	inline Vector3 perpendicular(void) const
548	{
549	static const Real fSquareZero = 1e-06 * 1e-06;
550
551	Vector3 perp = this->crossProduct( Vector3::UNIT_X );
552
553	// Check length
554	if( perp.squaredLength() < fSquareZero )
555	{
556	/* This vector is the Y axis multiplied by a scalar, so we have
557	to use another axis.
558	*/
559	perp = this->crossProduct( Vector3::UNIT_Y );
560	}
561	perp.normalise();
562
563	return perp;
564	}
565	/** Generates a new random vector which deviates from this vector by a
566	given angle in a random direction.
567	@remarks
568	This method assumes that the random number generator has already
569	been seeded appropriately.
570	@param
571	angle The angle at which to deviate
572	@param
573	up Any vector perpendicular to this one (which could generated
574	by cross-product of this vector and any other non-colinear
575	vector). If you choose not to provide this the function will
576	derive one on it's own, however if you provide one yourself the
577	function will be faster (this allows you to reuse up vectors if
578	you call this method more than once)
579	@returns
580	A random vector which deviates from this vector by angle. This
581	vector will not be normalised, normalise it if you wish
582	afterwards.
583	*/
584	inline Vector3 randomDeviant(
585	const Radian& angle,
586	const Vector3& up = Vector3::ZERO ) const
587	{
588	Vector3 newUp;
589
590	if (up == Vector3::ZERO)
591	{
592	// Generate an up vector
593	newUp = this->perpendicular();
594	}
595	else
596	{
597	newUp = up;
598	}
599
600	// Rotate up vector by random amount around this
601	Quaternion q;
602	q.FromAngleAxis( Radian(Math::UnitRandom() * Math::TWO_PI), *this );
603	newUp = q * newUp;
604
605	// Finally rotate this by given angle around randomised up
606	q.FromAngleAxis( angle, newUp );
607	return q * (*this);
608	}
609
610	/** Gets the angle between 2 vectors.
611	@remarks
612	Vectors do not have to be unit-length but must represent directions.
613	*/
614	inline Radian angleBetween(const Vector3& dest)
615	{
616	Real lenProduct = length() * dest.length();
617
618	// Divide by zero check
619	if(lenProduct < 1e-6f)
620	lenProduct = 1e-6f;
621
622	Real f = dotProduct(dest) / lenProduct;
623
624	f = Math::Clamp(f, (Real)-1.0, (Real)1.0);
625	return Math::ACos(f);
626
627	}
628	/** Gets the shortest arc quaternion to rotate this vector to the destination
629	vector.
630	@remarks
631	If you call this with a dest vector that is close to the inverse
632	of this vector, we will rotate 180 degrees around the 'fallbackAxis'
633	(if specified, or a generated axis if not) since in this case
634	ANY axis of rotation is valid.
635	*/
636	Quaternion getRotationTo(const Vector3& dest,
637	const Vector3& fallbackAxis = Vector3::ZERO) const
638	{
639	// Based on Stan Melax's article in Game Programming Gems
640	Quaternion q;
641	// Copy, since cannot modify local
642	Vector3 v0 = *this;
643	Vector3 v1 = dest;
644	v0.normalise();
645	v1.normalise();
646
647	Real d = v0.dotProduct(v1);
648	// If dot == 1, vectors are the same
649	if (d >= 1.0f)
650	{
651	return Quaternion::IDENTITY;
652	}
653	if (d < (1e-6f - 1.0f))
654	{
655	if (fallbackAxis != Vector3::ZERO)
656	{
657	// rotate 180 degrees about the fallback axis
658	q.FromAngleAxis(Radian(Math::PI), fallbackAxis);
659	}
660	else
661	{
662	// Generate an axis
663	Vector3 axis = Vector3::UNIT_X.crossProduct(*this);
664	if (axis.isZeroLength()) // pick another if colinear
665	axis = Vector3::UNIT_Y.crossProduct(*this);
666	axis.normalise();
667	q.FromAngleAxis(Radian(Math::PI), axis);
668	}
669	}
670	else
671	{
672	Real s = Math::Sqrt( (1+d)*2 );
673	Real invs = 1 / s;
674
675	Vector3 c = v0.crossProduct(v1);
676
677	q.x = c.x * invs;
678	q.y = c.y * invs;
679	q.z = c.z * invs;
680	q.w = s * 0.5;
681	q.normalise();
682	}
683	return q;
684	}
685
686	/** Returns true if this vector is zero length. */
687	inline bool isZeroLength(void) const
688	{
689	Real sqlen = (x * x) + (y * y) + (z * z);
690	return (sqlen < (1e-06 * 1e-06));
691
692	}
693
694	/** As normalise, except that this vector is unaffected and the
695	normalised vector is returned as a copy. */
696	inline Vector3 normalisedCopy(void) const
697	{
698	Vector3 ret = *this;
699	ret.normalise();
700	return ret;
701	}
702
703	/** Calculates a reflection vector to the plane with the given normal .
704	@remarks NB assumes 'this' is pointing AWAY FROM the plane, invert if it is not.
705	*/
706	inline Vector3 reflect(const Vector3& normal) const
707	{
708	return Vector3( this - ( 2 this->dotProduct(normal) * normal ) );
709	}
710
711	/** Returns whether this vector is within a positional tolerance
712	of another vector.
713	@param rhs The vector to compare with
714	@param tolerance The amount that each element of the vector may vary by
715	and still be considered equal
716	*/
717	inline bool positionEquals(const Vector3& rhs, Real tolerance = 1e-03) const
718	{
719	return Math::RealEqual(x, rhs.x, tolerance) &&
720	Math::RealEqual(y, rhs.y, tolerance) &&
721	Math::RealEqual(z, rhs.z, tolerance);
722
723	}
724
725	/** Returns whether this vector is within a positional tolerance
726	of another vector, also take scale of the vectors into account.
727	@param rhs The vector to compare with
728	@param tolerance The amount (related to the scale of vectors) that distance
729	of the vector may vary by and still be considered close
730	*/
731	inline bool positionCloses(const Vector3& rhs, Real tolerance = 1e-03f) const
732	{
733	return squaredDistance(rhs) <=
734	(squaredLength() + rhs.squaredLength()) * tolerance;
735	}
736
737	/** Returns whether this vector is within a directional tolerance
738	of another vector.
739	@param rhs The vector to compare with
740	@param tolerance The maximum angle by which the vectors may vary and
741	still be considered equal
742	@note Both vectors should be normalised.
743	*/
744	inline bool directionEquals(const Vector3& rhs,
745	const Radian& tolerance) const
746	{
747	Real dot = dotProduct(rhs);
748	Radian angle = Math::ACos(dot);
749
750	return Math::Abs(angle.valueRadians()) <= tolerance.valueRadians();
751
752	}
753
754	// special points
755	static const Vector3 ZERO;
756	static const Vector3 UNIT_X;
757	static const Vector3 UNIT_Y;
758	static const Vector3 UNIT_Z;
759	static const Vector3 NEGATIVE_UNIT_X;
760	static const Vector3 NEGATIVE_UNIT_Y;
761	static const Vector3 NEGATIVE_UNIT_Z;
762	static const Vector3 UNIT_SCALE;
763
764	/** Function for writing to a stream.
765	*/
766	inline _OgreExport friend std::ostream& operator <<
767	( std::ostream& o, const Vector3& v )
768	{
769	o << "Vector3(" << v.x << ", " << v.y << ", " << v.z << ")";
770	return o;
771	}
772	};
773
774	}
775	#endif

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source: sandbox_light/src/external/ogremath/OgreVector3.h @ 7187

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