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OgreMath.h @ 7908

Last change on this file since 7908 was 7908, checked in by rgrieder, 13 years ago
Stripped down trunk to form a new light sandbox.
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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 __Math_H__
30	#define __Math_H__
31
32	#include "OgrePrerequisites.h"
33
34	#include <cassert>
35	#include <cmath>
36	#include <vector>
37	#include <utility>
38	#include <list>
39	#include <limits>
40
41	namespace Ogre
42	{
43	/** Wrapper class which indicates a given angle value is in Radians.
44	@remarks
45	Radian values are interchangeable with Degree values, and conversions
46	will be done automatically between them.
47	*/
48	class Radian
49	{
50	Real mRad;
51
52	public:
53	explicit Radian ( Real r=0 ) : mRad(r) {}
54	Radian ( const Degree& d );
55	Radian& operator = ( const Real& f ) { mRad = f; return *this; }
56	Radian& operator = ( const Radian& r ) { mRad = r.mRad; return *this; }
57	Radian& operator = ( const Degree& d );
58
59	Real valueDegrees() const; // see bottom of this file
60	Real valueRadians() const { return mRad; }
61	Real valueAngleUnits() const;
62
63	const Radian& operator + () const { return *this; }
64	Radian operator + ( const Radian& r ) const { return Radian ( mRad + r.mRad ); }
65	Radian operator + ( const Degree& d ) const;
66	Radian& operator += ( const Radian& r ) { mRad += r.mRad; return *this; }
67	Radian& operator += ( const Degree& d );
68	Radian operator - () const { return Radian(-mRad); }
69	Radian operator - ( const Radian& r ) const { return Radian ( mRad - r.mRad ); }
70	Radian operator - ( const Degree& d ) const;
71	Radian& operator -= ( const Radian& r ) { mRad -= r.mRad; return *this; }
72	Radian& operator -= ( const Degree& d );
73	Radian operator * ( Real f ) const { return Radian ( mRad * f ); }
74	Radian operator * ( const Radian& f ) const { return Radian ( mRad * f.mRad ); }
75	Radian& operator = ( Real f ) { mRad = f; return *this; }
76	Radian operator / ( Real f ) const { return Radian ( mRad / f ); }
77	Radian& operator /= ( Real f ) { mRad /= f; return *this; }
78
79	bool operator < ( const Radian& r ) const { return mRad < r.mRad; }
80	bool operator <= ( const Radian& r ) const { return mRad <= r.mRad; }
81	bool operator == ( const Radian& r ) const { return mRad == r.mRad; }
82	bool operator != ( const Radian& r ) const { return mRad != r.mRad; }
83	bool operator >= ( const Radian& r ) const { return mRad >= r.mRad; }
84	bool operator > ( const Radian& r ) const { return mRad > r.mRad; }
85	};
86
87	/** Wrapper class which indicates a given angle value is in Degrees.
88	@remarks
89	Degree values are interchangeable with Radian values, and conversions
90	will be done automatically between them.
91	*/
92	class Degree
93	{
94	Real mDeg; // if you get an error here - make sure to define/typedef 'Real' first
95
96	public:
97	explicit Degree ( Real d=0 ) : mDeg(d) {}
98	Degree ( const Radian& r ) : mDeg(r.valueDegrees()) {}
99	Degree& operator = ( const Real& f ) { mDeg = f; return *this; }
100	Degree& operator = ( const Degree& d ) { mDeg = d.mDeg; return *this; }
101	Degree& operator = ( const Radian& r ) { mDeg = r.valueDegrees(); return *this; }
102
103	Real valueDegrees() const { return mDeg; }
104	Real valueRadians() const; // see bottom of this file
105	Real valueAngleUnits() const;
106
107	const Degree& operator + () const { return *this; }
108	Degree operator + ( const Degree& d ) const { return Degree ( mDeg + d.mDeg ); }
109	Degree operator + ( const Radian& r ) const { return Degree ( mDeg + r.valueDegrees() ); }
110	Degree& operator += ( const Degree& d ) { mDeg += d.mDeg; return *this; }
111	Degree& operator += ( const Radian& r ) { mDeg += r.valueDegrees(); return *this; }
112	Degree operator - () const { return Degree(-mDeg); }
113	Degree operator - ( const Degree& d ) const { return Degree ( mDeg - d.mDeg ); }
114	Degree operator - ( const Radian& r ) const { return Degree ( mDeg - r.valueDegrees() ); }
115	Degree& operator -= ( const Degree& d ) { mDeg -= d.mDeg; return *this; }
116	Degree& operator -= ( const Radian& r ) { mDeg -= r.valueDegrees(); return *this; }
117	Degree operator * ( Real f ) const { return Degree ( mDeg * f ); }
118	Degree operator * ( const Degree& f ) const { return Degree ( mDeg * f.mDeg ); }
119	Degree& operator = ( Real f ) { mDeg = f; return *this; }
120	Degree operator / ( Real f ) const { return Degree ( mDeg / f ); }
121	Degree& operator /= ( Real f ) { mDeg /= f; return *this; }
122
123	bool operator < ( const Degree& d ) const { return mDeg < d.mDeg; }
124	bool operator <= ( const Degree& d ) const { return mDeg <= d.mDeg; }
125	bool operator == ( const Degree& d ) const { return mDeg == d.mDeg; }
126	bool operator != ( const Degree& d ) const { return mDeg != d.mDeg; }
127	bool operator >= ( const Degree& d ) const { return mDeg >= d.mDeg; }
128	bool operator > ( const Degree& d ) const { return mDeg > d.mDeg; }
129	};
130
131	/** Wrapper class which identifies a value as the currently default angle
132	type, as defined by Math::setAngleUnit.
133	@remarks
134	Angle values will be automatically converted between radians and degrees,
135	as appropriate.
136	*/
137	class Angle
138	{
139	Real mAngle;
140	public:
141	explicit Angle ( Real angle ) : mAngle(angle) {}
142	operator Radian() const;
143	operator Degree() const;
144	};
145
146	// these functions could not be defined within the class definition of class
147	// Radian because they required class Degree to be defined
148	inline Radian::Radian ( const Degree& d ) : mRad(d.valueRadians()) {
149	}
150	inline Radian& Radian::operator = ( const Degree& d ) {
151	mRad = d.valueRadians(); return *this;
152	}
153	inline Radian Radian::operator + ( const Degree& d ) const {
154	return Radian ( mRad + d.valueRadians() );
155	}
156	inline Radian& Radian::operator += ( const Degree& d ) {
157	mRad += d.valueRadians();
158	return *this;
159	}
160	inline Radian Radian::operator - ( const Degree& d ) const {
161	return Radian ( mRad - d.valueRadians() );
162	}
163	inline Radian& Radian::operator -= ( const Degree& d ) {
164	mRad -= d.valueRadians();
165	return *this;
166	}
167
168	/** Class to provide access to common mathematical functions.
169	@remarks
170	Most of the maths functions are aliased versions of the C runtime
171	library functions. They are aliased here to provide future
172	optimisation opportunities, either from faster RTLs or custom
173	math approximations.
174	@note
175	<br>This is based on MgcMath.h from
176	<a href="http://www.geometrictools.com/">Wild Magic</a>.
177	*/
178	class _OgreExport Math
179	{
180	public:
181	/** The angular units used by the API. This functionality is now deprecated in favor
182	of discreet angular unit types ( see Degree and Radian above ). The only place
183	this functionality is actually still used is when parsing files. Search for
184	usage of the Angle class for those instances
185	*/
186	enum AngleUnit
187	{
188	AU_DEGREE,
189	AU_RADIAN
190	};
191
192	protected:
193	// angle units used by the api
194	static AngleUnit msAngleUnit;
195
196	/// Size of the trig tables as determined by constructor.
197	static int mTrigTableSize;
198
199	/// Radian -> index factor value ( mTrigTableSize / 2 * PI )
200	static Real mTrigTableFactor;
201	static Real* mSinTable;
202	static Real* mTanTable;
203
204	/** Private function to build trig tables.
205	*/
206	void buildTrigTables();
207
208	static Real SinTable (Real fValue);
209	static Real TanTable (Real fValue);
210	public:
211	/** Default constructor.
212	@param
213	trigTableSize Optional parameter to set the size of the
214	tables used to implement Sin, Cos, Tan
215	*/
216	Math(unsigned int trigTableSize = 4096);
217
218	/** Default destructor.
219	*/
220	~Math();
221
222	static inline int IAbs (int iValue) { return ( iValue >= 0 ? iValue : -iValue ); }
223	static inline int ICeil (float fValue) { return int(ceil(fValue)); }
224	static inline int IFloor (float fValue) { return int(floor(fValue)); }
225	static int ISign (int iValue);
226
227	static inline Real Abs (Real fValue) { return Real(fabs(fValue)); }
228	static inline Degree Abs (const Degree& dValue) { return Degree(fabs(dValue.valueDegrees())); }
229	static inline Radian Abs (const Radian& rValue) { return Radian(fabs(rValue.valueRadians())); }
230	static Radian ACos (Real fValue);
231	static Radian ASin (Real fValue);
232	static inline Radian ATan (Real fValue) { return Radian(atan(fValue)); }
233	static inline Radian ATan2 (Real fY, Real fX) { return Radian(atan2(fY,fX)); }
234	static inline Real Ceil (Real fValue) { return Real(ceil(fValue)); }
235
236	/** Cosine function.
237	@param
238	fValue Angle in radians
239	@param
240	useTables If true, uses lookup tables rather than
241	calculation - faster but less accurate.
242	*/
243	static inline Real Cos (const Radian& fValue, bool useTables = false) {
244	return (!useTables) ? Real(cos(fValue.valueRadians())) : SinTable(fValue.valueRadians() + HALF_PI);
245	}
246	/** Cosine function.
247	@param
248	fValue Angle in radians
249	@param
250	useTables If true, uses lookup tables rather than
251	calculation - faster but less accurate.
252	*/
253	static inline Real Cos (Real fValue, bool useTables = false) {
254	return (!useTables) ? Real(cos(fValue)) : SinTable(fValue + HALF_PI);
255	}
256
257	static inline Real Exp (Real fValue) { return Real(exp(fValue)); }
258
259	static inline Real Floor (Real fValue) { return Real(floor(fValue)); }
260
261	static inline Real Log (Real fValue) { return Real(log(fValue)); }
262
263	static inline Real Pow (Real fBase, Real fExponent) { return Real(pow(fBase,fExponent)); }
264
265	static Real Sign (Real fValue);
266	static inline Radian Sign ( const Radian& rValue )
267	{
268	return Radian(Sign(rValue.valueRadians()));
269	}
270	static inline Degree Sign ( const Degree& dValue )
271	{
272	return Degree(Sign(dValue.valueDegrees()));
273	}
274
275	/** Sine function.
276	@param
277	fValue Angle in radians
278	@param
279	useTables If true, uses lookup tables rather than
280	calculation - faster but less accurate.
281	*/
282	static inline Real Sin (const Radian& fValue, bool useTables = false) {
283	return (!useTables) ? Real(sin(fValue.valueRadians())) : SinTable(fValue.valueRadians());
284	}
285	/** Sine function.
286	@param
287	fValue Angle in radians
288	@param
289	useTables If true, uses lookup tables rather than
290	calculation - faster but less accurate.
291	*/
292	static inline Real Sin (Real fValue, bool useTables = false) {
293	return (!useTables) ? Real(sin(fValue)) : SinTable(fValue);
294	}
295
296	static inline Real Sqr (Real fValue) { return fValue*fValue; }
297
298	static inline Real Sqrt (Real fValue) { return Real(sqrt(fValue)); }
299
300	static inline Radian Sqrt (const Radian& fValue) { return Radian(sqrt(fValue.valueRadians())); }
301
302	static inline Degree Sqrt (const Degree& fValue) { return Degree(sqrt(fValue.valueDegrees())); }
303
304	/** Inverse square root i.e. 1 / Sqrt(x), good for vector
305	normalisation.
306	*/
307	static Real InvSqrt(Real fValue);
308
309	static Real UnitRandom (); // in [0,1]
310
311	static Real RangeRandom (Real fLow, Real fHigh); // in [fLow,fHigh]
312
313	static Real SymmetricRandom (); // in [-1,1]
314
315	/** Tangent function.
316	@param
317	fValue Angle in radians
318	@param
319	useTables If true, uses lookup tables rather than
320	calculation - faster but less accurate.
321	*/
322	static inline Real Tan (const Radian& fValue, bool useTables = false) {
323	return (!useTables) ? Real(tan(fValue.valueRadians())) : TanTable(fValue.valueRadians());
324	}
325	/** Tangent function.
326	@param
327	fValue Angle in radians
328	@param
329	useTables If true, uses lookup tables rather than
330	calculation - faster but less accurate.
331	*/
332	static inline Real Tan (Real fValue, bool useTables = false) {
333	return (!useTables) ? Real(tan(fValue)) : TanTable(fValue);
334	}
335
336	static inline Real DegreesToRadians(Real degrees) { return degrees * fDeg2Rad; }
337	static inline Real RadiansToDegrees(Real radians) { return radians * fRad2Deg; }
338
339	/** These functions used to set the assumed angle units (radians or degrees)
340	expected when using the Angle type.
341	@par
342	You can set this directly after creating a new Root, and also before/after resource creation,
343	depending on whether you want the change to affect resource files.
344	*/
345	static void setAngleUnit(AngleUnit unit);
346	/** Get the unit being used for angles. */
347	static AngleUnit getAngleUnit(void);
348
349	/** Convert from the current AngleUnit to radians. */
350	static Real AngleUnitsToRadians(Real units);
351	/** Convert from radians to the current AngleUnit . */
352	static Real RadiansToAngleUnits(Real radians);
353	/** Convert from the current AngleUnit to degrees. */
354	static Real AngleUnitsToDegrees(Real units);
355	/** Convert from degrees to the current AngleUnit. */
356	static Real DegreesToAngleUnits(Real degrees);
357
358	/** Checks whether a given point is inside a triangle, in a
359	2-dimensional (Cartesian) space.
360	@remarks
361	The vertices of the triangle must be given in either
362	trigonometrical (anticlockwise) or inverse trigonometrical
363	(clockwise) order.
364	@param
365	p The point.
366	@param
367	a The triangle's first vertex.
368	@param
369	b The triangle's second vertex.
370	@param
371	c The triangle's third vertex.
372	@returns
373	If the point resides in the triangle, <b>true</b> is
374	returned.
375	@par
376	If the point is outside the triangle, <b>false</b> is
377	returned.
378	*/
379	static bool pointInTri2D(const Vector2& p, const Vector2& a,
380	const Vector2& b, const Vector2& c);
381
382	/** Checks whether a given 3D point is inside a triangle.
383	@remarks
384	The vertices of the triangle must be given in either
385	trigonometrical (anticlockwise) or inverse trigonometrical
386	(clockwise) order, and the point must be guaranteed to be in the
387	same plane as the triangle
388	@param
389	p The point.
390	@param
391	a The triangle's first vertex.
392	@param
393	b The triangle's second vertex.
394	@param
395	c The triangle's third vertex.
396	@param
397	normal The triangle plane's normal (passed in rather than calculated
398	on demand since the caller may already have it)
399	@returns
400	If the point resides in the triangle, <b>true</b> is
401	returned.
402	@par
403	If the point is outside the triangle, <b>false</b> is
404	returned.
405	*/
406	static bool pointInTri3D(const Vector3& p, const Vector3& a,
407	const Vector3& b, const Vector3& c, const Vector3& normal);
408
409	/** Compare 2 reals, using tolerance for inaccuracies.
410	*/
411	static bool RealEqual(Real a, Real b,
412	Real tolerance = std::numeric_limits<Real>::epsilon());
413
414	/** Calculates the tangent space vector for a given set of positions / texture coords. */
415	static Vector3 calculateTangentSpaceVector(
416	const Vector3& position1, const Vector3& position2, const Vector3& position3,
417	Real u1, Real v1, Real u2, Real v2, Real u3, Real v3);
418
419	/** Calculate a face normal, including the w component which is the offset from the origin. */
420	static Vector4 calculateFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3);
421	/** Calculate a face normal, no w-information. */
422	static Vector3 calculateBasicFaceNormal(const Vector3& v1, const Vector3& v2, const Vector3& v3);
423	/** Calculate a face normal without normalize, including the w component which is the offset from the origin. */
424	static Vector4 calculateFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3);
425	/** Calculate a face normal without normalize, no w-information. */
426	static Vector3 calculateBasicFaceNormalWithoutNormalize(const Vector3& v1, const Vector3& v2, const Vector3& v3);
427
428	/** Generates a value based on the Gaussian (normal) distribution function
429	with the given offset and scale parameters.
430	*/
431	static Real gaussianDistribution(Real x, Real offset = 0.0f, Real scale = 1.0f);
432
433	/** Clamp a value within an inclusive range. */
434	template <typename T>
435	static T Clamp(T val, T minval, T maxval)
436	{
437	assert (minval < maxval && "Invalid clamp range");
438	return std::max(std::min(val, maxval), minval);
439	}
440
441	static Matrix4 makeViewMatrix(const Vector3& position, const Quaternion& orientation,
442	const Matrix4* reflectMatrix = 0);
443
444
445
446	static const Real POS_INFINITY;
447	static const Real NEG_INFINITY;
448	static const Real PI;
449	static const Real TWO_PI;
450	static const Real HALF_PI;
451	static const Real fDeg2Rad;
452	static const Real fRad2Deg;
453
454	};
455
456	// these functions must be defined down here, because they rely on the
457	// angle unit conversion functions in class Math:
458
459	inline Real Radian::valueDegrees() const
460	{
461	return Math::RadiansToDegrees ( mRad );
462	}
463
464	inline Real Radian::valueAngleUnits() const
465	{
466	return Math::RadiansToAngleUnits ( mRad );
467	}
468
469	inline Real Degree::valueRadians() const
470	{
471	return Math::DegreesToRadians ( mDeg );
472	}
473
474	inline Real Degree::valueAngleUnits() const
475	{
476	return Math::DegreesToAngleUnits ( mDeg );
477	}
478
479	inline Angle::operator Radian() const
480	{
481	return Radian(Math::AngleUnitsToRadians(mAngle));
482	}
483
484	inline Angle::operator Degree() const
485	{
486	return Degree(Math::AngleUnitsToDegrees(mAngle));
487	}
488
489	inline Radian operator * ( Real a, const Radian& b )
490	{
491	return Radian ( a * b.valueRadians() );
492	}
493
494	inline Radian operator / ( Real a, const Radian& b )
495	{
496	return Radian ( a / b.valueRadians() );
497	}
498
499	inline Degree operator * ( Real a, const Degree& b )
500	{
501	return Degree ( a * b.valueDegrees() );
502	}
503
504	inline Degree operator / ( Real a, const Degree& b )
505	{
506	return Degree ( a / b.valueDegrees() );
507	}
508
509	}
510	#endif

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