source: OGRE/trunk/ogrenew/OgreMain/include/OgreMatrix4.h @ 692

Revision 692, 20.6 KB checked in by mattausch, 19 years ago (diff)

adding ogre 1.2 and dependencies
Line 
1/*
2-----------------------------------------------------------------------------
3This source file is part of OGRE
4    (Object-oriented Graphics Rendering Engine)
5For the latest info, see http://www.ogre3d.org/
6
7Copyright (c) 2000-2005 The OGRE Team
8Also see acknowledgements in Readme.html
9
10This program is free software; you can redistribute it and/or modify it under
11the terms of the GNU Lesser General Public License as published by the Free Software
12Foundation; either version 2 of the License, or (at your option) any later
13version.
14
15This program is distributed in the hope that it will be useful, but WITHOUT
16ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
17FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.
18
19You should have received a copy of the GNU Lesser General Public License along with
20this program; if not, write to the Free Software Foundation, Inc., 59 Temple
21Place - Suite 330, Boston, MA 02111-1307, USA, or go to
22http://www.gnu.org/copyleft/lesser.txt.
23-----------------------------------------------------------------------------
24*/
25#ifndef __Matrix4__
26#define __Matrix4__
27
28// Precompiler options
29#include "OgrePrerequisites.h"
30
31#include "OgreVector3.h"
32#include "OgreMatrix3.h"
33#include "OgreVector4.h"
34#include "OgrePlane.h"
35namespace Ogre
36{
37    /** Class encapsulating a standard 4x4 homogenous matrix.
38        @remarks
39            OGRE uses column vectors when applying matrix multiplications,
40            This means a vector is represented as a single column, 4-row
41            matrix. This has the effect that the tranformations implemented
42            by the matrices happens right-to-left e.g. if vector V is to be
43            transformed by M1 then M2 then M3, the calculation would be
44            M3 * M2 * M1 * V. The order that matrices are concatenated is
45            vital since matrix multiplication is not cummatative, i.e. you
46            can get a different result if you concatenate in the wrong order.
47        @par
48            The use of column vectors and right-to-left ordering is the
49            standard in most mathematical texts, and id the same as used in
50            OpenGL. It is, however, the opposite of Direct3D, which has
51            inexplicably chosen to differ from the accepted standard and uses
52            row vectors and left-to-right matrix multiplication.
53        @par
54            OGRE deals with the differences between D3D and OpenGL etc.
55            internally when operating through different render systems. OGRE
56            users only need to conform to standard maths conventions, i.e.
57            right-to-left matrix multiplication, (OGRE transposes matrices it
58            passes to D3D to compensate).
59        @par
60            The generic form M * V which shows the layout of the matrix
61            entries is shown below:
62            <pre>
63                [ m[0][0]  m[0][1]  m[0][2]  m[0][3] ]   {x}
64                | m[1][0]  m[1][1]  m[1][2]  m[1][3] | * {y}
65                | m[2][0]  m[2][1]  m[2][2]  m[2][3] |   {z}
66                [ m[3][0]  m[3][1]  m[3][2]  m[3][3] ]   {1}
67            </pre>
68    */
69    class _OgreExport Matrix4
70    {
71    protected:
72        /// The matrix entries, indexed by [row][col].
73        union {
74            Real m[4][4];
75            Real _m[16];
76        };
77    public:
78        /** Default constructor.
79            @note
80                It does <b>NOT</b> initialize the matrix for efficiency.
81        */
82        inline Matrix4()
83        {
84        }
85
86        inline Matrix4(
87            Real m00, Real m01, Real m02, Real m03,
88            Real m10, Real m11, Real m12, Real m13,
89            Real m20, Real m21, Real m22, Real m23,
90            Real m30, Real m31, Real m32, Real m33 )
91        {
92            m[0][0] = m00;
93            m[0][1] = m01;
94            m[0][2] = m02;
95            m[0][3] = m03;
96            m[1][0] = m10;
97            m[1][1] = m11;
98            m[1][2] = m12;
99            m[1][3] = m13;
100            m[2][0] = m20;
101            m[2][1] = m21;
102            m[2][2] = m22;
103            m[2][3] = m23;
104            m[3][0] = m30;
105            m[3][1] = m31;
106            m[3][2] = m32;
107            m[3][3] = m33;
108        }
109
110        /** Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling 3x3 matrix.
111         */
112
113        inline Matrix4(const Matrix3& m3x3)
114        {
115          operator=(IDENTITY);
116          operator=(m3x3);
117        }
118
119        /** Creates a standard 4x4 transformation matrix with a zero translation part from a rotation/scaling Quaternion.
120         */
121       
122        inline Matrix4(const Quaternion& rot)
123        {
124          Matrix3 m3x3;
125          rot.ToRotationMatrix(m3x3);
126          operator=(IDENTITY);
127          operator=(m3x3);
128        }
129       
130
131        inline Real* operator [] ( size_t iRow )
132        {
133            assert( iRow < 4 );
134            return m[iRow];
135        }
136
137        inline const Real *const operator [] ( size_t iRow ) const
138        {
139            assert( iRow < 4 );
140            return m[iRow];
141        }
142
143        inline Matrix4 concatenate(const Matrix4 &m2) const
144        {
145            Matrix4 r;
146            r.m[0][0] = m[0][0] * m2.m[0][0] + m[0][1] * m2.m[1][0] + m[0][2] * m2.m[2][0] + m[0][3] * m2.m[3][0];
147            r.m[0][1] = m[0][0] * m2.m[0][1] + m[0][1] * m2.m[1][1] + m[0][2] * m2.m[2][1] + m[0][3] * m2.m[3][1];
148            r.m[0][2] = m[0][0] * m2.m[0][2] + m[0][1] * m2.m[1][2] + m[0][2] * m2.m[2][2] + m[0][3] * m2.m[3][2];
149            r.m[0][3] = m[0][0] * m2.m[0][3] + m[0][1] * m2.m[1][3] + m[0][2] * m2.m[2][3] + m[0][3] * m2.m[3][3];
150
151            r.m[1][0] = m[1][0] * m2.m[0][0] + m[1][1] * m2.m[1][0] + m[1][2] * m2.m[2][0] + m[1][3] * m2.m[3][0];
152            r.m[1][1] = m[1][0] * m2.m[0][1] + m[1][1] * m2.m[1][1] + m[1][2] * m2.m[2][1] + m[1][3] * m2.m[3][1];
153            r.m[1][2] = m[1][0] * m2.m[0][2] + m[1][1] * m2.m[1][2] + m[1][2] * m2.m[2][2] + m[1][3] * m2.m[3][2];
154            r.m[1][3] = m[1][0] * m2.m[0][3] + m[1][1] * m2.m[1][3] + m[1][2] * m2.m[2][3] + m[1][3] * m2.m[3][3];
155
156            r.m[2][0] = m[2][0] * m2.m[0][0] + m[2][1] * m2.m[1][0] + m[2][2] * m2.m[2][0] + m[2][3] * m2.m[3][0];
157            r.m[2][1] = m[2][0] * m2.m[0][1] + m[2][1] * m2.m[1][1] + m[2][2] * m2.m[2][1] + m[2][3] * m2.m[3][1];
158            r.m[2][2] = m[2][0] * m2.m[0][2] + m[2][1] * m2.m[1][2] + m[2][2] * m2.m[2][2] + m[2][3] * m2.m[3][2];
159            r.m[2][3] = m[2][0] * m2.m[0][3] + m[2][1] * m2.m[1][3] + m[2][2] * m2.m[2][3] + m[2][3] * m2.m[3][3];
160
161            r.m[3][0] = m[3][0] * m2.m[0][0] + m[3][1] * m2.m[1][0] + m[3][2] * m2.m[2][0] + m[3][3] * m2.m[3][0];
162            r.m[3][1] = m[3][0] * m2.m[0][1] + m[3][1] * m2.m[1][1] + m[3][2] * m2.m[2][1] + m[3][3] * m2.m[3][1];
163            r.m[3][2] = m[3][0] * m2.m[0][2] + m[3][1] * m2.m[1][2] + m[3][2] * m2.m[2][2] + m[3][3] * m2.m[3][2];
164            r.m[3][3] = m[3][0] * m2.m[0][3] + m[3][1] * m2.m[1][3] + m[3][2] * m2.m[2][3] + m[3][3] * m2.m[3][3];
165
166            return r;
167        }
168
169        /** Matrix concatenation using '*'.
170        */
171        inline Matrix4 operator * ( const Matrix4 &m2 ) const
172        {
173            return concatenate( m2 );
174        }
175
176        /** Vector transformation using '*'.
177            @remarks
178                Transforms the given 3-D vector by the matrix, projecting the
179                result back into <i>w</i> = 1.
180            @note
181                This means that the initial <i>w</i> is considered to be 1.0,
182                and then all the tree elements of the resulting 3-D vector are
183                divided by the resulting <i>w</i>.
184        */
185        inline Vector3 operator * ( const Vector3 &v ) const
186        {
187            Vector3 r;
188
189            Real fInvW = 1.0 / ( m[3][0] * v.x + m[3][1] * v.y + m[3][2] * v.z + m[3][3] );
190
191            r.x = ( m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3] ) * fInvW;
192            r.y = ( m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3] ) * fInvW;
193            r.z = ( m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3] ) * fInvW;
194
195            return r;
196        }
197        inline Vector4 operator * (const Vector4& v) const
198        {
199            return Vector4(
200                m[0][0] * v.x + m[0][1] * v.y + m[0][2] * v.z + m[0][3] * v.w,
201                m[1][0] * v.x + m[1][1] * v.y + m[1][2] * v.z + m[1][3] * v.w,
202                m[2][0] * v.x + m[2][1] * v.y + m[2][2] * v.z + m[2][3] * v.w,
203                m[3][0] * v.x + m[3][1] * v.y + m[3][2] * v.z + m[3][3] * v.w
204                );
205        }
206        inline Plane operator * (const Plane& p) const
207        {
208            Plane ret;
209                        Matrix4 invTrans = inverse().transpose();
210            ret.normal.x =
211                invTrans[0][0] * p.normal.x + invTrans[0][1] * p.normal.y + invTrans[0][2] * p.normal.z;
212            ret.normal.y =
213                invTrans[1][0] * p.normal.x + invTrans[1][1] * p.normal.y + invTrans[1][2] * p.normal.z;
214            ret.normal.z =
215                invTrans[2][0] * p.normal.x + invTrans[2][1] * p.normal.y + invTrans[2][2] * p.normal.z;
216            Vector3 pt = p.normal * -p.d;
217            pt = *this * pt;
218            ret.d = - pt.dotProduct(ret.normal);
219            return ret;
220        }
221
222
223        /** Matrix addition.
224        */
225        inline Matrix4 operator + ( const Matrix4 &m2 ) const
226        {
227            Matrix4 r;
228
229            r.m[0][0] = m[0][0] + m2.m[0][0];
230            r.m[0][1] = m[0][1] + m2.m[0][1];
231            r.m[0][2] = m[0][2] + m2.m[0][2];
232            r.m[0][3] = m[0][3] + m2.m[0][3];
233
234            r.m[1][0] = m[1][0] + m2.m[1][0];
235            r.m[1][1] = m[1][1] + m2.m[1][1];
236            r.m[1][2] = m[1][2] + m2.m[1][2];
237            r.m[1][3] = m[1][3] + m2.m[1][3];
238
239            r.m[2][0] = m[2][0] + m2.m[2][0];
240            r.m[2][1] = m[2][1] + m2.m[2][1];
241            r.m[2][2] = m[2][2] + m2.m[2][2];
242            r.m[2][3] = m[2][3] + m2.m[2][3];
243
244            r.m[3][0] = m[3][0] + m2.m[3][0];
245            r.m[3][1] = m[3][1] + m2.m[3][1];
246            r.m[3][2] = m[3][2] + m2.m[3][2];
247            r.m[3][3] = m[3][3] + m2.m[3][3];
248
249            return r;
250        }
251
252        /** Matrix subtraction.
253        */
254        inline Matrix4 operator - ( const Matrix4 &m2 ) const
255        {
256            Matrix4 r;
257            r.m[0][0] = m[0][0] - m2.m[0][0];
258            r.m[0][1] = m[0][1] - m2.m[0][1];
259            r.m[0][2] = m[0][2] - m2.m[0][2];
260            r.m[0][3] = m[0][3] - m2.m[0][3];
261
262            r.m[1][0] = m[1][0] - m2.m[1][0];
263            r.m[1][1] = m[1][1] - m2.m[1][1];
264            r.m[1][2] = m[1][2] - m2.m[1][2];
265            r.m[1][3] = m[1][3] - m2.m[1][3];
266
267            r.m[2][0] = m[2][0] - m2.m[2][0];
268            r.m[2][1] = m[2][1] - m2.m[2][1];
269            r.m[2][2] = m[2][2] - m2.m[2][2];
270            r.m[2][3] = m[2][3] - m2.m[2][3];
271
272            r.m[3][0] = m[3][0] - m2.m[3][0];
273            r.m[3][1] = m[3][1] - m2.m[3][1];
274            r.m[3][2] = m[3][2] - m2.m[3][2];
275            r.m[3][3] = m[3][3] - m2.m[3][3];
276
277            return r;
278        }
279
280        /** Tests 2 matrices for equality.
281        */
282        inline bool operator == ( const Matrix4& m2 ) const
283        {
284            if(
285                m[0][0] != m2.m[0][0] || m[0][1] != m2.m[0][1] || m[0][2] != m2.m[0][2] || m[0][3] != m2.m[0][3] ||
286                m[1][0] != m2.m[1][0] || m[1][1] != m2.m[1][1] || m[1][2] != m2.m[1][2] || m[1][3] != m2.m[1][3] ||
287                m[2][0] != m2.m[2][0] || m[2][1] != m2.m[2][1] || m[2][2] != m2.m[2][2] || m[2][3] != m2.m[2][3] ||
288                m[3][0] != m2.m[3][0] || m[3][1] != m2.m[3][1] || m[3][2] != m2.m[3][2] || m[3][3] != m2.m[3][3] )
289                return false;
290            return true;
291        }
292
293        /** Tests 2 matrices for inequality.
294        */
295        inline bool operator != ( const Matrix4& m2 ) const
296        {
297            if(
298                m[0][0] != m2.m[0][0] || m[0][1] != m2.m[0][1] || m[0][2] != m2.m[0][2] || m[0][3] != m2.m[0][3] ||
299                m[1][0] != m2.m[1][0] || m[1][1] != m2.m[1][1] || m[1][2] != m2.m[1][2] || m[1][3] != m2.m[1][3] ||
300                m[2][0] != m2.m[2][0] || m[2][1] != m2.m[2][1] || m[2][2] != m2.m[2][2] || m[2][3] != m2.m[2][3] ||
301                m[3][0] != m2.m[3][0] || m[3][1] != m2.m[3][1] || m[3][2] != m2.m[3][2] || m[3][3] != m2.m[3][3] )
302                return true;
303            return false;
304        }
305
306        /** Assignment from 3x3 matrix.
307        */
308        inline void operator = ( const Matrix3& mat3 )
309        {
310            m[0][0] = mat3.m[0][0]; m[0][1] = mat3.m[0][1]; m[0][2] = mat3.m[0][2];
311            m[1][0] = mat3.m[1][0]; m[1][1] = mat3.m[1][1]; m[1][2] = mat3.m[1][2];
312            m[2][0] = mat3.m[2][0]; m[2][1] = mat3.m[2][1]; m[2][2] = mat3.m[2][2];
313        }
314
315        inline Matrix4 transpose(void) const
316        {
317            return Matrix4(m[0][0], m[1][0], m[2][0], m[3][0],
318                           m[0][1], m[1][1], m[2][1], m[3][1],
319                           m[0][2], m[1][2], m[2][2], m[3][2],
320                           m[0][3], m[1][3], m[2][3], m[3][3]);
321        }
322
323        /*
324        -----------------------------------------------------------------------
325        Translation Transformation
326        -----------------------------------------------------------------------
327        */
328        /** Sets the translation transformation part of the matrix.
329        */
330        inline void setTrans( const Vector3& v )
331        {
332            m[0][3] = v.x;
333            m[1][3] = v.y;
334            m[2][3] = v.z;
335        }
336
337        /** Extracts the translation transformation part of the matrix.
338         */
339        inline Vector3 getTrans() const
340        {
341          return Vector3(m[0][3], m[1][3], m[2][3]);
342        }
343       
344
345        /** Builds a translation matrix
346        */
347        inline void makeTrans( const Vector3& v )
348        {
349            m[0][0] = 1.0; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = v.x;
350            m[1][0] = 0.0; m[1][1] = 1.0; m[1][2] = 0.0; m[1][3] = v.y;
351            m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = 1.0; m[2][3] = v.z;
352            m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0;
353        }
354
355        inline void makeTrans( Real tx, Real ty, Real tz )
356        {
357            m[0][0] = 1.0; m[0][1] = 0.0; m[0][2] = 0.0; m[0][3] = tx;
358            m[1][0] = 0.0; m[1][1] = 1.0; m[1][2] = 0.0; m[1][3] = ty;
359            m[2][0] = 0.0; m[2][1] = 0.0; m[2][2] = 1.0; m[2][3] = tz;
360            m[3][0] = 0.0; m[3][1] = 0.0; m[3][2] = 0.0; m[3][3] = 1.0;
361        }
362
363        /** Gets a translation matrix.
364        */
365        inline static Matrix4 getTrans( const Vector3& v )
366        {
367            Matrix4 r;
368
369            r.m[0][0] = 1.0; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = v.x;
370            r.m[1][0] = 0.0; r.m[1][1] = 1.0; r.m[1][2] = 0.0; r.m[1][3] = v.y;
371            r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = 1.0; r.m[2][3] = v.z;
372            r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;
373
374            return r;
375        }
376
377        /** Gets a translation matrix - variation for not using a vector.
378        */
379        inline static Matrix4 getTrans( Real t_x, Real t_y, Real t_z )
380        {
381            Matrix4 r;
382
383            r.m[0][0] = 1.0; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = t_x;
384            r.m[1][0] = 0.0; r.m[1][1] = 1.0; r.m[1][2] = 0.0; r.m[1][3] = t_y;
385            r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = 1.0; r.m[2][3] = t_z;
386            r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;
387
388            return r;
389        }
390
391        /*
392        -----------------------------------------------------------------------
393        Scale Transformation
394        -----------------------------------------------------------------------
395        */
396        /** Sets the scale part of the matrix.
397        */
398        inline void setScale( const Vector3& v )
399        {
400            m[0][0] = v.x;
401            m[1][1] = v.y;
402            m[2][2] = v.z;
403        }
404
405        /** Gets a scale matrix.
406        */
407        inline static Matrix4 getScale( const Vector3& v )
408        {
409            Matrix4 r;
410            r.m[0][0] = v.x; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = 0.0;
411            r.m[1][0] = 0.0; r.m[1][1] = v.y; r.m[1][2] = 0.0; r.m[1][3] = 0.0;
412            r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = v.z; r.m[2][3] = 0.0;
413            r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;
414
415            return r;
416        }
417
418        /** Gets a scale matrix - variation for not using a vector.
419        */
420        inline static Matrix4 getScale( Real s_x, Real s_y, Real s_z )
421        {
422            Matrix4 r;
423            r.m[0][0] = s_x; r.m[0][1] = 0.0; r.m[0][2] = 0.0; r.m[0][3] = 0.0;
424            r.m[1][0] = 0.0; r.m[1][1] = s_y; r.m[1][2] = 0.0; r.m[1][3] = 0.0;
425            r.m[2][0] = 0.0; r.m[2][1] = 0.0; r.m[2][2] = s_z; r.m[2][3] = 0.0;
426            r.m[3][0] = 0.0; r.m[3][1] = 0.0; r.m[3][2] = 0.0; r.m[3][3] = 1.0;
427
428            return r;
429        }
430
431        /** Extracts the rotation / scaling part of the Matrix as a 3x3 matrix.
432        @param m3x3 Destination Matrix3
433        */
434        inline void extract3x3Matrix(Matrix3& m3x3) const
435        {
436            m3x3.m[0][0] = m[0][0];
437            m3x3.m[0][1] = m[0][1];
438            m3x3.m[0][2] = m[0][2];
439            m3x3.m[1][0] = m[1][0];
440            m3x3.m[1][1] = m[1][1];
441            m3x3.m[1][2] = m[1][2];
442            m3x3.m[2][0] = m[2][0];
443            m3x3.m[2][1] = m[2][1];
444            m3x3.m[2][2] = m[2][2];
445
446        }
447
448        /** Extracts the rotation / scaling part as a quaternion from the Matrix.
449         */
450        inline Quaternion extractQuaternion() const
451        {
452          Matrix3 m3x3;
453          extract3x3Matrix(m3x3);
454          return Quaternion(m3x3);
455        }
456
457        static const Matrix4 ZERO;
458        static const Matrix4 IDENTITY;
459        /** Useful little matrix which takes 2D clipspace {-1, 1} to {0,1}
460            and inverts the Y. */
461        static const Matrix4 CLIPSPACE2DTOIMAGESPACE;
462
463        inline Matrix4 operator*(Real scalar)
464        {
465            return Matrix4(
466                scalar*m[0][0], scalar*m[0][1], scalar*m[0][2], scalar*m[0][3],
467                scalar*m[1][0], scalar*m[1][1], scalar*m[1][2], scalar*m[1][3],
468                scalar*m[2][0], scalar*m[2][1], scalar*m[2][2], scalar*m[2][3],
469                scalar*m[3][0], scalar*m[3][1], scalar*m[3][2], scalar*m[3][3]);
470        }
471
472        /** Function for writing to a stream.
473        */
474        inline _OgreExport friend std::ostream& operator <<
475            ( std::ostream& o, const Matrix4& m )
476        {
477            o << "Matrix4(";
478                        for (size_t i = 0; i < 4; ++i)
479            {
480                o << " row" << (unsigned)i << "{";
481                for(size_t j = 0; j < 4; ++j)
482                {
483                    o << m[i][j] << " ";
484                }
485                o << "}";
486            }
487            o << ")";
488            return o;
489        }
490               
491                Matrix4 adjoint() const;
492                Real determinant() const;
493                Matrix4 inverse() const;
494
495        /** Building a Matrix4 from orientation / scale / position.
496        @remarks
497            Transform is performed in the order scale, rotate, translation, i.e. translation is independent
498            of orientation axes, scale does not affect size of translation, rotation and scaling are always
499            centered on the origin.
500        */
501        void makeTransform(const Vector3& position, const Vector3& scale, const Quaternion& orientation);
502
503        /** Building an inverse Matrix4 from orientation / scale / position.
504        @remarks
505            As makeTransform except it build the inverse given the same data as makeTransform, so
506            performing -translation, -rotate, 1/scale in that order.
507        */
508        void makeInverseTransform(const Vector3& position, const Vector3& scale, const Quaternion& orientation);
509    };
510
511    /* Removed from Vector4 and made a non-member here because otherwise
512       OgreMatrix4.h and OgreVector4.h have to try to include and inline each
513       other, which frankly doesn't work ;)
514   */
515    inline Vector4 operator * (const Vector4& v, const Matrix4& mat)
516    {
517        return Vector4(
518            v.x*mat[0][0] + v.y*mat[1][0] + v.z*mat[2][0] + v.w*mat[3][0],
519            v.x*mat[0][1] + v.y*mat[1][1] + v.z*mat[2][1] + v.w*mat[3][1],
520            v.x*mat[0][2] + v.y*mat[1][2] + v.z*mat[2][2] + v.w*mat[3][2],
521            v.x*mat[0][3] + v.y*mat[1][3] + v.z*mat[2][3] + v.w*mat[3][3]
522            );
523    }
524
525}
526#endif
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