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Reference Guide
TEveTrans.cxx
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1// @(#)root/eve:$Id$
2// Authors: Matevz Tadel & Alja Mrak-Tadel: 2006, 2007
3
4/*************************************************************************
5 * Copyright (C) 1995-2007, Rene Brun and Fons Rademakers. *
6 * All rights reserved. *
7 * *
8 * For the licensing terms see $ROOTSYS/LICENSE. *
9 * For the list of contributors see $ROOTSYS/README/CREDITS. *
10 *************************************************************************/
11
12#include "TEveTrans.h"
13#include "TEveUtil.h"
14
15#include "TBuffer.h"
16#include "TClass.h"
17#include "TMath.h"
18
19#include "Riostream.h"
20
21#include <cctype>
22
23#define F00 0
24#define F01 4
25#define F02 8
26#define F03 12
27
28#define F10 1
29#define F11 5
30#define F12 9
31#define F13 13
32
33#define F20 2
34#define F21 6
35#define F22 10
36#define F23 14
37
38#define F30 3
39#define F31 7
40#define F32 11
41#define F33 15
42
43/** \class TEveTrans
44\ingroup TEve
45TEveTrans is a 4x4 transformation matrix for homogeneous coordinates
46stored internally in a column-major order to allow direct usage by
47GL. The element type is Double32_t as statically the floats would
48be precise enough but continuous operations on the matrix must
49retain precision of column vectors.
50
51Cartan angles are stored in fA[1-3] (+z, -y, +x). They are
52recalculated on demand.
53
54Direct element access (first two should be used with care):
55 - operator[i] direct access to elements, i:0->15
56 - CM(i,j) element 4*j + i; i,j:0->3 { CM ~ c-matrix }
57 - operator(i,j) element 4*(j-1) + i - 1 i,j:1->4
58
59Column-vector access:
60USet Get/SetBaseVec(), Get/SetPos() and Arr[XYZT]() methods.
61
62For all methods taking the matrix indices:
631->X, 2->Y, 3->Z; 4->Position (if applicable). 0 reserved for time.
64
65Shorthands in method-names:
66LF ~ LocalFrame; PF ~ ParentFrame; IP ~ InPlace
67*/
68
70
71////////////////////////////////////////////////////////////////////////////////
72/// Default constructor.
73
75 TObject(),
76 fA1(0), fA2(0), fA3(0), fAsOK(kFALSE),
77 fUseTrans (kTRUE),
78 fEditTrans(kFALSE),
79 fEditRotation(kTRUE),
80 fEditScale(kTRUE)
81{
82 UnitTrans();
83}
84
85////////////////////////////////////////////////////////////////////////////////
86/// Constructor.
87
89 TObject(),
90 fA1(t.fA1), fA2(t.fA2), fA3(t.fA3), fAsOK(t.fAsOK),
91 fUseTrans (t.fUseTrans),
92 fEditTrans(t.fEditTrans),
93 fEditRotation(kTRUE),
94 fEditScale(kTRUE)
95{
96 SetTrans(t, kFALSE);
97}
98
99////////////////////////////////////////////////////////////////////////////////
100/// Constructor.
101
103 TObject(),
104 fA1(0), fA2(0), fA3(0), fAsOK(kFALSE),
105 fUseTrans (kTRUE),
106 fEditTrans(kFALSE),
107 fEditRotation(kTRUE),
108 fEditScale(kTRUE)
109{
110 SetFromArray(arr);
111}
112
113////////////////////////////////////////////////////////////////////////////////
114/// Constructor.
115
117 TObject(),
118 fA1(0), fA2(0), fA3(0), fAsOK(kFALSE),
119 fUseTrans (kTRUE),
120 fEditTrans(kFALSE),
121 fEditRotation(kTRUE),
122 fEditScale(kTRUE)
123{
124 SetFromArray(arr);
125}
126
127////////////////////////////////////////////////////////////////////////////////
128/// Reset matrix to unity.
129
131{
132 memset(fM, 0, 16*sizeof(Double_t));
133 fM[F00] = fM[F11] = fM[F22] = fM[F33] = 1;
134 fA1 = fA2 = fA3 = 0;
135 fAsOK = kTRUE;
136}
137
138////////////////////////////////////////////////////////////////////////////////
139/// Reset matrix to zero, only the perspective scaling is set to w
140/// (1 by default).
141
143{
144 memset(fM, 0, 16*sizeof(Double_t));
145 fM[F33] = w;
146 fA1 = fA2 = fA3 = 0;
147 fAsOK = kFALSE;
148}
149
150////////////////////////////////////////////////////////////////////////////////
151/// Reset rotation part of the matrix to unity.
152
154{
155 memset(fM, 0, 12*sizeof(Double_t));
156 fM[F00] = fM[F11] = fM[F22] = 1;
157 fA1 = fA2 = fA3 = 0;
158 fAsOK = kTRUE;
159}
160
161////////////////////////////////////////////////////////////////////////////////
162/// Set matrix from another,
163
164void TEveTrans::SetTrans(const TEveTrans& t, Bool_t copyAngles)
165{
166 memcpy(fM, t.fM, sizeof(fM));
167 if (copyAngles && t.fAsOK) {
168 fAsOK = kTRUE;
169 fA1 = t.fA1; fA2 = t.fA2; fA3 = t.fA3;
170 } else {
171 fAsOK = kFALSE;
172 }
173}
174
175////////////////////////////////////////////////////////////////////////////////
176/// Set matrix from Double_t array.
177
179{
180 for(Int_t i=0; i<16; ++i) fM[i] = arr[i];
181 fAsOK = kFALSE;
182}
183
184////////////////////////////////////////////////////////////////////////////////
185/// Set matrix from Float_t array.
186
188{
189 for(Int_t i=0; i<16; ++i) fM[i] = arr[i];
190 fAsOK = kFALSE;
191}
192
193////////////////////////////////////////////////////////////////////////////////
194/// Setup the matrix as an elementary rotation.
195/// Optimized versions of left/right multiplication with an elementary
196/// rotation matrix are implemented in RotatePF/RotateLF.
197/// Expects identity matrix.
198
200{
201 if(i == j) return;
202 TEveTrans& t = *this;
203 t(i,i) = t(j,j) = TMath::Cos(f);
205 t(i,j) = -s; t(j,i) = s;
206 fAsOK = kFALSE;
207}
208
209////////////////////////////////////////////////////////////////////////////////
210/// A function for creating a rotation matrix that rotates a vector called
211/// "from" into another vector called "to".
212/// Input : from[3], to[3] which both must be *normalized* non-zero vectors
213/// Output: mtx[3][3] -- a 3x3 matrix in column-major form
214///
215/// Authors: Tomas Möller, John Hughes
216/// "Efficiently Building a Matrix to Rotate One Vector to Another"
217/// Journal of Graphics Tools, 4(4):1-4, 1999
218
220{
221 static const float kFromToEpsilon = 0.000001f;
222
223 ZeroTrans();
224
225 Float_t e, f;
226 e = from.Dot(to);
227 f = (e < 0.0f) ? -e : e;
228
229 if (f > 1.0f - kFromToEpsilon) /* "from" and "to"-vector almost parallel */
230 {
231 TEveVector u, v; /* temporary storage vectors */
232 TEveVector x; /* vector most nearly orthogonal to "from" */
233 Float_t c1, c2, c3; /* coefficients for later use */
234
235 x.fX = (from.fX > 0.0f) ? from.fX : -from.fX;
236 x.fY = (from.fY > 0.0f) ? from.fY : -from.fY;
237 x.fZ = (from.fZ > 0.0f) ? from.fZ : -from.fZ;
238
239 if (x.fX < x.fY)
240 {
241 if (x.fX < x.fZ) {
242 x.fX = 1.0f; x.fY = x.fZ = 0.0f;
243 } else {
244 x.fZ = 1.0f; x.fX = x.fY = 0.0f;
245 }
246 }
247 else
248 {
249 if (x.fY < x.fZ) {
250 x.fY = 1.0f; x.fX = x.fZ = 0.0f;
251 } else {
252 x.fZ = 1.0f; x.fX = x.fY = 0.0f;
253 }
254 }
255
256 u.Sub(x, from);
257 v.Sub(x, to);
258
259 c1 = 2.0f / u.Mag2();
260 c2 = 2.0f / v.Mag2();
261 c3 = c1 * c2 * u.Dot(v);
262
263 for (int i = 0; i < 3; i++) {
264 for (int j = 0; j < 3; j++) {
265 CM(i, j) = - c1 * u[i] * u[j]
266 - c2 * v[i] * v[j]
267 + c3 * v[i] * u[j];
268 }
269 CM(i, i) += 1.0;
270 }
271 }
272 else /* the most common case, unless "from"="to", or "from"=-"to" */
273 {
274 TEveVector v = from.Cross(to);
275
276 Float_t h, hvx, hvz, hvxy, hvxz, hvyz;
277 h = 1.0f/(1.0f + e);
278 hvx = h * v.fX;
279 hvz = h * v.fZ;
280 hvxy = hvx * v.fY;
281 hvxz = hvx * v.fZ;
282 hvyz = hvz * v.fY;
283
284 CM(0, 0) = e + hvx * v.fX;
285 CM(0, 1) = hvxy - v.fZ;
286 CM(0, 2) = hvxz + v.fY;
287
288 CM(1, 0) = hvxy + v.fZ;
289 CM(1, 1) = e + h * v.fY * v.fY;
290 CM(1, 2) = hvyz - v.fX;
291
292 CM(2, 0) = hvxz - v.fY;
293 CM(2, 1) = hvyz + v.fX;
294 CM(2, 2) = e + hvz * v.fZ;
295 }
296}
297
298////////////////////////////////////////////////////////////////////////////////
299/// Multiply from left: this = t * this.
300
302{
303 Double_t buf[4];
304 Double_t* col = fM;
305 for(int c=0; c<4; ++c, col+=4) {
306 const Double_t* row = t.fM;
307 for(int r=0; r<4; ++r, ++row)
308 buf[r] = row[0]*col[0] + row[4]*col[1] + row[8]*col[2] + row[12]*col[3];
309 col[0] = buf[0]; col[1] = buf[1]; col[2] = buf[2]; col[3] = buf[3];
310 }
311 fAsOK = kFALSE;
312}
313
314////////////////////////////////////////////////////////////////////////////////
315/// Multiply from right: this = this * t.
316
318{
319 Double_t buf[4];
320 Double_t* row = fM;
321 for(int r=0; r<4; ++r, ++row) {
322 const Double_t* col = t.fM;
323 for(int c=0; c<4; ++c, col+=4)
324 buf[c] = row[0]*col[0] + row[4]*col[1] + row[8]*col[2] + row[12]*col[3];
325 row[0] = buf[0]; row[4] = buf[1]; row[8] = buf[2]; row[12] = buf[3];
326 }
327 fAsOK = kFALSE;
328}
329
330////////////////////////////////////////////////////////////////////////////////
331/// Copy, multiply from right and return product.
332/// Avoid unless necessary.
333
335{
336 TEveTrans b(*this);
337 b.MultRight(t);
338 return b;
339}
340
341////////////////////////////////////////////////////////////////////////////////
342/// Transpose 3x3 rotation sub-matrix.
343
345{
346 Double_t x;
347 x = fM[F01]; fM[F01] = fM[F10]; fM[F10] = x;
348 x = fM[F02]; fM[F02] = fM[F20]; fM[F20] = x;
349 x = fM[F12]; fM[F12] = fM[F21]; fM[F21] = x;
350 fAsOK = kFALSE;
351}
352
353////////////////////////////////////////////////////////////////////////////////
354/// Move in local-frame along axis with index ai.
355
357{
358 const Double_t *col = fM + 4*--ai;
359 fM[F03] += amount*col[0]; fM[F13] += amount*col[1]; fM[F23] += amount*col[2];
360}
361
362////////////////////////////////////////////////////////////////////////////////
363/// General move in local-frame.
364
366{
367 fM[F03] += x*fM[0] + y*fM[4] + z*fM[8];
368 fM[F13] += x*fM[1] + y*fM[5] + z*fM[9];
369 fM[F23] += x*fM[2] + y*fM[6] + z*fM[10];
370}
371
372////////////////////////////////////////////////////////////////////////////////
373/// Rotate in local frame. Does optimised version of MultRight.
374
376{
377 if(i1 == i2) return;
378 // Algorithm: TEveTrans a; a.SetupRotation(i1, i2, amount); MultRight(a);
379 // Optimized version:
380 const Double_t cos = TMath::Cos(amount), sin = TMath::Sin(amount);
381 Double_t b1, b2;
382 Double_t* row = fM;
383 --i1 <<= 2; --i2 <<= 2; // column major
384 for (int r=0; r<4; ++r, ++row) {
385 b1 = cos*row[i1] + sin*row[i2];
386 b2 = cos*row[i2] - sin*row[i1];
387 row[i1] = b1; row[i2] = b2;
388 }
389 fAsOK = kFALSE;
390}
391
392////////////////////////////////////////////////////////////////////////////////
393/// Move in parent-frame along axis index ai.
394
396{
397 fM[F03 + --ai] += amount;
398}
399
400////////////////////////////////////////////////////////////////////////////////
401/// General move in parent-frame.
402
404{
405 fM[F03] += x;
406 fM[F13] += y;
407 fM[F23] += z;
408}
409
410////////////////////////////////////////////////////////////////////////////////
411/// Rotate in parent frame. Does optimised version of MultLeft.
412
414{
415 if(i1 == i2) return;
416 // Algorithm: TEveTrans a; a.SetupRotation(i1, i2, amount); MultLeft(a);
417
418 // Optimized version:
419 const Double_t cos = TMath::Cos(amount), sin = TMath::Sin(amount);
420 Double_t b1, b2;
421 Double_t* col = fM;
422 --i1; --i2;
423 for(int c=0; c<4; ++c, col+=4) {
424 b1 = cos*col[i1] - sin*col[i2];
425 b2 = cos*col[i2] + sin*col[i1];
426 col[i1] = b1; col[i2] = b2;
427 }
428 fAsOK = kFALSE;
429}
430
431////////////////////////////////////////////////////////////////////////////////
432/// Move in a's coord-system along axis-index ai.
433
434void TEveTrans::Move(const TEveTrans& a, Int_t ai, Double_t amount)
435{
436 const Double_t* vec = a.fM + 4*--ai;
437 fM[F03] += amount*vec[0];
438 fM[F13] += amount*vec[1];
439 fM[F23] += amount*vec[2];
440}
441
442////////////////////////////////////////////////////////////////////////////////
443/// General move in a's coord-system.
444
446{
447 const Double_t* m = a.fM;
448 fM[F03] += x*m[F00] + y*m[F01] + z*m[F02];
449 fM[F13] += x*m[F10] + y*m[F11] + z*m[F12];
450 fM[F23] += x*m[F20] + y*m[F21] + z*m[F22];
451}
452
453////////////////////////////////////////////////////////////////////////////////
454/// Rotate in a's coord-system, rotating base vector with index i1
455/// into i2.
456
457void TEveTrans::Rotate(const TEveTrans& a, Int_t i1, Int_t i2, Double_t amount)
458{
459 if(i1 == i2) return;
460 TEveTrans x(a);
461 x.Invert();
462 MultLeft(x);
463 RotatePF(i1, i2, amount);
464 MultLeft(a);
465 fAsOK = kFALSE;
466}
467
468////////////////////////////////////////////////////////////////////////////////
469/// Set base-vector with index b.
470
472{
473 Double_t* col = fM + 4*--b;
474 col[0] = x; col[1] = y; col[2] = z;
475 fAsOK = kFALSE;
476}
477
478////////////////////////////////////////////////////////////////////////////////
479/// Set base-vector with index b.
480
482{
483 Double_t* col = fM + 4*--b;
484 v.GetXYZ(col);
485 fAsOK = kFALSE;
486}
487
488////////////////////////////////////////////////////////////////////////////////
489/// Get base-vector with index b.
490
492{
493 return TVector3(&fM[4*--b]);
494}
495
497{
498 // Get base-vector with index b.
499
500 const Double_t* col = fM + 4*--b;
501 v.SetXYZ(col[0], col[1], col[2]);
502}
503
504////////////////////////////////////////////////////////////////////////////////
505/// Set position (base-vec 4).
506
508{
509 fM[F03] = x; fM[F13] = y; fM[F23] = z;
510}
511
513{
514 // Set position (base-vec 4).
515 fM[F03] = x[0]; fM[F13] = x[1]; fM[F23] = x[2];
516}
517
519{
520 // Set position (base-vec 4).
521 fM[F03] = x[0]; fM[F13] = x[1]; fM[F23] = x[2];
522}
523
525{
526 // Set position (base-vec 4).
527 const Double_t* m = t.fM;
528 fM[F03] = m[F03]; fM[F13] = m[F13]; fM[F23] = m[F23];
529}
530
531////////////////////////////////////////////////////////////////////////////////
532/// Get position (base-vec 4).
533
535{
536 x = fM[F03]; y = fM[F13]; z = fM[F23];
537}
538
540{
541 // Get position (base-vec 4).
542 x[0] = fM[F03]; x[1] = fM[F13]; x[2] = fM[F23];
543}
544
546{
547 // Get position (base-vec 4).
548 x[0] = fM[F03]; x[1] = fM[F13]; x[2] = fM[F23];
549}
550
552{
553 // Get position (base-vec 4).
554 v.SetXYZ(fM[F03], fM[F13], fM[F23]);
555}
556
558{
559 // Get position (base-vec 4).
560 return TVector3(fM[F03], fM[F13], fM[F23]);
561}
562
563namespace
564{
565inline void clamp_angle(Float_t& a)
566{
567 while(a < -TMath::TwoPi()) a += TMath::TwoPi();
568 while(a > TMath::TwoPi()) a -= TMath::TwoPi();
569}
570}
571
573{
574 // Sets Rotation part as given by angles:
575 // a1 around z, -a2 around y, a3 around x.
576
577 clamp_angle(a1); clamp_angle(a2); clamp_angle(a3);
578
579 Double_t a, b, c, d, e, f;
580 a = TMath::Cos(a3); b = TMath::Sin(a3);
581 c = TMath::Cos(a2); d = TMath::Sin(a2); // should be -sin(a2) for positive direction
582 e = TMath::Cos(a1); f = TMath::Sin(a1);
583 Double_t ad = a*d, bd = b*d;
584
585 fM[F00] = c*e; fM[F01] = -bd*e - a*f; fM[F02] = -ad*e + b*f;
586 fM[F10] = c*f; fM[F11] = -bd*f + a*e; fM[F12] = -ad*f - b*e;
587 fM[F20] = d; fM[F21] = b*c; fM[F22] = a*c;
588
589 fA1 = a1; fA2 = a2; fA3 = a3;
590 fAsOK = kTRUE;
591}
592
593////////////////////////////////////////////////////////////////////////////////
594/// Sets Rotation part as given by angles a1, a1, a3 and pattern pat.
595/// Pattern consists of "XxYyZz" characters.
596/// eg: x means rotate about x axis, X means rotate in negative direction
597/// xYz -> R_x(a3) * R_y(-a2) * R_z(a1); (standard Gled representation)
598/// Note that angles and pattern elements have inverted order!
599///
600/// Implements Eulerian/Cardanian angles in a uniform way.
601
603 const char* pat)
604{
605 int n = strspn(pat, "XxYyZz"); if(n > 3) n = 3;
606 // Build Trans ... assign ...
607 Float_t a[] = { a3, a2, a1 };
608 UnitRot();
609 for(int i=0; i<n; i++) {
610 if(isupper(pat[i])) a[i] = -a[i];
611 switch(pat[i]) {
612 case 'x': case 'X': RotateLF(2, 3, a[i]); break;
613 case 'y': case 'Y': RotateLF(3, 1, a[i]); break;
614 case 'z': case 'Z': RotateLF(1, 2, a[i]); break;
615 }
616 }
617 fAsOK = kFALSE;
618}
619
620////////////////////////////////////////////////////////////////////////////////
621/// Get Cardan rotation angles (pattern xYz above).
622
624{
625 if(!fAsOK) {
626 Double_t sx, sy, sz;
627 GetScale(sx, sy, sz);
628 Double_t d = fM[F20]/sx;
629 if(d>1) d=1; else if(d<-1) d=-1; // Fix numerical errors
630 fA2 = TMath::ASin(d);
632 if(TMath::Abs(cos) > 8.7e-6) {
633 fA1 = TMath::ATan2(fM[F10], fM[F00]);
634 fA3 = TMath::ATan2(fM[F21]/sy, fM[F22]/sz);
635 } else {
636 fA1 = TMath::ATan2(fM[F10]/sx, fM[F11]/sy);
637 fA3 = 0;
638 }
639 fAsOK = kTRUE;
640 }
641 x[0] = fA1; x[1] = fA2; x[2] = fA3;
642}
643
644////////////////////////////////////////////////////////////////////////////////
645/// Scale matrix. Translation part untouched.
646
648{
649 fM[F00] *= sx; fM[F10] *= sx; fM[F20] *= sx;
650 fM[F01] *= sy; fM[F11] *= sy; fM[F21] *= sy;
651 fM[F02] *= sz; fM[F12] *= sz; fM[F22] *= sz;
652}
653
654////////////////////////////////////////////////////////////////////////////////
655/// Remove scaling, make all base vectors of unit length.
656
658{
659 Double_t sx, sy, sz;
660 Unscale(sx, sy, sz);
661 return (sx + sy + sz)/3;
662}
663
664////////////////////////////////////////////////////////////////////////////////
665/// Remove scaling, make all base vectors of unit length.
666
668{
669 GetScale(sx, sy, sz);
670 fM[F00] /= sx; fM[F10] /= sx; fM[F20] /= sx;
671 fM[F01] /= sy; fM[F11] /= sy; fM[F21] /= sy;
672 fM[F02] /= sz; fM[F12] /= sz; fM[F22] /= sz;
673}
674
675////////////////////////////////////////////////////////////////////////////////
676/// Deduce scales from sizes of base vectors.
677
679{
680 sx = TMath::Sqrt( fM[F00]*fM[F00] + fM[F10]*fM[F10] + fM[F20]*fM[F20] );
681 sy = TMath::Sqrt( fM[F01]*fM[F01] + fM[F11]*fM[F11] + fM[F21]*fM[F21] );
682 sz = TMath::Sqrt( fM[F02]*fM[F02] + fM[F12]*fM[F12] + fM[F22]*fM[F22] );
683}
684
685////////////////////////////////////////////////////////////////////////////////
686/// Set scaling.
687
689{
690 sx /= TMath::Sqrt( fM[F00]*fM[F00] + fM[F10]*fM[F10] + fM[F20]*fM[F20] );
691 sy /= TMath::Sqrt( fM[F01]*fM[F01] + fM[F11]*fM[F11] + fM[F21]*fM[F21] );
692 sz /= TMath::Sqrt( fM[F02]*fM[F02] + fM[F12]*fM[F12] + fM[F22]*fM[F22] );
693
694 fM[F00] *= sx; fM[F10] *= sx; fM[F20] *= sx;
695 fM[F01] *= sy; fM[F11] *= sy; fM[F21] *= sy;
696 fM[F02] *= sz; fM[F12] *= sz; fM[F22] *= sz;
697}
698
699////////////////////////////////////////////////////////////////////////////////
700/// Change x scaling.
701
703{
704 sx /= TMath::Sqrt( fM[F00]*fM[F00] + fM[F10]*fM[F10] + fM[F20]*fM[F20] );
705 fM[F00] *= sx; fM[F10] *= sx; fM[F20] *= sx;
706}
707
708////////////////////////////////////////////////////////////////////////////////
709/// Change y scaling.
710
712{
713 sy /= TMath::Sqrt( fM[F01]*fM[F01] + fM[F11]*fM[F11] + fM[F21]*fM[F21] );
714 fM[F01] *= sy; fM[F11] *= sy; fM[F21] *= sy;
715}
716
717////////////////////////////////////////////////////////////////////////////////
718/// Change z scaling.
719
721{
722 sz /= TMath::Sqrt( fM[F02]*fM[F02] + fM[F12]*fM[F12] + fM[F22]*fM[F22] );
723 fM[F02] *= sz; fM[F12] *= sz; fM[F22] *= sz;
724}
725
726////////////////////////////////////////////////////////////////////////////////
727/// Multiply vector in-place.
728
730{
731 v.SetXYZ(fM[F00]*v.x() + fM[F01]*v.y() + fM[F02]*v.z() + fM[F03]*w,
732 fM[F10]*v.x() + fM[F11]*v.y() + fM[F12]*v.z() + fM[F13]*w,
733 fM[F20]*v.x() + fM[F21]*v.y() + fM[F22]*v.z() + fM[F23]*w);
734}
735
736////////////////////////////////////////////////////////////////////////////////
737/// Multiply vector in-place.
738
740{
741 Double_t r[3] = { v[0], v[1], v[2] };
742 v[0] = fM[F00]*r[0] + fM[F01]*r[1] + fM[F02]*r[2] + fM[F03]*w;
743 v[1] = fM[F10]*r[0] + fM[F11]*r[1] + fM[F12]*r[2] + fM[F13]*w;
744 v[2] = fM[F20]*r[0] + fM[F21]*r[1] + fM[F22]*r[2] + fM[F23]*w;
745}
746
747////////////////////////////////////////////////////////////////////////////////
748/// Multiply vector in-place.
749
751{
752 Double_t r[3] = { v[0], v[1], v[2] };
753 v[0] = fM[F00]*r[0] + fM[F01]*r[1] + fM[F02]*r[2] + fM[F03]*w;
754 v[1] = fM[F10]*r[0] + fM[F11]*r[1] + fM[F12]*r[2] + fM[F13]*w;
755 v[2] = fM[F20]*r[0] + fM[F21]*r[1] + fM[F22]*r[2] + fM[F23]*w;
756}
757
758////////////////////////////////////////////////////////////////////////////////
759/// Multiply vector and return it.
760
762{
763 return TVector3(fM[F00]*v.x() + fM[F01]*v.y() + fM[F02]*v.z() + fM[F03]*w,
764 fM[F10]*v.x() + fM[F11]*v.y() + fM[F12]*v.z() + fM[F13]*w,
765 fM[F20]*v.x() + fM[F21]*v.y() + fM[F22]*v.z() + fM[F23]*w);
766}
767
768////////////////////////////////////////////////////////////////////////////////
769/// Multiply vector and fill output array vout.
770
771void TEveTrans::Multiply(const Double_t *vin, Double_t* vout, Double_t w) const
772{
773 vout[0] = fM[F00]*vin[0] + fM[F01]*vin[1] + fM[F02]*vin[2] + fM[F03]*w;
774 vout[1] = fM[F10]*vin[0] + fM[F11]*vin[1] + fM[F12]*vin[1] + fM[F13]*w;
775 vout[2] = fM[F20]*vin[0] + fM[F21]*vin[1] + fM[F22]*vin[1] + fM[F23]*w;
776}
777
778////////////////////////////////////////////////////////////////////////////////
779/// Rotate vector in-place. Translation is NOT applied.
780
782{
783 v.SetXYZ(fM[F00]*v.x() + fM[F01]*v.y() + fM[F02]*v.z(),
784 fM[F10]*v.x() + fM[F11]*v.y() + fM[F12]*v.z(),
785 fM[F20]*v.x() + fM[F21]*v.y() + fM[F22]*v.z());
786}
787
788////////////////////////////////////////////////////////////////////////////////
789/// Rotate vector in-place. Translation is NOT applied.
790
792{
793 Double_t t[3] = { v[0], v[1], v[2] };
794
795 v[0] = fM[F00]*t[0] + fM[F01]*t[1] + fM[F02]*t[2];
796 v[1] = fM[F10]*t[0] + fM[F11]*t[1] + fM[F12]*t[2];
797 v[2] = fM[F20]*t[0] + fM[F21]*t[1] + fM[F22]*t[2];
798}
799
800////////////////////////////////////////////////////////////////////////////////
801/// Rotate vector in-place. Translation is NOT applied.
802
804{
805 Double_t t[3] = { v[0], v[1], v[2] };
806
807 v[0] = fM[F00]*t[0] + fM[F01]*t[1] + fM[F02]*t[2];
808 v[1] = fM[F10]*t[0] + fM[F11]*t[1] + fM[F12]*t[2];
809 v[2] = fM[F20]*t[0] + fM[F21]*t[1] + fM[F22]*t[2];
810}
811
812////////////////////////////////////////////////////////////////////////////////
813/// Rotate vector and return the rotated vector. Translation is NOT applied.
814
816{
817 return TVector3(fM[F00]*v.x() + fM[F01]*v.y() + fM[F02]*v.z(),
818 fM[F10]*v.x() + fM[F11]*v.y() + fM[F12]*v.z(),
819 fM[F20]*v.x() + fM[F21]*v.y() + fM[F22]*v.z());
820}
821
822////////////////////////////////////////////////////////////////////////////////
823/// Norm 3-vector in column col.
824
826{
827 Double_t* c = fM + 4*--col;
828 const Double_t l = TMath::Sqrt(c[0]*c[0] + c[1]*c[1] + c[2]*c[2]);
829 c[0] /= l; c[1] /= l; c[2] /= l;
830 return l;
831}
832
833////////////////////////////////////////////////////////////////////////////////
834/// Orto-norm 3-vector in column col with respect to column ref.
835
837{
838 Double_t* c = fM + 4*--col;
839 Double_t* rc = fM + 4*--ref;
840 const Double_t dp = c[0]*rc[0] + c[1]*rc[1] + c[2]*rc[2];
841 c[0] -= rc[0]*dp; c[1] -= rc[1]*dp; c[2] -= rc[2]*dp;
842 return dp;
843}
844
845////////////////////////////////////////////////////////////////////////////////
846/// Orto-norm columns 1 to 3.
847
849{
850 Norm3Column(1);
851 Orto3Column(2,1); Norm3Column(2);
852 fM[F02] = fM[F10]*fM[F21] - fM[F11]*fM[F20];
853 fM[F12] = fM[F20]*fM[F01] - fM[F21]*fM[F00];
854 fM[F22] = fM[F00]*fM[F11] - fM[F01]*fM[F10];
855 // Cross-product faster than the following.
856 // Orto3Column(3,1); Orto3Column(3,2); Norm3Column(3);
857}
858
859////////////////////////////////////////////////////////////////////////////////
860/// Invert matrix.
861/// Copied from ROOT's TMatrixFCramerInv.
862
864{
865 static const TEveException eh("TEveTrans::Invert ");
866
867 // Find all NECESSARY 2x2 dets: (18 of them)
868 const Double_t det2_12_01 = fM[F10]*fM[F21] - fM[F11]*fM[F20];
869 const Double_t det2_12_02 = fM[F10]*fM[F22] - fM[F12]*fM[F20];
870 const Double_t det2_12_03 = fM[F10]*fM[F23] - fM[F13]*fM[F20];
871 const Double_t det2_12_13 = fM[F11]*fM[F23] - fM[F13]*fM[F21];
872 const Double_t det2_12_23 = fM[F12]*fM[F23] - fM[F13]*fM[F22];
873 const Double_t det2_12_12 = fM[F11]*fM[F22] - fM[F12]*fM[F21];
874 const Double_t det2_13_01 = fM[F10]*fM[F31] - fM[F11]*fM[F30];
875 const Double_t det2_13_02 = fM[F10]*fM[F32] - fM[F12]*fM[F30];
876 const Double_t det2_13_03 = fM[F10]*fM[F33] - fM[F13]*fM[F30];
877 const Double_t det2_13_12 = fM[F11]*fM[F32] - fM[F12]*fM[F31];
878 const Double_t det2_13_13 = fM[F11]*fM[F33] - fM[F13]*fM[F31];
879 const Double_t det2_13_23 = fM[F12]*fM[F33] - fM[F13]*fM[F32];
880 const Double_t det2_23_01 = fM[F20]*fM[F31] - fM[F21]*fM[F30];
881 const Double_t det2_23_02 = fM[F20]*fM[F32] - fM[F22]*fM[F30];
882 const Double_t det2_23_03 = fM[F20]*fM[F33] - fM[F23]*fM[F30];
883 const Double_t det2_23_12 = fM[F21]*fM[F32] - fM[F22]*fM[F31];
884 const Double_t det2_23_13 = fM[F21]*fM[F33] - fM[F23]*fM[F31];
885 const Double_t det2_23_23 = fM[F22]*fM[F33] - fM[F23]*fM[F32];
886
887 // Find all NECESSARY 3x3 dets: (16 of them)
888 const Double_t det3_012_012 = fM[F00]*det2_12_12 - fM[F01]*det2_12_02 + fM[F02]*det2_12_01;
889 const Double_t det3_012_013 = fM[F00]*det2_12_13 - fM[F01]*det2_12_03 + fM[F03]*det2_12_01;
890 const Double_t det3_012_023 = fM[F00]*det2_12_23 - fM[F02]*det2_12_03 + fM[F03]*det2_12_02;
891 const Double_t det3_012_123 = fM[F01]*det2_12_23 - fM[F02]*det2_12_13 + fM[F03]*det2_12_12;
892 const Double_t det3_013_012 = fM[F00]*det2_13_12 - fM[F01]*det2_13_02 + fM[F02]*det2_13_01;
893 const Double_t det3_013_013 = fM[F00]*det2_13_13 - fM[F01]*det2_13_03 + fM[F03]*det2_13_01;
894 const Double_t det3_013_023 = fM[F00]*det2_13_23 - fM[F02]*det2_13_03 + fM[F03]*det2_13_02;
895 const Double_t det3_013_123 = fM[F01]*det2_13_23 - fM[F02]*det2_13_13 + fM[F03]*det2_13_12;
896 const Double_t det3_023_012 = fM[F00]*det2_23_12 - fM[F01]*det2_23_02 + fM[F02]*det2_23_01;
897 const Double_t det3_023_013 = fM[F00]*det2_23_13 - fM[F01]*det2_23_03 + fM[F03]*det2_23_01;
898 const Double_t det3_023_023 = fM[F00]*det2_23_23 - fM[F02]*det2_23_03 + fM[F03]*det2_23_02;
899 const Double_t det3_023_123 = fM[F01]*det2_23_23 - fM[F02]*det2_23_13 + fM[F03]*det2_23_12;
900 const Double_t det3_123_012 = fM[F10]*det2_23_12 - fM[F11]*det2_23_02 + fM[F12]*det2_23_01;
901 const Double_t det3_123_013 = fM[F10]*det2_23_13 - fM[F11]*det2_23_03 + fM[F13]*det2_23_01;
902 const Double_t det3_123_023 = fM[F10]*det2_23_23 - fM[F12]*det2_23_03 + fM[F13]*det2_23_02;
903 const Double_t det3_123_123 = fM[F11]*det2_23_23 - fM[F12]*det2_23_13 + fM[F13]*det2_23_12;
904
905 // Find the 4x4 det:
906 const Double_t det = fM[F00]*det3_123_123 - fM[F01]*det3_123_023 +
907 fM[F02]*det3_123_013 - fM[F03]*det3_123_012;
908
909 if(det == 0) {
910 throw(eh + "matrix is singular.");
911 }
912
913 const Double_t oneOverDet = 1.0/det;
914 const Double_t mn1OverDet = - oneOverDet;
915
916 fM[F00] = det3_123_123 * oneOverDet;
917 fM[F01] = det3_023_123 * mn1OverDet;
918 fM[F02] = det3_013_123 * oneOverDet;
919 fM[F03] = det3_012_123 * mn1OverDet;
920
921 fM[F10] = det3_123_023 * mn1OverDet;
922 fM[F11] = det3_023_023 * oneOverDet;
923 fM[F12] = det3_013_023 * mn1OverDet;
924 fM[F13] = det3_012_023 * oneOverDet;
925
926 fM[F20] = det3_123_013 * oneOverDet;
927 fM[F21] = det3_023_013 * mn1OverDet;
928 fM[F22] = det3_013_013 * oneOverDet;
929 fM[F23] = det3_012_013 * mn1OverDet;
930
931 fM[F30] = det3_123_012 * mn1OverDet;
932 fM[F31] = det3_023_012 * oneOverDet;
933 fM[F32] = det3_013_012 * mn1OverDet;
934 fM[F33] = det3_012_012 * oneOverDet;
935
936 fAsOK = kFALSE;
937 return det;
938}
939
940////////////////////////////////////////////////////////////////////////////////
941/// Stream an object of class TEveTrans.
942
943void TEveTrans::Streamer(TBuffer &R__b)
944{
945 if (R__b.IsReading()) {
946 TEveTrans::Class()->ReadBuffer(R__b, this);
947 fAsOK = kFALSE;
948 } else {
949 TEveTrans::Class()->WriteBuffer(R__b, this);
950 }
951}
952
953////////////////////////////////////////////////////////////////////////////////
954/// Print in reasonable format.
955
956void TEveTrans::Print(Option_t* /*option*/) const
957{
958 const Double_t* row = fM;
959 for(Int_t i=0; i<4; ++i, ++row)
960 printf("%8.3f %8.3f %8.3f | %8.3f\n", row[0], row[4], row[8], row[12]);
961}
962
963#include <iomanip>
964
965////////////////////////////////////////////////////////////////////////////////
966/// Print to std::ostream.
967
968std::ostream& operator<<(std::ostream& s, const TEveTrans& t)
969{
970 s.setf(std::ios::fixed, std::ios::floatfield);
971 s.precision(3);
972 for(Int_t i=1; i<=4; i++)
973 for(Int_t j=1; j<=4; j++)
974 s << t(i,j) << ((j==4) ? "\n" : "\t");
975 return s;
976}
977
978#include "TGeoMatrix.h"
979#include "TBuffer3D.h"
980
982{
983 // Initialize from array.
984
986 memcpy(fM, carr, 16*sizeof(Double_t));
987 fAsOK = kFALSE;
988}
989
990////////////////////////////////////////////////////////////////////////////////
991/// Initialize from TGeoMatrix.
992
994{
996 const Double_t *r = mat.GetRotationMatrix();
997 const Double_t *t = mat.GetTranslation();
998 Double_t *m = fM;
999 if (mat.IsScale())
1000 {
1001 const Double_t *s = mat.GetScale();
1002 m[0] = r[0]*s[0]; m[1] = r[3]*s[0]; m[2] = r[6]*s[0]; m[3] = 0;
1003 m[4] = r[1]*s[1]; m[5] = r[4]*s[1]; m[6] = r[7]*s[1]; m[7] = 0;
1004 m[8] = r[2]*s[2]; m[9] = r[5]*s[2]; m[10] = r[8]*s[2]; m[11] = 0;
1005 m[12] = t[0]; m[13] = t[1]; m[14] = t[2]; m[15] = 1;
1006 }
1007 else
1008 {
1009 m[0] = r[0]; m[1] = r[3]; m[2] = r[6]; m[3] = 0;
1010 m[4] = r[1]; m[5] = r[4]; m[6] = r[7]; m[7] = 0;
1011 m[8] = r[2]; m[9] = r[5]; m[10] = r[8]; m[11] = 0;
1012 m[12] = t[0]; m[13] = t[1]; m[14] = t[2]; m[15] = 1;
1013 }
1014 fAsOK = kFALSE;
1015}
1016
1017////////////////////////////////////////////////////////////////////////////////
1018/// Set TGeoHMatrix mat.
1019
1021{
1022 Double_t *r = mat.GetRotationMatrix();
1023 Double_t *t = mat.GetTranslation();
1024 Double_t *s = mat.GetScale();
1025 if (fUseTrans)
1026 {
1028 Double_t *m = fM;
1029 GetScale(s[0], s[1], s[2]);
1030 r[0] = m[0]/s[0]; r[3] = m[1]/s[0]; r[6] = m[2]/s[0]; m += 4;
1031 r[1] = m[0]/s[1]; r[4] = m[1]/s[1]; r[7] = m[2]/s[1]; m += 4;
1032 r[2] = m[0]/s[2]; r[5] = m[1]/s[2]; r[8] = m[2]/s[2]; m += 4;
1033 t[0] = m[0]; t[1] = m[1]; t[2] = m[2];
1034 }
1035 else
1036 {
1038 r[0] = 1; r[3] = 0; r[6] = 0;
1039 r[1] = 0; r[4] = 1; r[7] = 0;
1040 r[2] = 0; r[5] = 0; r[8] = 1;
1041 s[0] = s[1] = s[2] = 1;
1042 t[0] = t[1] = t[2] = 0;
1043 }
1044}
1045
1046////////////////////////////////////////////////////////////////////////////////
1047/// Fill transformation part TBuffer3D core section.
1048
1050{
1051 buff.fLocalFrame = fUseTrans;
1052 if (fUseTrans) {
1053 // In phys-shape ctor the rotation part is transposed, due to
1054 // TGeo's convention for rotation matrix. So we have to transpose
1055 // it here, also.
1056 Double_t *m = buff.fLocalMaster;
1057 m[0] = fM[0]; m[1] = fM[4]; m[2] = fM[8]; m[3] = fM[3];
1058 m[4] = fM[1]; m[5] = fM[5]; m[6] = fM[9]; m[7] = fM[7];
1059 m[8] = fM[2]; m[9] = fM[6]; m[10] = fM[10]; m[11] = fM[11];
1060 m[12] = fM[12]; m[13] = fM[13]; m[14] = fM[14]; m[15] = fM[15];
1061 // Otherwise this would do:
1062 // memcpy(buff.fLocalMaster, fM, 16*sizeof(Double_t));
1063 }
1064}
1065
1066////////////////////////////////////////////////////////////////////////////////
1067/// Test if the transformation is a scale.
1068/// To be used by ROOT TGLObject descendants that potentially need to
1069/// use GL_NORMALIZE.
1070/// The low/high limits are expected to be squares of actual limits.
1071///
1072/// Ideally this should be done by the TGLViewer [but is not].
1073
1075{
1076 if (!fUseTrans) return kFALSE;
1077 Double_t s;
1078 s = fM[F00]*fM[F00] + fM[F10]*fM[F10] + fM[F20]*fM[F20];
1079 if (s < low || s > high) return kTRUE;
1080 s = fM[F01]*fM[F01] + fM[F11]*fM[F11] + fM[F21]*fM[F21];
1081 if (s < low || s > high) return kTRUE;
1082 s = fM[F02]*fM[F02] + fM[F12]*fM[F12] + fM[F22]*fM[F22];
1083 if (s < low || s > high) return kTRUE;
1084 return kFALSE;
1085}
void Class()
Definition: Class.C:29
SVector< double, 2 > v
Definition: Dict.h:5
ROOT::R::TRInterface & r
Definition: Object.C:4
#define d(i)
Definition: RSha256.hxx:102
#define b(i)
Definition: RSha256.hxx:100
#define f(i)
Definition: RSha256.hxx:104
#define c(i)
Definition: RSha256.hxx:101
#define h(i)
Definition: RSha256.hxx:106
#define e(i)
Definition: RSha256.hxx:103
int Int_t
Definition: RtypesCore.h:41
const Bool_t kFALSE
Definition: RtypesCore.h:88
bool Bool_t
Definition: RtypesCore.h:59
double Double_t
Definition: RtypesCore.h:55
float Float_t
Definition: RtypesCore.h:53
const Bool_t kTRUE
Definition: RtypesCore.h:87
const char Option_t
Definition: RtypesCore.h:62
#define ClassImp(name)
Definition: Rtypes.h:365
#define F01
Definition: TEveTrans.cxx:24
#define F22
Definition: TEveTrans.cxx:35
#define F00
Definition: TEveTrans.cxx:23
#define F02
Definition: TEveTrans.cxx:25
std::ostream & operator<<(std::ostream &s, const TEveTrans &t)
Print to std::ostream.
Definition: TEveTrans.cxx:968
#define F31
Definition: TEveTrans.cxx:39
#define F32
Definition: TEveTrans.cxx:40
#define F21
Definition: TEveTrans.cxx:34
#define F03
Definition: TEveTrans.cxx:26
#define F30
Definition: TEveTrans.cxx:38
#define F11
Definition: TEveTrans.cxx:29
#define F10
Definition: TEveTrans.cxx:28
#define F33
Definition: TEveTrans.cxx:41
#define F20
Definition: TEveTrans.cxx:33
#define F12
Definition: TEveTrans.cxx:30
#define F23
Definition: TEveTrans.cxx:36
#define F13
Definition: TEveTrans.cxx:31
double cos(double)
double sin(double)
Generic 3D primitive description class.
Definition: TBuffer3D.h:18
Double_t fLocalMaster[16]
Definition: TBuffer3D.h:92
Bool_t fLocalFrame
Definition: TBuffer3D.h:90
Buffer base class used for serializing objects.
Definition: TBuffer.h:42
Bool_t IsReading() const
Definition: TBuffer.h:85
Exception class thrown by TEve classes and macros.
Definition: TEveUtil.h:103
TEveTrans is a 4x4 transformation matrix for homogeneous coordinates stored internally in a column-ma...
Definition: TEveTrans.h:27
void SetGeoHMatrix(TGeoHMatrix &mat)
Set TGeoHMatrix mat.
Definition: TEveTrans.cxx:1020
void OrtoNorm3()
Orto-norm columns 1 to 3.
Definition: TEveTrans.cxx:848
void MultLeft(const TEveTrans &t)
Multiply from left: this = t * this.
Definition: TEveTrans.cxx:301
void UnitRot()
Reset rotation part of the matrix to unity.
Definition: TEveTrans.cxx:153
Bool_t fAsOK
Definition: TEveTrans.h:37
Bool_t IsScale(Double_t low=0.9, Double_t high=1.1) const
Test if the transformation is a scale.
Definition: TEveTrans.cxx:1074
void SetBaseVec(Int_t b, Double_t x, Double_t y, Double_t z)
Set base-vector with index b.
Definition: TEveTrans.cxx:471
Double_t Orto3Column(Int_t col, Int_t ref)
Orto-norm 3-vector in column col with respect to column ref.
Definition: TEveTrans.cxx:836
Float_t fA3
Definition: TEveTrans.h:36
void MoveLF(Int_t ai, Double_t amount)
Move in local-frame along axis with index ai.
Definition: TEveTrans.cxx:356
Float_t fA2
Definition: TEveTrans.h:35
TEveTrans operator*(const TEveTrans &t)
Copy, multiply from right and return product.
Definition: TEveTrans.cxx:334
TEveTrans()
Default constructor.
Definition: TEveTrans.cxx:74
void Move(const TEveTrans &a, Int_t ai, Double_t amount)
Move in a's coord-system along axis-index ai.
Definition: TEveTrans.cxx:434
void SetFromArray(const Double_t arr[16])
Set matrix from Double_t array.
Definition: TEveTrans.cxx:178
Bool_t fUseTrans
Definition: TEveTrans.h:40
void Scale(Double_t sx, Double_t sy, Double_t sz)
Scale matrix. Translation part untouched.
Definition: TEveTrans.cxx:647
void Rotate(const TEveTrans &a, Int_t i1, Int_t i2, Double_t amount)
Rotate in a's coord-system, rotating base vector with index i1 into i2.
Definition: TEveTrans.cxx:457
void MultRight(const TEveTrans &t)
Multiply from right: this = this * t.
Definition: TEveTrans.cxx:317
void RotateIP(TVector3 &v) const
Rotate vector in-place. Translation is NOT applied.
Definition: TEveTrans.cxx:781
TVector3 GetBaseVec(Int_t b) const
Get base-vector with index b.
Definition: TEveTrans.cxx:491
TVector3 Multiply(const TVector3 &v, Double_t w=1) const
Multiply vector and return it.
Definition: TEveTrans.cxx:761
void Move3(const TEveTrans &a, Double_t x, Double_t y, Double_t z)
General move in a's coord-system.
Definition: TEveTrans.cxx:445
void RotatePF(Int_t i1, Int_t i2, Double_t amount)
Rotate in parent frame. Does optimised version of MultLeft.
Definition: TEveTrans.cxx:413
void SetScale(Double_t sx, Double_t sy, Double_t sz)
Set scaling.
Definition: TEveTrans.cxx:688
void SetRotByAngles(Float_t a1, Float_t a2, Float_t a3)
Definition: TEveTrans.cxx:572
void SetScaleX(Double_t sx)
Change x scaling.
Definition: TEveTrans.cxx:702
void RotateLF(Int_t i1, Int_t i2, Double_t amount)
Rotate in local frame. Does optimised version of MultRight.
Definition: TEveTrans.cxx:375
void UnitTrans()
Reset matrix to unity.
Definition: TEveTrans.cxx:130
void SetScaleY(Double_t sy)
Change y scaling.
Definition: TEveTrans.cxx:711
Double_t Norm3Column(Int_t col)
Norm 3-vector in column col.
Definition: TEveTrans.cxx:825
void SetRotByAnyAngles(Float_t a1, Float_t a2, Float_t a3, const char *pat)
Sets Rotation part as given by angles a1, a1, a3 and pattern pat.
Definition: TEveTrans.cxx:602
void SetupFromToVec(const TEveVector &from, const TEveVector &to)
A function for creating a rotation matrix that rotates a vector called "from" into another vector cal...
Definition: TEveTrans.cxx:219
void MovePF(Int_t ai, Double_t amount)
Move in parent-frame along axis index ai.
Definition: TEveTrans.cxx:395
Double_t Invert()
Invert matrix.
Definition: TEveTrans.cxx:863
virtual void Print(Option_t *option="") const
Print in reasonable format.
Definition: TEveTrans.cxx:956
Float_t fA1
Definition: TEveTrans.h:34
void Move3LF(Double_t x, Double_t y, Double_t z)
General move in local-frame.
Definition: TEveTrans.cxx:365
TVector3 GetPos() const
Definition: TEveTrans.cxx:557
Double32_t fM[16]
Definition: TEveTrans.h:32
void TransposeRotationPart()
Transpose 3x3 rotation sub-matrix.
Definition: TEveTrans.cxx:344
void SetupRotation(Int_t i, Int_t j, Double_t f)
Setup the matrix as an elementary rotation.
Definition: TEveTrans.cxx:199
void SetBuffer3D(TBuffer3D &buff)
Fill transformation part TBuffer3D core section.
Definition: TEveTrans.cxx:1049
void GetScale(Double_t &sx, Double_t &sy, Double_t &sz) const
Deduce scales from sizes of base vectors.
Definition: TEveTrans.cxx:678
void MultiplyIP(TVector3 &v, Double_t w=1) const
Multiply vector in-place.
Definition: TEveTrans.cxx:729
Double_t Unscale()
Remove scaling, make all base vectors of unit length.
Definition: TEveTrans.cxx:657
void SetFrom(Double_t *carr)
Definition: TEveTrans.cxx:981
void SetTrans(const TEveTrans &t, Bool_t copyAngles=kTRUE)
Set matrix from another,.
Definition: TEveTrans.cxx:164
void Move3PF(Double_t x, Double_t y, Double_t z)
General move in parent-frame.
Definition: TEveTrans.cxx:403
void SetScaleZ(Double_t sz)
Change z scaling.
Definition: TEveTrans.cxx:720
void GetRotAngles(Float_t *x) const
Get Cardan rotation angles (pattern xYz above).
Definition: TEveTrans.cxx:623
void SetPos(Double_t x, Double_t y, Double_t z)
Set position (base-vec 4).
Definition: TEveTrans.cxx:507
Double_t CM(Int_t i, Int_t j) const
Definition: TEveTrans.h:103
void ZeroTrans(Double_t w=1.0)
Reset matrix to zero, only the perspective scaling is set to w (1 by default).
Definition: TEveTrans.cxx:142
TEveVectorT Cross(const TEveVectorT &a) const
Definition: TEveVector.h:174
TT Dot(const TEveVectorT &a) const
Definition: TEveVector.h:167
TEveVectorT & Sub(const TEveVectorT &a, const TEveVectorT &b)
Definition: TEveVector.h:185
TT Mag2() const
Definition: TEveVector.h:97
Matrix class used for computing global transformations Should NOT be used for node definition.
Definition: TGeoMatrix.h:421
virtual const Double_t * GetScale() const
Definition: TGeoMatrix.h:469
virtual const Double_t * GetTranslation() const
Definition: TGeoMatrix.h:467
virtual const Double_t * GetRotationMatrix() const
Definition: TGeoMatrix.h:468
Geometrical transformation package.
Definition: TGeoMatrix.h:41
Bool_t IsScale() const
Definition: TGeoMatrix.h:70
@ kGeoGenTrans
Definition: TGeoMatrix.h:54
virtual const Double_t * GetTranslation() const =0
virtual const Double_t * GetScale() const =0
virtual const Double_t * GetRotationMatrix() const =0
Mother of all ROOT objects.
Definition: TObject.h:37
void SetBit(UInt_t f, Bool_t set)
Set or unset the user status bits as specified in f.
Definition: TObject.cxx:694
void ResetBit(UInt_t f)
Definition: TObject.h:171
TVector3 is a general three vector class, which can be used for the description of different vectors ...
Definition: TVector3.h:22
return c1
Definition: legend1.C:41
Double_t y[n]
Definition: legend1.C:17
Double_t x[n]
Definition: legend1.C:17
const Int_t n
Definition: legend1.C:16
return c2
Definition: legend2.C:14
return c3
Definition: legend3.C:15
static constexpr double s
Double_t ASin(Double_t)
Definition: TMath.h:649
Double_t ATan2(Double_t, Double_t)
Definition: TMath.h:667
Double_t Sqrt(Double_t x)
Definition: TMath.h:679
Double_t Cos(Double_t)
Definition: TMath.h:629
Double_t Sin(Double_t)
Definition: TMath.h:625
Short_t Abs(Short_t d)
Definition: TMathBase.h:120
constexpr Double_t TwoPi()
Definition: TMath.h:45
auto * m
Definition: textangle.C:8
auto * l
Definition: textangle.C:4
auto * a
Definition: textangle.C:12