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TGeoHype.cxx
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1// @(#)root/geom:$Id$
2// Author: Mihaela Gheata 20/11/04
3
4/*************************************************************************
5 * Copyright (C) 1995-2000, 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
13#include <iostream>
14
15#include "TGeoManager.h"
16#include "TGeoVolume.h"
17#include "TVirtualGeoPainter.h"
18#include "TGeoHype.h"
19#include "TBuffer3D.h"
20#include "TBuffer3DTypes.h"
21#include "TMath.h"
22
23/** \class TGeoHype
24\ingroup Geometry_classes
25
26Hyperboloid class defined by 5 parameters. Bounded by:
27 - Two z planes at z=+/-dz
28 - Inner and outer lateral surfaces. These represent the surfaces
29 described by the revolution of 2 hyperbolas about the Z axis:
30 r^2 - (t*z)^2 = a^2
31
32 - r = distance between hyperbola and Z axis at coordinate z
33 - t = tangent of the stereo angle (angle made by hyperbola
34 asymptotic lines and Z axis). t=0 means cylindrical surface.
35 - a = distance between hyperbola and Z axis at z=0
36
37The inner hyperbolic surface is described by:
38 r^2 - (tin*z)^2 = rin^2
39 - absence of the inner surface (filled hyperboloid can be forced
40 by rin=0 and sin=0
41The outer hyperbolic surface is described by:
42 r^2 - (tout*z)^2 = rout^2
43TGeoHype parameters: dz[cm], rin[cm], sin[deg], rout[cm], sout[deg].
44MANDATORY conditions:
45
46 - rin < rout
47 - rout > 0
48 - rin^2 + (tin*dz)^2 > rout^2 + (tout*dz)^2
49
50SUPPORTED CASES:
51
52 - rin = 0, tin != 0 => inner surface conical
53 - tin=0 AND/OR tout=0 => corresponding surface(s) cylindrical
54 e.g. tin=0 AND tout=0 => shape becomes a tube with: rmin,rmax,dz
55*/
56
58
59////////////////////////////////////////////////////////////////////////////////
60/// Default constructor
61
63{
65 fStIn = 0.;
66 fStOut = 0.;
67 fTin = 0.;
68 fTinsq = 0.;
69 fTout = 0.;
70 fToutsq = 0.;
71}
72
73
74////////////////////////////////////////////////////////////////////////////////
75/// Constructor specifying hyperboloid parameters.
76
78 :TGeoTube(rin, rout, dz)
79{
81 SetHypeDimensions(rin, stin, rout, stout, dz);
82 // dz<0 can be used to force dz of hyperboloid fit the container volume
85}
86////////////////////////////////////////////////////////////////////////////////
87/// Constructor specifying parameters and name.
88
89TGeoHype::TGeoHype(const char *name,Double_t rin, Double_t stin, Double_t rout, Double_t stout, Double_t dz)
90 :TGeoTube(name, rin, rout, dz)
91{
93 SetHypeDimensions(rin, stin, rout, stout, dz);
94 // dz<0 can be used to force dz of hyperboloid fit the container volume
97}
98
99////////////////////////////////////////////////////////////////////////////////
100/// Default constructor specifying a list of parameters
101/// - param[0] = dz
102/// - param[1] = rin
103/// - param[2] = stin
104/// - param[3] = rout
105/// - param[4] = stout
106
108 :TGeoTube(param[1],param[3],param[0])
109{
111 SetDimensions(param);
112 // dz<0 can be used to force dz of hyperboloid fit the container volume
114 ComputeBBox();
115}
116
117////////////////////////////////////////////////////////////////////////////////
118/// destructor
119
121{
122}
123
124////////////////////////////////////////////////////////////////////////////////
125/// Computes capacity of the shape in [length^3]
126
128{
129 Double_t capacity = 2.*TMath::Pi()*fDz*(fRmax*fRmax-fRmin*fRmin) +
130 (2.*TMath::Pi()/3.)*fDz*fDz*fDz*(fToutsq-fTinsq);
131 return capacity;
132}
133
134////////////////////////////////////////////////////////////////////////////////
135/// Compute bounding box of the hyperboloid
136
138{
139 if (fRmin<0.) {
140 Warning("ComputeBBox", "Shape %s has invalid rmin=%g ! SET TO 0.", GetName(),fRmin);
141 fRmin = 0.;
142 }
145 Error("ComputeBBox", "Shape %s hyperbolic surfaces are malformed: rin=%g, stin=%g, rout=%g, stout=%g",
147 return;
148 }
149
151 fDZ = fDz;
152}
153
154////////////////////////////////////////////////////////////////////////////////
155/// Compute normal to closest surface from POINT.
156
157void TGeoHype::ComputeNormal(const Double_t *point, const Double_t *dir, Double_t *norm)
158{
159 Double_t saf[3];
160 Double_t rsq = point[0]*point[0]+point[1]*point[1];
161 Double_t r = TMath::Sqrt(rsq);
162 Double_t rin = (HasInner())?(TMath::Sqrt(RadiusHypeSq(point[2],kTRUE))):0.;
163 Double_t rout = TMath::Sqrt(RadiusHypeSq(point[2],kFALSE));
164 saf[0] = TMath::Abs(fDz-TMath::Abs(point[2]));
165 saf[1] = (HasInner())?TMath::Abs(rin-r):TGeoShape::Big();
166 saf[2] = TMath::Abs(rout-r);
167 Int_t i = TMath::LocMin(3,saf);
168 if (i==0 || r<1.E-10) {
169 norm[0] = norm[1] = 0.;
170 norm[2] = TMath::Sign(1.,dir[2]);
171 return;
172 }
173 Double_t t = (i==1)?fTinsq:fToutsq;;
174 t *= -point[2]/r;
175 Double_t ct = TMath::Sqrt(1./(1.+t*t));
176 Double_t st = t * ct;
177 Double_t phi = TMath::ATan2(point[1], point[0]);
178 Double_t cphi = TMath::Cos(phi);
179 Double_t sphi = TMath::Sin(phi);
180
181 norm[0] = ct*cphi;
182 norm[1] = ct*sphi;
183 norm[2] = st;
184 if (norm[0]*dir[0]+norm[1]*dir[1]+norm[2]*dir[2]<0) {
185 norm[0] = -norm[0];
186 norm[1] = -norm[1];
187 norm[2] = -norm[2];
188 }
189}
190
191////////////////////////////////////////////////////////////////////////////////
192/// test if point is inside this tube
193
195{
196 if (TMath::Abs(point[2]) > fDz) return kFALSE;
197 Double_t r2 = point[0]*point[0]+point[1]*point[1];
198 Double_t routsq = RadiusHypeSq(point[2], kFALSE);
199 if (r2>routsq) return kFALSE;
200 if (!HasInner()) return kTRUE;
201 Double_t rinsq = RadiusHypeSq(point[2], kTRUE);
202 if (r2<rinsq) return kFALSE;
203 return kTRUE;
204}
205
206////////////////////////////////////////////////////////////////////////////////
207/// compute closest distance from point px,py to each corner
208
210{
211 Int_t numPoints = GetNmeshVertices();
212 return ShapeDistancetoPrimitive(numPoints, px, py);
213}
214
215////////////////////////////////////////////////////////////////////////////////
216/// Compute distance from inside point to surface of the hyperboloid.
217
218Double_t TGeoHype::DistFromInside(const Double_t *point, const Double_t *dir, Int_t iact, Double_t step, Double_t *safe) const
219{
220 if (iact<3 && safe) {
221 *safe = Safety(point, kTRUE);
222 if (iact==0) return TGeoShape::Big();
223 if ((iact==1) && (*safe>step)) return TGeoShape::Big();
224 }
225 // compute distance to surface
226 // Do Z
228 if (dir[2]>0) {
229 sz = (fDz-point[2])/dir[2];
230 if (sz<=0.) return 0.;
231 } else {
232 if (dir[2]<0) {
233 sz = -(fDz+point[2])/dir[2];
234 if (sz<=0.) return 0.;
235 }
236 }
237
238
239 // Do R
240 Double_t srin = TGeoShape::Big();
241 Double_t srout = TGeoShape::Big();
242 Double_t sr;
243 // inner and outer surfaces
244 Double_t s[2];
245 Int_t npos;
246 npos = DistToHype(point, dir, s, kTRUE, kTRUE);
247 if (npos) srin = s[0];
248 npos = DistToHype(point, dir, s, kFALSE, kTRUE);
249 if (npos) srout = s[0];
250 sr = TMath::Min(srin, srout);
251 return TMath::Min(sz,sr);
252}
253
254
255////////////////////////////////////////////////////////////////////////////////
256/// compute distance from outside point to surface of the hyperboloid.
257
258Double_t TGeoHype::DistFromOutside(const Double_t *point, const Double_t *dir, Int_t iact, Double_t step, Double_t *safe) const
259{
260 if (iact<3 && safe) {
261 *safe = Safety(point, kFALSE);
262 if (iact==0) return TGeoShape::Big();
263 if ((iact==1) && (step<=*safe)) return TGeoShape::Big();
264 }
265// Check if the bounding box is crossed within the requested distance
266 Double_t sdist = TGeoBBox::DistFromOutside(point,dir, fDX, fDY, fDZ, fOrigin, step);
267 if (sdist>=step) return TGeoShape::Big();
268 // find distance to shape
269 // Do Z
270 Double_t xi, yi, zi;
272 if (TMath::Abs(point[2])>=fDz) {
273 // We might find Z plane crossing
274 if ((point[2]*dir[2]) < 0) {
275 // Compute distance to Z (always positive)
276 sz = (TMath::Abs(point[2])-fDz)/TMath::Abs(dir[2]);
277 // Extrapolate
278 xi = point[0]+sz*dir[0];
279 yi = point[1]+sz*dir[1];
280 Double_t r2 = xi*xi + yi*yi;
281 Double_t rmin2 = RadiusHypeSq(fDz, kTRUE);
282 if (r2 >= rmin2) {
284 if (r2 <= rmax2) return sz;
285 }
286 }
287 }
288 // We do not cross Z planes.
290 Double_t sout = TGeoShape::Big();
291 Double_t s[2];
292 Int_t npos;
293 npos = DistToHype(point, dir, s, kTRUE, kFALSE);
294 if (npos) {
295 zi = point[2] + s[0]*dir[2];
296 if (TMath::Abs(zi) <= fDz) sin = s[0];
297 else if (npos==2) {
298 zi = point[2] + s[1]*dir[2];
299 if (TMath::Abs(zi) <= fDz) sin = s[1];
300 }
301 }
302 npos = DistToHype(point, dir, s, kFALSE, kFALSE);
303 if (npos) {
304 zi = point[2] + s[0]*dir[2];
305 if (TMath::Abs(zi) <= fDz) sout = s[0];
306 else if (npos==2) {
307 zi = point[2] + s[1]*dir[2];
308 if (TMath::Abs(zi) <= fDz) sout = s[1];
309 }
310 }
311 return TMath::Min(sin, sout);
312}
313
314////////////////////////////////////////////////////////////////////////////////
315/// Compute distance from an arbitrary point to inner/outer surface of hyperboloid.
316/// Returns number of positive solutions. S[2] contains the solutions.
317
318Int_t TGeoHype::DistToHype(const Double_t *point, const Double_t *dir, Double_t *s, Bool_t inner, Bool_t in) const
319{
320 Double_t r0, t0, snext;
321 if (inner) {
322 if (!HasInner()) return 0;
323 r0 = fRmin;
324 t0 = fTinsq;
325 } else {
326 r0 = fRmax;
327 t0 = fToutsq;
328 }
329 Double_t a = dir[0]*dir[0] + dir[1]*dir[1] - t0*dir[2]*dir[2];
330 Double_t b = t0*point[2]*dir[2] - point[0]*dir[0] - point[1]*dir[1];
331 Double_t c = point[0]*point[0] + point[1]*point[1] - t0*point[2]*point[2] - r0*r0;
332
334 if (TMath::Abs(b) < TGeoShape::Tolerance()) return 0;
335 snext = 0.5*c/b;
336 if (snext < 0.) return 0;
337 s[0] = snext;
338 return 1;
339 }
340
341 Double_t delta = b*b - a*c;
342 Double_t ainv = 1./a;
343 Int_t npos = 0;
344 if (delta < 0.) return 0;
345 delta = TMath::Sqrt(delta);
346 Double_t sone = TMath::Sign(1.,ainv);
347 Int_t i = -1;
348 while (i<2) {
349 snext = (b + i*sone*delta)*ainv;
350 i += 2;
351 if (snext<0) continue;
352 if (snext<1.E-8) {
353 Double_t r = TMath::Sqrt(point[0]*point[0]+point[1]*point[1]);
354 Double_t t = (inner)?fTinsq:fToutsq;
355 t *= -point[2]/r;
356 Double_t phi = TMath::ATan2(point[1], point[0]);
357 Double_t ndotd = TMath::Cos(phi)*dir[0]+TMath::Sin(phi)*dir[1]+t*dir[2];
358 if (inner) ndotd *= -1;
359 if (in) ndotd *= -1;
360 if (ndotd<0) s[npos++] = snext;
361 } else s[npos++] = snext;
362 }
363 return npos;
364}
365
366////////////////////////////////////////////////////////////////////////////////
367/// Cannot divide hyperboloids.
368
369TGeoVolume *TGeoHype::Divide(TGeoVolume * /*voldiv*/, const char *divname, Int_t /*iaxis*/, Int_t /*ndiv*/,
370 Double_t /*start*/, Double_t /*step*/)
371{
372 Error("Divide", "Hyperboloids cannot be divided. Division volume %s not created", divname);
373 return 0;
374}
375
376////////////////////////////////////////////////////////////////////////////////
377/// Get range of shape for a given axis.
378
380{
381 xlo = 0;
382 xhi = 0;
383 Double_t dx = 0;
384 switch (iaxis) {
385 case 1: // R
386 xlo = fRmin;
388 dx = xhi-xlo;
389 return dx;
390 case 2: // Phi
391 xlo = 0;
392 xhi = 360;
393 dx = 360;
394 return dx;
395 case 3: // Z
396 xlo = -fDz;
397 xhi = fDz;
398 dx = xhi-xlo;
399 return dx;
400 }
401 return dx;
402}
403
404////////////////////////////////////////////////////////////////////////////////
405/// Fill vector param[4] with the bounding cylinder parameters. The order
406/// is the following : Rmin, Rmax, Phi1, Phi2, dZ
407
409{
410 param[0] = fRmin; // Rmin
411 param[0] *= param[0];
412 param[1] = TMath::Sqrt(RadiusHypeSq(fDz, kFALSE)); // Rmax
413 param[1] *= param[1];
414 param[2] = 0.; // Phi1
415 param[3] = 360.; // Phi2
416}
417
418////////////////////////////////////////////////////////////////////////////////
419/// in case shape has some negative parameters, these has to be computed
420/// in order to fit the mother
421
423{
424 if (!TestShapeBit(kGeoRunTimeShape)) return 0;
425 Double_t dz;
426 Double_t zmin,zmax;
427 dz = fDz;
428 if (fDz<0) {
429 mother->GetAxisRange(3,zmin,zmax);
430 if (zmax<0) return 0;
431 dz=zmax;
432 } else {
433 Error("GetMakeRuntimeShape", "Shape %s does not have negative Z range", GetName());
434 return 0;
435 }
436 TGeoShape *hype = new TGeoHype(GetName(), dz, fRmax, fStOut, fRmin, fStIn);
437 return hype;
438}
439
440////////////////////////////////////////////////////////////////////////////////
441/// print shape parameters
442
444{
445 printf("*** Shape %s: TGeoHype ***\n", GetName());
446 printf(" Rin = %11.5f\n", fRmin);
447 printf(" sin = %11.5f\n", fStIn);
448 printf(" Rout = %11.5f\n", fRmax);
449 printf(" sout = %11.5f\n", fStOut);
450 printf(" dz = %11.5f\n", fDz);
451
452 printf(" Bounding box:\n");
454}
455
456////////////////////////////////////////////////////////////////////////////////
457/// Creates a TBuffer3D describing *this* shape.
458/// Coordinates are in local reference frame.
459
461{
463 Bool_t hasRmin = HasInner();
464 Int_t nbPnts = (hasRmin)?(2*n*n):(n*n+2);
465 Int_t nbSegs = (hasRmin)?(4*n*n):(n*(2*n+1));
466 Int_t nbPols = (hasRmin)?(2*n*n):(n*(n+1));
467
469 nbPnts, 3*nbPnts, nbSegs, 3*nbSegs, nbPols, 6*nbPols);
470 if (buff)
471 {
472 SetPoints(buff->fPnts);
473 SetSegsAndPols(*buff);
474 }
475
476 return buff;
477}
478
479////////////////////////////////////////////////////////////////////////////////
480/// Fill TBuffer3D structure for segments and polygons.
481
483{
485 Int_t i, j, n;
487 Bool_t hasRmin = HasInner();
488 Int_t irin = 0;
489 Int_t irout = (hasRmin)?(n*n):2;
490 // Fill segments
491 // Case hasRmin:
492 // Inner circles: [isin = 0], n (per circle) * n ( circles)
493 // iseg = isin+n*i+j , i = 0, n-1 , j = 0, n-1
494 // seg(i=1,n; j=1,n) = [irin+n*i+j] and [irin+n*i+(j+1)%n]
495 // Inner generators: [isgenin = isin+n*n], n (per circle) *(n-1) (slices)
496 // iseg = isgenin + i*n + j, i=0,n-2, j=0,n-1
497 // seg(i,j) = [irin+n*i+j] and [irin+n*(i+1)+j]
498 // Outer circles: [isout = isgenin+n*(n-1)], n (per circle) * n ( circles)
499 // iseg = isout + i*n + j , iz = 0, n-1 , j = 0, n-1
500 // seg(i=1,n; j=1,n) = [irout+n*i+j] and [irout+n*i+(j+1)%n]
501 // Outer generators: [isgenout = isout+n*n], n (per circle) *(n-1) (slices)
502 // iseg = isgenout + i*n + j, i=0,n-2, j=0,n-1
503 // seg(i,j) = [irout+n*i+j] and [irout+n*(i+1)+j]
504 // Lower cap : [islow = isgenout + n*(n-1)], n radial segments
505 // iseg = islow + j, j=0,n-1
506 // seg(j) = [irin + j] and [irout+j]
507 // Upper cap: [ishi = islow + n], nradial segments
508 // iseg = ishi + j, j=0,n-1
509 // seg[j] = [irin + n*(n-1) + j] and [irout+n*(n-1) + j]
510 //
511 // Case !hasRmin:
512 // Outer circles: [isout=0], same outer circles (n*n)
513 // Outer generators: isgenout = isout + n*n
514 // Lower cap: [islow = isgenout+n*(n-1)], n seg.
515 // iseg = islow + j, j=0,n-1
516 // seg[j] = [irin] and [irout+j]
517 // Upper cap: [ishi = islow +n]
518 // iseg = ishi + j, j=0,n-1
519 // seg[j] = [irin+1] and [irout+n*(n-1) + j]
520
521 Int_t isin = 0;
522 Int_t isgenin = (hasRmin)?(isin+n*n):0;
523 Int_t isout = (hasRmin)?(isgenin+n*(n-1)):0;
524 Int_t isgenout = isout+n*n;
525 Int_t islo = isgenout+n*(n-1);
526 Int_t ishi = islo + n;
527
528 Int_t npt = 0;
529 // Fill inner circle segments (n*n)
530 if (hasRmin) {
531 for (i=0; i<n; i++) {
532 for (j=0; j<n; j++) {
533 npt = 3*(isin+n*i+j);
534 buff.fSegs[npt] = c;
535 buff.fSegs[npt+1] = irin+n*i+j;
536 buff.fSegs[npt+2] = irin+n*i+((j+1)%n);
537 }
538 }
539 // Fill inner generators (n*(n-1))
540 for (i=0; i<n-1; i++) {
541 for (j=0; j<n; j++) {
542 npt = 3*(isgenin+n*i+j);
543 buff.fSegs[npt] = c;
544 buff.fSegs[npt+1] = irin+n*i+j;
545 buff.fSegs[npt+2] = irin+n*(i+1)+j;
546 }
547 }
548 }
549 // Fill outer circle segments (n*n)
550 for (i=0; i<n; i++) {
551 for (j=0; j<n; j++) {
552 npt = 3*(isout + n*i+j);
553 buff.fSegs[npt] = c;
554 buff.fSegs[npt+1] = irout+n*i+j;
555 buff.fSegs[npt+2] = irout+n*i+((j+1)%n);
556 }
557 }
558 // Fill outer generators (n*(n-1))
559 for (i=0; i<n-1; i++) {
560 for (j=0; j<n; j++) {
561 npt = 3*(isgenout+n*i+j);
562 buff.fSegs[npt] = c;
563 buff.fSegs[npt+1] = irout+n*i+j;
564 buff.fSegs[npt+2] = irout+n*(i+1)+j;
565 }
566 }
567 // Fill lower cap (n)
568 for (j=0; j<n; j++) {
569 npt = 3*(islo+j);
570 buff.fSegs[npt] = c;
571 buff.fSegs[npt+1] = irin;
572 if (hasRmin) buff.fSegs[npt+1] += j;
573 buff.fSegs[npt+2] = irout + j;
574 }
575 // Fill upper cap (n)
576 for (j=0; j<n; j++) {
577 npt = 3*(ishi+j);
578 buff.fSegs[npt] = c;
579 buff.fSegs[npt+1] = irin+1;
580 if (hasRmin) buff.fSegs[npt+1] += n*(n-1)+j-1;
581 buff.fSegs[npt+2] = irout + n*(n-1)+j;
582 }
583
584 // Fill polygons
585 // Inner polygons: [ipin = 0] (n-1) slices * n (edges)
586 // ipoly = ipin + n*i + j; i=0,n-2 j=0,n-1
587 // poly[i,j] = [isin+n*i+j] [isgenin+i*n+(j+1)%n] [isin+n*(i+1)+j] [isgenin+i*n+j]
588 // Outer polygons: [ipout = ipin+n*(n-1)] also (n-1)*n
589 // ipoly = ipout + n*i + j; i=0,n-2 j=0,n-1
590 // poly[i,j] = [isout+n*i+j] [isgenout+i*n+j] [isout+n*(i+1)+j] [isgenout+i*n+(j+1)%n]
591 // Lower cap: [iplow = ipout+n*(n-1): n polygons
592 // ipoly = iplow + j; j=0,n-1
593 // poly[i=0,j] = [isin+j] [islow+j] [isout+j] [islow+(j+1)%n]
594 // Upper cap: [ipup = iplow+n] : n polygons
595 // ipoly = ipup + j; j=0,n-1
596 // poly[i=n-1, j] = [isin+n*(n-1)+j] [ishi+(j+1)%n] [isout+n*(n-1)+j] [ishi+j]
597 //
598 // Case !hasRmin:
599 // ipin = 0 no inner polygons
600 // ipout = 0 same outer polygons
601 // Lower cap: iplow = ipout+n*(n-1): n polygons with 3 segments
602 // poly[i=0,j] = [isout+j] [islow+(j+1)%n] [islow+j]
603 // Upper cap: ipup = iplow+n;
604 // poly[i=n-1,j] = [isout+n*(n-1)+j] [ishi+j] [ishi+(j+1)%n]
605
606 Int_t ipin = 0;
607 Int_t ipout = (hasRmin)?(ipin+n*(n-1)):0;
608 Int_t iplo = ipout+n*(n-1);
609 Int_t ipup = iplo+n;
610 // Inner polygons n*(n-1)
611 if (hasRmin) {
612 for (i=0; i<n-1; i++) {
613 for (j=0; j<n; j++) {
614 npt = 6*(ipin+n*i+j);
615 buff.fPols[npt] = c;
616 buff.fPols[npt+1] = 4;
617 buff.fPols[npt+2] = isin+n*i+j;
618 buff.fPols[npt+3] = isgenin+i*n+((j+1)%n);
619 buff.fPols[npt+4] = isin+n*(i+1)+j;
620 buff.fPols[npt+5] = isgenin+i*n+j;
621 }
622 }
623 }
624 // Outer polygons n*(n-1)
625 for (i=0; i<n-1; i++) {
626 for (j=0; j<n; j++) {
627 npt = 6*(ipout+n*i+j);
628 buff.fPols[npt] = c;
629 buff.fPols[npt+1] = 4;
630 buff.fPols[npt+2] = isout+n*i+j;
631 buff.fPols[npt+3] = isgenout+i*n+j;
632 buff.fPols[npt+4] = isout+n*(i+1)+j;
633 buff.fPols[npt+5] = isgenout+i*n+((j+1)%n);
634 }
635 }
636 // End caps
637 if (hasRmin) {
638 for (j=0; j<n; j++) {
639 npt = 6*(iplo+j);
640 buff.fPols[npt] = c+1;
641 buff.fPols[npt+1] = 4;
642 buff.fPols[npt+2] = isin+j;
643 buff.fPols[npt+3] = islo+j;
644 buff.fPols[npt+4] = isout+j;
645 buff.fPols[npt+5] = islo+((j+1)%n);
646 }
647 for (j=0; j<n; j++) {
648 npt = 6*(ipup+j);
649 buff.fPols[npt] = c+2;
650 buff.fPols[npt+1] = 4;
651 buff.fPols[npt+2] = isin+n*(n-1)+j;
652 buff.fPols[npt+3] = ishi+((j+1)%n);
653 buff.fPols[npt+4] = isout+n*(n-1)+j;
654 buff.fPols[npt+5] = ishi+j;
655 }
656 } else {
657 for (j=0; j<n; j++) {
658 npt = 6*iplo+5*j;
659 buff.fPols[npt] = c+1;
660 buff.fPols[npt+1] = 3;
661 buff.fPols[npt+2] = isout+j;
662 buff.fPols[npt+3] = islo+((j+1)%n);
663 buff.fPols[npt+4] = islo+j;
664 }
665 for (j=0; j<n; j++) {
666 npt = 6*iplo+5*(n+j);
667 buff.fPols[npt] = c+2;
668 buff.fPols[npt+1] = 3;
669 buff.fPols[npt+2] = isout+n*(n-1)+j;
670 buff.fPols[npt+3] = ishi+j;
671 buff.fPols[npt+4] = ishi+((j+1)%n);
672 }
673 }
674}
675
676////////////////////////////////////////////////////////////////////////////////
677/// Compute r^2 = x^2 + y^2 at a given z coordinate, for either inner or outer hyperbolas.
678
680{
681 Double_t r0, tsq;
682 if (inner) {
683 r0 = fRmin;
684 tsq = fTinsq;
685 } else {
686 r0 = fRmax;
687 tsq = fToutsq;
688 }
689 return (r0*r0+tsq*z*z);
690}
691
692////////////////////////////////////////////////////////////////////////////////
693/// Compute z^2 at a given r^2, for either inner or outer hyperbolas.
694
696{
697 Double_t r0, tsq;
698 if (inner) {
699 r0 = fRmin;
700 tsq = fTinsq;
701 } else {
702 r0 = fRmax;
703 tsq = fToutsq;
704 }
705 if (TMath::Abs(tsq) < TGeoShape::Tolerance()) return TGeoShape::Big();
706 return ((r*r-r0*r0)/tsq);
707}
708
709////////////////////////////////////////////////////////////////////////////////
710/// computes the closest distance from given point to this shape, according
711/// to option. The matching point on the shape is stored in spoint.
712
714{
715 Double_t safe, safrmin, safrmax;
716 if (in) {
717 safe = fDz-TMath::Abs(point[2]);
718 safrmin = SafetyToHype(point, kTRUE, in);
719 if (safrmin < safe) safe = safrmin;
720 safrmax = SafetyToHype(point, kFALSE,in);
721 if (safrmax < safe) safe = safrmax;
722 } else {
723 safe = -fDz+TMath::Abs(point[2]);
724 safrmin = SafetyToHype(point, kTRUE, in);
725 if (safrmin > safe) safe = safrmin;
726 safrmax = SafetyToHype(point, kFALSE,in);
727 if (safrmax > safe) safe = safrmax;
728 }
729 return safe;
730}
731
732////////////////////////////////////////////////////////////////////////////////
733/// Compute an underestimate of the closest distance from a point to inner or
734/// outer infinite hyperbolas.
735
737{
738 Double_t r, rsq, rhsq, rh, dr, tsq, saf;
739 if (inner && !HasInner()) return (in)?TGeoShape::Big():-TGeoShape::Big();
740 rsq = point[0]*point[0]+point[1]*point[1];
741 r = TMath::Sqrt(rsq);
742 rhsq = RadiusHypeSq(point[2], inner);
743 rh = TMath::Sqrt(rhsq);
744 dr = r - rh;
745 if (inner) {
746 if (!in && dr>0) return -TGeoShape::Big();
747 if (TMath::Abs(fStIn) < TGeoShape::Tolerance()) return TMath::Abs(dr);
749 tsq = fTinsq;
750 } else {
751 if (!in && dr<0) return -TGeoShape::Big();
753 tsq = fToutsq;
754 }
755 if (TMath::Abs(dr)<TGeoShape::Tolerance()) return 0.;
756 // 1. dr<0 => approximate safety with distance to tangent to hyperbola in z = |point[2]|
757 Double_t m;
758 if (dr<0) {
759 m = rh/(tsq*TMath::Abs(point[2]));
760 saf = -m*dr/TMath::Sqrt(1.+m*m);
761 return saf;
762 }
763 // 2. dr>0 => approximate safety with distance from point to segment P1(r(z0),z0) and P2(r0, z(r0))
764 m = (TMath::Sqrt(ZHypeSq(r,inner)) - TMath::Abs(point[2]))/dr;
765 saf = m*dr/TMath::Sqrt(1.+m*m);
766 return saf;
767}
768
769////////////////////////////////////////////////////////////////////////////////
770/// Save a primitive as a C++ statement(s) on output stream "out".
771
772void TGeoHype::SavePrimitive(std::ostream &out, Option_t * /*option*/ /*= ""*/)
773{
775 out << " // Shape: " << GetName() << " type: " << ClassName() << std::endl;
776 out << " rin = " << fRmin << ";" << std::endl;
777 out << " stin = " << fStIn << ";" << std::endl;
778 out << " rout = " << fRmax << ";" << std::endl;
779 out << " stout = " << fStOut << ";" << std::endl;
780 out << " dz = " << fDz << ";" << std::endl;
781 out << " TGeoShape *" << GetPointerName() << " = new TGeoHype(\"" << GetName() << "\",rin,stin,rout,stout,dz);" << std::endl;
783}
784
785////////////////////////////////////////////////////////////////////////////////
786/// Set dimensions of the hyperboloid.
787
789{
790 fRmin = rin;
791 fRmax = rout;
792 fDz = dz;
793 fStIn = stin;
794 fStOut = stout;
796 fTinsq = fTin*fTin;
799 if ((fRmin==0) && (fStIn==0)) SetShapeBit(kGeoRSeg, kTRUE);
801}
802
803////////////////////////////////////////////////////////////////////////////////
804/// Set dimensions of the hyperboloid starting from an array.
805/// - param[0] = dz
806/// - param[1] = rin
807/// - param[2] = stin
808/// - param[3] = rout
809/// - param[4] = stout
810
812{
813 Double_t dz = param[0];
814 Double_t rin = param[1];
815 Double_t stin = param[2];
816 Double_t rout = param[3];
817 Double_t stout = param[4];
818 SetHypeDimensions(rin, stin, rout, stout, dz);
819}
820
821////////////////////////////////////////////////////////////////////////////////
822/// create tube mesh points
823
825{
826 Double_t z,dz,r;
827 Int_t i,j, n;
828 if (!points) return;
830 Double_t dphi = 360./n;
831 Double_t phi = 0;
832 dz = 2.*fDz/(n-1);
833
834 Int_t indx = 0;
835
836 if (HasInner()) {
837 // Inner surface points
838 for (i=0; i<n; i++) {
839 z = -fDz+i*dz;
841 for (j=0; j<n; j++) {
842 phi = j*dphi*TMath::DegToRad();
843 points[indx++] = r * TMath::Cos(phi);
844 points[indx++] = r * TMath::Sin(phi);
845 points[indx++] = z;
846 }
847 }
848 } else {
849 points[indx++] = 0.;
850 points[indx++] = 0.;
851 points[indx++] = -fDz;
852 points[indx++] = 0.;
853 points[indx++] = 0.;
854 points[indx++] = fDz;
855 }
856 // Outer surface points
857 for (i=0; i<n; i++) {
858 z = -fDz + i*dz;
860 for (j=0; j<n; j++) {
861 phi = j*dphi*TMath::DegToRad();
862 points[indx++] = r * TMath::Cos(phi);
863 points[indx++] = r * TMath::Sin(phi);
864 points[indx++] = z;
865 }
866 }
867}
868
869////////////////////////////////////////////////////////////////////////////////
870/// create tube mesh points
871
873{
874 Double_t z,dz,r;
875 Int_t i,j, n;
876 if (!points) return;
878 Double_t dphi = 360./n;
879 Double_t phi = 0;
880 dz = 2.*fDz/(n-1);
881
882 Int_t indx = 0;
883
884 if (HasInner()) {
885 // Inner surface points
886 for (i=0; i<n; i++) {
887 z = -fDz+i*dz;
889 for (j=0; j<n; j++) {
890 phi = j*dphi*TMath::DegToRad();
891 points[indx++] = r * TMath::Cos(phi);
892 points[indx++] = r * TMath::Sin(phi);
893 points[indx++] = z;
894 }
895 }
896 } else {
897 points[indx++] = 0.;
898 points[indx++] = 0.;
899 points[indx++] = -fDz;
900 points[indx++] = 0.;
901 points[indx++] = 0.;
902 points[indx++] = fDz;
903 }
904 // Outer surface points
905 for (i=0; i<n; i++) {
906 z = -fDz + i*dz;
908 for (j=0; j<n; j++) {
909 phi = j*dphi*TMath::DegToRad();
910 points[indx++] = r * TMath::Cos(phi);
911 points[indx++] = r * TMath::Sin(phi);
912 points[indx++] = z;
913 }
914 }
915}
916
917////////////////////////////////////////////////////////////////////////////////
918/// Returns numbers of vertices, segments and polygons composing the shape mesh.
919
920void TGeoHype::GetMeshNumbers(Int_t &nvert, Int_t &nsegs, Int_t &npols) const
921{
923 Bool_t hasRmin = HasInner();
924 nvert = (hasRmin)?(2*n*n):(n*n+2);
925 nsegs = (hasRmin)?(4*n*n):(n*(2*n+1));
926 npols = (hasRmin)?(2*n*n):(n*(n+1));
927}
928
929////////////////////////////////////////////////////////////////////////////////
930/// Return number of vertices of the mesh representation
931
933{
935 Int_t numPoints = (HasRmin())?(2*n*n):(n*n+2);
936 return numPoints;
937}
938
939////////////////////////////////////////////////////////////////////////////////
940/// fill size of this 3-D object
941
943{
944}
945
946////////////////////////////////////////////////////////////////////////////////
947/// Fills a static 3D buffer and returns a reference.
948
949const TBuffer3D & TGeoHype::GetBuffer3D(Int_t reqSections, Bool_t localFrame) const
950{
951 static TBuffer3D buffer(TBuffer3DTypes::kGeneric);
952
953 TGeoBBox::FillBuffer3D(buffer, reqSections, localFrame);
954
955 if (reqSections & TBuffer3D::kRawSizes) {
957 Bool_t hasRmin = HasInner();
958 Int_t nbPnts = (hasRmin)?(2*n*n):(n*n+2);
959 Int_t nbSegs = (hasRmin)?(4*n*n):(n*(2*n+1));
960 Int_t nbPols = (hasRmin)?(2*n*n):(n*(n+1));
961 if (buffer.SetRawSizes(nbPnts, 3*nbPnts, nbSegs, 3*nbSegs, nbPols, 6*nbPols)) {
963 }
964 }
965 if ((reqSections & TBuffer3D::kRaw) && buffer.SectionsValid(TBuffer3D::kRawSizes)) {
966 SetPoints(buffer.fPnts);
967 if (!buffer.fLocalFrame) {
968 TransformPoints(buffer.fPnts, buffer.NbPnts());
969 }
970
971 SetSegsAndPols(buffer);
973 }
974
975 return buffer;
976}
977
978////////////////////////////////////////////////////////////////////////////////
979/// Check the inside status for each of the points in the array.
980/// Input: Array of point coordinates + vector size
981/// Output: Array of Booleans for the inside of each point
982
983void TGeoHype::Contains_v(const Double_t *points, Bool_t *inside, Int_t vecsize) const
984{
985 for (Int_t i=0; i<vecsize; i++) inside[i] = Contains(&points[3*i]);
986}
987
988////////////////////////////////////////////////////////////////////////////////
989/// Compute the normal for an array o points so that norm.dot.dir is positive
990/// Input: Arrays of point coordinates and directions + vector size
991/// Output: Array of normal directions
992
993void TGeoHype::ComputeNormal_v(const Double_t *points, const Double_t *dirs, Double_t *norms, Int_t vecsize)
994{
995 for (Int_t i=0; i<vecsize; i++) ComputeNormal(&points[3*i], &dirs[3*i], &norms[3*i]);
996}
997
998////////////////////////////////////////////////////////////////////////////////
999/// Compute distance from array of input points having directions specified by dirs. Store output in dists
1000
1001void TGeoHype::DistFromInside_v(const Double_t *points, const Double_t *dirs, Double_t *dists, Int_t vecsize, Double_t* step) const
1002{
1003 for (Int_t i=0; i<vecsize; i++) dists[i] = DistFromInside(&points[3*i], &dirs[3*i], 3, step[i]);
1004}
1005
1006////////////////////////////////////////////////////////////////////////////////
1007/// Compute distance from array of input points having directions specified by dirs. Store output in dists
1008
1009void TGeoHype::DistFromOutside_v(const Double_t *points, const Double_t *dirs, Double_t *dists, Int_t vecsize, Double_t* step) const
1010{
1011 for (Int_t i=0; i<vecsize; i++) dists[i] = DistFromOutside(&points[3*i], &dirs[3*i], 3, step[i]);
1012}
1013
1014////////////////////////////////////////////////////////////////////////////////
1015/// Compute safe distance from each of the points in the input array.
1016/// Input: Array of point coordinates, array of statuses for these points, size of the arrays
1017/// Output: Safety values
1018
1019void TGeoHype::Safety_v(const Double_t *points, const Bool_t *inside, Double_t *safe, Int_t vecsize) const
1020{
1021 for (Int_t i=0; i<vecsize; i++) safe[i] = Safety(&points[3*i], inside[i]);
1022}
ROOT::R::TRInterface & r
Definition Object.C:4
#define b(i)
Definition RSha256.hxx:100
#define c(i)
Definition RSha256.hxx:101
#define a(i)
Definition RSha256.hxx:99
const Bool_t kFALSE
Definition RtypesCore.h:92
double Double_t
Definition RtypesCore.h:59
float Float_t
Definition RtypesCore.h:57
const Bool_t kTRUE
Definition RtypesCore.h:91
const char Option_t
Definition RtypesCore.h:66
#define ClassImp(name)
Definition Rtypes.h:364
void Error(const char *location, const char *msgfmt,...)
Use this function in case an error occurred.
Definition TError.cxx:187
void Warning(const char *location, const char *msgfmt,...)
Use this function in warning situations.
Definition TError.cxx:231
char name[80]
Definition TGX11.cxx:110
R__EXTERN TGeoManager * gGeoManager
double sin(double)
#define isin(address, start, length)
point * points
Definition X3DBuffer.c:22
Generic 3D primitive description class.
Definition TBuffer3D.h:18
Int_t * fPols
Definition TBuffer3D.h:114
UInt_t NbPnts() const
Definition TBuffer3D.h:80
Bool_t SectionsValid(UInt_t mask) const
Definition TBuffer3D.h:67
void SetSectionsValid(UInt_t mask)
Definition TBuffer3D.h:65
Int_t * fSegs
Definition TBuffer3D.h:113
Bool_t fLocalFrame
Definition TBuffer3D.h:90
Bool_t SetRawSizes(UInt_t reqPnts, UInt_t reqPntsCapacity, UInt_t reqSegs, UInt_t reqSegsCapacity, UInt_t reqPols, UInt_t reqPolsCapacity)
Set kRaw tessellation section of buffer with supplied sizes.
Double_t * fPnts
Definition TBuffer3D.h:112
Double_t fDX
Definition TGeoBBox.h:21
virtual Double_t DistFromOutside(const Double_t *point, const Double_t *dir, Int_t iact=1, Double_t step=TGeoShape::Big(), Double_t *safe=0) const
Compute distance from outside point to surface of the box.
Definition TGeoBBox.cxx:429
virtual void InspectShape() const
Prints shape parameters.
Definition TGeoBBox.cxx:792
Double_t fOrigin[3]
Definition TGeoBBox.h:24
Double_t fDY
Definition TGeoBBox.h:22
Double_t fDZ
Definition TGeoBBox.h:23
virtual void FillBuffer3D(TBuffer3D &buffer, Int_t reqSections, Bool_t localFrame) const
Fills the supplied buffer, with sections in desired frame See TBuffer3D.h for explanation of sections...
Hyperboloid class defined by 5 parameters.
Definition TGeoHype.h:18
virtual TGeoVolume * Divide(TGeoVolume *voldiv, const char *divname, Int_t iaxis, Int_t ndiv, Double_t start, Double_t step)
Cannot divide hyperboloids.
Definition TGeoHype.cxx:369
virtual void SetPoints(Double_t *points) const
create tube mesh points
Definition TGeoHype.cxx:824
Double_t SafetyToHype(const Double_t *point, Bool_t inner, Bool_t in) const
Compute an underestimate of the closest distance from a point to inner or outer infinite hyperbolas.
Definition TGeoHype.cxx:736
Double_t ZHypeSq(Double_t r, Bool_t inner) const
Compute z^2 at a given r^2, for either inner or outer hyperbolas.
Definition TGeoHype.cxx:695
virtual TGeoShape * GetMakeRuntimeShape(TGeoShape *mother, TGeoMatrix *mat) const
in case shape has some negative parameters, these has to be computed in order to fit the mother
Definition TGeoHype.cxx:422
virtual void Safety_v(const Double_t *points, const Bool_t *inside, Double_t *safe, Int_t vecsize) const
Compute safe distance from each of the points in the input array.
virtual const TBuffer3D & GetBuffer3D(Int_t reqSections, Bool_t localFrame) const
Fills a static 3D buffer and returns a reference.
Definition TGeoHype.cxx:949
Double_t RadiusHypeSq(Double_t z, Bool_t inner) const
Compute r^2 = x^2 + y^2 at a given z coordinate, for either inner or outer hyperbolas.
Definition TGeoHype.cxx:679
virtual void GetMeshNumbers(Int_t &nvert, Int_t &nsegs, Int_t &npols) const
Returns numbers of vertices, segments and polygons composing the shape mesh.
Definition TGeoHype.cxx:920
virtual Double_t Capacity() const
Computes capacity of the shape in [length^3].
Definition TGeoHype.cxx:127
virtual void DistFromInside_v(const Double_t *points, const Double_t *dirs, Double_t *dists, Int_t vecsize, Double_t *step) const
Compute distance from array of input points having directions specified by dirs. Store output in dist...
virtual void GetBoundingCylinder(Double_t *param) const
Fill vector param[4] with the bounding cylinder parameters.
Definition TGeoHype.cxx:408
Int_t DistToHype(const Double_t *point, const Double_t *dir, Double_t *s, Bool_t inner, Bool_t in) const
Compute distance from an arbitrary point to inner/outer surface of hyperboloid.
Definition TGeoHype.cxx:318
virtual Int_t DistancetoPrimitive(Int_t px, Int_t py)
compute closest distance from point px,py to each corner
Definition TGeoHype.cxx:209
virtual Double_t Safety(const Double_t *point, Bool_t in=kTRUE) const
computes the closest distance from given point to this shape, according to option.
Definition TGeoHype.cxx:713
virtual TBuffer3D * MakeBuffer3D() const
Creates a TBuffer3D describing this shape.
Definition TGeoHype.cxx:460
virtual void Contains_v(const Double_t *points, Bool_t *inside, Int_t vecsize) const
Check the inside status for each of the points in the array.
Definition TGeoHype.cxx:983
virtual void SetDimensions(Double_t *param)
Set dimensions of the hyperboloid starting from an array.
Definition TGeoHype.cxx:811
TGeoHype()
Default constructor.
Definition TGeoHype.cxx:62
Double_t fStIn
Definition TGeoHype.h:24
Double_t fToutsq
Definition TGeoHype.h:32
virtual void ComputeNormal_v(const Double_t *points, const Double_t *dirs, Double_t *norms, Int_t vecsize)
Compute the normal for an array o points so that norm.dot.dir is positive Input: Arrays of point coor...
Definition TGeoHype.cxx:993
virtual void InspectShape() const
print shape parameters
Definition TGeoHype.cxx:443
virtual ~TGeoHype()
destructor
Definition TGeoHype.cxx:120
virtual void SavePrimitive(std::ostream &out, Option_t *option="")
Save a primitive as a C++ statement(s) on output stream "out".
Definition TGeoHype.cxx:772
virtual Int_t GetNmeshVertices() const
Return number of vertices of the mesh representation.
Definition TGeoHype.cxx:932
virtual Bool_t Contains(const Double_t *point) const
test if point is inside this tube
Definition TGeoHype.cxx:194
void SetHypeDimensions(Double_t rin, Double_t stin, Double_t rout, Double_t stout, Double_t dz)
Set dimensions of the hyperboloid.
Definition TGeoHype.cxx:788
Double_t fStOut
Definition TGeoHype.h:25
virtual void ComputeBBox()
Compute bounding box of the hyperboloid.
Definition TGeoHype.cxx:137
Double_t fTinsq
Definition TGeoHype.h:31
virtual void ComputeNormal(const Double_t *point, const Double_t *dir, Double_t *norm)
Compute normal to closest surface from POINT.
Definition TGeoHype.cxx:157
virtual void DistFromOutside_v(const Double_t *points, const Double_t *dirs, Double_t *dists, Int_t vecsize, Double_t *step) const
Compute distance from array of input points having directions specified by dirs. Store output in dist...
virtual Double_t GetAxisRange(Int_t iaxis, Double_t &xlo, Double_t &xhi) const
Get range of shape for a given axis.
Definition TGeoHype.cxx:379
Double_t fTout
Definition TGeoHype.h:30
virtual void Sizeof3D() const
fill size of this 3-D object
Definition TGeoHype.cxx:942
virtual Double_t DistFromInside(const Double_t *point, const Double_t *dir, Int_t iact=1, Double_t step=TGeoShape::Big(), Double_t *safe=0) const
Compute distance from inside point to surface of the hyperboloid.
Definition TGeoHype.cxx:218
virtual Double_t DistFromOutside(const Double_t *point, const Double_t *dir, Int_t iact=1, Double_t step=TGeoShape::Big(), Double_t *safe=0) const
compute distance from outside point to surface of the hyperboloid.
Definition TGeoHype.cxx:258
Double_t fTin
Definition TGeoHype.h:29
virtual void SetSegsAndPols(TBuffer3D &buff) const
Fill TBuffer3D structure for segments and polygons.
Definition TGeoHype.cxx:482
Bool_t HasInner() const
Definition TGeoHype.h:70
Int_t GetNsegments() const
Get number of segments approximating circles.
Geometrical transformation package.
Definition TGeoMatrix.h:41
Base abstract class for all shapes.
Definition TGeoShape.h:26
static Double_t Big()
Definition TGeoShape.h:88
virtual Double_t GetAxisRange(Int_t iaxis, Double_t &xlo, Double_t &xhi) const =0
Int_t GetBasicColor() const
Get the basic color (0-7).
void TransformPoints(Double_t *points, UInt_t NbPoints) const
Tranform a set of points (LocalToMaster)
void SetShapeBit(UInt_t f, Bool_t set)
Equivalent of TObject::SetBit.
const char * GetPointerName() const
Provide a pointer name containing uid.
Int_t ShapeDistancetoPrimitive(Int_t numpoints, Int_t px, Int_t py) const
Returns distance to shape primitive mesh.
virtual const char * GetName() const
Get the shape name.
@ kGeoSavePrimitive
Definition TGeoShape.h:65
@ kGeoInvalidShape
Definition TGeoShape.h:42
@ kGeoRunTimeShape
Definition TGeoShape.h:41
static Double_t Tolerance()
Definition TGeoShape.h:91
Bool_t TestShapeBit(UInt_t f) const
Definition TGeoShape.h:163
Cylindrical tube class.
Definition TGeoTube.h:18
Double_t fRmin
Definition TGeoTube.h:21
Double_t fDz
Definition TGeoTube.h:23
Double_t fRmax
Definition TGeoTube.h:22
Bool_t HasRmin() const
Definition TGeoTube.h:69
TGeoVolume, TGeoVolumeMulti, TGeoVolumeAssembly are the volume classes.
Definition TGeoVolume.h:49
R__ALWAYS_INLINE Bool_t TestBit(UInt_t f) const
Definition TObject.h:187
virtual const char * ClassName() const
Returns name of class to which the object belongs.
Definition TObject.cxx:130
void SetBit(UInt_t f, Bool_t set)
Set or unset the user status bits as specified in f.
Definition TObject.cxx:696
const Int_t n
Definition legend1.C:16
Long64_t LocMin(Long64_t n, const T *a)
Return index of array with the minimum element.
Definition TMath.h:972
T1 Sign(T1 a, T2 b)
Definition TMathBase.h:165
Double_t ATan2(Double_t y, Double_t x)
Definition TMath.h:679
constexpr Double_t DegToRad()
Conversion from degree to radian:
Definition TMath.h:81
Double_t Sqrt(Double_t x)
Definition TMath.h:691
Short_t Min(Short_t a, Short_t b)
Definition TMathBase.h:180
Double_t Cos(Double_t)
Definition TMath.h:643
constexpr Double_t Pi()
Definition TMath.h:37
Double_t Sin(Double_t)
Definition TMath.h:639
Double_t Tan(Double_t)
Definition TMath.h:647
Short_t Abs(Short_t d)
Definition TMathBase.h:120
auto * m
Definition textangle.C:8
#define snext(osub1, osub2)
Definition triangle.c:1167