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[occt.git] / src / BRepGProp / BRepGProp_Gauss.cxx
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9bd59d1c 1// Copyright (c) 2008-2015 OPEN CASCADE SAS
2//
3// This file is part of Open CASCADE Technology software library.
4//
5// This library is free software; you can redistribute it and/or modify it under
6// the terms of the GNU Lesser General Public License version 2.1 as published
7// by the Free Software Foundation, with special exception defined in the file
8// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
9// distribution for complete text of the license and disclaimer of any warranty.
10//
11// Alternatively, this file may be used under the terms of Open CASCADE
12// commercial license or contractual agreement.
13
14#include <math.hxx>
15#include <Precision.hxx>
16#include <TColStd_Array1OfReal.hxx>
17#include <Standard_Assert.hxx>
18#include <BRepGProp_Face.hxx>
19#include <BRepGProp_Domain.hxx>
20#include <BRepGProp_Gauss.hxx>
21
22// If the following is defined the error of algorithm is calculated by static moments
23#define IS_MIN_DIM
24
25namespace
26{
27 // Minimal value of interval's range for computation | minimal value of "dim" | ...
28 static const Standard_Real EPS_PARAM = 1.e-12;
29 static const Standard_Real EPS_DIM = 1.e-30;
30 static const Standard_Real ERROR_ALGEBR_RATIO = 2.0 / 3.0;
31
32 // Maximum of GaussPoints on a subinterval and maximum of subintervals
33 static const Standard_Integer GPM = math::GaussPointsMax();
34 static const Standard_Integer SUBS_POWER = 32;
35 static const Standard_Integer SM = SUBS_POWER * GPM + 1;
36
37 // Auxiliary inner functions to perform arithmetic operations.
38 static Standard_Real Add(const Standard_Real theA, const Standard_Real theB)
39 {
40 return theA + theB;
41 }
42
43 static Standard_Real AddInf(const Standard_Real theA, const Standard_Real theB)
44 {
45 if (Precision::IsPositiveInfinite(theA))
46 {
47 if (Precision::IsNegativeInfinite(theB))
48 return 0.0;
49 else
50 return Precision::Infinite();
51 }
52
53 if (Precision::IsPositiveInfinite(theB))
54 {
55 if (Precision::IsNegativeInfinite(theA))
56 return 0.0;
57 else
58 return Precision::Infinite();
59 }
60
61 if (Precision::IsNegativeInfinite(theA))
62 {
63 if (Precision::IsPositiveInfinite(theB))
64 return 0.0;
65 else
66 return -Precision::Infinite();
67 }
68
69 if (Precision::IsNegativeInfinite(theB))
70 {
71 if (Precision::IsPositiveInfinite(theA))
72 return 0.0;
73 else
74 return -Precision::Infinite();
75 }
76
77 return theA + theB;
78 }
79
80 static Standard_Real Mult(const Standard_Real theA, const Standard_Real theB)
81 {
82 return theA * theB;
83 }
84
85 static Standard_Real MultInf(const Standard_Real theA, const Standard_Real theB)
86 {
87 if ((theA == 0.0) || (theB == 0.0)) //strictly zerro (without any tolerances)
88 return 0.0;
89
90 if (Precision::IsPositiveInfinite(theA))
91 {
92 if (theB < 0.0)
93 return -Precision::Infinite();
94 else
95 return Precision::Infinite();
96 }
97
98 if (Precision::IsPositiveInfinite(theB))
99 {
100 if (theA < 0.0)
101 return -Precision::Infinite();
102 else
103 return Precision::Infinite();
104 }
105
106 if (Precision::IsNegativeInfinite(theA))
107 {
108 if (theB < 0.0)
109 return +Precision::Infinite();
110 else
111 return -Precision::Infinite();
112 }
113
114 if (Precision::IsNegativeInfinite(theB))
115 {
116 if (theA < 0.0)
117 return +Precision::Infinite();
118 else
119 return -Precision::Infinite();
120 }
121
122 return theA * theB;
123 }
124}
125
126//=======================================================================
127//function : BRepGProp_Gauss::Inert::Inert
128//purpose : Constructor
129//=======================================================================
130BRepGProp_Gauss::Inertia::Inertia()
131: Mass(0.0),
132 Ix (0.0),
133 Iy (0.0),
134 Iz (0.0),
135 Ixx (0.0),
136 Iyy (0.0),
137 Izz (0.0),
138 Ixy (0.0),
139 Ixz (0.0),
140 Iyz (0.0)
141{
142}
143
144//=======================================================================
145//function : Inertia::Reset
146//purpose : Zeroes all values.
147//=======================================================================
148void BRepGProp_Gauss::Inertia::Reset()
149{
150 memset(reinterpret_cast<void*>(this), 0, sizeof(BRepGProp_Gauss::Inertia));
151}
152
153//=======================================================================
154//function : BRepGProp_Gauss
155//purpose : Constructor
156//=======================================================================
157BRepGProp_Gauss::BRepGProp_Gauss(const BRepGProp_GaussType theType)
158: myType(theType)
159{
160 add = (::Add );
161 mult = (::Mult);
162}
163
164//=======================================================================
165//function : MaxSubs
166//purpose :
167//=======================================================================
168Standard_Integer BRepGProp_Gauss::MaxSubs(const Standard_Integer theN,
169 const Standard_Integer theCoeff)
170{
171 return IntegerLast() / theCoeff < theN ?
172 IntegerLast() : theN * theCoeff + 1;
173}
174
175//=======================================================================
176//function : Init
177//purpose :
178//=======================================================================
c04c30b3 179void BRepGProp_Gauss::Init(NCollection_Handle<math_Vector>& theOutVec,
9bd59d1c 180 const Standard_Real theValue,
181 const Standard_Integer theFirst,
182 const Standard_Integer theLast)
183{
184 if(theLast - theFirst == 0)
185 {
186 theOutVec->Init(theValue);
187 }
188 else
189 {
190 for (Standard_Integer i = theFirst; i <= theLast; ++i)
191 theOutVec->Value(i) = theValue;
192 }
193}
194
195//=======================================================================
196//function : InitMass
197//purpose :
198//=======================================================================
199void BRepGProp_Gauss::InitMass(const Standard_Real theValue,
200 const Standard_Integer theFirst,
201 const Standard_Integer theLast,
202 InertiaArray& theArray)
203{
204 if (theArray.IsNull())
205 return;
206
207 Standard_Integer aFirst = theFirst;
208 Standard_Integer aLast = theLast;
209
210 if (theLast - theFirst == 0)
211 {
212 aFirst = theArray->Lower();
213 aLast = theArray->Upper();
214 }
215
216 for (Standard_Integer i = aFirst; i <= aLast; ++i)
217 theArray->ChangeValue(i).Mass = theValue;
218}
219
220//=======================================================================
221//function : FillIntervalBounds
222//purpose :
223//=======================================================================
224Standard_Integer BRepGProp_Gauss::FillIntervalBounds(
225 const Standard_Real theA,
226 const Standard_Real theB,
227 const TColStd_Array1OfReal& theKnots,
228 const Standard_Integer theNumSubs,
229 InertiaArray& theInerts,
c04c30b3 230 NCollection_Handle<math_Vector>& theParam1,
231 NCollection_Handle<math_Vector>& theParam2,
232 NCollection_Handle<math_Vector>& theError,
233 NCollection_Handle<math_Vector>& theCommonError)
9bd59d1c 234{
235 const Standard_Integer aSize =
236 Max(theKnots.Upper(), MaxSubs(theKnots.Upper() - 1, theNumSubs));
237
238 if (aSize - 1 > theParam1->Upper())
239 {
240 theInerts = new NCollection_Array1<Inertia>(1, aSize);
241 theParam1 = new math_Vector(1, aSize);
242 theParam2 = new math_Vector(1, aSize);
243 theError = new math_Vector(1, aSize, 0.0);
244
245 if (theCommonError.IsNull() == Standard_False)
246 theCommonError = new math_Vector(1, aSize, 0.0);
247 }
248
249 Standard_Integer j = 1, k = 1;
250 theParam1->Value(j++) = theA;
251
252 const Standard_Integer aLength = theKnots.Upper();
253 for (Standard_Integer i = 1; i <= aLength; ++i)
254 {
255 const Standard_Real kn = theKnots(i);
256 if (theA < kn)
257 {
258 if (kn < theB)
259 {
260 theParam1->Value(j++) = kn;
261 theParam2->Value(k++) = kn;
262 }
263 else
264 break;
265 }
266 }
267
268 theParam2->Value(k) = theB;
269 return k;
270}
271
272
273
274//=======================================================================
275//function : computeVInertiaOfElementaryPart
276//purpose :
277//=======================================================================
278void BRepGProp_Gauss::computeVInertiaOfElementaryPart(
279 const gp_Pnt& thePoint,
280 const gp_Vec& theNormal,
281 const gp_Pnt& theLocation,
282 const Standard_Real theWeight,
283 const Standard_Real theCoeff[],
284 const Standard_Boolean theIsByPoint,
285 BRepGProp_Gauss::Inertia& theOutInertia)
286{
287 Standard_Real x = thePoint.X() - theLocation.X();
288 Standard_Real y = thePoint.Y() - theLocation.Y();
289 Standard_Real z = thePoint.Z() - theLocation.Z();
290
291 const Standard_Real xn = theNormal.X() * theWeight;
292 const Standard_Real yn = theNormal.Y() * theWeight;
293 const Standard_Real zn = theNormal.Z() * theWeight;
294
295 if (theIsByPoint)
296 {
297 ///////////////////// ///////////////////////
298 // OFV code // // Initial code //
299 ///////////////////// ///////////////////////
300 // modified by APO
301
302 Standard_Real dv = x * xn + y * yn + z * zn; //xyz = x * y * z;
303 theOutInertia.Mass += dv / 3.0; //Ixyi += zn * xyz;
304 theOutInertia.Ix += 0.25 * x * dv; //Iyzi += xn * xyz;
305 theOutInertia.Iy += 0.25 * y * dv; //Ixzi += yn * xyz;
306 theOutInertia.Iz += 0.25 * z * dv; //xi = x * x * x * xn / 3.0;
307 x -= theCoeff[0]; //yi = y * y * y * yn / 3.0;
308 y -= theCoeff[1]; //zi = z * z * z * zn / 3.0;
309 z -= theCoeff[2]; //Ixxi += (yi + zi);
310 dv *= 0.2; //Iyyi += (xi + zi);
311 theOutInertia.Ixy -= x * y * dv; //Izzi += (xi + yi);
312 theOutInertia.Iyz -= y * z * dv; //x -= Coeff[0];
313 theOutInertia.Ixz -= x * z * dv; //y -= Coeff[1];
314 x *= x; //z -= Coeff[2];
315 y *= y; //dv = x * xn + y * yn + z * zn;
316 z *= z; //dvi += dv;
317 theOutInertia.Ixx += (y + z) * dv; //Ixi += x * dv;
318 theOutInertia.Iyy += (x + z) * dv; //Iyi += y * dv;
319 theOutInertia.Izz += (x + y) * dv; //Izi += z * dv;
320 }
321 else
322 { // By plane
323 const Standard_Real s = xn * theCoeff[0] + yn * theCoeff[1] + zn * theCoeff[2];
324
325 Standard_Real d1 = theCoeff[0] * x + theCoeff[1] * y + theCoeff[2] * z - theCoeff[3];
326 Standard_Real d2 = d1 * d1;
327 Standard_Real d3 = d1 * d2 / 3.0;
328 Standard_Real dv = s * d1;
329
330 theOutInertia.Mass += dv;
331 theOutInertia.Ix += (x - (theCoeff[0] * d1 * 0.5)) * dv;
332 theOutInertia.Iy += (y - (theCoeff[1] * d1 * 0.5)) * dv;
333 theOutInertia.Iz += (z - (theCoeff[2] * d1 * 0.5)) * dv;
334
335 const Standard_Real px = x - theCoeff[0] * d1;
336 const Standard_Real py = y - theCoeff[1] * d1;
337 const Standard_Real pz = z - theCoeff[2] * d1;
338
339 x = px * px * d1 + px * theCoeff[0] * d2 + theCoeff[0] * theCoeff[0] * d3;
340 y = py * py * d1 + py * theCoeff[1] * d2 + theCoeff[1] * theCoeff[1] * d3;
341 z = pz * pz * d1 + pz * theCoeff[2] * d2 + theCoeff[2] * theCoeff[2] * d3;
342
343 theOutInertia.Ixx += (y + z) * s;
344 theOutInertia.Iyy += (x + z) * s;
345 theOutInertia.Izz += (x + y) * s;
346
347 d2 *= 0.5;
348 x = (py * pz * d1) + (py * theCoeff[2] * d2) + (pz * theCoeff[1] * d2) + (theCoeff[1] * theCoeff[2] * d3);
349 y = (px * pz * d1) + (pz * theCoeff[0] * d2) + (px * theCoeff[2] * d2) + (theCoeff[0] * theCoeff[2] * d3);
350 z = (px * py * d1) + (px * theCoeff[1] * d2) + (py * theCoeff[0] * d2) + (theCoeff[0] * theCoeff[1] * d3);
351
352 theOutInertia.Ixy -= z * s;
353 theOutInertia.Iyz -= x * s;
354 theOutInertia.Ixz -= y * s;
355 }
356}
357
358//=======================================================================
359//function : computeSInertiaOfElementaryPart
360//purpose :
361//=======================================================================
362void BRepGProp_Gauss::computeSInertiaOfElementaryPart(
363 const gp_Pnt& thePoint,
364 const gp_Vec& theNormal,
365 const gp_Pnt& theLocation,
366 const Standard_Real theWeight,
367 BRepGProp_Gauss::Inertia& theOutInertia)
368{
369 // ds - Jacobien (x, y, z) -> (u, v) = ||n||
370 const Standard_Real ds = mult(theNormal.Magnitude(), theWeight);
371 const Standard_Real x = add(thePoint.X(), -theLocation.X());
372 const Standard_Real y = add(thePoint.Y(), -theLocation.Y());
373 const Standard_Real z = add(thePoint.Z(), -theLocation.Z());
374
375 theOutInertia.Mass = add(theOutInertia.Mass, ds);
376
377 const Standard_Real XdS = mult(x, ds);
378 const Standard_Real YdS = mult(y, ds);
379 const Standard_Real ZdS = mult(z, ds);
380
381 theOutInertia.Ix = add(theOutInertia.Ix, XdS);
382 theOutInertia.Iy = add(theOutInertia.Iy, YdS);
383 theOutInertia.Iz = add(theOutInertia.Iz, ZdS);
384 theOutInertia.Ixy = add(theOutInertia.Ixy, mult(x, YdS));
385 theOutInertia.Iyz = add(theOutInertia.Iyz, mult(y, ZdS));
386 theOutInertia.Ixz = add(theOutInertia.Ixz, mult(x, ZdS));
387
388 const Standard_Real XXdS = mult(x, XdS);
389 const Standard_Real YYdS = mult(y, YdS);
390 const Standard_Real ZZdS = mult(z, ZdS);
391
392 theOutInertia.Ixx = add(theOutInertia.Ixx, add(YYdS, ZZdS));
393 theOutInertia.Iyy = add(theOutInertia.Iyy, add(XXdS, ZZdS));
394 theOutInertia.Izz = add(theOutInertia.Izz, add(XXdS, YYdS));
395}
396
397//=======================================================================
398//function : checkBounds
399//purpose :
400//=======================================================================
401void BRepGProp_Gauss::checkBounds(const Standard_Real theU1,
402 const Standard_Real theU2,
403 const Standard_Real theV1,
404 const Standard_Real theV2)
405{
406 if (Precision::IsInfinite(theU1) || Precision::IsInfinite(theU2) ||
407 Precision::IsInfinite(theV1) || Precision::IsInfinite(theV2))
408 {
409 add = (::AddInf);
410 mult = (::MultInf);
411 }
412}
413
414//=======================================================================
415//function : addAndRestoreInertia
416//purpose :
417//=======================================================================
418void BRepGProp_Gauss::addAndRestoreInertia(
419 const BRepGProp_Gauss::Inertia& theInInertia,
420 BRepGProp_Gauss::Inertia& theOutInertia)
421{
422 theOutInertia.Mass = add(theOutInertia.Mass, theInInertia.Mass);
423 theOutInertia.Ix = add(theOutInertia.Ix, theInInertia.Ix);
424 theOutInertia.Iy = add(theOutInertia.Iy, theInInertia.Iy);
425 theOutInertia.Iz = add(theOutInertia.Iz, theInInertia.Iz);
426 theOutInertia.Ixx = add(theOutInertia.Ixx, theInInertia.Ixx);
427 theOutInertia.Iyy = add(theOutInertia.Iyy, theInInertia.Iyy);
428 theOutInertia.Izz = add(theOutInertia.Izz, theInInertia.Izz);
429 theOutInertia.Ixy = add(theOutInertia.Ixy, theInInertia.Ixy);
430 theOutInertia.Ixz = add(theOutInertia.Ixz, theInInertia.Ixz);
431 theOutInertia.Iyz = add(theOutInertia.Iyz, theInInertia.Iyz);
432}
433
434//=======================================================================
435//function : multAndRestoreInertia
436//purpose :
437//=======================================================================
438void BRepGProp_Gauss::multAndRestoreInertia(
439 const Standard_Real theValue,
440 BRepGProp_Gauss::Inertia& theInOutInertia)
441{
442 theInOutInertia.Mass = mult(theInOutInertia.Mass, theValue);
443 theInOutInertia.Ix = mult(theInOutInertia.Ix, theValue);
444 theInOutInertia.Iy = mult(theInOutInertia.Iy, theValue);
445 theInOutInertia.Iz = mult(theInOutInertia.Iz, theValue);
446 theInOutInertia.Ixx = mult(theInOutInertia.Ixx, theValue);
447 theInOutInertia.Iyy = mult(theInOutInertia.Iyy, theValue);
448 theInOutInertia.Izz = mult(theInOutInertia.Izz, theValue);
449 theInOutInertia.Ixy = mult(theInOutInertia.Ixy, theValue);
450 theInOutInertia.Ixz = mult(theInOutInertia.Ixz, theValue);
451 theInOutInertia.Iyz = mult(theInOutInertia.Iyz, theValue);
452}
453
454//=======================================================================
455//function : convert
456//purpose :
457//=======================================================================
458void BRepGProp_Gauss::convert(const BRepGProp_Gauss::Inertia& theInertia,
459 gp_Pnt& theOutGravityCenter,
460 gp_Mat& theOutMatrixOfInertia,
461 Standard_Real& theOutMass)
462{
463 if (Abs(theInertia.Mass) >= EPS_DIM)
464 {
465 const Standard_Real anInvMass = 1.0 / theInertia.Mass;
466 theOutGravityCenter.SetX(theInertia.Ix * anInvMass);
467 theOutGravityCenter.SetY(theInertia.Iy * anInvMass);
468 theOutGravityCenter.SetZ(theInertia.Iz * anInvMass);
469
470 theOutMass = theInertia.Mass;
471 }
472 else
473 {
474 theOutMass = 0.0;
475 theOutGravityCenter.SetCoord(0.0, 0.0, 0.0);
476 }
477
478 theOutMatrixOfInertia = gp_Mat(
479 gp_XYZ ( theInertia.Ixx, -theInertia.Ixy, -theInertia.Ixz),
480 gp_XYZ (-theInertia.Ixy, theInertia.Iyy, -theInertia.Iyz),
481 gp_XYZ (-theInertia.Ixz, -theInertia.Iyz, theInertia.Izz));
482}
483
484//=======================================================================
485//function : convert
486//purpose :
487//=======================================================================
488void BRepGProp_Gauss::convert(const BRepGProp_Gauss::Inertia& theInertia,
489 const Standard_Real theCoeff[],
490 const Standard_Boolean theIsByPoint,
491 gp_Pnt& theOutGravityCenter,
492 gp_Mat& theOutMatrixOfInertia,
493 Standard_Real& theOutMass)
494{
495 convert(theInertia, theOutGravityCenter, theOutMatrixOfInertia, theOutMass);
496 if (Abs(theInertia.Mass) >= EPS_DIM && theIsByPoint)
497 {
498 const Standard_Real anInvMass = 1.0 / theInertia.Mass;
499 if (theIsByPoint == Standard_True)
500 {
501 theOutGravityCenter.SetX(theCoeff[0] + theInertia.Ix * anInvMass);
502 theOutGravityCenter.SetY(theCoeff[1] + theInertia.Iy * anInvMass);
503 theOutGravityCenter.SetZ(theCoeff[2] + theInertia.Iz * anInvMass);
504 }
505 else
506 {
507 theOutGravityCenter.SetX(theInertia.Ix * anInvMass);
508 theOutGravityCenter.SetY(theInertia.Iy * anInvMass);
509 theOutGravityCenter.SetZ(theInertia.Iz * anInvMass);
510 }
511
512 theOutMass = theInertia.Mass;
513 }
514 else
515 {
516 theOutMass = 0.0;
517 theOutGravityCenter.SetCoord(0.0, 0.0, 0.0);
518 }
519
520 theOutMatrixOfInertia = gp_Mat(
521 gp_XYZ (theInertia.Ixx, theInertia.Ixy, theInertia.Ixz),
522 gp_XYZ (theInertia.Ixy, theInertia.Iyy, theInertia.Iyz),
523 gp_XYZ (theInertia.Ixz, theInertia.Iyz, theInertia.Izz));
524}
525
526//=======================================================================
527//function : Compute
528//purpose :
529//=======================================================================
530Standard_Real BRepGProp_Gauss::Compute(
531 BRepGProp_Face& theSurface,
532 BRepGProp_Domain& theDomain,
533 const gp_Pnt& theLocation,
534 const Standard_Real theEps,
535 const Standard_Real theCoeff[],
536 const Standard_Boolean theIsByPoint,
537 Standard_Real& theOutMass,
538 gp_Pnt& theOutGravityCenter,
539 gp_Mat& theOutInertia)
540{
541 const Standard_Boolean isErrorCalculation =
542 ( 0.0 > theEps || theEps < 0.001 ) ? Standard_True : Standard_False;
543 const Standard_Boolean isVerifyComputation =
544 ( 0.0 < theEps && theEps < 0.001 ) ? Standard_True : Standard_False;
545
546 Standard_Real anEpsilon= Abs(theEps);
547
548 BRepGProp_Gauss::Inertia anInertia;
549 InertiaArray anInertiaL = new NCollection_Array1<Inertia>(1, SM);
550 InertiaArray anInertiaU = new NCollection_Array1<Inertia>(1, SM);
551
552 // Prepare Gauss points and weights
c04c30b3 553 NCollection_Handle<math_Vector> LGaussP[2];
554 NCollection_Handle<math_Vector> LGaussW[2];
555 NCollection_Handle<math_Vector> UGaussP[2];
556 NCollection_Handle<math_Vector> UGaussW[2];
9bd59d1c 557
558 const Standard_Integer aNbGaussPoint =
559 RealToInt(Ceiling(ERROR_ALGEBR_RATIO * GPM));
560
561 LGaussP[0] = new math_Vector(1, GPM);
562 LGaussP[1] = new math_Vector(1, aNbGaussPoint);
563 LGaussW[0] = new math_Vector(1, GPM);
564 LGaussW[1] = new math_Vector(1, aNbGaussPoint);
565
566 UGaussP[0] = new math_Vector(1, GPM);
567 UGaussP[1] = new math_Vector(1, aNbGaussPoint);
568 UGaussW[0] = new math_Vector(1, GPM);
569 UGaussW[1] = new math_Vector(1, aNbGaussPoint);
570
c04c30b3 571 NCollection_Handle<math_Vector> L1 = new math_Vector(1, SM);
572 NCollection_Handle<math_Vector> L2 = new math_Vector(1, SM);
573 NCollection_Handle<math_Vector> U1 = new math_Vector(1, SM);
574 NCollection_Handle<math_Vector> U2 = new math_Vector(1, SM);
9bd59d1c 575
c04c30b3 576 NCollection_Handle<math_Vector> ErrL = new math_Vector(1, SM, 0.0);
577 NCollection_Handle<math_Vector> ErrU = new math_Vector(1, SM, 0.0);
578 NCollection_Handle<math_Vector> ErrUL = new math_Vector(1, SM, 0.0);
9bd59d1c 579
580 // Face parametrization in U and V direction
581 Standard_Real BV1, BV2, BU1, BU2;
582 theSurface.Bounds(BU1, BU2, BV1, BV2);
583 checkBounds(BU1, BU2, BV1, BV2);
584
585 //
586 const Standard_Integer NumSubs = SUBS_POWER;
5b0f2540 587 const TopoDS_Face& aF = theSurface.GetFace();
588 TopoDS_Iterator aWIter(aF);
589 const Standard_Boolean isNaturalRestriction = !aWIter.More(); //theSurface.NaturalRestriction();
9bd59d1c 590
591 Standard_Real CIx, CIy, CIz, CIxy, CIxz, CIyz;
592 Standard_Real CDim[2], CIxx[2], CIyy[2], CIzz[2];
593
594 // Boundary curve parametrization
595 Standard_Real u1 = BU1, u2, l1, l2, lm, lr, l, v;
596
597 // On the boundary curve u-v
598 gp_Pnt2d Puv;
599 gp_Vec2d Vuv;
600 Standard_Real Dul; // Dul = Du / Dl
601
602 Standard_Integer iLS, iLSubEnd, iGL, iGLEnd, NbLGaussP[2], LRange[2], iL, kL, kLEnd, IL, JL;
603 Standard_Integer i, iUSubEnd, NbUGaussP[2], URange[2], kU, kUEnd, IU, JU;
604 Standard_Integer UMaxSubs, LMaxSubs;
605
606 Standard_Real ErrorU, ErrorL, ErrorLMax = 0.0, Eps = 0.0, EpsL = 0.0, EpsU = 0.0;
607 iGLEnd = isErrorCalculation ? 2 : 1;
608
609 NbUGaussP[0] = theSurface.SIntOrder(anEpsilon);
610 NbUGaussP[1] = RealToInt( Ceiling(ERROR_ALGEBR_RATIO * NbUGaussP[0]) );
611
612 math::GaussPoints (NbUGaussP[0], *UGaussP[0]);
613 math::GaussWeights(NbUGaussP[0], *UGaussW[0]);
614 math::GaussPoints (NbUGaussP[1], *UGaussP[1]);
615 math::GaussWeights(NbUGaussP[1], *UGaussW[1]);
616
617 const Standard_Integer aNbUSubs = theSurface.SUIntSubs();
618 TColStd_Array1OfReal UKnots(1, aNbUSubs + 1);
619 theSurface.UKnots(UKnots);
620
621 while (isNaturalRestriction || theDomain.More())
622 {
623 if (isNaturalRestriction)
624 {
625 NbLGaussP[0] = Min(2 * NbUGaussP[0], math::GaussPointsMax());
626 }
627 else
628 {
629 theSurface.Load(theDomain.Value());
630 NbLGaussP[0] = theSurface.LIntOrder(anEpsilon);
631 }
632
633 NbLGaussP[1] = RealToInt( Ceiling(ERROR_ALGEBR_RATIO * NbLGaussP[0]) );
634
635 math::GaussPoints (NbLGaussP[0], *LGaussP[0]);
636 math::GaussWeights(NbLGaussP[0], *LGaussW[0]);
637 math::GaussPoints (NbLGaussP[1], *LGaussP[1]);
638 math::GaussWeights(NbLGaussP[1], *LGaussW[1]);
639
640 const Standard_Integer aNbLSubs =
641 isNaturalRestriction ? theSurface.SVIntSubs(): theSurface.LIntSubs();
642 TColStd_Array1OfReal LKnots(1, aNbLSubs + 1);
643
644 if (isNaturalRestriction)
645 {
646 theSurface.VKnots(LKnots);
647 l1 = BV1;
648 l2 = BV2;
649 }
650 else
651 {
652 theSurface.LKnots(LKnots);
653 l1 = theSurface.FirstParameter();
654 l2 = theSurface.LastParameter();
655 }
656 ErrorL = 0.0;
657 kLEnd = 1; JL = 0;
658
659 if (Abs(l2 - l1) > EPS_PARAM)
660 {
661 iLSubEnd = FillIntervalBounds(l1, l2, LKnots, NumSubs, anInertiaL, L1, L2, ErrL, ErrUL);
662 LMaxSubs = BRepGProp_Gauss::MaxSubs(iLSubEnd);
663
664 if (LMaxSubs > SM)
665 LMaxSubs = SM;
666
667 BRepGProp_Gauss::InitMass(0.0, 1, LMaxSubs, anInertiaL);
668 BRepGProp_Gauss::Init(ErrL, 0.0, 1, LMaxSubs);
669 BRepGProp_Gauss::Init(ErrUL, 0.0, 1, LMaxSubs);
670
671 do // while: L
672 {
673 if (++JL > iLSubEnd)
674 {
675 LRange[0] = IL = ErrL->Max();
676 LRange[1] = JL;
677 L1->Value(JL) = (L1->Value(IL) + L2->Value(IL)) * 0.5;
678 L2->Value(JL) = L2->Value(IL);
679 L2->Value(IL) = L1->Value(JL);
680 }
681 else
682 LRange[0] = IL = JL;
683
684 if (JL == LMaxSubs || Abs(L2->Value(JL) - L1->Value(JL)) < EPS_PARAM)
685 {
686 if (kLEnd == 1)
687 {
688 anInertiaL->ChangeValue(JL).Reset();
689 ErrL->Value(JL) = 0.0;
690 }
691 else
692 {
693 --JL;
694 EpsL = ErrorL;
695 Eps = EpsL / 0.9;
696 break;
697 }
698 }
699 else
700 for (kL = 0; kL < kLEnd; kL++)
701 {
702 iLS = LRange[kL];
703 lm = 0.5 * (L2->Value(iLS) + L1->Value(iLS));
704 lr = 0.5 * (L2->Value(iLS) - L1->Value(iLS));
705
706 CIx = CIy = CIz = CIxy = CIxz = CIyz = 0.0;
707
708 for (iGL = 0; iGL < iGLEnd; ++iGL)
709 {
710 CDim[iGL] = CIxx[iGL] = CIyy[iGL] = CIzz[iGL] = 0.0;
711
712 for (iL = 1; iL <= NbLGaussP[iGL]; iL++)
713 {
714 l = lm + lr * LGaussP[iGL]->Value(iL);
715 if (isNaturalRestriction)
716 {
717 v = l;
718 u2 = BU2;
719 Dul = LGaussW[iGL]->Value(iL);
720 }
721 else
722 {
723 theSurface.D12d (l, Puv, Vuv);
724 Dul = Vuv.Y() * LGaussW[iGL]->Value(iL); // Dul = Du / Dl
725
726 if (Abs(Dul) < EPS_PARAM)
727 continue;
728
729 v = Puv.Y();
730 u2 = Puv.X();
731
732 // Check on cause out off bounds of value current parameter
733 if (v < BV1)
734 v = BV1;
735 else if (v > BV2)
736 v = BV2;
737
738 if (u2 < BU1)
739 u2 = BU1;
740 else if (u2 > BU2)
741 u2 = BU2;
742 }
743
744 ErrUL->Value(iLS) = 0.0;
745 kUEnd = 1;
746 JU = 0;
747
748 if (Abs(u2 - u1) < EPS_PARAM)
749 continue;
750
c04c30b3 751 NCollection_Handle<math_Vector> aDummy;
9bd59d1c 752 iUSubEnd = FillIntervalBounds(u1, u2, UKnots, NumSubs, anInertiaU, U1, U2, ErrU, aDummy);
753 UMaxSubs = BRepGProp_Gauss::MaxSubs(iUSubEnd);
754
755 if (UMaxSubs > SM)
756 UMaxSubs = SM;
757
758 BRepGProp_Gauss::InitMass(0.0, 1, UMaxSubs, anInertiaU);
759 BRepGProp_Gauss::Init(ErrU, 0.0, 1, UMaxSubs);
760 ErrorU = 0.0;
761
762 do
763 {//while: U
764 if (++JU > iUSubEnd)
765 {
766 URange[0] = IU = ErrU->Max();
767 URange[1] = JU;
768
769 U1->Value(JU) = (U1->Value(IU) + U2->Value(IU)) * 0.5;
770 U2->Value(JU) = U2->Value(IU);
771 U2->Value(IU) = U1->Value(JU);
772 }
773 else
774 URange[0] = IU = JU;
775
776 if (JU == UMaxSubs || Abs(U2->Value(JU) - U1->Value(JU)) < EPS_PARAM)
777 if (kUEnd == 1)
778 {
779 ErrU->Value(JU) = 0.0;
780 anInertiaU->ChangeValue(JU).Reset();
781 }
782 else
783 {
784 --JU;
785 EpsU = ErrorU;
786 Eps = 10. * EpsU * Abs((u2 - u1) * Dul);
787 EpsL = 0.9 * Eps;
788 break;
789 }
790 else
791 {
792 gp_Pnt aPoint;
793 gp_Vec aNormal;
794
795 for (kU = 0; kU < kUEnd; ++kU)
796 {
797 BRepGProp_Gauss::Inertia aLocal[2];
798
799 Standard_Integer iUS = URange[kU];
800 const Standard_Integer aLength = iGLEnd - iGL;
801
802 const Standard_Real um = 0.5 * (U2->Value(iUS) + U1->Value(iUS));
803 const Standard_Real ur = 0.5 * (U2->Value(iUS) - U1->Value(iUS));
804
805 for (Standard_Integer iGU = 0; iGU < aLength; ++iGU)
806 {
807 for (Standard_Integer iU = 1; iU <= NbUGaussP[iGU]; ++iU)
808 {
809 Standard_Real w = UGaussW[iGU]->Value(iU);
810 const Standard_Real u = um + ur * UGaussP[iGU]->Value(iU);
811
812 theSurface.Normal(u, v, aPoint, aNormal);
813
814 if (myType == Vinert)
815 {
816 computeVInertiaOfElementaryPart(
817 aPoint, aNormal, theLocation, w, theCoeff, theIsByPoint, aLocal[iGU]);
818 }
819 else
820 {
821 if (iGU > 0)
822 aLocal[iGU].Mass += (w * aNormal.Magnitude());
823 else
824 {
825 computeSInertiaOfElementaryPart(
826 aPoint, aNormal, theLocation, w, aLocal[iGU]);
827 }
828 }
829 }
830 }
831
832 BRepGProp_Gauss::Inertia& anUI =
833 anInertiaU->ChangeValue(iUS);
834
835 anUI.Mass = mult(aLocal[0].Mass, ur);
836
837 if (myType == Vinert)
838 {
839 anUI.Ixx = mult(aLocal[0].Ixx, ur);
840 anUI.Iyy = mult(aLocal[0].Iyy, ur);
841 anUI.Izz = mult(aLocal[0].Izz, ur);
842 }
843
844 if (iGL > 0)
845 continue;
846
847 Standard_Real aDMass = Abs(aLocal[1].Mass - aLocal[0].Mass);
848
849 if (myType == Vinert)
850 {
851 aLocal[1].Ixx = Abs(aLocal[1].Ixx - aLocal[0].Ixx);
852 aLocal[1].Iyy = Abs(aLocal[1].Iyy - aLocal[0].Iyy);
853 aLocal[1].Izz = Abs(aLocal[1].Izz - aLocal[0].Izz);
854
855 anUI.Ix = mult(aLocal[0].Ix, ur);
856 anUI.Iy = mult(aLocal[0].Iy, ur);
857 anUI.Iz = mult(aLocal[0].Iz, ur);
858
859 anUI.Ixy = mult(aLocal[0].Ixy, ur);
860 anUI.Ixz = mult(aLocal[0].Ixz, ur);
861 anUI.Iyz = mult(aLocal[0].Iyz, ur);
862
863 #ifndef IS_MIN_DIM
864 aDMass = aLocal[1].Ixx + aLocal[1].Iyy + aLocal[1].Izz;
865 #endif
866
867 ErrU->Value(iUS) = mult(aDMass, ur);
868 }
869 else
870 {
871 anUI.Ix = mult(aLocal[0].Ix, ur);
872 anUI.Iy = mult(aLocal[0].Iy, ur);
873 anUI.Iz = mult(aLocal[0].Iz, ur);
874 anUI.Ixx = mult(aLocal[0].Ixx, ur);
875 anUI.Iyy = mult(aLocal[0].Iyy, ur);
876 anUI.Izz = mult(aLocal[0].Izz, ur);
877 anUI.Ixy = mult(aLocal[0].Ixy, ur);
878 anUI.Ixz = mult(aLocal[0].Ixz, ur);
879 anUI.Iyz = mult(aLocal[0].Iyz, ur);
880
881 ErrU->Value(iUS) = mult(aDMass, ur);
882 }
883 }
884 }
885
886 if (JU == iUSubEnd)
887 {
888 kUEnd = 2;
889 ErrorU = ErrU->Value(ErrU->Max());
890 }
891 } while ( (ErrorU - EpsU > 0.0 && EpsU != 0.0) || kUEnd == 1 );
892
893 for (i = 1; i <= JU; ++i)
894 {
895 const BRepGProp_Gauss::Inertia& anIU =
896 anInertiaU->Value(i);
897
898 CDim[iGL] = add(CDim[iGL], mult(anIU.Mass, Dul));
899 CIxx[iGL] = add(CIxx[iGL], mult(anIU.Ixx, Dul));
900 CIyy[iGL] = add(CIyy[iGL], mult(anIU.Iyy, Dul));
901 CIzz[iGL] = add(CIzz[iGL], mult(anIU.Izz, Dul));
902 }
903
904 if (iGL > 0)
905 continue;
906
907 ErrUL->Value(iLS) = ErrorU * Abs((u2 - u1) * Dul);
908
909 for (i = 1; i <= JU; ++i)
910 {
911 const BRepGProp_Gauss::Inertia& anIU =
912 anInertiaU->Value(i);
913
914 CIx = add(CIx, mult(anIU.Ix, Dul));
915 CIy = add(CIy, mult(anIU.Iy, Dul));
916 CIz = add(CIz, mult(anIU.Iz, Dul));
917
918 CIxy = add(CIxy, mult(anIU.Ixy, Dul));
919 CIxz = add(CIxz, mult(anIU.Ixz, Dul));
920 CIyz = add(CIyz, mult(anIU.Iyz, Dul));
921 }
922 }//for: iL
923 }//for: iGL
924
925 BRepGProp_Gauss::Inertia& aLI = anInertiaL->ChangeValue(iLS);
926
927 aLI.Mass = mult(CDim[0], lr);
928 aLI.Ixx = mult(CIxx[0], lr);
929 aLI.Iyy = mult(CIyy[0], lr);
930 aLI.Izz = mult(CIzz[0], lr);
931
932 if (iGLEnd == 2)
933 {
934 Standard_Real aSubDim = Abs(CDim[1] - CDim[0]);
935
936 if (myType == Vinert)
937 {
938 ErrorU = ErrUL->Value(iLS);
939
940 CIxx[1] = Abs(CIxx[1] - CIxx[0]);
941 CIyy[1] = Abs(CIyy[1] - CIyy[0]);
942 CIzz[1] = Abs(CIzz[1] - CIzz[0]);
943
944 #ifndef IS_MIN_DIM
945 aSubDim = CIxx[1] + CIyy[1] + CIzz[1];
946 #endif
947
948 ErrL->Value(iLS) = add(mult(aSubDim, lr), ErrorU);
949 }
950 else
951 {
952 ErrL->Value(iLS) = add(mult(aSubDim, lr), ErrUL->Value(iLS));
953 }
954 }
955
956 aLI.Ix = mult(CIx, lr);
957 aLI.Iy = mult(CIy, lr);
958 aLI.Iz = mult(CIz, lr);
959
960 aLI.Ixy = mult(CIxy, lr);
961 aLI.Ixz = mult(CIxz, lr);
962 aLI.Iyz = mult(CIyz, lr);
963 }//for: (kL)iLS
964
965 // Calculate/correct epsilon of computation by current value of dim
966 // That is need for not spend time for
967 if (JL == iLSubEnd)
968 {
969 kLEnd = 2;
970
971 Standard_Real DDim = 0.0;
972 for (i = 1; i <= JL; ++i)
973 DDim += anInertiaL->Value(i).Mass;
974
975 #ifndef IS_MIN_DIM
976 {
977 if (myType == Vinert)
978 {
979 Standard_Real DIxx = 0.0, DIyy = 0.0, DIzz = 0.0;
980 for (i = 1; i <= JL; ++i)
981 {
982 const BRepGProp_Gauss::Inertia& aLocalL =
983 anInertiaL->Value(i);
984
985 DIxx += aLocalL.Ixx;
986 DIyy += aLocalL.Iyy;
987 DIzz += aLocalL.Izz;
988 }
989
990 DDim = Abs(DIxx) + Abs(DIyy) + Abs(DIzz);
991 }
992 }
993 #endif
994
995 DDim = Abs(DDim * anEpsilon);
996
997 if (DDim > Eps)
998 {
999 Eps = DDim;
1000 EpsL = 0.9 * Eps;
1001 }
1002 }
1003 if (kLEnd == 2)
1004 {
1005 ErrorL = ErrL->Value(ErrL->Max());
1006 }
1007 } while ( (ErrorL - EpsL > 0.0 && isVerifyComputation) || kLEnd == 1 );
1008
1009 for ( i = 1; i <= JL; i++ )
1010 addAndRestoreInertia(anInertiaL->Value(i), anInertia);
1011
1012 ErrorLMax = Max(ErrorLMax, ErrorL);
1013 }
1014
1015 if (isNaturalRestriction)
1016 break;
1017
1018 theDomain.Next();
1019 }
1020
1021 if (myType == Vinert)
1022 convert(anInertia, theCoeff, theIsByPoint, theOutGravityCenter, theOutInertia, theOutMass);
1023 else
1024 convert(anInertia, theOutGravityCenter, theOutInertia, theOutMass);
1025
1026 if (iGLEnd == 2)
1027 {
1028 if (theOutMass != 0.0)
1029 {
1030 Eps = ErrorLMax / Abs(theOutMass);
1031
1032 #ifndef IS_MIN_DIM
1033 {
1034 if (myType == Vinert)
1035 Eps = ErrorLMax / (Abs(anInertia.Ixx) +
1036 Abs(anInertia.Iyy) +
1037 Abs(anInertia.Izz));
1038 }
1039 #endif
1040 }
1041 else
1042 {
1043 Eps = 0.0;
1044 }
1045 }
1046 else
1047 {
1048 Eps = anEpsilon;
1049 }
1050
1051 return Eps;
1052}
1053
1054//=======================================================================
1055//function : Compute
1056//purpose :
1057//=======================================================================
1058Standard_Real BRepGProp_Gauss::Compute(BRepGProp_Face& theSurface,
1059 BRepGProp_Domain& theDomain,
1060 const gp_Pnt& theLocation,
1061 const Standard_Real theEps,
1062 Standard_Real& theOutMass,
1063 gp_Pnt& theOutGravityCenter,
1064 gp_Mat& theOutInertia)
1065{
1066 Standard_ASSERT_RAISE(myType == Sinert, "BRepGProp_Gauss: Incorrect type");
1067
1068 return Compute(theSurface,
1069 theDomain,
1070 theLocation,
1071 theEps,
1072 NULL,
1073 Standard_True,
1074 theOutMass,
1075 theOutGravityCenter,
1076 theOutInertia);
1077}
1078
1079//=======================================================================
1080//function : Compute
1081//purpose :
1082//=======================================================================
1083void BRepGProp_Gauss::Compute(BRepGProp_Face& theSurface,
1084 BRepGProp_Domain& theDomain,
1085 const gp_Pnt& theLocation,
1086 Standard_Real& theOutMass,
1087 gp_Pnt& theOutGravityCenter,
1088 gp_Mat& theOutInertia)
1089{
1090 Standard_ASSERT_RAISE(myType == Sinert, "BRepGProp_Gauss: Incorrect type");
1091
1092 Standard_Real u1, u2, v1, v2;
1093 theSurface.Bounds (u1, u2, v1, v2);
1094 checkBounds(u1, u2, v1, v2);
1095
1096 const Standard_Integer NbUGaussgp_Pnts =
1097 Min(theSurface.UIntegrationOrder(), math::GaussPointsMax());
1098
1099 const Standard_Integer NbVGaussgp_Pnts =
1100 Min(theSurface.VIntegrationOrder(), math::GaussPointsMax());
1101
1102 const Standard_Integer NbGaussgp_Pnts =
1103 Max(NbUGaussgp_Pnts, NbVGaussgp_Pnts);
1104
1105 // Number of Gauss points for the integration on the face
1106 math_Vector GaussSPV (1, NbGaussgp_Pnts);
1107 math_Vector GaussSWV (1, NbGaussgp_Pnts);
1108 math::GaussPoints (NbGaussgp_Pnts, GaussSPV);
1109 math::GaussWeights(NbGaussgp_Pnts, GaussSWV);
1110
1111 BRepGProp_Gauss::Inertia anInertia;
1112 while (theDomain.More())
1113 {
1114 theSurface.Load(theDomain.Value());
1115
5b0f2540 1116 Standard_Integer NbCGaussgp_Pnts =
9bd59d1c 1117 Min(theSurface.IntegrationOrder(), math::GaussPointsMax());
1118
5b0f2540 1119 NbCGaussgp_Pnts = Max(NbCGaussgp_Pnts, NbGaussgp_Pnts);
1120
9bd59d1c 1121 math_Vector GaussCP(1, NbCGaussgp_Pnts);
1122 math_Vector GaussCW(1, NbCGaussgp_Pnts);
1123 math::GaussPoints (NbCGaussgp_Pnts, GaussCP);
1124 math::GaussWeights(NbCGaussgp_Pnts, GaussCW);
1125
1126
1127 const Standard_Real l1 = theSurface.FirstParameter();
1128 const Standard_Real l2 = theSurface.LastParameter ();
1129 const Standard_Real lm = 0.5 * (l2 + l1);
1130 const Standard_Real lr = 0.5 * (l2 - l1);
1131
1132 BRepGProp_Gauss::Inertia aCInertia;
1133 for (Standard_Integer i = 1; i <= NbCGaussgp_Pnts; ++i)
1134 {
1135 const Standard_Real l = lm + lr * GaussCP(i);
1136
1137 gp_Pnt2d Puv;
1138 gp_Vec2d Vuv;
1139 theSurface.D12d(l, Puv, Vuv);
1140
1141 const Standard_Real v = Puv.Y();
1142 u2 = Puv.X();
1143
1144 const Standard_Real Dul = Vuv.Y() * GaussCW(i);
1145 const Standard_Real um = 0.5 * (u2 + u1);
1146 const Standard_Real ur = 0.5 * (u2 - u1);
1147
1148 BRepGProp_Gauss::Inertia aLocalInertia;
1149 for (Standard_Integer j = 1; j <= NbGaussgp_Pnts; ++j)
1150 {
1151 const Standard_Real u = add(um, mult(ur, GaussSPV(j)));
1152 const Standard_Real aWeight = Dul * GaussSWV(j);
1153
1154 gp_Pnt aPoint;
1155 gp_Vec aNormal;
1156 theSurface.Normal (u, v, aPoint, aNormal);
1157
1158 computeSInertiaOfElementaryPart(aPoint, aNormal, theLocation, aWeight, aLocalInertia);
1159 }
1160
1161 multAndRestoreInertia(ur, aLocalInertia);
1162 addAndRestoreInertia (aLocalInertia, aCInertia);
1163 }
1164
1165 multAndRestoreInertia(lr, aCInertia);
1166 addAndRestoreInertia (aCInertia, anInertia);
1167
1168 theDomain.Next();
1169 }
1170
1171 convert(anInertia, theOutGravityCenter, theOutInertia, theOutMass);
1172}
1173
1174//=======================================================================
1175//function : Compute
1176//purpose :
1177//=======================================================================
1178void BRepGProp_Gauss::Compute(BRepGProp_Face& theSurface,
1179 BRepGProp_Domain& theDomain,
1180 const gp_Pnt& theLocation,
1181 const Standard_Real theCoeff[],
1182 const Standard_Boolean theIsByPoint,
1183 Standard_Real& theOutMass,
1184 gp_Pnt& theOutGravityCenter,
1185 gp_Mat& theOutInertia)
1186{
1187 Standard_ASSERT_RAISE(myType == Vinert, "BRepGProp_Gauss: Incorrect type");
1188
1189 Standard_Real u1, v1, u2, v2;
1190 theSurface.Bounds (u1, u2, v1, v2);
1191 checkBounds(u1, u2, v1, v2);
1192
1193 Standard_Real _u2 = u2; //OCC104
1194
1195 BRepGProp_Gauss::Inertia anInertia;
1196 while (theDomain.More())
1197 {
1198 theSurface.Load(theDomain.Value());
1199
1200 const Standard_Integer aVNbCGaussgp_Pnts =
1201 theSurface.VIntegrationOrder();
1202
1203 const Standard_Integer aNbGaussgp_Pnts =
1204 Min( Max(theSurface.IntegrationOrder(), aVNbCGaussgp_Pnts), math::GaussPointsMax() );
1205
1206 math_Vector GaussP(1, aNbGaussgp_Pnts);
1207 math_Vector GaussW(1, aNbGaussgp_Pnts);
1208 math::GaussPoints (aNbGaussgp_Pnts, GaussP);
1209 math::GaussWeights(aNbGaussgp_Pnts, GaussW);
1210
1211 const Standard_Real l1 = theSurface.FirstParameter();
1212 const Standard_Real l2 = theSurface.LastParameter();
1213 const Standard_Real lm = 0.5 * (l2 + l1);
1214 const Standard_Real lr = 0.5 * (l2 - l1);
1215
1216 BRepGProp_Gauss::Inertia aCInertia;
1217 for (Standard_Integer i = 1; i <= aNbGaussgp_Pnts; ++i)
1218 {
1219 const Standard_Real l = lm + lr * GaussP(i);
1220
1221 gp_Pnt2d Puv;
1222 gp_Vec2d Vuv;
1223
1224 theSurface.D12d(l, Puv, Vuv);
1225
1226 u2 = Puv.X();
1227 u2 = Min( Max(u1, u2), _u2 ); // OCC104
1228 const Standard_Real v = Min(Max(Puv.Y(), v1), v2);
1229
1230 const Standard_Real Dul = Vuv.Y() * GaussW(i);
1231 const Standard_Real um = 0.5 * (u2 + u1);
1232 const Standard_Real ur = 0.5 * (u2 - u1);
1233
1234 BRepGProp_Gauss::Inertia aLocalInertia;
1235 for (Standard_Integer j = 1; j <= aNbGaussgp_Pnts; ++j)
1236 {
1237 const Standard_Real u = um + ur * GaussP(j);
1238 const Standard_Real aWeight = Dul * GaussW(j);
1239
1240 gp_Pnt aPoint;
1241 gp_Vec aNormal;
1242
1243 theSurface.Normal(u, v, aPoint, aNormal);
1244
1245 computeVInertiaOfElementaryPart(
1246 aPoint,
1247 aNormal,
1248 theLocation,
1249 aWeight,
1250 theCoeff,
1251 theIsByPoint,
1252 aLocalInertia);
1253 }
1254
1255 multAndRestoreInertia(ur, aLocalInertia);
1256 addAndRestoreInertia (aLocalInertia, aCInertia);
1257 }
1258
1259 multAndRestoreInertia(lr, aCInertia);
1260 addAndRestoreInertia (aCInertia, anInertia);
1261
1262 theDomain.Next();
1263 }
1264
1265 convert(anInertia, theCoeff, theIsByPoint, theOutGravityCenter, theOutInertia, theOutMass);
1266}
1267
1268//=======================================================================
1269//function : Compute
1270//purpose :
1271//=======================================================================
1272void BRepGProp_Gauss::Compute(const BRepGProp_Face& theSurface,
1273 const gp_Pnt& theLocation,
1274 const Standard_Real theCoeff[],
1275 const Standard_Boolean theIsByPoint,
1276 Standard_Real& theOutMass,
1277 gp_Pnt& theOutGravityCenter,
1278 gp_Mat& theOutInertia)
1279{
1280 Standard_Real LowerU, UpperU, LowerV, UpperV;
1281 theSurface.Bounds(LowerU, UpperU, LowerV, UpperV);
1282 checkBounds(LowerU, UpperU, LowerV, UpperV);
1283
1284 const Standard_Integer UOrder =
1285 Min(theSurface.UIntegrationOrder(), math::GaussPointsMax());
1286 const Standard_Integer VOrder =
1287 Min(theSurface.VIntegrationOrder(), math::GaussPointsMax());
1288
1289 // Gauss points and weights
1290 math_Vector GaussPU(1, UOrder);
1291 math_Vector GaussWU(1, UOrder);
1292 math_Vector GaussPV(1, VOrder);
1293 math_Vector GaussWV(1, VOrder);
1294
1295 math::GaussPoints (UOrder, GaussPU);
1296 math::GaussWeights(UOrder, GaussWU);
1297 math::GaussPoints (VOrder, GaussPV);
1298 math::GaussWeights(VOrder, GaussWV);
1299
1300 const Standard_Real um = 0.5 * add(UpperU, LowerU);
1301 const Standard_Real vm = 0.5 * add(UpperV, LowerV);
1302 Standard_Real ur = 0.5 * add(UpperU, -LowerU);
1303 Standard_Real vr = 0.5 * add(UpperV, -LowerV);
1304
1305 gp_Pnt aPoint;
1306 gp_Vec aNormal;
1307
1308 BRepGProp_Gauss::Inertia anInertia;
1309 for (Standard_Integer j = 1; j <= VOrder; ++j)
1310 {
1311 BRepGProp_Gauss::Inertia anInertiaOfElementaryPart;
1312 const Standard_Real v = add(vm, mult(vr, GaussPV(j)));
1313
1314 for (Standard_Integer i = 1; i <= UOrder; ++i)
1315 {
1316 const Standard_Real aWeight = GaussWU(i);
1317 const Standard_Real u = add(um, mult(ur, GaussPU (i)));
1318 theSurface.Normal(u, v, aPoint, aNormal);
1319
1320 if (myType == Vinert)
1321 {
1322 computeVInertiaOfElementaryPart(
1323 aPoint,
1324 aNormal,
1325 theLocation,
1326 aWeight,
1327 theCoeff,
1328 theIsByPoint,
1329 anInertiaOfElementaryPart);
1330 }
1331 else // Sinert
1332 {
1333 computeSInertiaOfElementaryPart(
1334 aPoint,
1335 aNormal,
1336 theLocation,
1337 aWeight,
1338 anInertiaOfElementaryPart);
1339 }
1340 }
1341
1342 multAndRestoreInertia(GaussWV(j), anInertiaOfElementaryPart);
1343 addAndRestoreInertia (anInertiaOfElementaryPart, anInertia);
1344 }
1345 vr = mult(vr, ur);
1346 anInertia.Ixx = mult(vr, anInertia.Ixx);
1347 anInertia.Iyy = mult(vr, anInertia.Iyy);
1348 anInertia.Izz = mult(vr, anInertia.Izz);
1349 anInertia.Ixy = mult(vr, anInertia.Ixy);
1350 anInertia.Ixz = mult(vr, anInertia.Ixz);
1351 anInertia.Iyz = mult(vr, anInertia.Iyz);
1352
1353 if (myType == Vinert)
1354 {
1355 convert(anInertia, theCoeff, theIsByPoint, theOutGravityCenter, theOutInertia, theOutMass);
1356 }
1357 else // Sinert
1358 {
1359 convert(anInertia, theOutGravityCenter, theOutInertia, theOutMass);
1360 }
1361
1362 theOutMass *= vr;
1363}
1364
1365//=======================================================================
1366//function : Compute
1367//purpose :
1368//=======================================================================
1369void BRepGProp_Gauss::Compute(const BRepGProp_Face& theSurface,
1370 const gp_Pnt& theLocation,
1371 Standard_Real& theOutMass,
1372 gp_Pnt& theOutGravityCenter,
1373 gp_Mat& theOutInertia)
1374{
1375 Standard_ASSERT_RAISE(myType == Sinert, "BRepGProp_Gauss: Incorrect type");
1376
1377 Compute(theSurface,
1378 theLocation,
1379 NULL,
1380 Standard_True,
1381 theOutMass,
1382 theOutGravityCenter,
1383 theOutInertia);
1384}
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