CommitLineData
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{
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
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
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
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 {
410 mult = (::MultInf);
411 }
412}
413
414//=======================================================================
416//purpose :
417//=======================================================================
419 const BRepGProp_Gauss::Inertia& theInInertia,
420 BRepGProp_Gauss::Inertia& theOutInertia)
421{
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;
587 const Standard_Boolean isNaturalRestriction = theSurface.NaturalRestriction();
588
589 Standard_Real CIx, CIy, CIz, CIxy, CIxz, CIyz;
590 Standard_Real CDim[2], CIxx[2], CIyy[2], CIzz[2];
591
592 // Boundary curve parametrization
593 Standard_Real u1 = BU1, u2, l1, l2, lm, lr, l, v;
594
595 // On the boundary curve u-v
596 gp_Pnt2d Puv;
597 gp_Vec2d Vuv;
598 Standard_Real Dul; // Dul = Du / Dl
599
600 Standard_Integer iLS, iLSubEnd, iGL, iGLEnd, NbLGaussP[2], LRange[2], iL, kL, kLEnd, IL, JL;
601 Standard_Integer i, iUSubEnd, NbUGaussP[2], URange[2], kU, kUEnd, IU, JU;
602 Standard_Integer UMaxSubs, LMaxSubs;
603
604 Standard_Real ErrorU, ErrorL, ErrorLMax = 0.0, Eps = 0.0, EpsL = 0.0, EpsU = 0.0;
605 iGLEnd = isErrorCalculation ? 2 : 1;
606
607 NbUGaussP[0] = theSurface.SIntOrder(anEpsilon);
608 NbUGaussP[1] = RealToInt( Ceiling(ERROR_ALGEBR_RATIO * NbUGaussP[0]) );
609
610 math::GaussPoints (NbUGaussP[0], *UGaussP[0]);
611 math::GaussWeights(NbUGaussP[0], *UGaussW[0]);
612 math::GaussPoints (NbUGaussP[1], *UGaussP[1]);
613 math::GaussWeights(NbUGaussP[1], *UGaussW[1]);
614
615 const Standard_Integer aNbUSubs = theSurface.SUIntSubs();
616 TColStd_Array1OfReal UKnots(1, aNbUSubs + 1);
617 theSurface.UKnots(UKnots);
618
619 while (isNaturalRestriction || theDomain.More())
620 {
621 if (isNaturalRestriction)
622 {
623 NbLGaussP[0] = Min(2 * NbUGaussP[0], math::GaussPointsMax());
624 }
625 else
626 {
628 NbLGaussP[0] = theSurface.LIntOrder(anEpsilon);
629 }
630
631 NbLGaussP[1] = RealToInt( Ceiling(ERROR_ALGEBR_RATIO * NbLGaussP[0]) );
632
633 math::GaussPoints (NbLGaussP[0], *LGaussP[0]);
634 math::GaussWeights(NbLGaussP[0], *LGaussW[0]);
635 math::GaussPoints (NbLGaussP[1], *LGaussP[1]);
636 math::GaussWeights(NbLGaussP[1], *LGaussW[1]);
637
638 const Standard_Integer aNbLSubs =
639 isNaturalRestriction ? theSurface.SVIntSubs(): theSurface.LIntSubs();
640 TColStd_Array1OfReal LKnots(1, aNbLSubs + 1);
641
642 if (isNaturalRestriction)
643 {
644 theSurface.VKnots(LKnots);
645 l1 = BV1;
646 l2 = BV2;
647 }
648 else
649 {
650 theSurface.LKnots(LKnots);
651 l1 = theSurface.FirstParameter();
652 l2 = theSurface.LastParameter();
653 }
654 ErrorL = 0.0;
655 kLEnd = 1; JL = 0;
656
657 if (Abs(l2 - l1) > EPS_PARAM)
658 {
659 iLSubEnd = FillIntervalBounds(l1, l2, LKnots, NumSubs, anInertiaL, L1, L2, ErrL, ErrUL);
660 LMaxSubs = BRepGProp_Gauss::MaxSubs(iLSubEnd);
661
662 if (LMaxSubs > SM)
663 LMaxSubs = SM;
664
665 BRepGProp_Gauss::InitMass(0.0, 1, LMaxSubs, anInertiaL);
666 BRepGProp_Gauss::Init(ErrL, 0.0, 1, LMaxSubs);
667 BRepGProp_Gauss::Init(ErrUL, 0.0, 1, LMaxSubs);
668
669 do // while: L
670 {
671 if (++JL > iLSubEnd)
672 {
673 LRange[0] = IL = ErrL->Max();
674 LRange[1] = JL;
675 L1->Value(JL) = (L1->Value(IL) + L2->Value(IL)) * 0.5;
676 L2->Value(JL) = L2->Value(IL);
677 L2->Value(IL) = L1->Value(JL);
678 }
679 else
680 LRange[0] = IL = JL;
681
682 if (JL == LMaxSubs || Abs(L2->Value(JL) - L1->Value(JL)) < EPS_PARAM)
683 {
684 if (kLEnd == 1)
685 {
686 anInertiaL->ChangeValue(JL).Reset();
687 ErrL->Value(JL) = 0.0;
688 }
689 else
690 {
691 --JL;
692 EpsL = ErrorL;
693 Eps = EpsL / 0.9;
694 break;
695 }
696 }
697 else
698 for (kL = 0; kL < kLEnd; kL++)
699 {
700 iLS = LRange[kL];
701 lm = 0.5 * (L2->Value(iLS) + L1->Value(iLS));
702 lr = 0.5 * (L2->Value(iLS) - L1->Value(iLS));
703
704 CIx = CIy = CIz = CIxy = CIxz = CIyz = 0.0;
705
706 for (iGL = 0; iGL < iGLEnd; ++iGL)
707 {
708 CDim[iGL] = CIxx[iGL] = CIyy[iGL] = CIzz[iGL] = 0.0;
709
710 for (iL = 1; iL <= NbLGaussP[iGL]; iL++)
711 {
712 l = lm + lr * LGaussP[iGL]->Value(iL);
713 if (isNaturalRestriction)
714 {
715 v = l;
716 u2 = BU2;
717 Dul = LGaussW[iGL]->Value(iL);
718 }
719 else
720 {
721 theSurface.D12d (l, Puv, Vuv);
722 Dul = Vuv.Y() * LGaussW[iGL]->Value(iL); // Dul = Du / Dl
723
724 if (Abs(Dul) < EPS_PARAM)
725 continue;
726
727 v = Puv.Y();
728 u2 = Puv.X();
729
730 // Check on cause out off bounds of value current parameter
731 if (v < BV1)
732 v = BV1;
733 else if (v > BV2)
734 v = BV2;
735
736 if (u2 < BU1)
737 u2 = BU1;
738 else if (u2 > BU2)
739 u2 = BU2;
740 }
741
742 ErrUL->Value(iLS) = 0.0;
743 kUEnd = 1;
744 JU = 0;
745
746 if (Abs(u2 - u1) < EPS_PARAM)
747 continue;
748
9bd59d1c 750 iUSubEnd = FillIntervalBounds(u1, u2, UKnots, NumSubs, anInertiaU, U1, U2, ErrU, aDummy);
751 UMaxSubs = BRepGProp_Gauss::MaxSubs(iUSubEnd);
752
753 if (UMaxSubs > SM)
754 UMaxSubs = SM;
755
756 BRepGProp_Gauss::InitMass(0.0, 1, UMaxSubs, anInertiaU);
757 BRepGProp_Gauss::Init(ErrU, 0.0, 1, UMaxSubs);
758 ErrorU = 0.0;
759
760 do
761 {//while: U
762 if (++JU > iUSubEnd)
763 {
764 URange[0] = IU = ErrU->Max();
765 URange[1] = JU;
766
767 U1->Value(JU) = (U1->Value(IU) + U2->Value(IU)) * 0.5;
768 U2->Value(JU) = U2->Value(IU);
769 U2->Value(IU) = U1->Value(JU);
770 }
771 else
772 URange[0] = IU = JU;
773
774 if (JU == UMaxSubs || Abs(U2->Value(JU) - U1->Value(JU)) < EPS_PARAM)
775 if (kUEnd == 1)
776 {
777 ErrU->Value(JU) = 0.0;
778 anInertiaU->ChangeValue(JU).Reset();
779 }
780 else
781 {
782 --JU;
783 EpsU = ErrorU;
784 Eps = 10. * EpsU * Abs((u2 - u1) * Dul);
785 EpsL = 0.9 * Eps;
786 break;
787 }
788 else
789 {
790 gp_Pnt aPoint;
791 gp_Vec aNormal;
792
793 for (kU = 0; kU < kUEnd; ++kU)
794 {
795 BRepGProp_Gauss::Inertia aLocal[2];
796
797 Standard_Integer iUS = URange[kU];
798 const Standard_Integer aLength = iGLEnd - iGL;
799
800 const Standard_Real um = 0.5 * (U2->Value(iUS) + U1->Value(iUS));
801 const Standard_Real ur = 0.5 * (U2->Value(iUS) - U1->Value(iUS));
802
803 for (Standard_Integer iGU = 0; iGU < aLength; ++iGU)
804 {
805 for (Standard_Integer iU = 1; iU <= NbUGaussP[iGU]; ++iU)
806 {
807 Standard_Real w = UGaussW[iGU]->Value(iU);
808 const Standard_Real u = um + ur * UGaussP[iGU]->Value(iU);
809
810 theSurface.Normal(u, v, aPoint, aNormal);
811
812 if (myType == Vinert)
813 {
814 computeVInertiaOfElementaryPart(
815 aPoint, aNormal, theLocation, w, theCoeff, theIsByPoint, aLocal[iGU]);
816 }
817 else
818 {
819 if (iGU > 0)
820 aLocal[iGU].Mass += (w * aNormal.Magnitude());
821 else
822 {
823 computeSInertiaOfElementaryPart(
824 aPoint, aNormal, theLocation, w, aLocal[iGU]);
825 }
826 }
827 }
828 }
829
830 BRepGProp_Gauss::Inertia& anUI =
831 anInertiaU->ChangeValue(iUS);
832
833 anUI.Mass = mult(aLocal[0].Mass, ur);
834
835 if (myType == Vinert)
836 {
837 anUI.Ixx = mult(aLocal[0].Ixx, ur);
838 anUI.Iyy = mult(aLocal[0].Iyy, ur);
839 anUI.Izz = mult(aLocal[0].Izz, ur);
840 }
841
842 if (iGL > 0)
843 continue;
844
845 Standard_Real aDMass = Abs(aLocal[1].Mass - aLocal[0].Mass);
846
847 if (myType == Vinert)
848 {
849 aLocal[1].Ixx = Abs(aLocal[1].Ixx - aLocal[0].Ixx);
850 aLocal[1].Iyy = Abs(aLocal[1].Iyy - aLocal[0].Iyy);
851 aLocal[1].Izz = Abs(aLocal[1].Izz - aLocal[0].Izz);
852
853 anUI.Ix = mult(aLocal[0].Ix, ur);
854 anUI.Iy = mult(aLocal[0].Iy, ur);
855 anUI.Iz = mult(aLocal[0].Iz, ur);
856
857 anUI.Ixy = mult(aLocal[0].Ixy, ur);
858 anUI.Ixz = mult(aLocal[0].Ixz, ur);
859 anUI.Iyz = mult(aLocal[0].Iyz, ur);
860
861 #ifndef IS_MIN_DIM
862 aDMass = aLocal[1].Ixx + aLocal[1].Iyy + aLocal[1].Izz;
863 #endif
864
866 }
867 else
868 {
869 anUI.Ix = mult(aLocal[0].Ix, ur);
870 anUI.Iy = mult(aLocal[0].Iy, ur);
871 anUI.Iz = mult(aLocal[0].Iz, ur);
872 anUI.Ixx = mult(aLocal[0].Ixx, ur);
873 anUI.Iyy = mult(aLocal[0].Iyy, ur);
874 anUI.Izz = mult(aLocal[0].Izz, ur);
875 anUI.Ixy = mult(aLocal[0].Ixy, ur);
876 anUI.Ixz = mult(aLocal[0].Ixz, ur);
877 anUI.Iyz = mult(aLocal[0].Iyz, ur);
878
880 }
881 }
882 }
883
884 if (JU == iUSubEnd)
885 {
886 kUEnd = 2;
887 ErrorU = ErrU->Value(ErrU->Max());
888 }
889 } while ( (ErrorU - EpsU > 0.0 && EpsU != 0.0) || kUEnd == 1 );
890
891 for (i = 1; i <= JU; ++i)
892 {
893 const BRepGProp_Gauss::Inertia& anIU =
894 anInertiaU->Value(i);
895
896 CDim[iGL] = add(CDim[iGL], mult(anIU.Mass, Dul));
897 CIxx[iGL] = add(CIxx[iGL], mult(anIU.Ixx, Dul));
898 CIyy[iGL] = add(CIyy[iGL], mult(anIU.Iyy, Dul));
899 CIzz[iGL] = add(CIzz[iGL], mult(anIU.Izz, Dul));
900 }
901
902 if (iGL > 0)
903 continue;
904
905 ErrUL->Value(iLS) = ErrorU * Abs((u2 - u1) * Dul);
906
907 for (i = 1; i <= JU; ++i)
908 {
909 const BRepGProp_Gauss::Inertia& anIU =
910 anInertiaU->Value(i);
911
912 CIx = add(CIx, mult(anIU.Ix, Dul));
913 CIy = add(CIy, mult(anIU.Iy, Dul));
914 CIz = add(CIz, mult(anIU.Iz, Dul));
915
916 CIxy = add(CIxy, mult(anIU.Ixy, Dul));
917 CIxz = add(CIxz, mult(anIU.Ixz, Dul));
918 CIyz = add(CIyz, mult(anIU.Iyz, Dul));
919 }
920 }//for: iL
921 }//for: iGL
922
923 BRepGProp_Gauss::Inertia& aLI = anInertiaL->ChangeValue(iLS);
924
925 aLI.Mass = mult(CDim[0], lr);
926 aLI.Ixx = mult(CIxx[0], lr);
927 aLI.Iyy = mult(CIyy[0], lr);
928 aLI.Izz = mult(CIzz[0], lr);
929
930 if (iGLEnd == 2)
931 {
932 Standard_Real aSubDim = Abs(CDim[1] - CDim[0]);
933
934 if (myType == Vinert)
935 {
936 ErrorU = ErrUL->Value(iLS);
937
938 CIxx[1] = Abs(CIxx[1] - CIxx[0]);
939 CIyy[1] = Abs(CIyy[1] - CIyy[0]);
940 CIzz[1] = Abs(CIzz[1] - CIzz[0]);
941
942 #ifndef IS_MIN_DIM
943 aSubDim = CIxx[1] + CIyy[1] + CIzz[1];
944 #endif
945
946 ErrL->Value(iLS) = add(mult(aSubDim, lr), ErrorU);
947 }
948 else
949 {
950 ErrL->Value(iLS) = add(mult(aSubDim, lr), ErrUL->Value(iLS));
951 }
952 }
953
954 aLI.Ix = mult(CIx, lr);
955 aLI.Iy = mult(CIy, lr);
956 aLI.Iz = mult(CIz, lr);
957
958 aLI.Ixy = mult(CIxy, lr);
959 aLI.Ixz = mult(CIxz, lr);
960 aLI.Iyz = mult(CIyz, lr);
961 }//for: (kL)iLS
962
963 // Calculate/correct epsilon of computation by current value of dim
964 // That is need for not spend time for
965 if (JL == iLSubEnd)
966 {
967 kLEnd = 2;
968
969 Standard_Real DDim = 0.0;
970 for (i = 1; i <= JL; ++i)
971 DDim += anInertiaL->Value(i).Mass;
972
973 #ifndef IS_MIN_DIM
974 {
975 if (myType == Vinert)
976 {
977 Standard_Real DIxx = 0.0, DIyy = 0.0, DIzz = 0.0;
978 for (i = 1; i <= JL; ++i)
979 {
980 const BRepGProp_Gauss::Inertia& aLocalL =
981 anInertiaL->Value(i);
982
983 DIxx += aLocalL.Ixx;
984 DIyy += aLocalL.Iyy;
985 DIzz += aLocalL.Izz;
986 }
987
988 DDim = Abs(DIxx) + Abs(DIyy) + Abs(DIzz);
989 }
990 }
991 #endif
992
993 DDim = Abs(DDim * anEpsilon);
994
995 if (DDim > Eps)
996 {
997 Eps = DDim;
998 EpsL = 0.9 * Eps;
999 }
1000 }
1001 if (kLEnd == 2)
1002 {
1003 ErrorL = ErrL->Value(ErrL->Max());
1004 }
1005 } while ( (ErrorL - EpsL > 0.0 && isVerifyComputation) || kLEnd == 1 );
1006
1007 for ( i = 1; i <= JL; i++ )
1009
1010 ErrorLMax = Max(ErrorLMax, ErrorL);
1011 }
1012
1013 if (isNaturalRestriction)
1014 break;
1015
1016 theDomain.Next();
1017 }
1018
1019 if (myType == Vinert)
1020 convert(anInertia, theCoeff, theIsByPoint, theOutGravityCenter, theOutInertia, theOutMass);
1021 else
1022 convert(anInertia, theOutGravityCenter, theOutInertia, theOutMass);
1023
1024 if (iGLEnd == 2)
1025 {
1026 if (theOutMass != 0.0)
1027 {
1028 Eps = ErrorLMax / Abs(theOutMass);
1029
1030 #ifndef IS_MIN_DIM
1031 {
1032 if (myType == Vinert)
1033 Eps = ErrorLMax / (Abs(anInertia.Ixx) +
1034 Abs(anInertia.Iyy) +
1035 Abs(anInertia.Izz));
1036 }
1037 #endif
1038 }
1039 else
1040 {
1041 Eps = 0.0;
1042 }
1043 }
1044 else
1045 {
1046 Eps = anEpsilon;
1047 }
1048
1049 return Eps;
1050}
1051
1052//=======================================================================
1053//function : Compute
1054//purpose :
1055//=======================================================================
1056Standard_Real BRepGProp_Gauss::Compute(BRepGProp_Face& theSurface,
1057 BRepGProp_Domain& theDomain,
1058 const gp_Pnt& theLocation,
1059 const Standard_Real theEps,
1060 Standard_Real& theOutMass,
1061 gp_Pnt& theOutGravityCenter,
1062 gp_Mat& theOutInertia)
1063{
1064 Standard_ASSERT_RAISE(myType == Sinert, "BRepGProp_Gauss: Incorrect type");
1065
1066 return Compute(theSurface,
1067 theDomain,
1068 theLocation,
1069 theEps,
1070 NULL,
1071 Standard_True,
1072 theOutMass,
1073 theOutGravityCenter,
1074 theOutInertia);
1075}
1076
1077//=======================================================================
1078//function : Compute
1079//purpose :
1080//=======================================================================
1081void BRepGProp_Gauss::Compute(BRepGProp_Face& theSurface,
1082 BRepGProp_Domain& theDomain,
1083 const gp_Pnt& theLocation,
1084 Standard_Real& theOutMass,
1085 gp_Pnt& theOutGravityCenter,
1086 gp_Mat& theOutInertia)
1087{
1088 Standard_ASSERT_RAISE(myType == Sinert, "BRepGProp_Gauss: Incorrect type");
1089
1090 Standard_Real u1, u2, v1, v2;
1091 theSurface.Bounds (u1, u2, v1, v2);
1092 checkBounds(u1, u2, v1, v2);
1093
1094 const Standard_Integer NbUGaussgp_Pnts =
1095 Min(theSurface.UIntegrationOrder(), math::GaussPointsMax());
1096
1097 const Standard_Integer NbVGaussgp_Pnts =
1098 Min(theSurface.VIntegrationOrder(), math::GaussPointsMax());
1099
1100 const Standard_Integer NbGaussgp_Pnts =
1101 Max(NbUGaussgp_Pnts, NbVGaussgp_Pnts);
1102
1103 // Number of Gauss points for the integration on the face
1104 math_Vector GaussSPV (1, NbGaussgp_Pnts);
1105 math_Vector GaussSWV (1, NbGaussgp_Pnts);
1106 math::GaussPoints (NbGaussgp_Pnts, GaussSPV);
1107 math::GaussWeights(NbGaussgp_Pnts, GaussSWV);
1108
1109 BRepGProp_Gauss::Inertia anInertia;
1110 while (theDomain.More())
1111 {
1113
1114 const Standard_Integer NbCGaussgp_Pnts =
1115 Min(theSurface.IntegrationOrder(), math::GaussPointsMax());
1116
1117 math_Vector GaussCP(1, NbCGaussgp_Pnts);
1118 math_Vector GaussCW(1, NbCGaussgp_Pnts);
1119 math::GaussPoints (NbCGaussgp_Pnts, GaussCP);
1120 math::GaussWeights(NbCGaussgp_Pnts, GaussCW);
1121
1122
1123 const Standard_Real l1 = theSurface.FirstParameter();
1124 const Standard_Real l2 = theSurface.LastParameter ();
1125 const Standard_Real lm = 0.5 * (l2 + l1);
1126 const Standard_Real lr = 0.5 * (l2 - l1);
1127
1128 BRepGProp_Gauss::Inertia aCInertia;
1129 for (Standard_Integer i = 1; i <= NbCGaussgp_Pnts; ++i)
1130 {
1131 const Standard_Real l = lm + lr * GaussCP(i);
1132
1133 gp_Pnt2d Puv;
1134 gp_Vec2d Vuv;
1135 theSurface.D12d(l, Puv, Vuv);
1136
1137 const Standard_Real v = Puv.Y();
1138 u2 = Puv.X();
1139
1140 const Standard_Real Dul = Vuv.Y() * GaussCW(i);
1141 const Standard_Real um = 0.5 * (u2 + u1);
1142 const Standard_Real ur = 0.5 * (u2 - u1);
1143
1144 BRepGProp_Gauss::Inertia aLocalInertia;
1145 for (Standard_Integer j = 1; j <= NbGaussgp_Pnts; ++j)
1146 {
1147 const Standard_Real u = add(um, mult(ur, GaussSPV(j)));
1148 const Standard_Real aWeight = Dul * GaussSWV(j);
1149
1150 gp_Pnt aPoint;
1151 gp_Vec aNormal;
1152 theSurface.Normal (u, v, aPoint, aNormal);
1153
1154 computeSInertiaOfElementaryPart(aPoint, aNormal, theLocation, aWeight, aLocalInertia);
1155 }
1156
1157 multAndRestoreInertia(ur, aLocalInertia);
1159 }
1160
1161 multAndRestoreInertia(lr, aCInertia);
1163
1164 theDomain.Next();
1165 }
1166
1167 convert(anInertia, theOutGravityCenter, theOutInertia, theOutMass);
1168}
1169
1170//=======================================================================
1171//function : Compute
1172//purpose :
1173//=======================================================================
1174void BRepGProp_Gauss::Compute(BRepGProp_Face& theSurface,
1175 BRepGProp_Domain& theDomain,
1176 const gp_Pnt& theLocation,
1177 const Standard_Real theCoeff[],
1178 const Standard_Boolean theIsByPoint,
1179 Standard_Real& theOutMass,
1180 gp_Pnt& theOutGravityCenter,
1181 gp_Mat& theOutInertia)
1182{
1183 Standard_ASSERT_RAISE(myType == Vinert, "BRepGProp_Gauss: Incorrect type");
1184
1185 Standard_Real u1, v1, u2, v2;
1186 theSurface.Bounds (u1, u2, v1, v2);
1187 checkBounds(u1, u2, v1, v2);
1188
1189 Standard_Real _u2 = u2; //OCC104
1190
1191 BRepGProp_Gauss::Inertia anInertia;
1192 while (theDomain.More())
1193 {
1195
1196 const Standard_Integer aVNbCGaussgp_Pnts =
1197 theSurface.VIntegrationOrder();
1198
1199 const Standard_Integer aNbGaussgp_Pnts =
1200 Min( Max(theSurface.IntegrationOrder(), aVNbCGaussgp_Pnts), math::GaussPointsMax() );
1201
1202 math_Vector GaussP(1, aNbGaussgp_Pnts);
1203 math_Vector GaussW(1, aNbGaussgp_Pnts);
1204 math::GaussPoints (aNbGaussgp_Pnts, GaussP);
1205 math::GaussWeights(aNbGaussgp_Pnts, GaussW);
1206
1207 const Standard_Real l1 = theSurface.FirstParameter();
1208 const Standard_Real l2 = theSurface.LastParameter();
1209 const Standard_Real lm = 0.5 * (l2 + l1);
1210 const Standard_Real lr = 0.5 * (l2 - l1);
1211
1212 BRepGProp_Gauss::Inertia aCInertia;
1213 for (Standard_Integer i = 1; i <= aNbGaussgp_Pnts; ++i)
1214 {
1215 const Standard_Real l = lm + lr * GaussP(i);
1216
1217 gp_Pnt2d Puv;
1218 gp_Vec2d Vuv;
1219
1220 theSurface.D12d(l, Puv, Vuv);
1221
1222 u2 = Puv.X();
1223 u2 = Min( Max(u1, u2), _u2 ); // OCC104
1224 const Standard_Real v = Min(Max(Puv.Y(), v1), v2);
1225
1226 const Standard_Real Dul = Vuv.Y() * GaussW(i);
1227 const Standard_Real um = 0.5 * (u2 + u1);
1228 const Standard_Real ur = 0.5 * (u2 - u1);
1229
1230 BRepGProp_Gauss::Inertia aLocalInertia;
1231 for (Standard_Integer j = 1; j <= aNbGaussgp_Pnts; ++j)
1232 {
1233 const Standard_Real u = um + ur * GaussP(j);
1234 const Standard_Real aWeight = Dul * GaussW(j);
1235
1236 gp_Pnt aPoint;
1237 gp_Vec aNormal;
1238
1239 theSurface.Normal(u, v, aPoint, aNormal);
1240
1241 computeVInertiaOfElementaryPart(
1242 aPoint,
1243 aNormal,
1244 theLocation,
1245 aWeight,
1246 theCoeff,
1247 theIsByPoint,
1248 aLocalInertia);
1249 }
1250
1251 multAndRestoreInertia(ur, aLocalInertia);
1253 }
1254
1255 multAndRestoreInertia(lr, aCInertia);
1257
1258 theDomain.Next();
1259 }
1260
1261 convert(anInertia, theCoeff, theIsByPoint, theOutGravityCenter, theOutInertia, theOutMass);
1262}
1263
1264//=======================================================================
1265//function : Compute
1266//purpose :
1267//=======================================================================
1268void BRepGProp_Gauss::Compute(const BRepGProp_Face& theSurface,
1269 const gp_Pnt& theLocation,
1270 const Standard_Real theCoeff[],
1271 const Standard_Boolean theIsByPoint,
1272 Standard_Real& theOutMass,
1273 gp_Pnt& theOutGravityCenter,
1274 gp_Mat& theOutInertia)
1275{
1276 Standard_Real LowerU, UpperU, LowerV, UpperV;
1277 theSurface.Bounds(LowerU, UpperU, LowerV, UpperV);
1278 checkBounds(LowerU, UpperU, LowerV, UpperV);
1279
1280 const Standard_Integer UOrder =
1281 Min(theSurface.UIntegrationOrder(), math::GaussPointsMax());
1282 const Standard_Integer VOrder =
1283 Min(theSurface.VIntegrationOrder(), math::GaussPointsMax());
1284
1285 // Gauss points and weights
1286 math_Vector GaussPU(1, UOrder);
1287 math_Vector GaussWU(1, UOrder);
1288 math_Vector GaussPV(1, VOrder);
1289 math_Vector GaussWV(1, VOrder);
1290
1291 math::GaussPoints (UOrder, GaussPU);
1292 math::GaussWeights(UOrder, GaussWU);
1293 math::GaussPoints (VOrder, GaussPV);
1294 math::GaussWeights(VOrder, GaussWV);
1295
1296 const Standard_Real um = 0.5 * add(UpperU, LowerU);
1297 const Standard_Real vm = 0.5 * add(UpperV, LowerV);
1298 Standard_Real ur = 0.5 * add(UpperU, -LowerU);
1299 Standard_Real vr = 0.5 * add(UpperV, -LowerV);
1300
1301 gp_Pnt aPoint;
1302 gp_Vec aNormal;
1303
1304 BRepGProp_Gauss::Inertia anInertia;
1305 for (Standard_Integer j = 1; j <= VOrder; ++j)
1306 {
1307 BRepGProp_Gauss::Inertia anInertiaOfElementaryPart;
1308 const Standard_Real v = add(vm, mult(vr, GaussPV(j)));
1309
1310 for (Standard_Integer i = 1; i <= UOrder; ++i)
1311 {
1312 const Standard_Real aWeight = GaussWU(i);
1313 const Standard_Real u = add(um, mult(ur, GaussPU (i)));
1314 theSurface.Normal(u, v, aPoint, aNormal);
1315
1316 if (myType == Vinert)
1317 {
1318 computeVInertiaOfElementaryPart(
1319 aPoint,
1320 aNormal,
1321 theLocation,
1322 aWeight,
1323 theCoeff,
1324 theIsByPoint,
1325 anInertiaOfElementaryPart);
1326 }
1327 else // Sinert
1328 {
1329 computeSInertiaOfElementaryPart(
1330 aPoint,
1331 aNormal,
1332 theLocation,
1333 aWeight,
1334 anInertiaOfElementaryPart);
1335 }
1336 }
1337
1338 multAndRestoreInertia(GaussWV(j), anInertiaOfElementaryPart);
1340 }
1341 vr = mult(vr, ur);
1342 anInertia.Ixx = mult(vr, anInertia.Ixx);
1343 anInertia.Iyy = mult(vr, anInertia.Iyy);
1344 anInertia.Izz = mult(vr, anInertia.Izz);
1345 anInertia.Ixy = mult(vr, anInertia.Ixy);
1346 anInertia.Ixz = mult(vr, anInertia.Ixz);
1347 anInertia.Iyz = mult(vr, anInertia.Iyz);
1348
1349 if (myType == Vinert)
1350 {
1351 convert(anInertia, theCoeff, theIsByPoint, theOutGravityCenter, theOutInertia, theOutMass);
1352 }
1353 else // Sinert
1354 {
1355 convert(anInertia, theOutGravityCenter, theOutInertia, theOutMass);
1356 }
1357
1358 theOutMass *= vr;
1359}
1360
1361//=======================================================================
1362//function : Compute
1363//purpose :
1364//=======================================================================
1365void BRepGProp_Gauss::Compute(const BRepGProp_Face& theSurface,
1366 const gp_Pnt& theLocation,
1367 Standard_Real& theOutMass,
1368 gp_Pnt& theOutGravityCenter,
1369 gp_Mat& theOutInertia)
1370{
1371 Standard_ASSERT_RAISE(myType == Sinert, "BRepGProp_Gauss: Incorrect type");
1372
1373 Compute(theSurface,
1374 theLocation,
1375 NULL,
1376 Standard_True,
1377 theOutMass,
1378 theOutGravityCenter,
1379 theOutInertia);
1380}