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[occt.git] / src / IntAna / IntAna_QuadQuadGeo.cxx
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1// Created on: 1992-08-06
2// Created by: Laurent BUCHARD
3// Copyright (c) 1992-1999 Matra Datavision
4// Copyright (c) 1999-2014 OPEN CASCADE SAS
5//
6// This file is part of Open CASCADE Technology software library.
7//
8// This library is free software; you can redistribute it and/or modify it under
9// the terms of the GNU Lesser General Public License version 2.1 as published
10// by the Free Software Foundation, with special exception defined in the file
11// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
12// distribution for complete text of the license and disclaimer of any warranty.
13//
14// Alternatively, this file may be used under the terms of Open CASCADE
15// commercial license or contractual agreement.
16
17//----------------------------------------------------------------------
18//-- Purposse: Geometric Intersection between two Natural Quadric
19//-- If the intersection is not a conic,
20//-- analytical methods must be called.
21//----------------------------------------------------------------------
22#ifndef DEB
23#define No_Standard_RangeError
24#define No_Standard_OutOfRange
25#endif
26
27#include <IntAna_QuadQuadGeo.ixx>
28
29#include <IntAna_IntConicQuad.hxx>
30#include <StdFail_NotDone.hxx>
31#include <Standard_DomainError.hxx>
32#include <Standard_OutOfRange.hxx>
33#include <math_DirectPolynomialRoots.hxx>
34
35#include <gp.hxx>
36#include <gp_Pln.hxx>
37#include <gp_Vec.hxx>
38#include <ElSLib.hxx>
39#include <ElCLib.hxx>
40
41#include <gp_Dir.hxx>
42#include <gp_XYZ.hxx>
43#include <gp_Pnt2d.hxx>
44#include <gp_Vec2d.hxx>
45#include <gp_Dir2d.hxx>
46
47
48static
49 gp_Ax2 DirToAx2(const gp_Pnt& P,const gp_Dir& D);
50static
51 void RefineDir(gp_Dir& aDir);
52
53//=======================================================================
54//class :
55//purpose : O p e r a t i o n s D i v e r s e s s u r d e s A x 1
56//=======================================================================
57class AxeOperator {
58 public:
59 AxeOperator(const gp_Ax1& A1,const gp_Ax1& A2);
60
61 void Distance(Standard_Real& dist,
62 Standard_Real& Param1,
63 Standard_Real& Param2);
64
65 gp_Pnt PtIntersect() {
66 return ptintersect;
67 }
68 Standard_Boolean Coplanar(void) {
69 return thecoplanar;
70 }
71 Standard_Boolean Same(void) {
72 return theparallel && (thedistance<myEPSILON_DISTANCE);
73 }
74 Standard_Real Distance(void) {
75 return thedistance ;
76 }
77 Standard_Boolean Intersect(void) {
78 return (thecoplanar && (!theparallel));
79 }
80 Standard_Boolean Parallel(void) {
81 return theparallel;
82 }
83 Standard_Boolean Normal(void) {
84 return thenormal;
85 }
86
87 protected:
88 Standard_Real Det33(const Standard_Real a11,
89 const Standard_Real a12,
90 const Standard_Real a13,
91 const Standard_Real a21,
92 const Standard_Real a22,
93 const Standard_Real a23,
94 const Standard_Real a31,
95 const Standard_Real a32,
96 const Standard_Real a33) {
97 Standard_Real theReturn =
98 a11*(a22*a33-a32*a23) - a21*(a12*a33-a32*a13) + a31*(a12*a23-a22*a13) ;
99 return theReturn ;
100 }
101
102 private:
103 gp_Pnt ptintersect;
104 gp_Ax1 Axe1;
105 gp_Ax1 Axe2;
106 Standard_Real thedistance;
107 Standard_Boolean theparallel;
108 Standard_Boolean thecoplanar;
109 Standard_Boolean thenormal;
110 //
111 Standard_Real myEPSILON_DISTANCE;
112 Standard_Real myEPSILON_AXES_PARA;
113};
114
115//=======================================================================
116//function : AxeOperator::AxeOperator
117//purpose :
118//=======================================================================
119 AxeOperator::AxeOperator(const gp_Ax1& A1,const gp_Ax1& A2)
120{
121 myEPSILON_DISTANCE=0.00000000000001;
122 myEPSILON_AXES_PARA=0.000000000001;
123 Axe1=A1;
124 Axe2=A2;
125 //---------------------------------------------------------------------
126 gp_Dir V1=Axe1.Direction();
127 gp_Dir V2=Axe2.Direction();
128 gp_Pnt P1=Axe1.Location();
129 gp_Pnt P2=Axe2.Location();
130 //
131 RefineDir(V1);
132 RefineDir(V2);
133 thecoplanar= Standard_False;
134 thenormal = Standard_False;
135
136 //--- check if the two axis are parallel
137 theparallel=V1.IsParallel(V2, myEPSILON_AXES_PARA);
138 //--- Distance between the two axis
139 gp_XYZ perp(A1.Direction().XYZ().Crossed(A2.Direction().XYZ()));
140 if (theparallel) {
141 gp_Lin L1(A1);
142 thedistance = L1.Distance(A2.Location());
143 }
144 else {
145 thedistance = Abs(gp_Vec(perp.Normalized()).Dot(gp_Vec(Axe1.Location(),
146 Axe2.Location())));
147 }
148 //--- check if Axis are Coplanar
149 Standard_Real D33;
150 if(thedistance<myEPSILON_DISTANCE) {
151 D33=Det33(V1.X(),V1.Y(),V1.Z()
152 ,V2.X(),V2.Y(),V2.Z()
153 ,P1.X()-P2.X(),P1.Y()-P2.Y(),P1.Z()-P2.Z());
154 if(Abs(D33)<=myEPSILON_DISTANCE) {
155 thecoplanar=Standard_True;
156 }
157 }
158 else {
159 thecoplanar=Standard_True;
160 thenormal=(V1.Dot(V2)==0.0)? Standard_True : Standard_False;
161 }
162 //--- check if the two axis are concurrent
163 if(thecoplanar && (!theparallel)) {
164 Standard_Real smx=P2.X() - P1.X();
165 Standard_Real smy=P2.Y() - P1.Y();
166 Standard_Real smz=P2.Z() - P1.Z();
167 Standard_Real Det1,Det2,Det3,A;
168 Det1=V1.Y() * V2.X() - V1.X() * V2.Y();
169 Det2=V1.Z() * V2.Y() - V1.Y() * V2.Z();
170 Det3=V1.Z() * V2.X() - V1.X() * V2.Z();
171
172 if((Det1!=0.0) && ((Abs(Det1) >= Abs(Det2))&&(Abs(Det1) >= Abs(Det3)))) {
173 A=(smy * V2.X() - smx * V2.Y())/Det1;
174 }
175 else if((Det2!=0.0)
176 && ((Abs(Det2) >= Abs(Det1))
177 &&(Abs(Det2) >= Abs(Det3)))) {
178 A=(smz * V2.Y() - smy * V2.Z())/Det2;
179 }
180 else {
181 A=(smz * V2.X() - smx * V2.Z())/Det3;
182 }
183 ptintersect.SetCoord( P1.X() + A * V1.X()
184 ,P1.Y() + A * V1.Y()
185 ,P1.Z() + A * V1.Z());
186 }
187 else {
188 ptintersect.SetCoord(0,0,0); //-- Pour eviter des FPE
189 }
190}
191//=======================================================================
192//function : Distance
193//purpose :
194//=======================================================================
195 void AxeOperator::Distance(Standard_Real& dist,Standard_Real& Param1,Standard_Real& Param2)
196 {
197 gp_Vec O1O2(Axe1.Location(),Axe2.Location()); //-----------------------------
198 gp_Dir U1 = Axe1.Direction(); //-- juste pour voir.
199 gp_Dir U2 = Axe2.Direction();
200
201 gp_Dir N = U1.Crossed(U2);
202 Standard_Real D = Det33(U1.X(),U2.X(),N.X(),
203 U1.Y(),U2.Y(),N.Y(),
204 U1.Z(),U2.Z(),N.Z());
205 if(D) {
206 dist = Det33(U1.X(),U2.X(),O1O2.X(),
207 U1.Y(),U2.Y(),O1O2.Y(),
208 U1.Z(),U2.Z(),O1O2.Z()) / D;
209 Param1 = Det33(O1O2.X(),U2.X(),N.X(),
210 O1O2.Y(),U2.Y(),N.Y(),
211 O1O2.Z(),U2.Z(),N.Z()) / (-D);
212 //------------------------------------------------------------
213 //-- On resout P1 * Dir1 + P2 * Dir2 + d * N = O1O2
214 //-- soit : Segment perpendiculaire : O1+P1 D1
215 //-- O2-P2 D2
216 Param2 = Det33(U1.X(),O1O2.X(),N.X(),
217 U1.Y(),O1O2.Y(),N.Y(),
218 U1.Z(),O1O2.Z(),N.Z()) / (D);
219 }
220}
221//=======================================================================
222//function : DirToAx2
223//purpose : returns a gp_Ax2 where D is the main direction
224//=======================================================================
225gp_Ax2 DirToAx2(const gp_Pnt& P,const gp_Dir& D)
226{
227 Standard_Real x=D.X(); Standard_Real ax=Abs(x);
228 Standard_Real y=D.Y(); Standard_Real ay=Abs(y);
229 Standard_Real z=D.Z(); Standard_Real az=Abs(z);
230 if( (ax==0.0) || ((ax<ay) && (ax<az)) ) {
231 return(gp_Ax2(P,D,gp_Dir(gp_Vec(0.0,-z,y))));
232 }
233 else if( (ay==0.0) || ((ay<ax) && (ay<az)) ) {
234 return(gp_Ax2(P,D,gp_Dir(gp_Vec(-z,0.0,x))));
235 }
236 else {
237 return(gp_Ax2(P,D,gp_Dir(gp_Vec(-y,x,0.0))));
238 }
239}
240//=======================================================================
241//function : IntAna_QuadQuadGeo
242//purpose : Empty constructor
243//=======================================================================
244 IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(void)
245 : done(Standard_False),
246 nbint(0),
247 typeres(IntAna_Empty),
248 pt1(0,0,0),
249 pt2(0,0,0),
250 pt3(0,0,0),
251 pt4(0,0,0),
252 param1(0),
253 param2(0),
254 param3(0),
255 param4(0),
256 param1bis(0),
257 param2bis(0),
258 myCommonGen(Standard_False),
259 myPChar(0,0,0)
260{
261 InitTolerances();
262}
263//=======================================================================
264//function : InitTolerances
265//purpose :
266//=======================================================================
267 void IntAna_QuadQuadGeo::InitTolerances()
268{
269 myEPSILON_DISTANCE = 0.00000000000001;
270 myEPSILON_ANGLE_CONE = 0.000000000001;
271 myEPSILON_MINI_CIRCLE_RADIUS = 0.000000001;
272 myEPSILON_CYLINDER_DELTA_RADIUS = 0.0000000000001;
273 myEPSILON_CYLINDER_DELTA_DISTANCE= 0.0000001;
274 myEPSILON_AXES_PARA = 0.000000000001;
275}
276//=======================================================================
277//function : IntAna_QuadQuadGeo
278//purpose : Pln Pln
279//=======================================================================
280 IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Pln& P1,
281 const gp_Pln& P2,
282 const Standard_Real TolAng,
283 const Standard_Real Tol)
284: done(Standard_False),
285 nbint(0),
286 typeres(IntAna_Empty),
287 pt1(0,0,0),
288 pt2(0,0,0),
289 pt3(0,0,0),
290 pt4(0,0,0),
291 param1(0),
292 param2(0),
293 param3(0),
294 param4(0),
295 param1bis(0),
296 param2bis(0),
297 myCommonGen(Standard_False),
298 myPChar(0,0,0)
299{
300 InitTolerances();
301 Perform(P1,P2,TolAng,Tol);
302}
303//=======================================================================
304//function : Perform
305//purpose :
306//=======================================================================
307 void IntAna_QuadQuadGeo::Perform (const gp_Pln& P1,
308 const gp_Pln& P2,
309 const Standard_Real TolAng,
310 const Standard_Real Tol)
311{
312 done=Standard_False;
313 //
314 param2bis=0.0;
315
316 Standard_Real A1 = 0., B1 = 0., C1 = 0., D1 = 0., A2 = 0., B2 = 0., C2 = 0., D2 = 0.;
317 P1.Coefficients(A1,B1,C1,D1);
318 P2.Coefficients(A2,B2,C2,D2);
319
320 gp_Vec vd(gp_Vec(A1,B1,C1).Crossed(gp_Vec(A2,B2,C2)));
321 Standard_Real dist1= A2*P1.Location().X() + B2*P1.Location().Y() + C2*P1.Location().Z() + D2;
322 Standard_Real dist2= A1*P2.Location().X() + B1*P2.Location().Y() + C1*P2.Location().Z() + D1;
323
324 if(vd.Magnitude() <=TolAng) {
325 // normalles are collinear - planes are same or parallel
326 typeres = (Abs(dist1) <= Tol && Abs(dist2) <= Tol) ? IntAna_Same : IntAna_Empty;
327 }
328 else {
329 Standard_Real denom=A1*A2 + B1*B2 + C1*C2;
330
331 Standard_Real denom2 = denom*denom;
332 Standard_Real ddenom = 1. - denom2;
333 //denom = ( Abs(ddenom) <= 1.e-9 ) ? 1.e-9 : ddenom;
334 denom = ( Abs(ddenom) <= 1.e-16 ) ? 1.e-16 : ddenom;
335
336 Standard_Real par1 = dist1/denom;
337 Standard_Real par2 = -dist2/denom;
338
339 gp_Vec inter1(gp_Vec(A1,B1,C1).Crossed(vd));
340 gp_Vec inter2(gp_Vec(A2,B2,C2).Crossed(vd));
341
342 Standard_Real X1=P1.Location().X() + par1*inter1.X();
343 Standard_Real Y1=P1.Location().Y() + par1*inter1.Y();
344 Standard_Real Z1=P1.Location().Z() + par1*inter1.Z();
345 Standard_Real X2=P2.Location().X() + par2*inter2.X();
346 Standard_Real Y2=P2.Location().Y() + par2*inter2.Y();
347 Standard_Real Z2=P2.Location().Z() + par2*inter2.Z();
348
349 pt1=gp_Pnt((X1+X2)*0.5, (Y1+Y2)*0.5, (Z1+Z2)*0.5);
350 dir1 = gp_Dir(vd);
351 typeres = IntAna_Line;
352 nbint = 1;
353
354 }
355 done=Standard_True;
356}
357//=======================================================================
358//function : IntAna_QuadQuadGeo
359//purpose : Pln Cylinder
360//=======================================================================
361 IntAna_QuadQuadGeo::IntAna_QuadQuadGeo( const gp_Pln& P
362 ,const gp_Cylinder& Cl
363 ,const Standard_Real Tolang
364 ,const Standard_Real Tol
365 ,const Standard_Real H)
366 : done(Standard_False),
367 nbint(0),
368 typeres(IntAna_Empty),
369 pt1(0,0,0),
370 pt2(0,0,0),
371 pt3(0,0,0),
372 pt4(0,0,0),
373 param1(0),
374 param2(0),
375 param3(0),
376 param4(0),
377 param1bis(0),
378 param2bis(0),
379 myCommonGen(Standard_False),
380 myPChar(0,0,0)
381{
382 InitTolerances();
383 Perform(P,Cl,Tolang,Tol,H);
384}
385//=======================================================================
386//function : Perform
387//purpose :
388//=======================================================================
389 void IntAna_QuadQuadGeo::Perform( const gp_Pln& P
390 ,const gp_Cylinder& Cl
391 ,const Standard_Real Tolang
392 ,const Standard_Real Tol
393 ,const Standard_Real H)
394{
395 done = Standard_False;
396 Standard_Real dist,radius;
397 Standard_Real A,B,C,D;
398 Standard_Real X,Y,Z;
399 Standard_Real sint,cost,h;
400 gp_XYZ axex,axey,omega;
401
402
403 param2bis=0.0;
404 radius = Cl.Radius();
405
406 gp_Lin axec(Cl.Axis());
407 gp_XYZ normp(P.Axis().Direction().XYZ());
408
409 P.Coefficients(A,B,C,D);
410 axec.Location().Coord(X,Y,Z);
411 dist = A*X + B*Y + C*Z + D; // la distance axe/plan est evaluee a l origine de l axe.
412
413 Standard_Real tolang = Tolang;
414 Standard_Boolean newparams = Standard_False;
415
416 gp_Vec ldv( axec.Direction() );
417 gp_Vec npv( normp );
418 Standard_Real dA = Abs( ldv.Angle( npv ) );
419 if( dA > (M_PI/4.) )
420 {
421 Standard_Real dang = Abs( ldv.Angle( npv ) ) - M_PI/2.;
422 Standard_Real dangle = Abs( dang );
423 if( dangle > Tolang )
424 {
425 Standard_Real sinda = Abs( Sin( dangle ) );
426 Standard_Real dif = Abs( sinda - Tol );
427 if( dif < Tol )
428 {
429 tolang = sinda * 2.;
430 newparams = Standard_True;
431 }
432 }
433 }
434
435 nbint = 0;
436 IntAna_IntConicQuad inter(axec,P,tolang,Tol,H);
437
438 if (inter.IsParallel()) {
439 // Le resultat de l intersection Plan-Cylindre est de type droite.
440 // il y a 1 ou 2 droites
441
442 typeres = IntAna_Line;
443 omega.SetCoord(X-dist*A,Y-dist*B,Z-dist*C);
444
445 if (Abs(Abs(dist)-radius) < Tol)
446 {
447 nbint = 1;
448 pt1.SetXYZ(omega);
449
450 if( newparams )
451 {
452 gp_XYZ omegaXYZ(X,Y,Z);
453 gp_XYZ omegaXYZtrnsl( omegaXYZ + 100.*axec.Direction().XYZ() );
454 Standard_Real Xt,Yt,Zt,distt;
455 omegaXYZtrnsl.Coord(Xt,Yt,Zt);
456 distt = A*Xt + B*Yt + C*Zt + D;
457 gp_XYZ omega1( omegaXYZtrnsl.X()-distt*A, omegaXYZtrnsl.Y()-distt*B, omegaXYZtrnsl.Z()-distt*C );
458 gp_Pnt ppt1;
459 ppt1.SetXYZ( omega1 );
460 gp_Vec vv1(pt1,ppt1);
461 gp_Dir dd1( vv1 );
462 dir1 = dd1;
463 }
464 else
465 dir1 = axec.Direction();
466 }
467 else if (Abs(dist) < radius)
468 {
469 nbint = 2;
470 h = Sqrt(radius*radius - dist*dist);
471 axey = axec.Direction().XYZ().Crossed(normp); // axey est normalise
472
473 pt1.SetXYZ(omega - h*axey);
474 pt2.SetXYZ(omega + h*axey);
475
476 if( newparams )
477 {
478 gp_XYZ omegaXYZ(X,Y,Z);
479 gp_XYZ omegaXYZtrnsl( omegaXYZ + 100.*axec.Direction().XYZ() );
480 Standard_Real Xt,Yt,Zt,distt,ht;
481 omegaXYZtrnsl.Coord(Xt,Yt,Zt);
482 distt = A*Xt + B*Yt + C*Zt + D;
483 // ht = Sqrt(radius*radius - distt*distt);
484 Standard_Real anSqrtArg = radius*radius - distt*distt;
485 ht = (anSqrtArg > 0.) ? Sqrt(anSqrtArg) : 0.;
486
487 gp_XYZ omega1( omegaXYZtrnsl.X()-distt*A, omegaXYZtrnsl.Y()-distt*B, omegaXYZtrnsl.Z()-distt*C );
488 gp_Pnt ppt1,ppt2;
489 ppt1.SetXYZ( omega1 - ht*axey);
490 ppt2.SetXYZ( omega1 + ht*axey);
491 gp_Vec vv1(pt1,ppt1);
492 gp_Vec vv2(pt2,ppt2);
493 gp_Dir dd1( vv1 );
494 gp_Dir dd2( vv2 );
495 dir1 = dd1;
496 dir2 = dd2;
497 }
498 else
499 {
500 dir1 = axec.Direction();
501 dir2 = axec.Direction();
502 }
503 }
504 // else nbint = 0
505
506 // debug JAG : le nbint = 0 doit etre remplace par typeres = IntAna_Empty
507 // et ne pas etre seulement supprime...
508
509 else {
510 typeres = IntAna_Empty;
511 }
512 }
513 else { // Il y a un point d intersection. C est le centre du cercle
514 // ou de l ellipse solution.
515
516 nbint = 1;
517 axey = normp.Crossed(axec.Direction().XYZ());
518 sint = axey.Modulus();
519
520 pt1 = inter.Point(1);
521
522 if (sint < Tol/radius) {
523
524 // on construit un cercle avec comme axes X et Y ceux du cylindre
525 typeres = IntAna_Circle;
526
527 dir1 = axec.Direction(); // axe Z
528 dir2 = Cl.Position().XDirection();
529 param1 = radius;
530 }
531 else {
532
533 // on construit un ellipse
534 typeres = IntAna_Ellipse;
535 cost = Abs(axec.Direction().XYZ().Dot(normp));
536 axex = axey.Crossed(normp);
537
538 dir1.SetXYZ(normp); //Modif ds ce bloc
539 dir2.SetXYZ(axex);
540
541 param1 = radius/cost;
542 param1bis = radius;
543 }
544 }
545
546 done = Standard_True;
547}
548//=======================================================================
549//function : IntAna_QuadQuadGeo
550//purpose : Pln Cone
551//=======================================================================
552 IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Pln& P,
553 const gp_Cone& Co,
554 const Standard_Real Tolang,
555 const Standard_Real Tol)
556: done(Standard_False),
557 nbint(0),
558 typeres(IntAna_Empty),
559 pt1(0,0,0),
560 pt2(0,0,0),
561 pt3(0,0,0),
562 pt4(0,0,0),
563 param1(0),
564 param2(0),
565 param3(0),
566 param4(0),
567 param1bis(0),
568 param2bis(0),
569 myCommonGen(Standard_False),
570 myPChar(0,0,0)
571{
572 InitTolerances();
573 Perform(P,Co,Tolang,Tol);
574}
575//=======================================================================
576//function : Perform
577//purpose :
578//=======================================================================
579 void IntAna_QuadQuadGeo::Perform(const gp_Pln& P,
580 const gp_Cone& Co,
581 const Standard_Real Tolang,
582 const Standard_Real Tol)
583{
584
585 done = Standard_False;
586 nbint = 0;
587
588 Standard_Real A,B,C,D;
589 Standard_Real X,Y,Z;
590 Standard_Real dist,sint,cost,sina,cosa,angl,costa;
591 Standard_Real dh;
592 gp_XYZ axex,axey;
593
594 gp_Lin axec(Co.Axis());
595 P.Coefficients(A,B,C,D);
596 gp_Pnt apex(Co.Apex());
597
598 apex.Coord(X,Y,Z);
599 dist = A*X + B*Y + C*Z + D; // distance signee sommet du cone/ Plan
600
601 gp_XYZ normp = P.Axis().Direction().XYZ();
602 if(P.Direct()==Standard_False) { //-- lbr le 14 jan 97
603 normp.Reverse();
604 }
605
606 axey = normp.Crossed(Co.Axis().Direction().XYZ());
607 axex = axey.Crossed(normp);
608
609
610 angl = Co.SemiAngle();
611
612 cosa = Cos(angl);
613 sina = Abs(Sin(angl));
614
615
616 // Angle entre la normale au plan et l axe du cone, ramene entre 0. et PI/2.
617
618 sint = axey.Modulus();
619 cost = Abs(Co.Axis().Direction().XYZ().Dot(normp));
620
621 // Le calcul de costa permet de determiner si le plan contient
622 // un generatrice du cone : on calcul Sin((PI/2. - t) - angl)
623
624 costa = cost*cosa - sint*sina; // sin((PI/2 -t)-angl)=cos(t+angl)
625 // avec t ramene entre 0 et pi/2.
626
627 if (Abs(dist) < Tol) {
628 // on considere que le plan contient le sommet du cone.
629 // les solutions possibles sont donc : 1 point, 1 droite, 2 droites
630 // selon l inclinaison du plan.
631
632 if (Abs(costa) < Tolang) { // plan parallele a la generatrice
633 typeres = IntAna_Line;
634 nbint = 1;
635 gp_XYZ ptonaxe(apex.XYZ() + 10.*(Co.Axis().Direction().XYZ()));
636 // point sur l axe du cone cote z positif
637
638 dist = A*ptonaxe.X() + B*ptonaxe.Y() + C*ptonaxe.Z() + D;
639 ptonaxe = ptonaxe - dist*normp;
640 pt1 = apex;
641 dir1.SetXYZ(ptonaxe - pt1.XYZ());
642 }
643 else if (cost < sina) { // plan "interieur" au cone
644 typeres = IntAna_Line;
645 nbint = 2;
646 pt1 = apex;
647 pt2 = apex;
648 dh = Sqrt(sina*sina-cost*cost)/cosa;
649 dir1.SetXYZ(axex + dh*axey);
650 dir2.SetXYZ(axex - dh*axey);
651 }
652 else { // plan "exterieur" au cone
653 typeres = IntAna_Point;
654 nbint = 1;
655 pt1 = apex;
656 }
657 }
658 else {
659 // Solutions possibles : cercle, ellipse, parabole, hyperbole selon
660 // l inclinaison du plan.
661 Standard_Real deltacenter, distance;
662
663 if (cost < Tolang) {
664 // Le plan contient la direction de l axe du cone. La solution est
665 // l hyperbole
666 typeres = IntAna_Hyperbola;
667 nbint = 2;
668 pt1.SetXYZ(apex.XYZ()-dist*normp);
669 pt2 = pt1;
670 dir1=normp;
671 dir2.SetXYZ(axex);
672 param1 = param2 = Abs(dist/Tan(angl));
673 param1bis = param2bis = Abs(dist);
674 }
675 else {
676
677 IntAna_IntConicQuad inter(axec,P,Tolang); // on a necessairement 1 point.
678
679 gp_Pnt center(inter.Point(1));
680
681 // En fonction de la position de l intersection par rapport au sommet
682 // du cone, on change l axe x en -x et y en -y. Le parametre du sommet
683 // sur axec est negatif (voir definition du cone)
684
685 distance = apex.Distance(center);
686
687 if (inter.ParamOnConic(1) + Co.RefRadius()/Tan(angl) < 0.) {
688 axex.Reverse();
689 axey.Reverse();
690 }
691
692 if (Abs(costa) < Tolang) { // plan parallele a une generatrice
693 typeres = IntAna_Parabola;
694 nbint = 1;
695 deltacenter = distance/2./cosa;
696 axex.Normalize();
697 pt1.SetXYZ(center.XYZ()-deltacenter*axex);
698 dir1 = normp;
699 dir2.SetXYZ(axex);
700 param1 = deltacenter*sina*sina;
701 }
702 else if (sint < Tolang) { // plan perpendiculaire a l axe
703 typeres = IntAna_Circle;
704 nbint = 1;
705 pt1 = center;
706 dir1 = Co.Position().Direction();
707 dir2 = Co.Position().XDirection();
708 param1 = apex.Distance(center)*Abs(Tan(angl));
709 }
710 else if (cost < sina ) {
711 typeres = IntAna_Hyperbola;
712 nbint = 2;
713 axex.Normalize();
714
715 deltacenter = sint*sina*sina*distance/(sina*sina - cost*cost);
716 pt1.SetXYZ(center.XYZ() - deltacenter*axex);
717 pt2 = pt1;
718 dir1 = normp;
719 dir2.SetXYZ(axex);
720 param1 = param2 = cost*sina*cosa*distance /(sina*sina-cost*cost);
721 param1bis = param2bis = cost*sina*distance / Sqrt(sina*sina-cost*cost);
722
723 }
724 else { // on a alors cost > sina
725 typeres = IntAna_Ellipse;
726 nbint = 1;
727 Standard_Real radius = cost*sina*cosa*distance/(cost*cost-sina*sina);
728 deltacenter = sint*sina*sina*distance/(cost*cost-sina*sina);
729 axex.Normalize();
730 pt1.SetXYZ(center.XYZ() + deltacenter*axex);
731 dir1 = normp;
732 dir2.SetXYZ(axex);
733 param1 = radius;
734 param1bis = cost*sina*distance/ Sqrt(cost*cost - sina*sina);
735 }
736 }
737 }
738
739 //-- On a du mal a gerer plus loin (Value ProjLib, Params ... )
740 //-- des hyperboles trop bizarres
741 //-- On retourne False -> Traitement par biparametree
742 static Standard_Real EllipseLimit = 1.0E+9; //OCC513(apo) 1000000
743 static Standard_Real HyperbolaLimit = 2.0E+6; //OCC537(apo) 50000
744 if(typeres==IntAna_Ellipse && nbint>=1) {
745 if(Abs(param1) > EllipseLimit || Abs(param1bis) > EllipseLimit) {
746 done=Standard_False;
747 return;
748 }
749 }
750 if(typeres==IntAna_Hyperbola && nbint>=2) {
751 if(Abs(param2) > HyperbolaLimit || Abs(param2bis) > HyperbolaLimit) {
752 done = Standard_False;
753 return;
754 }
755 }
756 if(typeres==IntAna_Hyperbola && nbint>=1) {
757 if(Abs(param1) > HyperbolaLimit || Abs(param1bis) > HyperbolaLimit) {
758 done=Standard_False;
759 return;
760 }
761 }
762
763 done = Standard_True;
764}
765
766//=======================================================================
767//function : IntAna_QuadQuadGeo
768//purpose : Pln Sphere
769//=======================================================================
770 IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Pln& P,
771 const gp_Sphere& S)
772: done(Standard_False),
773 nbint(0),
774 typeres(IntAna_Empty),
775 pt1(0,0,0),
776 pt2(0,0,0),
777 pt3(0,0,0),
778 pt4(0,0,0),
779 param1(0),
780 param2(0),
781 param3(0),
782 param4(0),
783 param1bis(0),
784 param2bis(0),
785 myCommonGen(Standard_False),
786 myPChar(0,0,0)
787{
788 InitTolerances();
789 Perform(P,S);
790}
791//=======================================================================
792//function : Perform
793//purpose :
794//=======================================================================
795 void IntAna_QuadQuadGeo::Perform( const gp_Pln& P
796 ,const gp_Sphere& S)
797{
798
799 done = Standard_False;
800 Standard_Real A,B,C,D,dist, radius;
801 Standard_Real X,Y,Z;
802
803 nbint = 0;
804// debug JAG : on met typeres = IntAna_Empty par defaut...
805 typeres = IntAna_Empty;
806
807 P.Coefficients(A,B,C,D);
808 S.Location().Coord(X,Y,Z);
809 radius = S.Radius();
810
811 dist = A * X + B * Y + C * Z + D;
812
813 if (Abs( Abs(dist) - radius) < Epsilon(radius)) {
814 // on a une seule solution : le point projection du centre de la sphere
815 // sur le plan
816 nbint = 1;
817 typeres = IntAna_Point;
818 pt1.SetCoord(X - dist*A, Y - dist*B, Z - dist*C);
819 }
820 else if (Abs(dist) < radius) {
821 // on a un cercle solution
822 nbint = 1;
823 typeres = IntAna_Circle;
824 pt1.SetCoord(X - dist*A, Y - dist*B, Z - dist*C);
825 dir1 = P.Axis().Direction();
826 if(P.Direct()==Standard_False) dir1.Reverse();
827 dir2 = P.Position().XDirection();
828 param1 = Sqrt(radius*radius - dist*dist);
829 }
830 param2bis=0.0; //-- pour eviter param2bis not used ....
831 done = Standard_True;
832}
833
834//=======================================================================
835//function : IntAna_QuadQuadGeo
836//purpose : Cylinder - Cylinder
837//=======================================================================
838 IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Cylinder& Cyl1,
839 const gp_Cylinder& Cyl2,
840 const Standard_Real Tol)
841: done(Standard_False),
842 nbint(0),
843 typeres(IntAna_Empty),
844 pt1(0,0,0),
845 pt2(0,0,0),
846 pt3(0,0,0),
847 pt4(0,0,0),
848 param1(0),
849 param2(0),
850 param3(0),
851 param4(0),
852 param1bis(0),
853 param2bis(0),
854 myCommonGen(Standard_False),
855 myPChar(0,0,0)
856{
857 InitTolerances();
858 Perform(Cyl1,Cyl2,Tol);
859}
860//=======================================================================
861//function : Perform
862//purpose :
863//=======================================================================
864 void IntAna_QuadQuadGeo::Perform(const gp_Cylinder& Cyl1,
865 const gp_Cylinder& Cyl2,
866 const Standard_Real Tol)
867{
868 done=Standard_True;
869 //---------------------------- Parallel axes -------------------------
870 AxeOperator A1A2(Cyl1.Axis(),Cyl2.Axis());
871 Standard_Real R1=Cyl1.Radius();
872 Standard_Real R2=Cyl2.Radius();
873 Standard_Real RmR, RmR_Relative;
874 RmR=(R1>R2)? (R1-R2) : (R2-R1);
875 {
876 Standard_Real Rmax;
877 Rmax=(R1>R2)? R1 : R2;
878 RmR_Relative=RmR/Rmax;
879 }
880
881 Standard_Real DistA1A2=A1A2.Distance();
882
883 if(A1A2.Parallel()) {
884 if(DistA1A2<=Tol) {
885 if(RmR<=Tol) {
886 typeres=IntAna_Same;
887 }
888 else {
889 typeres=IntAna_Empty;
890 }
891 }
892 else { //-- DistA1A2 > Tol
893 gp_Pnt P1=Cyl1.Location();
894 gp_Pnt P2t=Cyl2.Location();
895 gp_Pnt P2;
896 //-- P2t is projected on the plane (P1,DirCylX,DirCylY)
897 gp_Dir DirCyl = Cyl1.Position().Direction();
898 Standard_Real ProjP2OnDirCyl1=gp_Vec(DirCyl).Dot(gp_Vec(P1,P2t));
899
900 P2.SetCoord( P2t.X() - ProjP2OnDirCyl1*DirCyl.X()
901 ,P2t.Y() - ProjP2OnDirCyl1*DirCyl.Y()
902 ,P2t.Z() - ProjP2OnDirCyl1*DirCyl.Z());
903 //--
904 Standard_Real R1pR2=R1+R2;
905 if(DistA1A2>(R1pR2+Tol)) {
906 typeres=IntAna_Empty;
907 nbint=0;
908 }
909 else if(DistA1A2>(R1pR2)) {
910 //-- 1 Tangent line -------------------------------------OK
911 typeres=IntAna_Line;
912
913 nbint=1;
914 dir1=DirCyl;
915 Standard_Real R1_R1pR2=R1/R1pR2;
916 pt1.SetCoord( P1.X() + R1_R1pR2 * (P2.X()-P1.X())
917 ,P1.Y() + R1_R1pR2 * (P2.Y()-P1.Y())
918 ,P1.Z() + R1_R1pR2 * (P2.Z()-P1.Z()));
919
920 }
921 else if(DistA1A2>RmR) {
922 //-- 2 lines ---------------------------------------------OK
923 typeres=IntAna_Line;
924 nbint=2;
925 dir1=DirCyl;
926 gp_Vec P1P2(P1,P2);
927 gp_Dir DirA1A2=gp_Dir(P1P2);
928 gp_Dir Ortho_dir1_P1P2 = dir1.Crossed(DirA1A2);
929 dir2=dir1;
930 Standard_Real Alpha=0.5*(R1*R1-R2*R2+DistA1A2*DistA1A2)/(DistA1A2);
931
932// Standard_Real Beta = Sqrt(R1*R1-Alpha*Alpha);
933 Standard_Real anSqrtArg = R1*R1-Alpha*Alpha;
934 Standard_Real Beta = (anSqrtArg > 0.) ? Sqrt(anSqrtArg) : 0.;
935
936 if((Beta+Beta)<Tol) {
937 nbint=1;
938 pt1.SetCoord( P1.X() + Alpha*DirA1A2.X()
939 ,P1.Y() + Alpha*DirA1A2.Y()
940 ,P1.Z() + Alpha*DirA1A2.Z());
941 }
942 else {
943 pt1.SetCoord( P1.X() + Alpha*DirA1A2.X() + Beta*Ortho_dir1_P1P2.X()
944 ,P1.Y() + Alpha*DirA1A2.Y() + Beta*Ortho_dir1_P1P2.Y()
945 ,P1.Z() + Alpha*DirA1A2.Z() + Beta*Ortho_dir1_P1P2.Z() );
946
947 pt2.SetCoord( P1.X() + Alpha*DirA1A2.X() - Beta*Ortho_dir1_P1P2.X()
948 ,P1.Y() + Alpha*DirA1A2.Y() - Beta*Ortho_dir1_P1P2.Y()
949 ,P1.Z() + Alpha*DirA1A2.Z() - Beta*Ortho_dir1_P1P2.Z());
950 }
951 }
952 else if(DistA1A2>(RmR-Tol)) {
953 //-- 1 Tangent ------------------------------------------OK
954 typeres=IntAna_Line;
955 nbint=1;
956 dir1=DirCyl;
957 Standard_Real R1_RmR=R1/RmR;
958
959 if(R1 < R2) R1_RmR = -R1_RmR;
960
961 pt1.SetCoord( P1.X() + R1_RmR * (P2.X()-P1.X())
962 ,P1.Y() + R1_RmR * (P2.Y()-P1.Y())
963 ,P1.Z() + R1_RmR * (P2.Z()-P1.Z()));
964 }
965 else {
966 nbint=0;
967 typeres=IntAna_Empty;
968 }
969 }
970 }
971 else { //-- No Parallel Axis ---------------------------------OK
972 if((RmR_Relative<=myEPSILON_CYLINDER_DELTA_RADIUS)
973 && (DistA1A2 <= myEPSILON_CYLINDER_DELTA_DISTANCE)) {
974 //-- PI/2 between the two axis and Intersection
975 //-- and identical radius
976 typeres=IntAna_Ellipse;
977 nbint=2;
978 gp_Dir DirCyl1=Cyl1.Position().Direction();
979 gp_Dir DirCyl2=Cyl2.Position().Direction();
980 pt1=pt2=A1A2.PtIntersect();
981
982 Standard_Real A=DirCyl1.Angle(DirCyl2);
983 Standard_Real B;
984 B=Abs(Sin(0.5*(M_PI-A)));
985 A=Abs(Sin(0.5*A));
986
987 if(A==0.0 || B==0.0) {
988 typeres=IntAna_Same;
989 return;
990 }
991
992
993 gp_Vec dircyl1(DirCyl1);gp_Vec dircyl2(DirCyl2);
994 dir1 = gp_Dir(dircyl1.Added(dircyl2));
995 dir2 = gp_Dir(dircyl1.Subtracted(dircyl2));
996
997 param2 = Cyl1.Radius() / A;
998 param1 = Cyl1.Radius() / B;
999 param2bis= param1bis = Cyl1.Radius();
1000 if(param1 < param1bis) {
1001 A=param1; param1=param1bis; param1bis=A;
1002 }
1003 if(param2 < param2bis) {
1004 A=param2; param2=param2bis; param2bis=A;
1005 }
1006 }
1007 else {
1008 if(Abs(DistA1A2-Cyl1.Radius()-Cyl2.Radius())<Tol) {
1009 typeres = IntAna_Point;
1010 Standard_Real d,p1,p2;
1011
1012 gp_Dir D1 = Cyl1.Axis().Direction();
1013 gp_Dir D2 = Cyl2.Axis().Direction();
1014 A1A2.Distance(d,p1,p2);
1015 gp_Pnt P = Cyl1.Axis().Location();
1016 gp_Pnt P1(P.X() - p1*D1.X(),
1017 P.Y() - p1*D1.Y(),
1018 P.Z() - p1*D1.Z());
1019 P = Cyl2.Axis().Location();
1020 gp_Pnt P2(P.X() - p2*D2.X(),
1021 P.Y() - p2*D2.Y(),
1022 P.Z() - p2*D2.Z());
1023 gp_Vec P1P2(P1,P2);
1024 D1=gp_Dir(P1P2);
1025 p1=Cyl1.Radius();
1026 pt1.SetCoord(P1.X() + p1*D1.X(),
1027 P1.Y() + p1*D1.Y(),
1028 P1.Z() + p1*D1.Z());
1029 nbint = 1;
1030 }
1031 else {
1032 typeres=IntAna_NoGeometricSolution;
1033 }
1034 }
1035 }
1036}
1037//=======================================================================
1038//function : IntAna_QuadQuadGeo
1039//purpose : Cylinder - Cone
1040//=======================================================================
1041 IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Cylinder& Cyl,
1042 const gp_Cone& Con,
1043 const Standard_Real Tol)
1044: done(Standard_False),
1045 nbint(0),
1046 typeres(IntAna_Empty),
1047 pt1(0,0,0),
1048 pt2(0,0,0),
1049 pt3(0,0,0),
1050 pt4(0,0,0),
1051 param1(0),
1052 param2(0),
1053 param3(0),
1054 param4(0),
1055 param1bis(0),
1056 param2bis(0),
1057 myCommonGen(Standard_False),
1058 myPChar(0,0,0)
1059{
1060 InitTolerances();
1061 Perform(Cyl,Con,Tol);
1062}
1063//=======================================================================
1064//function : Perform
1065//purpose :
1066//=======================================================================
1067 void IntAna_QuadQuadGeo::Perform(const gp_Cylinder& Cyl,
1068 const gp_Cone& Con,
1069 const Standard_Real )
1070{
1071 done=Standard_True;
1072 AxeOperator A1A2(Cyl.Axis(),Con.Axis());
1073 if(A1A2.Same()) {
1074 gp_Pnt Pt=Con.Apex();
1075 Standard_Real dist=Cyl.Radius()/(Tan(Con.SemiAngle()));
1076 gp_Dir dir=Cyl.Position().Direction();
1077 pt1.SetCoord( Pt.X() + dist*dir.X()
1078 ,Pt.Y() + dist*dir.Y()
1079 ,Pt.Z() + dist*dir.Z());
1080 pt2.SetCoord( Pt.X() - dist*dir.X()
1081 ,Pt.Y() - dist*dir.Y()
1082 ,Pt.Z() - dist*dir.Z());
1083 dir1=dir2=dir;
1084 param1=param2=Cyl.Radius();
1085 nbint=2;
1086 typeres=IntAna_Circle;
1087
1088 }
1089 else {
1090 typeres=IntAna_NoGeometricSolution;
1091 }
1092}
1093//=======================================================================
1094//function :
1095//purpose : Cylinder - Sphere
1096//=======================================================================
1097 IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Cylinder& Cyl,
1098 const gp_Sphere& Sph,
1099 const Standard_Real Tol)
1100: done(Standard_False),
1101 nbint(0),
1102 typeres(IntAna_Empty),
1103 pt1(0,0,0),
1104 pt2(0,0,0),
1105 pt3(0,0,0),
1106 pt4(0,0,0),
1107 param1(0),
1108 param2(0),
1109 param3(0),
1110 param4(0),
1111 param1bis(0),
1112 param2bis(0),
1113 myCommonGen(Standard_False),
1114 myPChar(0,0,0)
1115{
1116 InitTolerances();
1117 Perform(Cyl,Sph,Tol);
1118}
1119//=======================================================================
1120//function : Perform
1121//purpose :
1122//=======================================================================
1123 void IntAna_QuadQuadGeo::Perform( const gp_Cylinder& Cyl
1124 ,const gp_Sphere& Sph
1125 ,const Standard_Real)
1126{
1127 done=Standard_True;
1128 gp_Pnt Pt=Sph.Location();
1129 AxeOperator A1A2(Cyl.Axis(),Sph.Position().Axis());
1130 if((A1A2.Intersect() && Pt.Distance(A1A2.PtIntersect())==0.0 )
1131 || (A1A2.Same())) {
1132 if(Sph.Radius() < Cyl.Radius()) {
1133 typeres = IntAna_Empty;
1134 }
1135 else {
1136 Standard_Real dist=Sqrt( Sph.Radius() * Sph.Radius() - Cyl.Radius() * Cyl.Radius() );
1137 gp_Dir dir=Cyl.Position().Direction();
1138 dir1 = dir2 = dir;
1139 typeres=IntAna_Circle;
1140 pt1.SetCoord( Pt.X() + dist*dir.X()
1141 ,Pt.Y() + dist*dir.Y()
1142 ,Pt.Z() + dist*dir.Z());
1143 nbint=1;
1144 param1 = Cyl.Radius();
1145 if(dist>RealEpsilon()) {
1146 pt2.SetCoord( Pt.X() - dist*dir.X()
1147 ,Pt.Y() - dist*dir.Y()
1148 ,Pt.Z() - dist*dir.Z());
1149 param2=Cyl.Radius();
1150 nbint=2;
1151 }
1152 }
1153 }
1154 else {
1155 typeres=IntAna_NoGeometricSolution;
1156 }
1157}
1158
1159//=======================================================================
1160//function : IntAna_QuadQuadGeo
1161//purpose : Cone - Cone
1162//=======================================================================
1163 IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Cone& Con1,
1164 const gp_Cone& Con2,
1165 const Standard_Real Tol)
1166: done(Standard_False),
1167 nbint(0),
1168 typeres(IntAna_Empty),
1169 pt1(0,0,0),
1170 pt2(0,0,0),
1171 pt3(0,0,0),
1172 pt4(0,0,0),
1173 param1(0),
1174 param2(0),
1175 param3(0),
1176 param4(0),
1177 param1bis(0),
1178 param2bis(0),
1179 myCommonGen(Standard_False),
1180 myPChar(0,0,0)
1181{
1182 InitTolerances();
1183 Perform(Con1,Con2,Tol);
1184}
1185//
1186//=======================================================================
1187//function : Perform
1188//purpose :
1189//=======================================================================
1190 void IntAna_QuadQuadGeo::Perform(const gp_Cone& Con1,
1191 const gp_Cone& Con2,
1192 const Standard_Real Tol)
1193{
1194 done=Standard_True;
1195 //
1196 Standard_Real tg1, tg2, aDA1A2, aTol2;
1197 gp_Pnt aPApex1, aPApex2;
1198
1199 Standard_Real TOL_APEX_CONF = 1.e-10;
1200
1201 //
1202 tg1=Tan(Con1.SemiAngle());
1203 tg2=Tan(Con2.SemiAngle());
1204
1205 if((tg1 * tg2) < 0.) {
1206 tg2 = -tg2;
1207 }
1208 //
1209 aTol2=Tol*Tol;
1210 aPApex1=Con1.Apex();
1211 aPApex2=Con2.Apex();
1212 aDA1A2=aPApex1.SquareDistance(aPApex2);
1213 //
1214 AxeOperator A1A2(Con1.Axis(),Con2.Axis());
1215 //
1216 // 1
1217 if(A1A2.Same()) {
1218 //-- two circles
1219 Standard_Real x;
1220 gp_Pnt P=Con1.Apex();
1221 gp_Dir D=Con1.Position().Direction();
1222 Standard_Real d=gp_Vec(D).Dot(gp_Vec(P,Con2.Apex()));
1223
1224 if(Abs(tg1-tg2)>myEPSILON_ANGLE_CONE) {
1225 if (fabs(d) < TOL_APEX_CONF) {
1226 typeres = IntAna_Point;
1227 nbint = 1;
1228 pt1 = P;
1229 return;
1230 }
1231 x=(d*tg2)/(tg1+tg2);
1232 pt1.SetCoord( P.X() + x*D.X()
1233 ,P.Y() + x*D.Y()
1234 ,P.Z() + x*D.Z());
1235 param1=Abs(x*tg1);
1236
1237 x=(d*tg2)/(tg2-tg1);
1238 pt2.SetCoord( P.X() + x*D.X()
1239 ,P.Y() + x*D.Y()
1240 ,P.Z() + x*D.Z());
1241 param2=Abs(x*tg1);
1242 dir1 = dir2 = D;
1243 nbint=2;
1244 typeres=IntAna_Circle;
1245 }
1246 else {
1247 if (fabs(d) < TOL_APEX_CONF) {
1248 typeres=IntAna_Same;
1249 }
1250 else {
1251 typeres=IntAna_Circle;
1252 nbint=1;
1253 x=d*0.5;
1254 pt1.SetCoord( P.X() + x*D.X()
1255 ,P.Y() + x*D.Y()
1256 ,P.Z() + x*D.Z());
1257 param1 = Abs(x * tg1);
1258 dir1 = D;
1259 }
1260 }
1261 } //-- fin A1A2.Same
1262 // 2
1263 else if((Abs(tg1-tg2)<myEPSILON_ANGLE_CONE) && (A1A2.Parallel())) {
1264 //-- voir AnVer12mai98
1265 Standard_Real DistA1A2=A1A2.Distance();
1266 gp_Dir DA1=Con1.Position().Direction();
1267 gp_Vec O1O2(Con1.Apex(),Con2.Apex());
1268 gp_Dir O1O2n(O1O2); // normalization of the vector before projection
1269 Standard_Real O1O2_DA1=gp_Vec(DA1).Dot(gp_Vec(O1O2n));
1270
1271 gp_Vec O1_Proj_A2(O1O2n.X()-O1O2_DA1*DA1.X(),
1272 O1O2n.Y()-O1O2_DA1*DA1.Y(),
1273 O1O2n.Z()-O1O2_DA1*DA1.Z());
1274 gp_Dir DB1=gp_Dir(O1_Proj_A2);
1275
1276 Standard_Real yO1O2=O1O2.Dot(gp_Vec(DA1));
1277 Standard_Real ABSTG1 = Abs(tg1);
1278 Standard_Real X2 = (DistA1A2/ABSTG1 - yO1O2)*0.5;
1279 Standard_Real X1 = X2+yO1O2;
1280
1281 gp_Pnt P1(Con1.Apex().X() + X1*( DA1.X() + ABSTG1*DB1.X()),
1282 Con1.Apex().Y() + X1*( DA1.Y() + ABSTG1*DB1.Y()),
1283 Con1.Apex().Z() + X1*( DA1.Z() + ABSTG1*DB1.Z()));
1284
1285 gp_Pnt MO1O2(0.5*(Con1.Apex().X()+Con2.Apex().X()),
1286 0.5*(Con1.Apex().Y()+Con2.Apex().Y()),
1287 0.5*(Con1.Apex().Z()+Con2.Apex().Z()));
1288 gp_Vec P1MO1O2(P1,MO1O2);
1289
1290 gp_Dir DA1_X_DB1=DA1.Crossed(DB1);
1291 gp_Dir OrthoPln = DA1_X_DB1.Crossed(gp_Dir(P1MO1O2));
1292
1293 IntAna_QuadQuadGeo INTER_QUAD_PLN(gp_Pln(P1,OrthoPln),Con1,Tol,Tol);
1294 if(INTER_QUAD_PLN.IsDone()) {
1295 switch(INTER_QUAD_PLN.TypeInter()) {
1296 case IntAna_Ellipse: {
1297 typeres=IntAna_Ellipse;
1298 gp_Elips E=INTER_QUAD_PLN.Ellipse(1);
1299 pt1 = E.Location();
1300 dir1 = E.Position().Direction();
1301 dir2 = E.Position().XDirection();
1302 param1 = E.MajorRadius();
1303 param1bis = E.MinorRadius();
1304 nbint = 1;
1305 break;
1306 }
1307 case IntAna_Circle: {
1308 typeres=IntAna_Circle;
1309 gp_Circ C=INTER_QUAD_PLN.Circle(1);
1310 pt1 = C.Location();
1311 dir1 = C.Position().XDirection();
1312 dir2 = C.Position().YDirection();
1313 param1 = C.Radius();
1314 nbint = 1;
1315 break;
1316 }
1317 case IntAna_Hyperbola: {
1318 typeres=IntAna_Hyperbola;
1319 gp_Hypr H=INTER_QUAD_PLN.Hyperbola(1);
1320 pt1 = pt2 = H.Location();
1321 dir1 = H.Position().Direction();
1322 dir2 = H.Position().XDirection();
1323 param1 = param2 = H.MajorRadius();
1324 param1bis = param2bis = H.MinorRadius();
1325 nbint = 2;
1326 break;
1327 }
1328 case IntAna_Line: {
1329 typeres=IntAna_Line;
1330 gp_Lin H=INTER_QUAD_PLN.Line(1);
1331 pt1 = pt2 = H.Location();
1332 dir1 = dir2 = H.Position().Direction();
1333 param1 = param2 = 0.0;
1334 param1bis = param2bis = 0.0;
1335 nbint = 2;
1336 break;
1337 }
1338 default:
1339 typeres=IntAna_NoGeometricSolution;
1340 }
1341 }
1342 }// else if((Abs(tg1-tg2)<EPSILON_ANGLE_CONE) && (A1A2.Parallel()))
1343 // 3
1344 else if (aDA1A2<aTol2) {
1345 //
1346 // When apices are coinsided there can be 3 possible cases
1347 // 3.1 - empty solution (iRet=0)
1348 // 3.2 - one line when cone1 touches cone2 (iRet=1)
1349 // 3.3 - two lines when cone1 intersects cone2 (iRet=2)
1350 //
1351 Standard_Integer iRet;
1352 Standard_Real aGamma, aBeta1, aBeta2;
1353 Standard_Real aD1, aR1, aTgBeta1, aTgBeta2, aHalfPI;
1354 Standard_Real aCosGamma, aSinGamma, aDx, aR2, aRD2, aD2;
1355 gp_Pnt2d aP0, aPA1, aP1, aPA2;
1356 gp_Vec2d aVAx2;
1357 gp_Ax1 aAx1, aAx2;
1358 //
1359 // Preliminary analysis. Determination of iRet
1360 //
1361 iRet=0;
1362 aHalfPI=0.5*M_PI;
1363 aD1=1.;
1364 aPA1.SetCoord(aD1, 0.);
1365 aP0.SetCoord(0., 0.);
1366 //
1367 aAx1=Con1.Axis();
1368 aAx2=Con2.Axis();
1369 aGamma=aAx1.Angle(aAx2);
1370 if (aGamma>aHalfPI){
1371 aGamma=M_PI-aGamma;
1372 }
1373 aCosGamma=Cos(aGamma);
1374 aSinGamma=Sin(aGamma);
1375 //
1376 aBeta1=Con1.SemiAngle();
1377 aTgBeta1=Tan(aBeta1);
1378 aTgBeta1=Abs(aTgBeta1);
1379 //
1380 aBeta2=Con2.SemiAngle();
1381 aTgBeta2=Tan(aBeta2);
1382 aTgBeta2=Abs(aTgBeta2);
1383 //
1384 aR1=aD1*aTgBeta1;
1385 aP1.SetCoord(aD1, aR1);
1386 //
1387 // PA2
1388 aVAx2.SetCoord(aCosGamma, aSinGamma);
1389 gp_Dir2d aDAx2(aVAx2);
1390 gp_Lin2d aLAx2(aP0, aDAx2);
1391 //
1392 gp_Vec2d aV(aP0, aP1);
1393 aDx=aVAx2.Dot(aV);
1394 aPA2=aP0.Translated(aDx*aDAx2);
1395 //
1396 // aR2
1397 aDx=aPA2.Distance(aP0);
1398 aR2=aDx*aTgBeta2;
1399 //
1400 // aRD2
1401 aRD2=aPA2.Distance(aP1);
1402 //
1403 if (aRD2>(aR2+Tol)) {
1404 iRet=0;
1405 typeres=IntAna_Empty; //nothing
1406 return;
1407 }
1408 //
1409 iRet=1; //touch case => 1 line
1410 if (aRD2<(aR2-Tol)) {
1411 iRet=2;//intersection => couple of lines
1412 }
1413 //
1414 // Finding the solution in 3D
1415 //
1416 Standard_Real aDa;
1417 gp_Pnt aQApex1, aQA1, aQA2, aQX, aQX1, aQX2;
1418 gp_Dir aD3Ax1, aD3Ax2;
1419 gp_Lin aLin;
1420 IntAna_QuadQuadGeo aIntr;
1421 //
1422 aQApex1=Con1.Apex();
1423 aD3Ax1=aAx1.Direction();
1424 aQA1.SetCoord(aQApex1.X()+aD1*aD3Ax1.X(),
1425 aQApex1.Y()+aD1*aD3Ax1.Y(),
1426 aQApex1.Z()+aD1*aD3Ax1.Z());
1427 //
1428 aDx=aD3Ax1.Dot(aAx2.Direction());
1429 if (aDx<0.) {
1430 aAx2.Reverse();
1431 }
1432 aD3Ax2=aAx2.Direction();
1433 //
1434 aD2=aD1*sqrt((1.+aTgBeta1*aTgBeta1)/(1.+aTgBeta2*aTgBeta2));
1435 //
1436 aQA2.SetCoord(aQApex1.X()+aD2*aD3Ax2.X(),
1437 aQApex1.Y()+aD2*aD3Ax2.Y(),
1438 aQApex1.Z()+aD2*aD3Ax2.Z());
1439 //
1440 gp_Pln aPln1(aQA1, aD3Ax1);
1441 gp_Pln aPln2(aQA2, aD3Ax2);
1442 //
1443 aIntr.Perform(aPln1, aPln2, Tol, Tol);
1444 if (!aIntr.IsDone()) {
1445 iRet=-1; // just in case. it must not be so
1446 typeres=IntAna_NoGeometricSolution;
1447 return;
1448 }
1449 //
1450 aLin=aIntr.Line(1);
1451 const gp_Dir& aDLin=aLin.Direction();
1452 gp_Vec aVLin(aDLin);
1453 gp_Pnt aOrig=aLin.Location();
1454 gp_Vec aVr(aQA1, aOrig);
1455 aDx=aVLin.Dot(aVr);
1456 aQX=aOrig.Translated(aDx*aVLin);
1457 //
1458 // Final part
1459 //
1460 typeres=IntAna_Line;
1461 //
1462 param1=0.;
1463 param2 =0.;
1464 param1bis=0.;
1465 param2bis=0.;
1466 //
1467 if (iRet==1) {
1468 // one line
1469 nbint=1;
1470 pt1=aQApex1;
1471 gp_Vec aVX(aQApex1, aQX);
1472 dir1=gp_Dir(aVX);
1473 }
1474
1475 else {//iRet=2
1476 // two lines
1477 nbint=2;
1478 aDa=aQA1.Distance(aQX);
1479 aDx=sqrt(aR1*aR1-aDa*aDa);
1480 aQX1=aQX.Translated(aDx*aVLin);
1481 aQX2=aQX.Translated(-aDx*aVLin);
1482 //
1483 pt1=aQApex1;
1484 pt2=aQApex1;
1485 gp_Vec aVX1(aQApex1, aQX1);
1486 dir1=gp_Dir(aVX1);
1487 gp_Vec aVX2(aQApex1, aQX2);
1488 dir2=gp_Dir(aVX2);
1489 }
1490 } //else if (aDA1A2<aTol2) {
1491 //Case when cones have common generatrix
1492 else if(A1A2.Intersect()) {
1493 //Check if apex of one cone belongs another one
1494 Standard_Real u, v, tol2 = Tol*Tol;
1495 ElSLib::Parameters(Con2, aPApex1, u, v);
1496 gp_Pnt p = ElSLib::Value(u, v, Con2);
1497 if(aPApex1.SquareDistance(p) > tol2) {
1498 typeres=IntAna_NoGeometricSolution;
1499 return;
1500 }
1501 //
1502 ElSLib::Parameters(Con1, aPApex2, u, v);
1503 p = ElSLib::Value(u, v, Con1);
1504 if(aPApex2.SquareDistance(p) > tol2) {
1505 typeres=IntAna_NoGeometricSolution;
1506 return;
1507 }
1508
1509 //Cones have a common generatrix passing through apexes
1510 myCommonGen = Standard_True;
1511
1512 //common generatrix of cones
1513 gp_Lin aGen(aPApex1, gp_Dir(gp_Vec(aPApex1, aPApex2)));
1514
1515 //Intersection point of axes
1516 gp_Pnt aPAxeInt = A1A2.PtIntersect();
1517
1518 //Characteristic point of intersection curve
1519 u = ElCLib::Parameter(aGen, aPAxeInt);
1520 myPChar = ElCLib::Value(u, aGen);
1521
1522
1523 //Other generatrixes of cones laying in maximal plane
1524 gp_Lin aGen1 = aGen.Rotated(Con1.Axis(), M_PI);
1525 gp_Lin aGen2 = aGen.Rotated(Con2.Axis(), M_PI);
1526 //
1527 //Intersection point of generatrixes
1528 gp_Dir aN; //solution plane normal
1529 gp_Dir aD1 = aGen1.Direction();
1530
1531 gp_Dir aD2(aD1.Crossed(aGen.Direction()));
1532
1533 if(aD1.IsParallel(aGen2.Direction(), Precision::Angular())) {
1534 aN = aD1.Crossed(aD2);
1535 }
1536 else if(aGen1.SquareDistance(aGen2) > tol2) {
1537 //Something wrong ???
1538 typeres=IntAna_NoGeometricSolution;
1539 return;
1540 }
1541 else {
1542 gp_Dir D1 = aGen1.Position().Direction();
1543 gp_Dir D2 = aGen2.Position().Direction();
1544 gp_Pnt O1 = aGen1.Location();
1545 gp_Pnt O2 = aGen2.Location();
1546 Standard_Real D1DotD2 = D1.Dot(D2);
1547 Standard_Real aSin = 1.-D1DotD2*D1DotD2;
1548 gp_Vec O1O2 (O1,O2);
1549 Standard_Real U2 = (D1.XYZ()*(O1O2.Dot(D1))-(O1O2.XYZ())).Dot(D2.XYZ());
1550 U2 /= aSin;
1551 gp_Pnt aPGint(ElCLib::Value(U2, aGen2));
1552
1553 aD1 = gp_Dir(gp_Vec(aPGint, myPChar));
1554 aN = aD1.Crossed(aD2);
1555 }
1556 //Plane that must contain intersection curves
1557 gp_Pln anIntPln(myPChar, aN);
1558
1559 IntAna_QuadQuadGeo INTER_QUAD_PLN(anIntPln,Con1,Tol,Tol);
1560
1561 if(INTER_QUAD_PLN.IsDone()) {
1562 switch(INTER_QUAD_PLN.TypeInter()) {
1563 case IntAna_Ellipse: {
1564 typeres=IntAna_Ellipse;
1565 gp_Elips E=INTER_QUAD_PLN.Ellipse(1);
1566 pt1 = E.Location();
1567 dir1 = E.Position().Direction();
1568 dir2 = E.Position().XDirection();
1569 param1 = E.MajorRadius();
1570 param1bis = E.MinorRadius();
1571 nbint = 1;
1572 break;
1573 }
1574 case IntAna_Circle: {
1575 typeres=IntAna_Circle;
1576 gp_Circ C=INTER_QUAD_PLN.Circle(1);
1577 pt1 = C.Location();
1578 dir1 = C.Position().XDirection();
1579 dir2 = C.Position().YDirection();
1580 param1 = C.Radius();
1581 nbint = 1;
1582 break;
1583 }
1584 case IntAna_Parabola: {
1585 typeres=IntAna_Parabola;
1586 gp_Parab Prb=INTER_QUAD_PLN.Parabola(1);
1587 pt1 = Prb.Location();
1588 dir1 = Prb.Position().Direction();
1589 dir2 = Prb.Position().XDirection();
1590 param1 = Prb.Focal();
1591 nbint = 1;
1592 break;
1593 }
1594 case IntAna_Hyperbola: {
1595 typeres=IntAna_Hyperbola;
1596 gp_Hypr H=INTER_QUAD_PLN.Hyperbola(1);
1597 pt1 = pt2 = H.Location();
1598 dir1 = H.Position().Direction();
1599 dir2 = H.Position().XDirection();
1600 param1 = param2 = H.MajorRadius();
1601 param1bis = param2bis = H.MinorRadius();
1602 nbint = 2;
1603 break;
1604 }
1605 default:
1606 typeres=IntAna_NoGeometricSolution;
1607 }
1608 }
1609 }
1610
1611 else {
1612 typeres=IntAna_NoGeometricSolution;
1613 }
1614}
1615//=======================================================================
1616//function : IntAna_QuadQuadGeo
1617//purpose : Sphere - Cone
1618//=======================================================================
1619 IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Sphere& Sph,
1620 const gp_Cone& Con,
1621 const Standard_Real Tol)
1622: done(Standard_False),
1623 nbint(0),
1624 typeres(IntAna_Empty),
1625 pt1(0,0,0),
1626 pt2(0,0,0),
1627 pt3(0,0,0),
1628 pt4(0,0,0),
1629 param1(0),
1630 param2(0),
1631 param3(0),
1632 param4(0),
1633 param1bis(0),
1634 param2bis(0),
1635 myCommonGen(Standard_False),
1636 myPChar(0,0,0)
1637{
1638 InitTolerances();
1639 Perform(Sph,Con,Tol);
1640}
1641//=======================================================================
1642//function : Perform
1643//purpose :
1644//=======================================================================
1645 void IntAna_QuadQuadGeo::Perform(const gp_Sphere& Sph,
1646 const gp_Cone& Con,
1647 const Standard_Real)
1648{
1649
1650 //
1651 done=Standard_True;
1652 //
1653 AxeOperator A1A2(Con.Axis(),Sph.Position().Axis());
1654 gp_Pnt Pt=Sph.Location();
1655 //
1656 if((A1A2.Intersect() && (Pt.Distance(A1A2.PtIntersect())==0.0))
1657 || A1A2.Same()) {
1658 gp_Pnt ConApex= Con.Apex();
1659 Standard_Real dApexSphCenter=Pt.Distance(ConApex);
1660 gp_Dir ConDir;
1661 if(dApexSphCenter>RealEpsilon()) {
1662 ConDir = gp_Dir(gp_Vec(ConApex,Pt));
1663 }
1664 else {
1665 ConDir = Con.Position().Direction();
1666 }
1667
1668 Standard_Real Rad=Sph.Radius();
1669 Standard_Real tga=Tan(Con.SemiAngle());
1670
1671
1672 //-- 2 circles
1673 //-- x: Roots of (x**2 + y**2 = Rad**2)
1674 //-- tga = y / (x+dApexSphCenter)
1675 Standard_Real tgatga = tga * tga;
1676 math_DirectPolynomialRoots Eq( 1.0+tgatga
1677 ,2.0*tgatga*dApexSphCenter
1678 ,-Rad*Rad + dApexSphCenter*dApexSphCenter*tgatga);
1679 if(Eq.IsDone()) {
1680 Standard_Integer nbsol=Eq.NbSolutions();
1681 if(nbsol==0) {
1682 typeres=IntAna_Empty;
1683 }
1684 else {
1685 typeres=IntAna_Circle;
1686 if(nbsol>=1) {
1687 Standard_Real x = Eq.Value(1);
1688 Standard_Real dApexSphCenterpx = dApexSphCenter+x;
1689 nbint=1;
1690 pt1.SetCoord( ConApex.X() + (dApexSphCenterpx) * ConDir.X()
1691 ,ConApex.Y() + (dApexSphCenterpx) * ConDir.Y()
1692 ,ConApex.Z() + (dApexSphCenterpx) * ConDir.Z());
1693 param1 = tga * dApexSphCenterpx;
1694 param1 = Abs(param1);
1695 dir1 = ConDir;
1696 if(param1<=myEPSILON_MINI_CIRCLE_RADIUS) {
1697 typeres=IntAna_PointAndCircle;
1698 param1=0.0;
1699 }
1700 }
1701 if(nbsol>=2) {
1702 Standard_Real x=Eq.Value(2);
1703 Standard_Real dApexSphCenterpx = dApexSphCenter+x;
1704 nbint=2;
1705 pt2.SetCoord( ConApex.X() + (dApexSphCenterpx) * ConDir.X()
1706 ,ConApex.Y() + (dApexSphCenterpx) * ConDir.Y()
1707 ,ConApex.Z() + (dApexSphCenterpx) * ConDir.Z());
1708 param2 = tga * dApexSphCenterpx;
1709 param2 = Abs(param2);
1710 dir2=ConDir;
1711 if(param2<=myEPSILON_MINI_CIRCLE_RADIUS) {
1712 typeres=IntAna_PointAndCircle;
1713 param2=0.0;
1714 }
1715 }
1716 }
1717 }
1718 else {
1719 done=Standard_False;
1720 }
1721 }
1722 else {
1723 typeres=IntAna_NoGeometricSolution;
1724 }
1725}
1726
1727//=======================================================================
1728//function : IntAna_QuadQuadGeo
1729//purpose : Sphere - Sphere
1730//=======================================================================
1731 IntAna_QuadQuadGeo::IntAna_QuadQuadGeo( const gp_Sphere& Sph1
1732 ,const gp_Sphere& Sph2
1733 ,const Standard_Real Tol)
1734: done(Standard_False),
1735 nbint(0),
1736 typeres(IntAna_Empty),
1737 pt1(0,0,0),
1738 pt2(0,0,0),
1739 pt3(0,0,0),
1740 pt4(0,0,0),
1741 param1(0),
1742 param2(0),
1743 param3(0),
1744 param4(0),
1745 param1bis(0),
1746 param2bis(0),
1747 myCommonGen(Standard_False),
1748 myPChar(0,0,0)
1749{
1750 InitTolerances();
1751 Perform(Sph1,Sph2,Tol);
1752}
1753//=======================================================================
1754//function : Perform
1755//purpose :
1756//=======================================================================
1757 void IntAna_QuadQuadGeo::Perform(const gp_Sphere& Sph1,
1758 const gp_Sphere& Sph2,
1759 const Standard_Real Tol)
1760{
1761 done=Standard_True;
1762 gp_Pnt O1=Sph1.Location();
1763 gp_Pnt O2=Sph2.Location();
1764 Standard_Real dO1O2=O1.Distance(O2);
1765 Standard_Real R1=Sph1.Radius();
1766 Standard_Real R2=Sph2.Radius();
1767 Standard_Real Rmin,Rmax;
1768 typeres=IntAna_Empty;
1769 param2bis=0.0; //-- pour eviter param2bis not used ....
1770
1771 if(R1>R2) { Rmin=R2; Rmax=R1; } else { Rmin=R1; Rmax=R2; }
1772
1773 if(dO1O2<=Tol && (Abs(R1-R2) <= Tol)) {
1774 typeres = IntAna_Same;
1775 }
1776 else {
1777 if(dO1O2<=Tol) { return; }
1778 gp_Dir Dir=gp_Dir(gp_Vec(O1,O2));
1779 Standard_Real t = Rmax - dO1O2 - Rmin;
1780
1781 //----------------------------------------------------------------------
1782 //-- |----------------- R1 --------------------|
1783 //-- |----dO1O2-----|-----------R2----------|
1784 //-- --->--<-- t
1785 //--
1786 //-- |------ R1 ------|---------dO1O2----------|
1787 //-- |-------------------R2-----------------------|
1788 //-- --->--<-- t
1789 //----------------------------------------------------------------------
1790 if(t >= 0.0 && t <=Tol) {
1791 typeres = IntAna_Point;
1792 nbint = 1;
1793 Standard_Real t2;
1794 if(R1==Rmax) t2=(R1 + (R2 + dO1O2)) * 0.5;
1795 else t2=(-R1+(dO1O2-R2))*0.5;
1796
1797 pt1.SetCoord( O1.X() + t2*Dir.X()
1798 ,O1.Y() + t2*Dir.Y()
1799 ,O1.Z() + t2*Dir.Z());
1800 }
1801 else {
1802 //-----------------------------------------------------------------
1803 //-- |----------------- dO1O2 --------------------|
1804 //-- |----R1-----|-----------R2----------|-Tol-|
1805 //--
1806 //-- |----------------- Rmax --------------------|
1807 //-- |----Rmin----|-------dO1O2-------|-Tol-|
1808 //--
1809 //-----------------------------------------------------------------
1810 if((dO1O2 > (R1+R2+Tol)) || (Rmax > (dO1O2+Rmin+Tol))) {
1811 typeres=IntAna_Empty;
1812 }
1813 else {
1814 //---------------------------------------------------------------
1815 //--
1816 //--
1817 //---------------------------------------------------------------
1818 Standard_Real Alpha=0.5*(R1*R1-R2*R2+dO1O2*dO1O2)/(dO1O2);
1819 Standard_Real Beta = R1*R1-Alpha*Alpha;
1820 Beta = (Beta>0.0)? Sqrt(Beta) : 0.0;
1821
1822 if(Beta<= myEPSILON_MINI_CIRCLE_RADIUS) {
1823 typeres = IntAna_Point;
1824 Alpha = (R1 + (dO1O2 - R2)) * 0.5;
1825 }
1826 else {
1827 typeres = IntAna_Circle;
1828 dir1 = Dir;
1829 param1 = Beta;
1830 }
1831 pt1.SetCoord( O1.X() + Alpha*Dir.X()
1832 ,O1.Y() + Alpha*Dir.Y()
1833 ,O1.Z() + Alpha*Dir.Z());
1834
1835 nbint=1;
1836 }
1837 }
1838 }
1839}
1840
1841//=======================================================================
1842//function : IntAna_QuadQuadGeo
1843//purpose : Plane - Torus
1844//=======================================================================
1845IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Pln& Pln,
1846 const gp_Torus& Tor,
1847 const Standard_Real Tol)
1848: done(Standard_False),
1849 nbint(0),
1850 typeres(IntAna_Empty),
1851 pt1(0,0,0),
1852 pt2(0,0,0),
1853 pt3(0,0,0),
1854 pt4(0,0,0),
1855 param1(0),
1856 param2(0),
1857 param3(0),
1858 param4(0),
1859 param1bis(0),
1860 param2bis(0),
1861 myCommonGen(Standard_False),
1862 myPChar(0,0,0)
1863{
1864 InitTolerances();
1865 Perform(Pln,Tor,Tol);
1866}
1867//=======================================================================
1868//function : Perform
1869//purpose :
1870//=======================================================================
1871void IntAna_QuadQuadGeo::Perform(const gp_Pln& Pln,
1872 const gp_Torus& Tor,
1873 const Standard_Real Tol)
1874{
1875 done = Standard_True;
1876 //
1877 Standard_Real aRMin, aRMaj;
1878 //
1879 aRMin = Tor.MinorRadius();
1880 aRMaj = Tor.MajorRadius();
1881 if (aRMin >= aRMaj) {
1882 typeres = IntAna_NoGeometricSolution;
1883 return;
1884 }
1885 //
1886 const gp_Ax1 aPlnAx = Pln.Axis();
1887 const gp_Ax1 aTorAx = Tor.Axis();
1888 //
1889 Standard_Boolean bParallel, bNormal;
1890 //
1891 bParallel = aTorAx.IsParallel(aPlnAx, myEPSILON_AXES_PARA);
1892 bNormal = !bParallel ? aTorAx.IsNormal(aPlnAx, myEPSILON_AXES_PARA) : Standard_False;
1893 if (!bNormal && !bParallel) {
1894 typeres = IntAna_NoGeometricSolution;
1895 return;
1896 }
1897 //
1898 Standard_Real aDist;
1899 //
1900 gp_Pnt aTorLoc = aTorAx.Location();
1901 if (bParallel) {
1902 Standard_Real aDt, X, Y, Z, A, B, C, D;
1903 //
1904 Pln.Coefficients(A,B,C,D);
1905 aTorLoc.Coord(X,Y,Z);
1906 aDist = A*X + B*Y + C*Z + D;
1907 //
1908 if ((Abs(aDist) - aRMin) > Tol) {
1909 typeres=IntAna_Empty;
1910 return;
1911 }
1912 //
1913 typeres = IntAna_Circle;
1914 //
1915 pt1.SetCoord(X - aDist*A, Y - aDist*B, Z - aDist*C);
1916 aDt = Sqrt(Abs(aRMin*aRMin - aDist*aDist));
1917 param1 = aRMaj + aDt;
1918 dir1 = aTorAx.Direction();
1919 nbint = 1;
1920 if ((Abs(aDist) < aRMin) && (aDt > Tol)) {
1921 pt2 = pt1;
1922 param2 = aRMaj - aDt;
1923 dir2 = dir1;
1924 nbint = 2;
1925 }
1926 }
1927 //
1928 else {
1929 aDist = Pln.Distance(aTorLoc);
1930 if (aDist > myEPSILON_DISTANCE) {
1931 typeres = IntAna_NoGeometricSolution;
1932 return;
1933 }
1934 //
1935 typeres = IntAna_Circle;
1936 param2 = param1 = aRMin;
1937 dir2 = dir1 = aPlnAx.Direction();
1938 nbint = 2;
1939 //
1940 gp_Dir aDir = aTorAx.Direction()^dir1;
1941 pt1.SetXYZ(aTorLoc.XYZ() + aRMaj*aDir.XYZ());
1942 pt2.SetXYZ(aTorLoc.XYZ() - aRMaj*aDir.XYZ());
1943 }
1944}
1945
1946//=======================================================================
1947//function : IntAna_QuadQuadGeo
1948//purpose : Cylinder - Torus
1949//=======================================================================
1950IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Cylinder& Cyl,
1951 const gp_Torus& Tor,
1952 const Standard_Real Tol)
1953: done(Standard_False),
1954 nbint(0),
1955 typeres(IntAna_Empty),
1956 pt1(0,0,0),
1957 pt2(0,0,0),
1958 pt3(0,0,0),
1959 pt4(0,0,0),
1960 param1(0),
1961 param2(0),
1962 param3(0),
1963 param4(0),
1964 param1bis(0),
1965 param2bis(0),
1966 myCommonGen(Standard_False),
1967 myPChar(0,0,0)
1968{
1969 InitTolerances();
1970 Perform(Cyl,Tor,Tol);
1971}
1972//=======================================================================
1973//function : Perform
1974//purpose :
1975//=======================================================================
1976void IntAna_QuadQuadGeo::Perform(const gp_Cylinder& Cyl,
1977 const gp_Torus& Tor,
1978 const Standard_Real Tol)
1979{
1980 done = Standard_True;
1981 //
1982 Standard_Real aRMin, aRMaj;
1983 //
1984 aRMin = Tor.MinorRadius();
1985 aRMaj = Tor.MajorRadius();
1986 if (aRMin >= aRMaj) {
1987 typeres = IntAna_NoGeometricSolution;
1988 return;
1989 }
1990 //
1991 const gp_Ax1 aCylAx = Cyl.Axis();
1992 const gp_Ax1 aTorAx = Tor.Axis();
1993 //
1994 const gp_Lin aLin(aTorAx);
1995 const gp_Pnt aLocCyl = Cyl.Location();
1996 //
1997 if (!aTorAx.IsParallel(aCylAx, myEPSILON_AXES_PARA) ||
1998 (aLin.Distance(aLocCyl) > myEPSILON_DISTANCE)) {
1999 typeres = IntAna_NoGeometricSolution;
2000 return;
2001 }
2002 //
2003 Standard_Real aRCyl;
2004 //
2005 aRCyl = Cyl.Radius();
2006 if (((aRCyl + Tol) < (aRMaj - aRMin)) || ((aRCyl - Tol) > (aRMaj + aRMin))) {
2007 typeres = IntAna_Empty;
2008 return;
2009 }
2010 //
2011 typeres = IntAna_Circle;
2012 //
2013 Standard_Real aDist = Sqrt(Abs(aRMin*aRMin - (aRCyl-aRMaj)*(aRCyl-aRMaj)));
2014 gp_XYZ aTorLoc = aTorAx.Location().XYZ();
2015 //
2016 dir1 = aTorAx.Direction();
2017 pt1.SetXYZ(aTorLoc + aDist*dir1.XYZ());
2018 param1 = aRCyl;
2019 nbint = 1;
2020 if ((aDist > Tol) && (aRCyl > (aRMaj - aRMin)) &&
2021 (aRCyl < (aRMaj + aRMin))) {
2022 dir2 = dir1;
2023 pt2.SetXYZ(aTorLoc - aDist*dir2.XYZ());
2024 param2 = param1;
2025 nbint = 2;
2026 }
2027}
2028
2029//=======================================================================
2030//function : IntAna_QuadQuadGeo
2031//purpose : Cone - Torus
2032//=======================================================================
2033IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Cone& Con,
2034 const gp_Torus& Tor,
2035 const Standard_Real Tol)
2036: done(Standard_False),
2037 nbint(0),
2038 typeres(IntAna_Empty),
2039 pt1(0,0,0),
2040 pt2(0,0,0),
2041 pt3(0,0,0),
2042 pt4(0,0,0),
2043 param1(0),
2044 param2(0),
2045 param3(0),
2046 param4(0),
2047 param1bis(0),
2048 param2bis(0),
2049 myCommonGen(Standard_False),
2050 myPChar(0,0,0)
2051{
2052 InitTolerances();
2053 Perform(Con,Tor,Tol);
2054}
2055//=======================================================================
2056//function : Perform
2057//purpose :
2058//=======================================================================
2059void IntAna_QuadQuadGeo::Perform(const gp_Cone& Con,
2060 const gp_Torus& Tor,
2061 const Standard_Real Tol)
2062{
2063 done = Standard_True;
2064 //
2065 Standard_Real aRMin, aRMaj;
2066 //
2067 aRMin = Tor.MinorRadius();
2068 aRMaj = Tor.MajorRadius();
2069 if (aRMin >= aRMaj) {
2070 typeres = IntAna_NoGeometricSolution;
2071 return;
2072 }
2073 //
2074 const gp_Ax1 aConAx = Con.Axis();
2075 const gp_Ax1 aTorAx = Tor.Axis();
2076 //
2077 const gp_Lin aLin(aTorAx);
2078 const gp_Pnt aConApex = Con.Apex();
2079 //
2080 if (!aTorAx.IsParallel(aConAx, myEPSILON_AXES_PARA) ||
2081 (aLin.Distance(aConApex) > myEPSILON_DISTANCE)) {
2082 typeres = IntAna_NoGeometricSolution;
2083 return;
2084 }
2085 //
2086 Standard_Real anAngle, aDist, aParam[4], aDt;
2087 Standard_Integer i;
2088 gp_Pnt aTorLoc, aPCT, aPN, aPt[4];
2089 gp_Dir aDir[4];
2090 //
2091 anAngle = Con.SemiAngle();
2092 aTorLoc = aTorAx.Location();
2093 //
2094 aPN.SetXYZ(aTorLoc.XYZ() + aRMaj*Tor.YAxis().Direction().XYZ());
2095 gp_Dir aDN (gp_Vec(aTorLoc, aPN));
2096 gp_Ax1 anAxCLRot(aConApex, aDN);
2097 gp_Lin aConL = aLin.Rotated(anAxCLRot, anAngle);
2098 gp_Dir aDL = aConL.Position().Direction();
2099 gp_Dir aXDir = Tor.XAxis().Direction();
2100 //
2101 typeres = IntAna_Empty;
2102 //
2103 for (i = 0; i < 2; ++i) {
2104 if (i) {
2105 aXDir.Reverse();
2106 }
2107 aPCT.SetXYZ(aTorLoc.XYZ() + aRMaj*aXDir.XYZ());
2108 //
2109 aDist = aConL.Distance(aPCT);
2110 if (aDist > aRMin+Tol) {
2111 continue;
2112 }
2113 //
2114 typeres = IntAna_Circle;
2115 //
2116 gp_XYZ aPh = aPCT.XYZ() - aDist*aConL.Normal(aPCT).Direction().XYZ();
2117 aDt = Sqrt(Abs(aRMin*aRMin - aDist*aDist));
2118 //
2119 gp_Pnt aP;
2120 gp_XYZ aDVal = aDt*aDL.XYZ();
2121 aP.SetXYZ(aPh + aDVal);
2122 aParam[nbint] = aLin.Distance(aP);
2123 aPt[nbint].SetXYZ(aP.XYZ() - aParam[nbint]*aXDir.XYZ());
2124 aDir[nbint] = aTorAx.Direction();
2125 ++nbint;
2126 if ((aDist < aRMin) && (aDt > Tol)) {
2127 aP.SetXYZ(aPh - aDVal);
2128 aParam[nbint] = aLin.Distance(aP);
2129 aPt[nbint].SetXYZ(aP.XYZ() - aParam[nbint]*aXDir.XYZ());
2130 aDir[nbint] = aDir[nbint-1];
2131 ++nbint;
2132 }
2133 }
2134 //
2135 for (i = 0; i < nbint; ++i) {
2136 switch (i) {
2137 case 0:{
2138 pt1 = aPt[i];
2139 param1 = aParam[i];
2140 dir1 = aDir[i];
2141 break;
2142 }
2143 case 1:{
2144 pt2 = aPt[i];
2145 param2 = aParam[i];
2146 dir2 = aDir[i];
2147 break;
2148 }
2149 case 2:{
2150 pt3 = aPt[i];
2151 param3 = aParam[i];
2152 dir3 = aDir[i];
2153 break;
2154 }
2155 case 3:{
2156 pt4 = aPt[i];
2157 param4 = aParam[i];
2158 dir4 = aDir[i];
2159 break;
2160 }
2161 default:
2162 break;
2163 }
2164 }
2165}
2166
2167//=======================================================================
2168//function : IntAna_QuadQuadGeo
2169//purpose : Sphere - Torus
2170//=======================================================================
2171IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Sphere& Sph,
2172 const gp_Torus& Tor,
2173 const Standard_Real Tol)
2174: done(Standard_False),
2175 nbint(0),
2176 typeres(IntAna_Empty),
2177 pt1(0,0,0),
2178 pt2(0,0,0),
2179 pt3(0,0,0),
2180 pt4(0,0,0),
2181 param1(0),
2182 param2(0),
2183 param3(0),
2184 param4(0),
2185 param1bis(0),
2186 param2bis(0),
2187 myCommonGen(Standard_False),
2188 myPChar(0,0,0)
2189{
2190 InitTolerances();
2191 Perform(Sph,Tor,Tol);
2192}
2193//=======================================================================
2194//function : Perform
2195//purpose :
2196//=======================================================================
2197void IntAna_QuadQuadGeo::Perform(const gp_Sphere& Sph,
2198 const gp_Torus& Tor,
2199 const Standard_Real Tol)
2200{
2201 done = Standard_True;
2202 //
2203 Standard_Real aRMin, aRMaj;
2204 //
2205 aRMin = Tor.MinorRadius();
2206 aRMaj = Tor.MajorRadius();
2207 if (aRMin >= aRMaj) {
2208 typeres = IntAna_NoGeometricSolution;
2209 return;
2210 }
2211 //
2212 const gp_Ax1 aTorAx = Tor.Axis();
2213 const gp_Lin aLin(aTorAx);
2214 const gp_Pnt aSphLoc = Sph.Location();
2215 //
2216 if (aLin.Distance(aSphLoc) > myEPSILON_DISTANCE) {
2217 typeres = IntAna_NoGeometricSolution;
2218 return;
2219 }
2220 //
2221 Standard_Real aRSph, aDist;
2222 gp_Pnt aTorLoc;
2223 //
2224 gp_Dir aXDir = Tor.XAxis().Direction();
2225 aTorLoc.SetXYZ(aTorAx.Location().XYZ() + aRMaj*aXDir.XYZ());
2226 aRSph = Sph.Radius();
2227 //
2228 gp_Vec aVec12(aTorLoc, aSphLoc);
2229 aDist = aVec12.Magnitude();
2230 if (((aDist - Tol) > (aRMin + aRSph)) ||
2231 ((aDist + Tol) < Abs(aRMin - aRSph))) {
2232 typeres = IntAna_Empty;
2233 return;
2234 }
2235 //
2236 typeres = IntAna_Circle;
2237 //
2238 Standard_Real anAlpha, aBeta;
2239 //
2240 anAlpha = 0.5*(aRMin*aRMin - aRSph*aRSph + aDist*aDist ) / aDist;
2241 aBeta = Sqrt(Abs(aRMin*aRMin - anAlpha*anAlpha));
2242 //
2243 gp_Dir aDir12(aVec12);
2244 gp_XYZ aPh = aTorLoc.XYZ() + anAlpha*aDir12.XYZ();
2245 gp_Dir aDC = Tor.YAxis().Direction()^aDir12;
2246 //
2247 gp_Pnt aP;
2248 gp_XYZ aDVal = aBeta*aDC.XYZ();
2249 aP.SetXYZ(aPh + aDVal);
2250 param1 = aLin.Distance(aP);
2251 pt1.SetXYZ(aP.XYZ() - param1*aXDir.XYZ());
2252 dir1 = aTorAx.Direction();
2253 nbint = 1;
2254 if ((aDist < (aRSph + aRMin)) && (aDist > Abs(aRSph - aRMin)) &&
2255 (aDVal.Modulus() > Tol)) {
2256 aP.SetXYZ(aPh - aDVal);
2257 param2 = aLin.Distance(aP);
2258 pt2.SetXYZ(aP.XYZ() - param2*aXDir.XYZ());
2259 dir2 = dir1;
2260 nbint = 2;
2261 }
2262}
2263
2264//=======================================================================
2265//function : IntAna_QuadQuadGeo
2266//purpose : Torus - Torus
2267//=======================================================================
2268IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Torus& Tor1,
2269 const gp_Torus& Tor2,
2270 const Standard_Real Tol)
2271: done(Standard_False),
2272 nbint(0),
2273 typeres(IntAna_Empty),
2274 pt1(0,0,0),
2275 pt2(0,0,0),
2276 pt3(0,0,0),
2277 pt4(0,0,0),
2278 param1(0),
2279 param2(0),
2280 param3(0),
2281 param4(0),
2282 param1bis(0),
2283 param2bis(0),
2284 myCommonGen(Standard_False),
2285 myPChar(0,0,0)
2286{
2287 InitTolerances();
2288 Perform(Tor1,Tor2,Tol);
2289}
2290//=======================================================================
2291//function : Perform
2292//purpose :
2293//=======================================================================
2294void IntAna_QuadQuadGeo::Perform(const gp_Torus& Tor1,
2295 const gp_Torus& Tor2,
2296 const Standard_Real Tol)
2297{
2298 done = Standard_True;
2299 //
2300 Standard_Real aRMin1, aRMin2, aRMaj1, aRMaj2;
2301 //
2302 aRMin1 = Tor1.MinorRadius();
2303 aRMaj1 = Tor1.MajorRadius();
2304 aRMin2 = Tor2.MinorRadius();
2305 aRMaj2 = Tor2.MajorRadius();
2306 if (aRMin1 >= aRMaj1 || aRMin2 >= aRMaj2) {
2307 typeres = IntAna_NoGeometricSolution;
2308 return;
2309 }
2310 //
2311 const gp_Ax1 anAx1 = Tor1.Axis();
2312 const gp_Ax1 anAx2 = Tor2.Axis();
2313 //
2314 gp_Lin aL1(anAx1);
2315 if (!anAx1.IsParallel(anAx2, myEPSILON_AXES_PARA) ||
2316 (aL1.Distance(anAx2.Location()) > myEPSILON_DISTANCE)) {
2317 typeres = IntAna_NoGeometricSolution;
2318 return;
2319 }
2320 //
2321 gp_Pnt aLoc1, aLoc2;
2322 //
2323 aLoc1 = anAx1.Location();
2324 aLoc2 = anAx2.Location();
2325 //
2326 if (aLoc1.IsEqual(aLoc2, Tol) &&
2327 (Abs(aRMin1 - aRMin2) <= Tol) &&
2328 (Abs(aRMaj1 - aRMaj2) <= Tol)) {
2329 typeres = IntAna_Same;
2330 return;
2331 }
2332 //
2333 Standard_Real aDist;
2334 gp_Pnt aP1, aP2;
2335 //
2336 gp_Dir aXDir1 = Tor1.XAxis().Direction();
2337 aP1.SetXYZ(aLoc1.XYZ() + aRMaj1*aXDir1.XYZ());
2338 aP2.SetXYZ(aLoc2.XYZ() + aRMaj2*aXDir1.XYZ());
2339 //
2340 gp_Vec aV12(aP1, aP2);
2341 aDist = aV12.Magnitude();
2342 if (((aDist - Tol) > (aRMin1 + aRMin2)) ||
2343 ((aDist + Tol) < Abs(aRMin1 - aRMin2))) {
2344 typeres = IntAna_Empty;
2345 return;
2346 }
2347 //
2348 typeres = IntAna_Circle;
2349 //
2350 Standard_Real anAlpha, aBeta;
2351 //
2352 anAlpha = 0.5*(aRMin1*aRMin1 - aRMin2*aRMin2 + aDist*aDist ) / aDist;
2353 aBeta = Sqrt(Abs(aRMin1*aRMin1 - anAlpha*anAlpha));
2354 //
2355 gp_Dir aDir12(aV12);
2356 gp_XYZ aPh = aP1.XYZ() + anAlpha*aDir12.XYZ();
2357 gp_Dir aDC = Tor1.YAxis().Direction()^aDir12;
2358 //
2359 gp_Pnt aP;
2360 gp_XYZ aDVal = aBeta*aDC.XYZ();
2361 aP.SetXYZ(aPh + aDVal);
2362 param1 = aL1.Distance(aP);
2363 pt1.SetXYZ(aP.XYZ() - param1*aXDir1.XYZ());
2364 dir1 = anAx1.Direction();
2365 nbint = 1;
2366 if ((aDist < (aRMin1 + aRMin2)) && (aDist > Abs(aRMin1 - aRMin2)) &&
2367 aDVal.Modulus() > Tol) {
2368 aP.SetXYZ(aPh - aDVal);
2369 param2 = aL1.Distance(aP);
2370 pt2.SetXYZ(aP.XYZ() - param2*aXDir1.XYZ());
2371 dir2 = dir1;
2372 nbint = 2;
2373 }
2374}
2375
2376//=======================================================================
2377//function : Point
2378//purpose : Returns a Point
2379//=======================================================================
2380 gp_Pnt IntAna_QuadQuadGeo::Point(const Standard_Integer n) const
2381{
2382 if(!done) { StdFail_NotDone::Raise(); }
2383 if(n>nbint || n<1) { Standard_DomainError::Raise(); }
2384 if(typeres==IntAna_PointAndCircle) {
2385 if(n!=1) { Standard_DomainError::Raise(); }
2386 if(param1==0.0) return(pt1);
2387 return(pt2);
2388 }
2389 else if(typeres==IntAna_Point) {
2390 if(n==1) return(pt1);
2391 return(pt2);
2392 }
2393
2394 // WNT (what can you expect from MicroSoft ?)
2395 return gp_Pnt(0,0,0);
2396}
2397//=======================================================================
2398//function : Line
2399//purpose : Returns a Line
2400//=======================================================================
2401 gp_Lin IntAna_QuadQuadGeo::Line(const Standard_Integer n) const
2402{
2403 if(!done) { StdFail_NotDone::Raise(); }
2404 if((n>nbint) || (n<1) || (typeres!=IntAna_Line)) {
2405 Standard_DomainError::Raise();
2406 }
2407 if(n==1) { return(gp_Lin(pt1,dir1)); }
2408 else { return(gp_Lin(pt2,dir2)); }
2409}
2410//=======================================================================
2411//function : Circle
2412//purpose : Returns a Circle
2413//=======================================================================
2414 gp_Circ IntAna_QuadQuadGeo::Circle(const Standard_Integer n) const
2415{
2416 if(!done) { StdFail_NotDone::Raise(); }
2417 if(typeres==IntAna_PointAndCircle) {
2418 if(n!=1) { Standard_DomainError::Raise(); }
2419 if(param2==0.0) return(gp_Circ(DirToAx2(pt1,dir1),param1));
2420 return(gp_Circ(DirToAx2(pt2,dir2),param2));
2421 }
2422 else if((n>nbint) || (n<1) || (typeres!=IntAna_Circle)) {
2423 Standard_DomainError::Raise();
2424 }
2425 if (n==1) { return(gp_Circ(DirToAx2(pt1,dir1),param1));}
2426 else if (n==2) { return(gp_Circ(DirToAx2(pt2,dir2),param2));}
2427 else if (n==3) { return(gp_Circ(DirToAx2(pt3,dir3),param3));}
2428 else { return(gp_Circ(DirToAx2(pt4,dir4),param4));}
2429}
2430
2431//=======================================================================
2432//function : Ellipse
2433//purpose : Returns a Elips
2434//=======================================================================
2435 gp_Elips IntAna_QuadQuadGeo::Ellipse(const Standard_Integer n) const
2436{
2437 if(!done) { StdFail_NotDone::Raise(); }
2438 if((n>nbint) || (n<1) || (typeres!=IntAna_Ellipse)) {
2439 Standard_DomainError::Raise();
2440 }
2441
2442 if(n==1) {
2443 Standard_Real R1=param1, R2=param1bis, aTmp;
2444 if (R1<R2) {
2445 aTmp=R1; R1=R2; R2=aTmp;
2446 }
2447 gp_Ax2 anAx2(pt1, dir1 ,dir2);
2448 gp_Elips anElips (anAx2, R1, R2);
2449 return anElips;
2450 }
2451 else {
2452 Standard_Real R1=param2, R2=param2bis, aTmp;
2453 if (R1<R2) {
2454 aTmp=R1; R1=R2; R2=aTmp;
2455 }
2456 gp_Ax2 anAx2(pt2, dir2 ,dir1);
2457 gp_Elips anElips (anAx2, R1, R2);
2458 return anElips;
2459 }
2460}
2461//=======================================================================
2462//function : Parabola
2463//purpose : Returns a Parabola
2464//=======================================================================
2465 gp_Parab IntAna_QuadQuadGeo::Parabola(const Standard_Integer n) const
2466{
2467 if(!done) {
2468 StdFail_NotDone::Raise();
2469 }
2470 if (typeres!=IntAna_Parabola) {
2471 Standard_DomainError::Raise();
2472 }
2473 if((n>nbint) || (n!=1)) {
2474 Standard_OutOfRange::Raise();
2475 }
2476 return(gp_Parab(gp_Ax2( pt1
2477 ,dir1
2478 ,dir2)
2479 ,param1));
2480}
2481//=======================================================================
2482//function : Hyperbola
2483//purpose : Returns a Hyperbola
2484//=======================================================================
2485 gp_Hypr IntAna_QuadQuadGeo::Hyperbola(const Standard_Integer n) const
2486{
2487 if(!done) {
2488 StdFail_NotDone::Raise();
2489 }
2490 if((n>nbint) || (n<1) || (typeres!=IntAna_Hyperbola)) {
2491 Standard_DomainError::Raise();
2492 }
2493 if(n==1) {
2494 return(gp_Hypr(gp_Ax2( pt1
2495 ,dir1
2496 ,dir2)
2497 ,param1,param1bis));
2498 }
2499 else {
2500 return(gp_Hypr(gp_Ax2( pt2
2501 ,dir1
2502 ,dir2.Reversed())
2503 ,param2,param2bis));
2504 }
2505}
2506//=======================================================================
2507//function : HasCommonGen
2508//purpose :
2509//=======================================================================
2510Standard_Boolean IntAna_QuadQuadGeo::HasCommonGen() const
2511{
2512 return myCommonGen;
2513}
2514//=======================================================================
2515//function : PChar
2516//purpose :
2517//=======================================================================
2518const gp_Pnt& IntAna_QuadQuadGeo::PChar() const
2519{
2520 return myPChar;
2521}
2522//=======================================================================
2523//function : RefineDir
2524//purpose :
2525//=======================================================================
2526void RefineDir(gp_Dir& aDir)
2527{
2528 Standard_Integer k, m, n;
2529 Standard_Real aC[3];
2530 //
2531 aDir.Coord(aC[0], aC[1], aC[2]);
2532 //
2533 m=0;
2534 n=0;
2535 for (k=0; k<3; ++k) {
2536 if (aC[k]==1. || aC[k]==-1.) {
2537 ++m;
2538 }
2539 else if (aC[k]!=0.) {
2540 ++n;
2541 }
2542 }
2543 //
2544 if (m && n) {
2545 Standard_Real aEps, aR1, aR2, aNum;
2546 //
2547 aEps=RealEpsilon();
2548 aR1=1.-aEps;
2549 aR2=1.+aEps;
2550 //
2551 for (k=0; k<3; ++k) {
2552 m=(aC[k]>0.);
2553 aNum=(m)? aC[k] : -aC[k];
2554 if (aNum>aR1 && aNum<aR2) {
2555 if (m) {
2556 aC[k]=1.;
2557 }
2558 else {
2559 aC[k]=-1.;
2560 }
2561 //
2562 aC[(k+1)%3]=0.;
2563 aC[(k+2)%3]=0.;
2564 break;
2565 }
2566 }
2567 aDir.SetCoord(aC[0], aC[1], aC[2]);
2568 }
2569}
2570
2571
2572
Open CASCADE Technology repository