7fd59977 |
1 | // File: IntAna_QuadQuadGeo.cxx |
2 | // Created: Thu Aug 6 12:00:46 1992 |
3 | // Author: Laurent BUCHARD |
4 | // <lbr@sdsun2> |
5 | |
6 | |
7 | //---------------------------------------------------------------------- |
8 | //-- Purposse: Geometric Intersection between two Natural Quadric |
9 | //-- If the intersection is not a conic, |
10 | //-- analytical methods must be called. |
11 | //---------------------------------------------------------------------- |
12 | #ifndef DEB |
13 | #define No_Standard_RangeError |
14 | #define No_Standard_OutOfRange |
15 | #endif |
16 | |
17 | #include <IntAna_QuadQuadGeo.ixx> |
18 | |
19 | #include <IntAna_IntConicQuad.hxx> |
20 | #include <StdFail_NotDone.hxx> |
21 | #include <Standard_DomainError.hxx> |
22 | #include <Standard_OutOfRange.hxx> |
23 | #include <math_DirectPolynomialRoots.hxx> |
24 | |
25 | #include <gp.hxx> |
26 | #include <gp_Pln.hxx> |
27 | #include <gp_Vec.hxx> |
28 | #include <ElSLib.hxx> |
29 | #include <ElCLib.hxx> |
30 | |
31 | #include <gp_Dir.hxx> |
32 | #include <gp_XYZ.hxx> |
33 | #include <gp_Pnt2d.hxx> |
34 | #include <gp_Vec2d.hxx> |
35 | #include <gp_Dir2d.hxx> |
36 | |
37 | |
38 | static |
39 | gp_Ax2 DirToAx2(const gp_Pnt& P,const gp_Dir& D); |
40 | |
41 | //======================================================================= |
42 | //class : |
43 | //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 |
44 | //======================================================================= |
45 | class AxeOperator { |
46 | public: |
47 | AxeOperator(const gp_Ax1& A1,const gp_Ax1& A2); |
48 | |
49 | void Distance(Standard_Real& dist, |
50 | Standard_Real& Param1, |
51 | Standard_Real& Param2); |
52 | |
53 | gp_Pnt PtIntersect() { |
54 | return ptintersect; |
55 | } |
56 | Standard_Boolean Coplanar(void) { |
57 | return thecoplanar; |
58 | } |
59 | Standard_Boolean Same(void) { |
60 | return theparallel && (thedistance<myEPSILON_DISTANCE); |
61 | } |
62 | Standard_Real Distance(void) { |
63 | return thedistance ; |
64 | } |
65 | Standard_Boolean Intersect(void) { |
66 | return (thecoplanar && (!theparallel)); |
67 | } |
68 | Standard_Boolean Parallel(void) { |
69 | return theparallel; |
70 | } |
71 | Standard_Boolean Normal(void) { |
72 | return thenormal; |
73 | } |
74 | |
75 | protected: |
76 | Standard_Real Det33(const Standard_Real a11, |
77 | const Standard_Real a12, |
78 | const Standard_Real a13, |
79 | const Standard_Real a21, |
80 | const Standard_Real a22, |
81 | const Standard_Real a23, |
82 | const Standard_Real a31, |
83 | const Standard_Real a32, |
84 | const Standard_Real a33) { |
85 | Standard_Real theReturn = |
86 | a11*(a22*a33-a32*a23) - a21*(a12*a33-a32*a13) + a31*(a12*a23-a22*a13) ; |
87 | return theReturn ; |
88 | } |
89 | |
90 | private: |
91 | gp_Pnt ptintersect; |
92 | gp_Ax1 Axe1; |
93 | gp_Ax1 Axe2; |
94 | Standard_Real thedistance; |
95 | Standard_Boolean theparallel; |
96 | Standard_Boolean thecoplanar; |
97 | Standard_Boolean thenormal; |
98 | // |
99 | Standard_Real myEPSILON_DISTANCE; |
100 | Standard_Real myEPSILON_AXES_PARA; |
101 | }; |
102 | |
103 | //======================================================================= |
104 | //function : AxeOperator::AxeOperator |
105 | //purpose : |
106 | //======================================================================= |
107 | AxeOperator::AxeOperator(const gp_Ax1& A1,const gp_Ax1& A2) |
108 | { |
109 | myEPSILON_DISTANCE=0.00000000000001; |
110 | myEPSILON_AXES_PARA=0.000000000001; |
111 | Axe1=A1; |
112 | Axe2=A2; |
113 | //--------------------------------------------------------------------- |
114 | gp_Dir V1=Axe1.Direction(); |
115 | gp_Dir V2=Axe2.Direction(); |
116 | gp_Pnt P1=Axe1.Location(); |
117 | gp_Pnt P2=Axe2.Location(); |
118 | |
119 | thecoplanar= Standard_False; |
120 | thenormal = Standard_False; |
121 | |
122 | //--- check if the two axis are parallel |
123 | theparallel=V1.IsParallel(V2, myEPSILON_AXES_PARA); |
124 | //--- Distance between the two axis |
125 | gp_XYZ perp(A1.Direction().XYZ().Crossed(A2.Direction().XYZ())); |
126 | if (theparallel) { |
127 | gp_Lin L1(A1); |
128 | thedistance = L1.Distance(A2.Location()); |
129 | } |
130 | else { |
131 | thedistance = Abs(gp_Vec(perp.Normalized()).Dot(gp_Vec(Axe1.Location(), |
132 | Axe2.Location()))); |
133 | } |
134 | //--- check if Axis are Coplanar |
135 | Standard_Real D33; |
136 | if(thedistance<myEPSILON_DISTANCE) { |
137 | D33=Det33(V1.X(),V1.Y(),V1.Z() |
138 | ,V2.X(),V2.Y(),V2.Z() |
139 | ,P1.X()-P2.X(),P1.Y()-P2.Y(),P1.Z()-P2.Z()); |
140 | if(Abs(D33)<=myEPSILON_DISTANCE) { |
141 | thecoplanar=Standard_True; |
142 | } |
143 | } |
144 | else { |
145 | thecoplanar=Standard_True; |
146 | thenormal=(V1.Dot(V2)==0.0)? Standard_True : Standard_False; |
147 | } |
148 | //--- check if the two axis are concurrent |
149 | if(thecoplanar && (!theparallel)) { |
150 | Standard_Real smx=P2.X() - P1.X(); |
151 | Standard_Real smy=P2.Y() - P1.Y(); |
152 | Standard_Real smz=P2.Z() - P1.Z(); |
153 | Standard_Real Det1,Det2,Det3,A; |
154 | Det1=V1.Y() * V2.X() - V1.X() * V2.Y(); |
155 | Det2=V1.Z() * V2.Y() - V1.Y() * V2.Z(); |
156 | Det3=V1.Z() * V2.X() - V1.X() * V2.Z(); |
157 | |
158 | if((Det1!=0.0) && ((Abs(Det1) >= Abs(Det2))&&(Abs(Det1) >= Abs(Det3)))) { |
159 | A=(smy * V2.X() - smx * V2.Y())/Det1; |
160 | } |
161 | else if((Det2!=0.0) |
162 | && ((Abs(Det2) >= Abs(Det1)) |
163 | &&(Abs(Det2) >= Abs(Det3)))) { |
164 | A=(smz * V2.Y() - smy * V2.Z())/Det2; |
165 | } |
166 | else { |
167 | A=(smz * V2.X() - smx * V2.Z())/Det3; |
168 | } |
169 | ptintersect.SetCoord( P1.X() + A * V1.X() |
170 | ,P1.Y() + A * V1.Y() |
171 | ,P1.Z() + A * V1.Z()); |
172 | } |
173 | else { |
174 | ptintersect.SetCoord(0,0,0); //-- Pour eviter des FPE |
175 | } |
176 | } |
177 | //======================================================================= |
178 | //function : Distance |
179 | //purpose : |
180 | //======================================================================= |
181 | void AxeOperator::Distance(Standard_Real& dist,Standard_Real& Param1,Standard_Real& Param2) |
182 | { |
183 | gp_Vec O1O2(Axe1.Location(),Axe2.Location()); //----------------------------- |
184 | gp_Dir U1 = Axe1.Direction(); //-- juste pour voir. |
185 | gp_Dir U2 = Axe2.Direction(); |
186 | |
187 | gp_Dir N = U1.Crossed(U2); |
188 | Standard_Real D = Det33(U1.X(),U2.X(),N.X(), |
189 | U1.Y(),U2.Y(),N.Y(), |
190 | U1.Z(),U2.Z(),N.Z()); |
191 | if(D) { |
192 | dist = Det33(U1.X(),U2.X(),O1O2.X(), |
193 | U1.Y(),U2.Y(),O1O2.Y(), |
194 | U1.Z(),U2.Z(),O1O2.Z()) / D; |
195 | Param1 = Det33(O1O2.X(),U2.X(),N.X(), |
196 | O1O2.Y(),U2.Y(),N.Y(), |
197 | O1O2.Z(),U2.Z(),N.Z()) / (-D); |
198 | //------------------------------------------------------------ |
199 | //-- On resout P1 * Dir1 + P2 * Dir2 + d * N = O1O2 |
200 | //-- soit : Segment perpendiculaire : O1+P1 D1 |
201 | //-- O2-P2 D2 |
202 | Param2 = Det33(U1.X(),O1O2.X(),N.X(), |
203 | U1.Y(),O1O2.Y(),N.Y(), |
204 | U1.Z(),O1O2.Z(),N.Z()) / (D); |
205 | } |
206 | } |
207 | //======================================================================= |
208 | //function : DirToAx2 |
209 | //purpose : returns a gp_Ax2 where D is the main direction |
210 | //======================================================================= |
211 | gp_Ax2 DirToAx2(const gp_Pnt& P,const gp_Dir& D) |
212 | { |
213 | Standard_Real x=D.X(); Standard_Real ax=Abs(x); |
214 | Standard_Real y=D.Y(); Standard_Real ay=Abs(y); |
215 | Standard_Real z=D.Z(); Standard_Real az=Abs(z); |
216 | if( (ax==0.0) || ((ax<ay) && (ax<az)) ) { |
217 | return(gp_Ax2(P,D,gp_Dir(gp_Vec(0.0,-z,y)))); |
218 | } |
219 | else if( (ay==0.0) || ((ay<ax) && (ay<az)) ) { |
220 | return(gp_Ax2(P,D,gp_Dir(gp_Vec(-z,0.0,x)))); |
221 | } |
222 | else { |
223 | return(gp_Ax2(P,D,gp_Dir(gp_Vec(-y,x,0.0)))); |
224 | } |
225 | } |
226 | //======================================================================= |
227 | //function : IntAna_QuadQuadGeo |
228 | //purpose : Empty constructor |
229 | //======================================================================= |
230 | IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(void) |
231 | : done(Standard_False), |
232 | nbint(0), |
233 | typeres(IntAna_Empty), |
234 | pt1(0,0,0), |
235 | pt2(0,0,0), |
236 | param1(0), |
237 | param2(0), |
238 | param1bis(0), |
239 | param2bis(0), |
240 | myCommonGen(Standard_False), |
241 | myPChar(0,0,0) |
242 | { |
243 | InitTolerances(); |
244 | } |
245 | //======================================================================= |
246 | //function : InitTolerances |
247 | //purpose : |
248 | //======================================================================= |
249 | void IntAna_QuadQuadGeo::InitTolerances() |
250 | { |
251 | myEPSILON_DISTANCE = 0.00000000000001; |
252 | myEPSILON_ANGLE_CONE = 0.000000000001; |
253 | myEPSILON_MINI_CIRCLE_RADIUS = 0.000000001; |
254 | myEPSILON_CYLINDER_DELTA_RADIUS = 0.0000000000001; |
255 | myEPSILON_CYLINDER_DELTA_DISTANCE= 0.0000001; |
256 | myEPSILON_AXES_PARA = 0.000000000001; |
257 | } |
258 | //======================================================================= |
259 | //function : IntAna_QuadQuadGeo |
260 | //purpose : Pln Pln |
261 | //======================================================================= |
262 | IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Pln& P1, |
263 | const gp_Pln& P2, |
264 | const Standard_Real TolAng, |
265 | const Standard_Real Tol) |
266 | : done(Standard_False), |
267 | nbint(0), |
268 | typeres(IntAna_Empty), |
269 | pt1(0,0,0), |
270 | pt2(0,0,0), |
271 | param1(0), |
272 | param2(0), |
273 | param1bis(0), |
274 | param2bis(0), |
275 | myCommonGen(Standard_False), |
276 | myPChar(0,0,0) |
277 | { |
278 | InitTolerances(); |
279 | Perform(P1,P2,TolAng,Tol); |
280 | } |
281 | //======================================================================= |
282 | //function : Perform |
283 | //purpose : |
284 | //======================================================================= |
285 | void IntAna_QuadQuadGeo::Perform (const gp_Pln& P1, |
286 | const gp_Pln& P2, |
287 | const Standard_Real TolAng, |
288 | const Standard_Real Tol) |
289 | { |
290 | done=Standard_False; |
291 | // |
292 | param2bis=0.0; |
293 | |
294 | Standard_Real A1 = 0., B1 = 0., C1 = 0., D1 = 0., A2 = 0., B2 = 0., C2 = 0., D2 = 0.; |
295 | P1.Coefficients(A1,B1,C1,D1); |
296 | P2.Coefficients(A2,B2,C2,D2); |
297 | |
298 | gp_Vec vd(gp_Vec(A1,B1,C1).Crossed(gp_Vec(A2,B2,C2))); |
299 | Standard_Real dist1= A2*P1.Location().X() + B2*P1.Location().Y() + C2*P1.Location().Z() + D2; |
300 | Standard_Real dist2= A1*P2.Location().X() + B1*P2.Location().Y() + C1*P2.Location().Z() + D1; |
301 | |
302 | if(vd.Magnitude() <=TolAng) { |
303 | // normalles are collinear - planes are same or parallel |
304 | typeres = (Abs(dist1) <= Tol && Abs(dist2) <= Tol) ? IntAna_Same : IntAna_Empty; |
305 | } |
306 | else { |
307 | Standard_Real denom=A1*A2 + B1*B2 + C1*C2; |
308 | |
309 | Standard_Real denom2 = denom*denom; |
310 | Standard_Real ddenom = 1. - denom2; |
311 | denom = ( Abs(ddenom) <= 1.e-9 ) ? 1.e-9 : ddenom; |
312 | |
313 | Standard_Real par1 = dist1/denom; |
314 | Standard_Real par2 = -dist2/denom; |
315 | |
316 | gp_Vec inter1(gp_Vec(A1,B1,C1).Crossed(vd)); |
317 | gp_Vec inter2(gp_Vec(A2,B2,C2).Crossed(vd)); |
318 | |
319 | Standard_Real X1=P1.Location().X() + par1*inter1.X(); |
320 | Standard_Real Y1=P1.Location().Y() + par1*inter1.Y(); |
321 | Standard_Real Z1=P1.Location().Z() + par1*inter1.Z(); |
322 | Standard_Real X2=P2.Location().X() + par2*inter2.X(); |
323 | Standard_Real Y2=P2.Location().Y() + par2*inter2.Y(); |
324 | Standard_Real Z2=P2.Location().Z() + par2*inter2.Z(); |
325 | |
326 | pt1=gp_Pnt((X1+X2)*0.5, (Y1+Y2)*0.5, (Z1+Z2)*0.5); |
327 | dir1 = gp_Dir(vd); |
328 | typeres = IntAna_Line; |
329 | nbint = 1; |
330 | |
331 | } |
332 | done=Standard_True; |
333 | } |
334 | //======================================================================= |
335 | //function : IntAna_QuadQuadGeo |
336 | //purpose : Pln Cylinder |
337 | //======================================================================= |
338 | IntAna_QuadQuadGeo::IntAna_QuadQuadGeo( const gp_Pln& P |
339 | ,const gp_Cylinder& Cl |
340 | ,const Standard_Real Tolang |
341 | ,const Standard_Real Tol) |
342 | : done(Standard_False), |
343 | nbint(0), |
344 | typeres(IntAna_Empty), |
345 | pt1(0,0,0), |
346 | pt2(0,0,0), |
347 | param1(0), |
348 | param2(0), |
349 | param1bis(0), |
350 | param2bis(0), |
351 | myCommonGen(Standard_False), |
352 | myPChar(0,0,0) |
353 | { |
354 | InitTolerances(); |
355 | Perform(P,Cl,Tolang,Tol); |
356 | } |
357 | //======================================================================= |
358 | //function : Perform |
359 | //purpose : |
360 | //======================================================================= |
361 | void IntAna_QuadQuadGeo::Perform( const gp_Pln& P |
362 | ,const gp_Cylinder& Cl |
363 | ,const Standard_Real Tolang |
364 | ,const Standard_Real Tol) |
365 | { |
366 | done = Standard_False; |
367 | Standard_Real dist,radius; |
368 | Standard_Real A,B,C,D; |
369 | Standard_Real X,Y,Z; |
370 | Standard_Real sint,cost,h; |
371 | gp_XYZ axex,axey,omega; |
372 | |
373 | |
374 | param2bis=0.0; |
375 | radius = Cl.Radius(); |
376 | |
377 | gp_Lin axec(Cl.Axis()); |
378 | gp_XYZ normp(P.Axis().Direction().XYZ()); |
379 | |
380 | P.Coefficients(A,B,C,D); |
381 | axec.Location().Coord(X,Y,Z); |
382 | dist = A*X + B*Y + C*Z + D; // la distance axe/plan est evaluee a l origine de l axe. |
383 | |
384 | Standard_Real tolang = Tolang; |
385 | Standard_Boolean newparams = Standard_False; |
386 | |
387 | gp_Vec ldv( axec.Direction() ); |
388 | gp_Vec npv( normp ); |
389 | Standard_Real dA = Abs( ldv.Angle( npv ) ); |
390 | if( dA > (PI/4.) ) |
391 | { |
392 | Standard_Real dang = Abs( ldv.Angle( npv ) ) - PI/2.; |
393 | Standard_Real dangle = Abs( dang ); |
394 | if( dangle > Tolang ) |
395 | { |
396 | Standard_Real sinda = Abs( Sin( dangle ) ); |
397 | Standard_Real dif = Abs( sinda - Tol ); |
398 | if( dif < Tol ) |
399 | { |
400 | tolang = sinda * 2.; |
401 | newparams = Standard_True; |
402 | } |
403 | } |
404 | } |
405 | |
406 | nbint = 0; |
407 | IntAna_IntConicQuad inter(axec,P,tolang); |
408 | |
409 | if (inter.IsParallel()) { |
410 | // Le resultat de l intersection Plan-Cylindre est de type droite. |
411 | // il y a 1 ou 2 droites |
412 | |
413 | typeres = IntAna_Line; |
414 | omega.SetCoord(X-dist*A,Y-dist*B,Z-dist*C); |
415 | |
416 | if (Abs(Abs(dist)-radius) < Tol) |
417 | { |
418 | nbint = 1; |
419 | pt1.SetXYZ(omega); |
420 | |
421 | if( newparams ) |
422 | { |
423 | gp_XYZ omegaXYZ(X,Y,Z); |
424 | gp_XYZ omegaXYZtrnsl( omegaXYZ + 100.*axec.Direction().XYZ() ); |
425 | Standard_Real Xt,Yt,Zt,distt; |
426 | omegaXYZtrnsl.Coord(Xt,Yt,Zt); |
427 | distt = A*Xt + B*Yt + C*Zt + D; |
428 | gp_XYZ omega1( omegaXYZtrnsl.X()-distt*A, omegaXYZtrnsl.Y()-distt*B, omegaXYZtrnsl.Z()-distt*C ); |
429 | gp_Pnt ppt1; |
430 | ppt1.SetXYZ( omega1 ); |
431 | gp_Vec vv1(pt1,ppt1); |
432 | gp_Dir dd1( vv1 ); |
433 | dir1 = dd1; |
434 | } |
435 | else |
436 | dir1 = axec.Direction(); |
437 | } |
438 | else if (Abs(dist) < radius) |
439 | { |
440 | nbint = 2; |
441 | h = Sqrt(radius*radius - dist*dist); |
442 | axey = axec.Direction().XYZ().Crossed(normp); // axey est normalise |
443 | |
444 | pt1.SetXYZ(omega - h*axey); |
445 | pt2.SetXYZ(omega + h*axey); |
446 | |
447 | if( newparams ) |
448 | { |
449 | gp_XYZ omegaXYZ(X,Y,Z); |
450 | gp_XYZ omegaXYZtrnsl( omegaXYZ + 100.*axec.Direction().XYZ() ); |
451 | Standard_Real Xt,Yt,Zt,distt,ht; |
452 | omegaXYZtrnsl.Coord(Xt,Yt,Zt); |
453 | distt = A*Xt + B*Yt + C*Zt + D; |
454 | // ht = Sqrt(radius*radius - distt*distt); |
455 | Standard_Real anSqrtArg = radius*radius - distt*distt; |
456 | ht = (anSqrtArg > 0.) ? Sqrt(anSqrtArg) : 0.; |
457 | |
458 | gp_XYZ omega1( omegaXYZtrnsl.X()-distt*A, omegaXYZtrnsl.Y()-distt*B, omegaXYZtrnsl.Z()-distt*C ); |
459 | gp_Pnt ppt1,ppt2; |
460 | ppt1.SetXYZ( omega1 - ht*axey); |
461 | ppt2.SetXYZ( omega1 + ht*axey); |
462 | gp_Vec vv1(pt1,ppt1); |
463 | gp_Vec vv2(pt2,ppt2); |
464 | gp_Dir dd1( vv1 ); |
465 | gp_Dir dd2( vv2 ); |
466 | dir1 = dd1; |
467 | dir2 = dd2; |
468 | } |
469 | else |
470 | { |
471 | dir1 = axec.Direction(); |
472 | dir2 = axec.Direction(); |
473 | } |
474 | } |
475 | // else nbint = 0 |
476 | |
477 | // debug JAG : le nbint = 0 doit etre remplace par typeres = IntAna_Empty |
478 | // et ne pas etre seulement supprime... |
479 | |
480 | else { |
481 | typeres = IntAna_Empty; |
482 | } |
483 | } |
484 | else { // Il y a un point d intersection. C est le centre du cercle |
485 | // ou de l ellipse solution. |
486 | |
487 | nbint = 1; |
488 | axey = normp.Crossed(axec.Direction().XYZ()); |
489 | sint = axey.Modulus(); |
490 | |
491 | pt1 = inter.Point(1); |
492 | |
493 | if (sint < Tol/radius) { |
494 | |
495 | // on construit un cercle avec comme axes X et Y ceux du cylindre |
496 | typeres = IntAna_Circle; |
497 | |
498 | dir1 = axec.Direction(); // axe Z |
499 | dir2 = Cl.Position().XDirection(); |
500 | param1 = radius; |
501 | } |
502 | else { |
503 | |
504 | // on construit un ellipse |
505 | typeres = IntAna_Ellipse; |
506 | cost = Abs(axec.Direction().XYZ().Dot(normp)); |
507 | axex = axey.Crossed(normp); |
508 | |
509 | dir1.SetXYZ(normp); //Modif ds ce bloc |
510 | dir2.SetXYZ(axex); |
511 | |
512 | param1 = radius/cost; |
513 | param1bis = radius; |
514 | } |
515 | } |
516 | if(typeres == IntAna_Ellipse) { |
517 | if( param1>100000.0*param1bis |
518 | || param1bis>100000.0*param1) { |
519 | done = Standard_False; |
520 | return; |
521 | } |
522 | } |
523 | done = Standard_True; |
524 | } |
525 | //======================================================================= |
526 | //function : IntAna_QuadQuadGeo |
527 | //purpose : Pln Cone |
528 | //======================================================================= |
529 | IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Pln& P, |
530 | const gp_Cone& Co, |
531 | const Standard_Real Tolang, |
532 | const Standard_Real Tol) |
533 | : done(Standard_False), |
534 | nbint(0), |
535 | typeres(IntAna_Empty), |
536 | pt1(0,0,0), |
537 | pt2(0,0,0), |
538 | param1(0), |
539 | param2(0), |
540 | param1bis(0), |
541 | param2bis(0), |
542 | myCommonGen(Standard_False), |
543 | myPChar(0,0,0) |
544 | { |
545 | InitTolerances(); |
546 | Perform(P,Co,Tolang,Tol); |
547 | } |
548 | //======================================================================= |
549 | //function : Perform |
550 | //purpose : |
551 | //======================================================================= |
552 | void IntAna_QuadQuadGeo::Perform(const gp_Pln& P, |
553 | const gp_Cone& Co, |
554 | const Standard_Real Tolang, |
555 | const Standard_Real Tol) |
556 | { |
557 | |
558 | done = Standard_False; |
559 | nbint = 0; |
560 | |
561 | Standard_Real A,B,C,D; |
562 | Standard_Real X,Y,Z; |
563 | Standard_Real dist,sint,cost,sina,cosa,angl,costa; |
564 | Standard_Real dh; |
565 | gp_XYZ axex,axey; |
566 | |
567 | gp_Lin axec(Co.Axis()); |
568 | P.Coefficients(A,B,C,D); |
569 | gp_Pnt apex(Co.Apex()); |
570 | |
571 | apex.Coord(X,Y,Z); |
572 | dist = A*X + B*Y + C*Z + D; // distance signee sommet du cone/ Plan |
573 | |
574 | gp_XYZ normp = P.Axis().Direction().XYZ(); |
575 | if(P.Direct()==Standard_False) { //-- lbr le 14 jan 97 |
576 | normp.Reverse(); |
577 | } |
578 | |
579 | axey = normp.Crossed(Co.Axis().Direction().XYZ()); |
580 | axex = axey.Crossed(normp); |
581 | |
582 | |
583 | angl = Co.SemiAngle(); |
584 | |
585 | cosa = Cos(angl); |
586 | sina = Abs(Sin(angl)); |
587 | |
588 | |
589 | // Angle entre la normale au plan et l axe du cone, ramene entre 0. et PI/2. |
590 | |
591 | sint = axey.Modulus(); |
592 | cost = Abs(Co.Axis().Direction().XYZ().Dot(normp)); |
593 | |
594 | // Le calcul de costa permet de determiner si le plan contient |
595 | // un generatrice du cone : on calcul Sin((PI/2. - t) - angl) |
596 | |
597 | costa = cost*cosa - sint*sina; // sin((PI/2 -t)-angl)=cos(t+angl) |
598 | // avec t ramene entre 0 et pi/2. |
599 | |
600 | if (Abs(dist) < Tol) { |
601 | // on considere que le plan contient le sommet du cone. |
602 | // les solutions possibles sont donc : 1 point, 1 droite, 2 droites |
603 | // selon l inclinaison du plan. |
604 | |
605 | if (Abs(costa) < Tolang) { // plan parallele a la generatrice |
606 | typeres = IntAna_Line; |
607 | nbint = 1; |
608 | gp_XYZ ptonaxe(apex.XYZ() + 10.*(Co.Axis().Direction().XYZ())); |
609 | // point sur l axe du cone cote z positif |
610 | |
611 | dist = A*ptonaxe.X() + B*ptonaxe.Y() + C*ptonaxe.Z() + D; |
612 | ptonaxe = ptonaxe - dist*normp; |
613 | pt1 = apex; |
614 | dir1.SetXYZ(ptonaxe - pt1.XYZ()); |
615 | } |
616 | else if (cost < sina) { // plan "interieur" au cone |
617 | typeres = IntAna_Line; |
618 | nbint = 2; |
619 | pt1 = apex; |
620 | pt2 = apex; |
621 | dh = Sqrt(sina*sina-cost*cost)/cosa; |
622 | dir1.SetXYZ(axex + dh*axey); |
623 | dir2.SetXYZ(axex - dh*axey); |
624 | } |
625 | else { // plan "exterieur" au cone |
626 | typeres = IntAna_Point; |
627 | nbint = 1; |
628 | pt1 = apex; |
629 | } |
630 | } |
631 | else { |
632 | // Solutions possibles : cercle, ellipse, parabole, hyperbole selon |
633 | // l inclinaison du plan. |
634 | Standard_Real deltacenter, distance; |
635 | |
636 | if (cost < Tolang) { |
637 | // Le plan contient la direction de l axe du cone. La solution est |
638 | // l hyperbole |
639 | typeres = IntAna_Hyperbola; |
640 | nbint = 2; |
641 | pt1.SetXYZ(apex.XYZ()-dist*normp); |
642 | pt2 = pt1; |
643 | dir1=normp; |
644 | dir2.SetXYZ(axex); |
645 | param1 = param2 = Abs(dist/Tan(angl)); |
646 | param1bis = param2bis = Abs(dist); |
647 | } |
648 | else { |
649 | |
650 | IntAna_IntConicQuad inter(axec,P,Tolang); // on a necessairement 1 point. |
651 | |
652 | gp_Pnt center(inter.Point(1)); |
653 | |
654 | // En fonction de la position de l intersection par rapport au sommet |
655 | // du cone, on change l axe x en -x et y en -y. Le parametre du sommet |
656 | // sur axec est negatif (voir definition du cone) |
657 | |
658 | distance = apex.Distance(center); |
659 | |
660 | if (inter.ParamOnConic(1) + Co.RefRadius()/Tan(angl) < 0.) { |
661 | axex.Reverse(); |
662 | axey.Reverse(); |
663 | } |
664 | |
665 | if (Abs(costa) < Tolang) { // plan parallele a une generatrice |
666 | typeres = IntAna_Parabola; |
667 | nbint = 1; |
668 | deltacenter = distance/2./cosa; |
669 | axex.Normalize(); |
670 | pt1.SetXYZ(center.XYZ()-deltacenter*axex); |
671 | dir1 = normp; |
672 | dir2.SetXYZ(axex); |
673 | param1 = deltacenter*sina*sina; |
674 | } |
675 | else if (sint < Tolang) { // plan perpendiculaire a l axe |
676 | typeres = IntAna_Circle; |
677 | nbint = 1; |
678 | pt1 = center; |
679 | dir1 = Co.Position().Direction(); |
680 | dir2 = Co.Position().XDirection(); |
681 | param1 = apex.Distance(center)*Abs(Tan(angl)); |
682 | } |
683 | else if (cost < sina ) { |
684 | typeres = IntAna_Hyperbola; |
685 | nbint = 2; |
686 | axex.Normalize(); |
687 | |
688 | deltacenter = sint*sina*sina*distance/(sina*sina - cost*cost); |
689 | pt1.SetXYZ(center.XYZ() - deltacenter*axex); |
690 | pt2 = pt1; |
691 | dir1 = normp; |
692 | dir2.SetXYZ(axex); |
693 | param1 = param2 = cost*sina*cosa*distance /(sina*sina-cost*cost); |
694 | param1bis = param2bis = cost*sina*distance / Sqrt(sina*sina-cost*cost); |
695 | |
696 | } |
697 | else { // on a alors cost > sina |
698 | typeres = IntAna_Ellipse; |
699 | nbint = 1; |
700 | Standard_Real radius = cost*sina*cosa*distance/(cost*cost-sina*sina); |
701 | deltacenter = sint*sina*sina*distance/(cost*cost-sina*sina); |
702 | axex.Normalize(); |
703 | pt1.SetXYZ(center.XYZ() + deltacenter*axex); |
704 | dir1 = normp; |
705 | dir2.SetXYZ(axex); |
706 | param1 = radius; |
707 | param1bis = cost*sina*distance/ Sqrt(cost*cost - sina*sina); |
708 | } |
709 | } |
710 | } |
711 | |
712 | //-- On a du mal a gerer plus loin (Value ProjLib, Params ... ) |
713 | //-- des hyperboles trop bizarres |
714 | //-- On retourne False -> Traitement par biparametree |
715 | static Standard_Real EllipseLimit = 1.0E+9; //OCC513(apo) 1000000 |
716 | static Standard_Real HyperbolaLimit = 2.0E+6; //OCC537(apo) 50000 |
717 | if(typeres==IntAna_Ellipse && nbint>=1) { |
718 | if(Abs(param1) > EllipseLimit || Abs(param1bis) > EllipseLimit) { |
719 | done=Standard_False; |
720 | return; |
721 | } |
722 | } |
723 | if(typeres==IntAna_Hyperbola && nbint>=2) { |
724 | if(Abs(param2) > HyperbolaLimit || Abs(param2bis) > HyperbolaLimit) { |
725 | done = Standard_False; |
726 | return; |
727 | } |
728 | } |
729 | if(typeres==IntAna_Hyperbola && nbint>=1) { |
730 | if(Abs(param1) > HyperbolaLimit || Abs(param1bis) > HyperbolaLimit) { |
731 | done=Standard_False; |
732 | return; |
733 | } |
734 | } |
735 | |
736 | done = Standard_True; |
737 | } |
738 | |
739 | //======================================================================= |
740 | //function : IntAna_QuadQuadGeo |
741 | //purpose : Pln Sphere |
742 | //======================================================================= |
743 | IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Pln& P, |
744 | const gp_Sphere& S) |
745 | : done(Standard_False), |
746 | nbint(0), |
747 | typeres(IntAna_Empty), |
748 | pt1(0,0,0), |
749 | pt2(0,0,0), |
750 | param1(0), |
751 | param2(0), |
752 | param1bis(0), |
753 | param2bis(0), |
754 | myCommonGen(Standard_False), |
755 | myPChar(0,0,0) |
756 | { |
757 | InitTolerances(); |
758 | Perform(P,S); |
759 | } |
760 | //======================================================================= |
761 | //function : Perform |
762 | //purpose : |
763 | //======================================================================= |
764 | void IntAna_QuadQuadGeo::Perform( const gp_Pln& P |
765 | ,const gp_Sphere& S) |
766 | { |
767 | |
768 | done = Standard_False; |
769 | Standard_Real A,B,C,D,dist, radius; |
770 | Standard_Real X,Y,Z; |
771 | |
772 | nbint = 0; |
773 | // debug JAG : on met typeres = IntAna_Empty par defaut... |
774 | typeres = IntAna_Empty; |
775 | |
776 | P.Coefficients(A,B,C,D); |
777 | S.Location().Coord(X,Y,Z); |
778 | radius = S.Radius(); |
779 | |
780 | dist = A * X + B * Y + C * Z + D; |
781 | |
782 | if (Abs( Abs(dist) - radius) < Epsilon(radius)) { |
783 | // on a une seule solution : le point projection du centre de la sphere |
784 | // sur le plan |
785 | nbint = 1; |
786 | typeres = IntAna_Point; |
787 | pt1.SetCoord(X - dist*A, Y - dist*B, Z - dist*C); |
788 | } |
789 | else if (Abs(dist) < radius) { |
790 | // on a un cercle solution |
791 | nbint = 1; |
792 | typeres = IntAna_Circle; |
793 | pt1.SetCoord(X - dist*A, Y - dist*B, Z - dist*C); |
794 | dir1 = P.Axis().Direction(); |
795 | if(P.Direct()==Standard_False) dir1.Reverse(); |
796 | dir2 = P.Position().XDirection(); |
797 | param1 = Sqrt(radius*radius - dist*dist); |
798 | } |
799 | param2bis=0.0; //-- pour eviter param2bis not used .... |
800 | done = Standard_True; |
801 | } |
802 | |
803 | //======================================================================= |
804 | //function : IntAna_QuadQuadGeo |
805 | //purpose : Cylinder - Cylinder |
806 | //======================================================================= |
807 | IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Cylinder& Cyl1, |
808 | const gp_Cylinder& Cyl2, |
809 | const Standard_Real Tol) |
810 | : done(Standard_False), |
811 | nbint(0), |
812 | typeres(IntAna_Empty), |
813 | pt1(0,0,0), |
814 | pt2(0,0,0), |
815 | param1(0), |
816 | param2(0), |
817 | param1bis(0), |
818 | param2bis(0), |
819 | myCommonGen(Standard_False), |
820 | myPChar(0,0,0) |
821 | { |
822 | InitTolerances(); |
823 | Perform(Cyl1,Cyl2,Tol); |
824 | } |
825 | //======================================================================= |
826 | //function : Perform |
827 | //purpose : |
828 | //======================================================================= |
829 | void IntAna_QuadQuadGeo::Perform(const gp_Cylinder& Cyl1, |
830 | const gp_Cylinder& Cyl2, |
831 | const Standard_Real Tol) |
832 | { |
833 | done=Standard_True; |
834 | //---------------------------- Parallel axes ------------------------- |
835 | AxeOperator A1A2(Cyl1.Axis(),Cyl2.Axis()); |
836 | Standard_Real R1=Cyl1.Radius(); |
837 | Standard_Real R2=Cyl2.Radius(); |
838 | Standard_Real RmR, RmR_Relative; |
839 | RmR=(R1>R2)? (R1-R2) : (R2-R1); |
840 | { |
841 | Standard_Real Rmax, Rmin; |
842 | Rmax=(R1>R2)? R1 : R2; |
843 | Rmin=(R1>R2)? R2 : R1; |
844 | RmR_Relative=RmR/Rmax; |
845 | } |
846 | |
847 | Standard_Real DistA1A2=A1A2.Distance(); |
848 | |
849 | if(A1A2.Parallel()) { |
850 | if(DistA1A2<=Tol) { |
851 | if(RmR<=Tol) { |
852 | typeres=IntAna_Same; |
853 | } |
854 | else { |
855 | typeres=IntAna_Empty; |
856 | } |
857 | } |
858 | else { //-- DistA1A2 > Tol |
859 | gp_Pnt P1=Cyl1.Location(); |
860 | gp_Pnt P2t=Cyl2.Location(); |
861 | gp_Pnt P2; |
862 | //-- P2t is projected on the plane (P1,DirCylX,DirCylY) |
863 | gp_Dir DirCyl = Cyl1.Position().Direction(); |
864 | Standard_Real ProjP2OnDirCyl1=gp_Vec(DirCyl).Dot(gp_Vec(P1,P2t)); |
865 | |
866 | P2.SetCoord( P2t.X() - ProjP2OnDirCyl1*DirCyl.X() |
867 | ,P2t.Y() - ProjP2OnDirCyl1*DirCyl.Y() |
868 | ,P2t.Z() - ProjP2OnDirCyl1*DirCyl.Z()); |
869 | //-- |
870 | Standard_Real R1pR2=R1+R2; |
871 | if(DistA1A2>(R1pR2+Tol)) { |
872 | typeres=IntAna_Empty; |
873 | nbint=0; |
874 | } |
875 | else if(DistA1A2>(R1pR2)) { |
876 | //-- 1 Tangent line -------------------------------------OK |
877 | typeres=IntAna_Line; |
878 | |
879 | nbint=1; |
880 | dir1=DirCyl; |
881 | Standard_Real R1_R1pR2=R1/R1pR2; |
882 | pt1.SetCoord( P1.X() + R1_R1pR2 * (P2.X()-P1.X()) |
883 | ,P1.Y() + R1_R1pR2 * (P2.Y()-P1.Y()) |
884 | ,P1.Z() + R1_R1pR2 * (P2.Z()-P1.Z())); |
885 | |
886 | } |
887 | else if(DistA1A2>RmR) { |
888 | //-- 2 lines ---------------------------------------------OK |
889 | typeres=IntAna_Line; |
890 | nbint=2; |
891 | dir1=DirCyl; |
892 | gp_Vec P1P2(P1,P2); |
893 | gp_Dir DirA1A2=gp_Dir(P1P2); |
894 | gp_Dir Ortho_dir1_P1P2 = dir1.Crossed(DirA1A2); |
895 | dir2=dir1; |
896 | Standard_Real Alpha=0.5*(R1*R1-R2*R2+DistA1A2*DistA1A2)/(DistA1A2); |
897 | |
898 | // Standard_Real Beta = Sqrt(R1*R1-Alpha*Alpha); |
899 | Standard_Real anSqrtArg = R1*R1-Alpha*Alpha; |
900 | Standard_Real Beta = (anSqrtArg > 0.) ? Sqrt(anSqrtArg) : 0.; |
901 | |
902 | if((Beta+Beta)<Tol) { |
903 | nbint=1; |
904 | pt1.SetCoord( P1.X() + Alpha*DirA1A2.X() |
905 | ,P1.Y() + Alpha*DirA1A2.Y() |
906 | ,P1.Z() + Alpha*DirA1A2.Z()); |
907 | } |
908 | else { |
909 | pt1.SetCoord( P1.X() + Alpha*DirA1A2.X() + Beta*Ortho_dir1_P1P2.X() |
910 | ,P1.Y() + Alpha*DirA1A2.Y() + Beta*Ortho_dir1_P1P2.Y() |
911 | ,P1.Z() + Alpha*DirA1A2.Z() + Beta*Ortho_dir1_P1P2.Z() ); |
912 | |
913 | pt2.SetCoord( P1.X() + Alpha*DirA1A2.X() - Beta*Ortho_dir1_P1P2.X() |
914 | ,P1.Y() + Alpha*DirA1A2.Y() - Beta*Ortho_dir1_P1P2.Y() |
915 | ,P1.Z() + Alpha*DirA1A2.Z() - Beta*Ortho_dir1_P1P2.Z()); |
916 | } |
917 | } |
918 | else if(DistA1A2>(RmR-Tol)) { |
919 | //-- 1 Tangent ------------------------------------------OK |
920 | typeres=IntAna_Line; |
921 | nbint=1; |
922 | dir1=DirCyl; |
923 | Standard_Real R1_RmR=R1/RmR; |
924 | |
925 | if(R1 < R2) R1_RmR = -R1_RmR; |
926 | |
927 | pt1.SetCoord( P1.X() + R1_RmR * (P2.X()-P1.X()) |
928 | ,P1.Y() + R1_RmR * (P2.Y()-P1.Y()) |
929 | ,P1.Z() + R1_RmR * (P2.Z()-P1.Z())); |
930 | } |
931 | else { |
932 | nbint=0; |
933 | typeres=IntAna_Empty; |
934 | } |
935 | } |
936 | } |
937 | else { //-- No Parallel Axis ---------------------------------OK |
938 | if((RmR_Relative<=myEPSILON_CYLINDER_DELTA_RADIUS) |
939 | && (DistA1A2 <= myEPSILON_CYLINDER_DELTA_DISTANCE)) { |
940 | //-- PI/2 between the two axis and Intersection |
941 | //-- and identical radius |
942 | typeres=IntAna_Ellipse; |
943 | nbint=2; |
944 | gp_Dir DirCyl1=Cyl1.Position().Direction(); |
945 | gp_Dir DirCyl2=Cyl2.Position().Direction(); |
946 | pt1=pt2=A1A2.PtIntersect(); |
947 | |
948 | Standard_Real A=DirCyl1.Angle(DirCyl2); |
949 | Standard_Real B; |
950 | B=Abs(Sin(0.5*(PI-A))); |
951 | A=Abs(Sin(0.5*A)); |
952 | |
953 | if(A==0.0 || B==0.0) { |
954 | typeres=IntAna_Same; |
955 | return; |
956 | } |
957 | |
958 | |
959 | gp_Vec dircyl1(DirCyl1);gp_Vec dircyl2(DirCyl2); |
960 | dir1 = gp_Dir(dircyl1.Added(dircyl2)); |
961 | dir2 = gp_Dir(dircyl1.Subtracted(dircyl2)); |
962 | |
963 | param2 = Cyl1.Radius() / A; |
964 | param1 = Cyl1.Radius() / B; |
965 | param2bis= param1bis = Cyl1.Radius(); |
966 | if(param1 < param1bis) { |
967 | A=param1; param1=param1bis; param1bis=A; |
968 | } |
969 | if(param2 < param2bis) { |
970 | A=param2; param2=param2bis; param2bis=A; |
971 | } |
972 | } |
973 | else { |
974 | if(Abs(DistA1A2-Cyl1.Radius()-Cyl2.Radius())<Tol) { |
975 | typeres = IntAna_Point; |
976 | Standard_Real d,p1,p2; |
977 | |
978 | gp_Dir D1 = Cyl1.Axis().Direction(); |
979 | gp_Dir D2 = Cyl2.Axis().Direction(); |
980 | A1A2.Distance(d,p1,p2); |
981 | gp_Pnt P = Cyl1.Axis().Location(); |
982 | gp_Pnt P1(P.X() - p1*D1.X(), |
983 | P.Y() - p1*D1.Y(), |
984 | P.Z() - p1*D1.Z()); |
985 | P = Cyl2.Axis().Location(); |
986 | gp_Pnt P2(P.X() - p2*D2.X(), |
987 | P.Y() - p2*D2.Y(), |
988 | P.Z() - p2*D2.Z()); |
989 | gp_Vec P1P2(P1,P2); |
990 | D1=gp_Dir(P1P2); |
991 | p1=Cyl1.Radius(); |
992 | pt1.SetCoord(P1.X() + p1*D1.X(), |
993 | P1.Y() + p1*D1.Y(), |
994 | P1.Z() + p1*D1.Z()); |
995 | nbint = 1; |
996 | } |
997 | else { |
998 | typeres=IntAna_NoGeometricSolution; |
999 | } |
1000 | } |
1001 | } |
1002 | } |
1003 | //======================================================================= |
1004 | //function : IntAna_QuadQuadGeo |
1005 | //purpose : Cylinder - Cone |
1006 | //======================================================================= |
1007 | IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Cylinder& Cyl, |
1008 | const gp_Cone& Con, |
1009 | const Standard_Real Tol) |
1010 | : done(Standard_False), |
1011 | nbint(0), |
1012 | typeres(IntAna_Empty), |
1013 | pt1(0,0,0), |
1014 | pt2(0,0,0), |
1015 | param1(0), |
1016 | param2(0), |
1017 | param1bis(0), |
1018 | param2bis(0), |
1019 | myCommonGen(Standard_False), |
1020 | myPChar(0,0,0) |
1021 | { |
1022 | InitTolerances(); |
1023 | Perform(Cyl,Con,Tol); |
1024 | } |
1025 | //======================================================================= |
1026 | //function : Perform |
1027 | //purpose : |
1028 | //======================================================================= |
1029 | void IntAna_QuadQuadGeo::Perform(const gp_Cylinder& Cyl, |
1030 | const gp_Cone& Con, |
1031 | const Standard_Real ) |
1032 | { |
1033 | done=Standard_True; |
1034 | AxeOperator A1A2(Cyl.Axis(),Con.Axis()); |
1035 | if(A1A2.Same()) { |
1036 | gp_Pnt Pt=Con.Apex(); |
1037 | Standard_Real dist=Cyl.Radius()/(Tan(Con.SemiAngle())); |
1038 | gp_Dir dir=Cyl.Position().Direction(); |
1039 | pt1.SetCoord( Pt.X() + dist*dir.X() |
1040 | ,Pt.Y() + dist*dir.Y() |
1041 | ,Pt.Z() + dist*dir.Z()); |
1042 | pt2.SetCoord( Pt.X() - dist*dir.X() |
1043 | ,Pt.Y() - dist*dir.Y() |
1044 | ,Pt.Z() - dist*dir.Z()); |
1045 | dir1=dir2=dir; |
1046 | param1=param2=Cyl.Radius(); |
1047 | nbint=2; |
1048 | typeres=IntAna_Circle; |
1049 | |
1050 | } |
1051 | else { |
1052 | typeres=IntAna_NoGeometricSolution; |
1053 | } |
1054 | } |
1055 | //======================================================================= |
1056 | //function : |
1057 | //purpose : Cylinder - Sphere |
1058 | //======================================================================= |
1059 | IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Cylinder& Cyl, |
1060 | const gp_Sphere& Sph, |
1061 | const Standard_Real Tol) |
1062 | : done(Standard_False), |
1063 | nbint(0), |
1064 | typeres(IntAna_Empty), |
1065 | pt1(0,0,0), |
1066 | pt2(0,0,0), |
1067 | param1(0), |
1068 | param2(0), |
1069 | param1bis(0), |
1070 | param2bis(0), |
1071 | myCommonGen(Standard_False), |
1072 | myPChar(0,0,0) |
1073 | { |
1074 | InitTolerances(); |
1075 | Perform(Cyl,Sph,Tol); |
1076 | } |
1077 | //======================================================================= |
1078 | //function : Perform |
1079 | //purpose : |
1080 | //======================================================================= |
1081 | void IntAna_QuadQuadGeo::Perform( const gp_Cylinder& Cyl |
1082 | ,const gp_Sphere& Sph |
1083 | ,const Standard_Real) |
1084 | { |
1085 | done=Standard_True; |
1086 | gp_Pnt Pt=Sph.Location(); |
1087 | AxeOperator A1A2(Cyl.Axis(),Sph.Position().Axis()); |
1088 | if((A1A2.Intersect() && Pt.Distance(A1A2.PtIntersect())==0.0 ) |
1089 | || (A1A2.Same())) { |
1090 | if(Sph.Radius() < Cyl.Radius()) { |
1091 | typeres = IntAna_Empty; |
1092 | } |
1093 | else { |
1094 | Standard_Real dist=Sqrt( Sph.Radius() * Sph.Radius() - Cyl.Radius() * Cyl.Radius() ); |
1095 | gp_Dir dir=Cyl.Position().Direction(); |
1096 | dir1 = dir2 = dir; |
1097 | typeres=IntAna_Circle; |
1098 | pt1.SetCoord( Pt.X() + dist*dir.X() |
1099 | ,Pt.Y() + dist*dir.Y() |
1100 | ,Pt.Z() + dist*dir.Z()); |
1101 | nbint=1; |
1102 | param1 = Cyl.Radius(); |
1103 | if(dist>RealEpsilon()) { |
1104 | pt2.SetCoord( Pt.X() - dist*dir.X() |
1105 | ,Pt.Y() - dist*dir.Y() |
1106 | ,Pt.Z() - dist*dir.Z()); |
1107 | param2=Cyl.Radius(); |
1108 | nbint=2; |
1109 | } |
1110 | } |
1111 | } |
1112 | else { |
1113 | typeres=IntAna_NoGeometricSolution; |
1114 | } |
1115 | } |
1116 | |
1117 | //======================================================================= |
1118 | //function : IntAna_QuadQuadGeo |
1119 | //purpose : Cone - Cone |
1120 | //======================================================================= |
1121 | IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Cone& Con1, |
1122 | const gp_Cone& Con2, |
1123 | const Standard_Real Tol) |
1124 | : done(Standard_False), |
1125 | nbint(0), |
1126 | typeres(IntAna_Empty), |
1127 | pt1(0,0,0), |
1128 | pt2(0,0,0), |
1129 | param1(0), |
1130 | param2(0), |
1131 | param1bis(0), |
1132 | param2bis(0), |
1133 | myCommonGen(Standard_False), |
1134 | myPChar(0,0,0) |
1135 | { |
1136 | InitTolerances(); |
1137 | Perform(Con1,Con2,Tol); |
1138 | } |
1139 | // |
1140 | //======================================================================= |
1141 | //function : Perform |
1142 | //purpose : |
1143 | //======================================================================= |
1144 | void IntAna_QuadQuadGeo::Perform(const gp_Cone& Con1, |
1145 | const gp_Cone& Con2, |
1146 | const Standard_Real Tol) |
1147 | { |
1148 | done=Standard_True; |
1149 | // |
1150 | Standard_Real tg1, tg2, aDA1A2, aTol2; |
1151 | gp_Pnt aPApex1, aPApex2; |
1152 | // |
1153 | tg1=Tan(Con1.SemiAngle()); |
1154 | tg2=Tan(Con2.SemiAngle()); |
1155 | |
1156 | if((tg1 * tg2) < 0.) { |
1157 | tg2 = -tg2; |
1158 | } |
1159 | // |
1160 | //modified by NIZNHY-PKV Thu Dec 1 16:49:47 2005f |
1161 | aTol2=Tol*Tol; |
1162 | aPApex1=Con1.Apex(); |
1163 | aPApex2=Con2.Apex(); |
1164 | aDA1A2=aPApex1.SquareDistance(aPApex2); |
1165 | //modified by NIZNHY-PKV Wed Nov 30 10:17:05 2005t |
1166 | // |
1167 | AxeOperator A1A2(Con1.Axis(),Con2.Axis()); |
1168 | // |
1169 | // 1 |
1170 | if(A1A2.Same()) { |
1171 | //-- two circles |
1172 | Standard_Real x; |
1173 | gp_Pnt P=Con1.Apex(); |
1174 | gp_Dir D=Con1.Position().Direction(); |
1175 | Standard_Real d=gp_Vec(D).Dot(gp_Vec(P,Con2.Apex())); |
1176 | |
1177 | if(Abs(tg1-tg2)>myEPSILON_ANGLE_CONE) { |
1178 | x=(d*tg2)/(tg1+tg2); |
1179 | pt1.SetCoord( P.X() + x*D.X() |
1180 | ,P.Y() + x*D.Y() |
1181 | ,P.Z() + x*D.Z()); |
1182 | param1=Abs(x*tg1); |
1183 | |
1184 | x=(d*tg2)/(tg2-tg1); |
1185 | pt2.SetCoord( P.X() + x*D.X() |
1186 | ,P.Y() + x*D.Y() |
1187 | ,P.Z() + x*D.Z()); |
1188 | param2=Abs(x*tg1); |
1189 | dir1 = dir2 = D; |
1190 | nbint=2; |
1191 | typeres=IntAna_Circle; |
1192 | } |
1193 | else { |
1194 | if (fabs(d)<1.e-10) { |
1195 | typeres=IntAna_Same; |
1196 | } |
1197 | else { |
1198 | typeres=IntAna_Circle; |
1199 | nbint=1; |
1200 | x=d*0.5; |
1201 | pt1.SetCoord( P.X() + x*D.X() |
1202 | ,P.Y() + x*D.Y() |
1203 | ,P.Z() + x*D.Z()); |
1204 | param1 = Abs(x * tg1); |
1205 | dir1 = D; |
1206 | } |
1207 | } |
1208 | } //-- fin A1A2.Same |
1209 | // 2 |
1210 | else if((Abs(tg1-tg2)<myEPSILON_ANGLE_CONE) && (A1A2.Parallel())) { |
1211 | //-- voir AnVer12mai98 |
1212 | Standard_Real DistA1A2=A1A2.Distance(); |
1213 | gp_Dir DA1=Con1.Position().Direction(); |
1214 | gp_Vec O1O2(Con1.Apex(),Con2.Apex()); |
1215 | Standard_Real O1O2_DA1=gp_Vec(DA1).Dot(O1O2); |
1216 | |
1217 | gp_Vec O1_Proj_A2(O1O2.X()-O1O2_DA1*DA1.X(), |
1218 | O1O2.Y()-O1O2_DA1*DA1.Y(), |
1219 | O1O2.Z()-O1O2_DA1*DA1.Z()); |
1220 | gp_Dir DB1=gp_Dir(O1_Proj_A2); |
1221 | |
1222 | Standard_Real yO1O2=O1O2.Dot(gp_Vec(DA1)); |
1223 | Standard_Real ABSTG1 = Abs(tg1); |
1224 | Standard_Real X2 = (DistA1A2/ABSTG1 - yO1O2)*0.5; |
1225 | Standard_Real X1 = X2+yO1O2; |
1226 | |
1227 | gp_Pnt P1(Con1.Apex().X() + X1*( DA1.X() + ABSTG1*DB1.X()), |
1228 | Con1.Apex().Y() + X1*( DA1.Y() + ABSTG1*DB1.Y()), |
1229 | Con1.Apex().Z() + X1*( DA1.Z() + ABSTG1*DB1.Z())); |
1230 | |
1231 | gp_Pnt MO1O2(0.5*(Con1.Apex().X()+Con2.Apex().X()), |
1232 | 0.5*(Con1.Apex().Y()+Con2.Apex().Y()), |
1233 | 0.5*(Con1.Apex().Z()+Con2.Apex().Z())); |
1234 | gp_Vec P1MO1O2(P1,MO1O2); |
1235 | |
1236 | gp_Dir DA1_X_DB1=DA1.Crossed(DB1); |
1237 | gp_Dir OrthoPln = DA1_X_DB1.Crossed(gp_Dir(P1MO1O2)); |
1238 | |
1239 | IntAna_QuadQuadGeo INTER_QUAD_PLN(gp_Pln(P1,OrthoPln),Con1,Tol,Tol); |
1240 | if(INTER_QUAD_PLN.IsDone()) { |
1241 | switch(INTER_QUAD_PLN.TypeInter()) { |
1242 | case IntAna_Ellipse: { |
1243 | typeres=IntAna_Ellipse; |
1244 | gp_Elips E=INTER_QUAD_PLN.Ellipse(1); |
1245 | pt1 = E.Location(); |
1246 | dir1 = E.Position().Direction(); |
1247 | dir2 = E.Position().XDirection(); |
1248 | param1 = E.MajorRadius(); |
1249 | param1bis = E.MinorRadius(); |
1250 | nbint = 1; |
1251 | break; |
1252 | } |
1253 | case IntAna_Circle: { |
1254 | typeres=IntAna_Circle; |
1255 | gp_Circ C=INTER_QUAD_PLN.Circle(1); |
1256 | pt1 = C.Location(); |
1257 | dir1 = C.Position().XDirection(); |
1258 | dir2 = C.Position().YDirection(); |
1259 | param1 = C.Radius(); |
1260 | nbint = 1; |
1261 | break; |
1262 | } |
1263 | case IntAna_Hyperbola: { |
1264 | typeres=IntAna_Hyperbola; |
1265 | gp_Hypr H=INTER_QUAD_PLN.Hyperbola(1); |
1266 | pt1 = pt2 = H.Location(); |
1267 | dir1 = H.Position().Direction(); |
1268 | dir2 = H.Position().XDirection(); |
1269 | param1 = param2 = H.MajorRadius(); |
1270 | param1bis = param2bis = H.MinorRadius(); |
1271 | nbint = 2; |
1272 | break; |
1273 | } |
1274 | case IntAna_Line: { |
1275 | typeres=IntAna_Line; |
1276 | gp_Lin H=INTER_QUAD_PLN.Line(1); |
1277 | pt1 = pt2 = H.Location(); |
1278 | dir1 = dir2 = H.Position().Direction(); |
1279 | param1 = param2 = 0.0; |
1280 | param1bis = param2bis = 0.0; |
1281 | nbint = 2; |
1282 | break; |
1283 | } |
1284 | default: |
1285 | typeres=IntAna_NoGeometricSolution; |
1286 | } |
1287 | } |
1288 | }// else if((Abs(tg1-tg2)<EPSILON_ANGLE_CONE) && (A1A2.Parallel())) |
1289 | //modified by NIZNHY-PKV Wed Nov 30 10:12:39 2005f |
1290 | // 3 |
1291 | else if (aDA1A2<aTol2) { |
1292 | // |
1293 | // by NIZNHY-PKV Thu Dec 1 2005 |
1294 | // |
1295 | // When apices are coinsided there can be 3 possible cases |
1296 | // 3.1 - empty solution (iRet=0) |
1297 | // 3.2 - one line when cone1 touches cone2 (iRet=1) |
1298 | // 3.3 - two lines when cone1 intersects cone2 (iRet=2) |
1299 | // |
1300 | Standard_Integer iRet; |
1301 | Standard_Real aGamma, aBeta1, aBeta2; |
1302 | Standard_Real aD1, aR1, aTgBeta1, aTgBeta2, aHalfPI; |
1303 | Standard_Real aCosGamma, aSinGamma, aDx, aR2, aRD2, aD2; |
1304 | gp_Pnt2d aP0, aPA1, aP1, aPA2; |
1305 | gp_Vec2d aVAx2; |
1306 | gp_Ax1 aAx1, aAx2; |
1307 | // |
1308 | // Preliminary analysis. Determination of iRet |
1309 | // |
1310 | iRet=0; |
1311 | aHalfPI=0.5*PI; |
1312 | aD1=1.; |
1313 | aPA1.SetCoord(aD1, 0.); |
1314 | aP0.SetCoord(0., 0.); |
1315 | // |
1316 | aAx1=Con1.Axis(); |
1317 | aAx2=Con2.Axis(); |
1318 | aGamma=aAx1.Angle(aAx2); |
1319 | if (aGamma>aHalfPI){ |
1320 | aGamma=PI-aGamma; |
1321 | } |
1322 | aCosGamma=Cos(aGamma); |
1323 | aSinGamma=Sin(aGamma); |
1324 | // |
1325 | aBeta1=Con1.SemiAngle(); |
1326 | aTgBeta1=Tan(aBeta1); |
1327 | aTgBeta1=Abs(aTgBeta1); |
1328 | // |
1329 | aBeta2=Con2.SemiAngle(); |
1330 | aTgBeta2=Tan(aBeta2); |
1331 | aTgBeta2=Abs(aTgBeta2); |
1332 | // |
1333 | aR1=aD1*aTgBeta1; |
1334 | aP1.SetCoord(aD1, aR1); |
1335 | // |
1336 | // PA2 |
1337 | aVAx2.SetCoord(aCosGamma, aSinGamma); |
1338 | gp_Dir2d aDAx2(aVAx2); |
1339 | gp_Lin2d aLAx2(aP0, aDAx2); |
1340 | // |
1341 | gp_Vec2d aV(aP0, aP1); |
1342 | aDx=aVAx2.Dot(aV); |
1343 | aPA2=aP0.Translated(aDx*aDAx2); |
1344 | // |
1345 | // aR2 |
1346 | aDx=aPA2.Distance(aP0); |
1347 | aR2=aDx*aTgBeta2; |
1348 | // |
1349 | // aRD2 |
1350 | aRD2=aPA2.Distance(aP1); |
1351 | // |
1352 | if (aRD2>(aR2+Tol)) { |
1353 | iRet=0; |
1354 | //printf(" * iRet=0 => IntAna_Empty\n"); |
1355 | typeres=IntAna_Empty; //nothing |
1356 | } |
1357 | // |
1358 | iRet=1; //touch case => 1 line |
1359 | if (aRD2<(aR2-Tol)) { |
1360 | iRet=2;//intersection => couple of lines |
1361 | } |
1362 | // |
1363 | // Finding the solution in 3D |
1364 | // |
1365 | Standard_Real aDa; |
1366 | gp_Pnt aQApex1, aQA1, aQA2, aQX, aQX1, aQX2; |
1367 | gp_Dir aD3Ax1, aD3Ax2; |
1368 | gp_Lin aLin; |
1369 | IntAna_QuadQuadGeo aIntr; |
1370 | // |
1371 | aQApex1=Con1.Apex(); |
1372 | aD3Ax1=aAx1.Direction(); |
1373 | aQA1.SetCoord(aQApex1.X()+aD1*aD3Ax1.X(), |
1374 | aQApex1.Y()+aD1*aD3Ax1.Y(), |
1375 | aQApex1.Z()+aD1*aD3Ax1.Z()); |
1376 | // |
1377 | aDx=aD3Ax1.Dot(aAx2.Direction()); |
1378 | if (aDx<0.) { |
1379 | aAx2.Reverse(); |
1380 | } |
1381 | aD3Ax2=aAx2.Direction(); |
1382 | // |
1383 | aD2=aD1*sqrt((1.+aTgBeta1*aTgBeta1)/(1.+aTgBeta2*aTgBeta2)); |
1384 | // |
1385 | aQA2.SetCoord(aQApex1.X()+aD2*aD3Ax2.X(), |
1386 | aQApex1.Y()+aD2*aD3Ax2.Y(), |
1387 | aQApex1.Z()+aD2*aD3Ax2.Z()); |
1388 | // |
1389 | gp_Pln aPln1(aQA1, aD3Ax1); |
1390 | gp_Pln aPln2(aQA2, aD3Ax2); |
1391 | // |
1392 | aIntr.Perform(aPln1, aPln2, Tol, Tol); |
1393 | if (!aIntr.IsDone()) { |
1394 | iRet=-1; // just in case. it must not be so |
1395 | typeres=IntAna_NoGeometricSolution; |
1396 | return; |
1397 | } |
1398 | // |
1399 | aLin=aIntr.Line(1); |
1400 | const gp_Dir& aDLin=aLin.Direction(); |
1401 | gp_Vec aVLin(aDLin); |
1402 | gp_Pnt aOrig=aLin.Location(); |
1403 | gp_Vec aVr(aQA1, aOrig); |
1404 | aDx=aVLin.Dot(aVr); |
1405 | aQX=aOrig.Translated(aDx*aVLin); |
1406 | // |
1407 | // Final part |
1408 | // |
1409 | typeres=IntAna_Line; |
1410 | // |
1411 | param1=0.; |
1412 | param2 =0.; |
1413 | param1bis=0.; |
1414 | param2bis=0.; |
1415 | // |
1416 | if (iRet==1) { |
1417 | // one line |
1418 | nbint=1; |
1419 | pt1=aQApex1; |
1420 | gp_Vec aVX(aQApex1, aQX); |
1421 | dir1=gp_Dir(aVX); |
1422 | /* |
1423 | printf(" line L1 %lf %lf %lf %lf %lf %lf\n", |
1424 | pt1.X(), pt1.Y(), pt1.Z(), |
1425 | dir1.X(), dir1.Y(), dir1.Z()); |
1426 | */ |
1427 | } |
1428 | |
1429 | else {//iRet=2 |
1430 | // two lines |
1431 | nbint=2; |
1432 | aDa=aQA1.Distance(aQX); |
1433 | aDx=sqrt(aR1*aR1-aDa*aDa); |
1434 | aQX1=aQX.Translated(aDx*aVLin); |
1435 | aQX2=aQX.Translated(-aDx*aVLin); |
1436 | // |
1437 | pt1=aQApex1; |
1438 | pt2=aQApex1; |
1439 | gp_Vec aVX1(aQApex1, aQX1); |
1440 | dir1=gp_Dir(aVX1); |
1441 | gp_Vec aVX2(aQApex1, aQX2); |
1442 | dir2=gp_Dir(aVX2); |
1443 | /* |
1444 | printf(" line L1 %lf %lf %lf %lf %lf %lf\n", |
1445 | pt1.X(), pt1.Y(), pt1.Z(), |
1446 | dir1.X(), dir1.Y(), dir1.Z()); |
1447 | printf(" line L2 %lf %lf %lf %lf %lf %lf\n", |
1448 | pt2.X(), pt2.Y(), pt2.Z(), |
1449 | dir2.X(), dir2.Y(), dir2.Z()); |
1450 | */ |
1451 | } |
1452 | } //else if (aDA1A2<aTol2) { |
1453 | //modified by NIZNHY-PKV Wed Nov 30 10:12:41 2005t |
1454 | //modified by NIZNHY-IFV Fry Sep 01 15:46:41 2006f |
1455 | //Case when cones have common generatrix |
1456 | else if(A1A2.Intersect()) { |
1457 | //Check if apex of one cone belongs another one |
1458 | Standard_Real u, v, tol2 = Tol*Tol; |
1459 | ElSLib::Parameters(Con2, aPApex1, u, v); |
1460 | gp_Pnt p = ElSLib::Value(u, v, Con2); |
1461 | if(aPApex1.SquareDistance(p) > tol2) { |
1462 | typeres=IntAna_NoGeometricSolution; |
1463 | return; |
1464 | } |
1465 | // |
1466 | ElSLib::Parameters(Con1, aPApex2, u, v); |
1467 | p = ElSLib::Value(u, v, Con1); |
1468 | if(aPApex2.SquareDistance(p) > tol2) { |
1469 | typeres=IntAna_NoGeometricSolution; |
1470 | return; |
1471 | } |
1472 | |
1473 | //Cones have a common generatrix passing through apexes |
1474 | myCommonGen = Standard_True; |
1475 | |
1476 | //common generatrix of cones |
1477 | gp_Lin aGen(aPApex1, gp_Dir(gp_Vec(aPApex1, aPApex2))); |
1478 | |
1479 | //Intersection point of axes |
1480 | gp_Pnt aPAxeInt = A1A2.PtIntersect(); |
1481 | |
1482 | //Characteristic point of intersection curve |
1483 | u = ElCLib::Parameter(aGen, aPAxeInt); |
1484 | myPChar = ElCLib::Value(u, aGen); |
1485 | |
1486 | |
1487 | //Other generatrixes of cones laying in maximal plane |
1488 | gp_Lin aGen1 = aGen.Rotated(Con1.Axis(), Standard_PI); |
1489 | gp_Lin aGen2 = aGen.Rotated(Con2.Axis(), Standard_PI); |
1490 | // |
1491 | //Intersection point of generatrixes |
1492 | gp_Dir aN; //solution plane normal |
1493 | gp_Dir aD1 = aGen1.Direction(); |
1494 | |
1495 | gp_Dir aD2(aD1.Crossed(aGen.Direction())); |
1496 | |
1497 | if(aD1.IsParallel(aGen2.Direction(), Precision::Angular())) { |
1498 | aN = aD1.Crossed(aD2); |
1499 | } |
1500 | else if(aGen1.SquareDistance(aGen2) > tol2) { |
1501 | //Something wrong ??? |
1502 | typeres=IntAna_NoGeometricSolution; |
1503 | return; |
1504 | } |
1505 | else { |
1506 | gp_Dir D1 = aGen1.Position().Direction(); |
1507 | gp_Dir D2 = aGen2.Position().Direction(); |
1508 | gp_Pnt O1 = aGen1.Location(); |
1509 | gp_Pnt O2 = aGen2.Location(); |
1510 | Standard_Real D1DotD2 = D1.Dot(D2); |
1511 | Standard_Real aSin = 1.-D1DotD2*D1DotD2; |
1512 | gp_Vec O1O2 (O1,O2); |
1513 | Standard_Real U2 = (D1.XYZ()*(O1O2.Dot(D1))-(O1O2.XYZ())).Dot(D2.XYZ()); |
1514 | U2 /= aSin; |
1515 | gp_Pnt aPGint(ElCLib::Value(U2, aGen2)); |
1516 | |
1517 | aD1 = gp_Dir(gp_Vec(aPGint, myPChar)); |
1518 | aN = aD1.Crossed(aD2); |
1519 | } |
1520 | //Plane that must contain intersection curves |
1521 | gp_Pln anIntPln(myPChar, aN); |
1522 | |
1523 | IntAna_QuadQuadGeo INTER_QUAD_PLN(anIntPln,Con1,Tol,Tol); |
1524 | |
1525 | if(INTER_QUAD_PLN.IsDone()) { |
1526 | switch(INTER_QUAD_PLN.TypeInter()) { |
1527 | case IntAna_Ellipse: { |
1528 | typeres=IntAna_Ellipse; |
1529 | gp_Elips E=INTER_QUAD_PLN.Ellipse(1); |
1530 | pt1 = E.Location(); |
1531 | dir1 = E.Position().Direction(); |
1532 | dir2 = E.Position().XDirection(); |
1533 | param1 = E.MajorRadius(); |
1534 | param1bis = E.MinorRadius(); |
1535 | nbint = 1; |
1536 | break; |
1537 | } |
1538 | case IntAna_Circle: { |
1539 | typeres=IntAna_Circle; |
1540 | gp_Circ C=INTER_QUAD_PLN.Circle(1); |
1541 | pt1 = C.Location(); |
1542 | dir1 = C.Position().XDirection(); |
1543 | dir2 = C.Position().YDirection(); |
1544 | param1 = C.Radius(); |
1545 | nbint = 1; |
1546 | break; |
1547 | } |
1548 | case IntAna_Parabola: { |
1549 | typeres=IntAna_Parabola; |
1550 | gp_Parab Prb=INTER_QUAD_PLN.Parabola(1); |
1551 | pt1 = Prb.Location(); |
1552 | dir1 = Prb.Position().Direction(); |
1553 | dir2 = Prb.Position().XDirection(); |
1554 | param1 = Prb.Focal(); |
1555 | nbint = 1; |
1556 | break; |
1557 | } |
1558 | case IntAna_Hyperbola: { |
1559 | typeres=IntAna_Hyperbola; |
1560 | gp_Hypr H=INTER_QUAD_PLN.Hyperbola(1); |
1561 | pt1 = pt2 = H.Location(); |
1562 | dir1 = H.Position().Direction(); |
1563 | dir2 = H.Position().XDirection(); |
1564 | param1 = param2 = H.MajorRadius(); |
1565 | param1bis = param2bis = H.MinorRadius(); |
1566 | nbint = 2; |
1567 | break; |
1568 | } |
1569 | default: |
1570 | typeres=IntAna_NoGeometricSolution; |
1571 | } |
1572 | } |
1573 | } |
1574 | //modified by NIZNHY-IFV Fry Sep 01 15:46:41 2006t |
1575 | // else if(A1A2.Intersect() { |
1576 | else { |
1577 | typeres=IntAna_NoGeometricSolution; |
1578 | } |
1579 | } |
1580 | //======================================================================= |
1581 | //function : IntAna_QuadQuadGeo |
1582 | //purpose : Sphere - Cone |
1583 | //======================================================================= |
1584 | IntAna_QuadQuadGeo::IntAna_QuadQuadGeo(const gp_Sphere& Sph, |
1585 | const gp_Cone& Con, |
1586 | const Standard_Real Tol) |
1587 | : done(Standard_False), |
1588 | nbint(0), |
1589 | typeres(IntAna_Empty), |
1590 | pt1(0,0,0), |
1591 | pt2(0,0,0), |
1592 | param1(0), |
1593 | param2(0), |
1594 | param1bis(0), |
1595 | param2bis(0), |
1596 | myCommonGen(Standard_False), |
1597 | myPChar(0,0,0) |
1598 | { |
1599 | InitTolerances(); |
1600 | Perform(Sph,Con,Tol); |
1601 | } |
1602 | //======================================================================= |
1603 | //function : Perform |
1604 | //purpose : |
1605 | //======================================================================= |
1606 | void IntAna_QuadQuadGeo::Perform(const gp_Sphere& Sph, |
1607 | const gp_Cone& Con, |
1608 | const Standard_Real) |
1609 | { |
1610 | done=Standard_True; |
1611 | AxeOperator A1A2(Con.Axis(),Sph.Position().Axis()); |
1612 | gp_Pnt Pt=Sph.Location(); |
1613 | if((A1A2.Intersect() && (Pt.Distance(A1A2.PtIntersect())==0.0)) |
1614 | || A1A2.Same()) { |
1615 | gp_Pnt ConApex= Con.Apex(); |
1616 | Standard_Real dApexSphCenter=Pt.Distance(ConApex); |
1617 | gp_Dir ConDir; |
1618 | if(dApexSphCenter>RealEpsilon()) { |
1619 | ConDir = gp_Dir(gp_Vec(ConApex,Pt)); |
1620 | } |
1621 | else { |
1622 | ConDir = Con.Position().Direction(); |
1623 | } |
1624 | |
1625 | Standard_Real Rad=Sph.Radius(); |
1626 | Standard_Real tga=Tan(Con.SemiAngle()); |
1627 | |
1628 | |
1629 | //-- 2 circles |
1630 | //-- x: Roots of (x**2 + y**2 = Rad**2) |
1631 | //-- tga = y / (x+dApexSphCenter) |
1632 | Standard_Real tgatga = tga * tga; |
1633 | math_DirectPolynomialRoots Eq( 1.0+tgatga |
1634 | ,2.0*tgatga*dApexSphCenter |
1635 | ,-Rad*Rad + dApexSphCenter*dApexSphCenter*tgatga); |
1636 | if(Eq.IsDone()) { |
1637 | Standard_Integer nbsol=Eq.NbSolutions(); |
1638 | if(nbsol==0) { |
1639 | typeres=IntAna_Empty; |
1640 | } |
1641 | else { |
1642 | typeres=IntAna_Circle; |
1643 | if(nbsol>=1) { |
1644 | Standard_Real x = Eq.Value(1); |
1645 | Standard_Real dApexSphCenterpx = dApexSphCenter+x; |
1646 | nbint=1; |
1647 | pt1.SetCoord( ConApex.X() + (dApexSphCenterpx) * ConDir.X() |
1648 | ,ConApex.Y() + (dApexSphCenterpx) * ConDir.Y() |
1649 | ,ConApex.Z() + (dApexSphCenterpx) * ConDir.Z()); |
1650 | param1 = tga * dApexSphCenterpx; |
1651 | param1 = Abs(param1); |
1652 | dir1 = ConDir; |
1653 | if(param1<=myEPSILON_MINI_CIRCLE_RADIUS) { |
1654 | typeres=IntAna_PointAndCircle; |
1655 | param1=0.0; |
1656 | } |
1657 | } |
1658 | if(nbsol>=2) { |
1659 | Standard_Real x=Eq.Value(2); |
1660 | Standard_Real dApexSphCenterpx = dApexSphCenter+x; |
1661 | nbint=2; |
1662 | pt2.SetCoord( ConApex.X() + (dApexSphCenterpx) * ConDir.X() |
1663 | ,ConApex.Y() + (dApexSphCenterpx) * ConDir.Y() |
1664 | ,ConApex.Z() + (dApexSphCenterpx) * ConDir.Z()); |
1665 | param2 = tga * dApexSphCenterpx; |
1666 | param2 = Abs(param2); |
1667 | dir2=ConDir; |
1668 | if(param2<=myEPSILON_MINI_CIRCLE_RADIUS) { |
1669 | typeres=IntAna_PointAndCircle; |
1670 | param2=0.0; |
1671 | } |
1672 | } |
1673 | } |
1674 | } |
1675 | else { |
1676 | done=Standard_False; |
1677 | } |
1678 | } |
1679 | else { |
1680 | typeres=IntAna_NoGeometricSolution; |
1681 | } |
1682 | } |
1683 | |
1684 | //======================================================================= |
1685 | //function : IntAna_QuadQuadGeo |
1686 | //purpose : Sphere - Sphere |
1687 | //======================================================================= |
1688 | IntAna_QuadQuadGeo::IntAna_QuadQuadGeo( const gp_Sphere& Sph1 |
1689 | ,const gp_Sphere& Sph2 |
1690 | ,const Standard_Real Tol) |
1691 | : done(Standard_False), |
1692 | nbint(0), |
1693 | typeres(IntAna_Empty), |
1694 | pt1(0,0,0), |
1695 | pt2(0,0,0), |
1696 | param1(0), |
1697 | param2(0), |
1698 | param1bis(0), |
1699 | param2bis(0), |
1700 | myCommonGen(Standard_False), |
1701 | myPChar(0,0,0) |
1702 | { |
1703 | InitTolerances(); |
1704 | Perform(Sph1,Sph2,Tol); |
1705 | } |
1706 | //======================================================================= |
1707 | //function : Perform |
1708 | //purpose : |
1709 | //======================================================================= |
1710 | void IntAna_QuadQuadGeo::Perform(const gp_Sphere& Sph1, |
1711 | const gp_Sphere& Sph2, |
1712 | const Standard_Real Tol) |
1713 | { |
1714 | done=Standard_True; |
1715 | gp_Pnt O1=Sph1.Location(); |
1716 | gp_Pnt O2=Sph2.Location(); |
1717 | Standard_Real dO1O2=O1.Distance(O2); |
1718 | Standard_Real R1=Sph1.Radius(); |
1719 | Standard_Real R2=Sph2.Radius(); |
1720 | Standard_Real Rmin,Rmax; |
1721 | typeres=IntAna_Empty; |
1722 | param2bis=0.0; //-- pour eviter param2bis not used .... |
1723 | |
1724 | if(R1>R2) { Rmin=R2; Rmax=R1; } else { Rmin=R1; Rmax=R2; } |
1725 | |
1726 | if(dO1O2<=Tol && (Abs(R1-R2) <= Tol)) { |
1727 | typeres = IntAna_Same; |
1728 | } |
1729 | else { |
1730 | if(dO1O2<=Tol) { return; } |
1731 | gp_Dir Dir=gp_Dir(gp_Vec(O1,O2)); |
1732 | Standard_Real t = Rmax - dO1O2 - Rmin; |
1733 | |
1734 | //---------------------------------------------------------------------- |
1735 | //-- |----------------- R1 --------------------| |
1736 | //-- |----dO1O2-----|-----------R2----------| |
1737 | //-- --->--<-- t |
1738 | //-- |
1739 | //-- |------ R1 ------|---------dO1O2----------| |
1740 | //-- |-------------------R2-----------------------| |
1741 | //-- --->--<-- t |
1742 | //---------------------------------------------------------------------- |
1743 | if(t >= 0.0 && t <=Tol) { |
1744 | typeres = IntAna_Point; |
1745 | nbint = 1; |
1746 | Standard_Real t2; |
1747 | if(R1==Rmax) t2=(R1 + (R2 + dO1O2)) * 0.5; |
1748 | else t2=(-R1+(dO1O2-R2))*0.5; |
1749 | |
1750 | pt1.SetCoord( O1.X() + t2*Dir.X() |
1751 | ,O1.Y() + t2*Dir.Y() |
1752 | ,O1.Z() + t2*Dir.Z()); |
1753 | } |
1754 | else { |
1755 | //----------------------------------------------------------------- |
1756 | //-- |----------------- dO1O2 --------------------| |
1757 | //-- |----R1-----|-----------R2----------|-Tol-| |
1758 | //-- |
1759 | //-- |----------------- Rmax --------------------| |
1760 | //-- |----Rmin----|-------dO1O2-------|-Tol-| |
1761 | //-- |
1762 | //----------------------------------------------------------------- |
1763 | if((dO1O2 > (R1+R2+Tol)) || (Rmax > (dO1O2+Rmin+Tol))) { |
1764 | typeres=IntAna_Empty; |
1765 | } |
1766 | else { |
1767 | //--------------------------------------------------------------- |
1768 | //-- |
1769 | //-- |
1770 | //--------------------------------------------------------------- |
1771 | Standard_Real Alpha=0.5*(R1*R1-R2*R2+dO1O2*dO1O2)/(dO1O2); |
1772 | Standard_Real Beta = R1*R1-Alpha*Alpha; |
1773 | Beta = (Beta>0.0)? Sqrt(Beta) : 0.0; |
1774 | |
1775 | if(Beta<= myEPSILON_MINI_CIRCLE_RADIUS) { |
1776 | typeres = IntAna_Point; |
1777 | Alpha = (R1 + (dO1O2 - R2)) * 0.5; |
1778 | } |
1779 | else { |
1780 | typeres = IntAna_Circle; |
1781 | dir1 = Dir; |
1782 | param1 = Beta; |
1783 | } |
1784 | pt1.SetCoord( O1.X() + Alpha*Dir.X() |
1785 | ,O1.Y() + Alpha*Dir.Y() |
1786 | ,O1.Z() + Alpha*Dir.Z()); |
1787 | |
1788 | nbint=1; |
1789 | } |
1790 | } |
1791 | } |
1792 | } |
1793 | //======================================================================= |
1794 | //function : Point |
1795 | //purpose : Returns a Point |
1796 | //======================================================================= |
1797 | gp_Pnt IntAna_QuadQuadGeo::Point(const Standard_Integer n) const |
1798 | { |
1799 | if(!done) { StdFail_NotDone::Raise(); } |
1800 | if(n>nbint || n<1) { Standard_DomainError::Raise(); } |
1801 | if(typeres==IntAna_PointAndCircle) { |
1802 | if(n!=1) { Standard_DomainError::Raise(); } |
1803 | if(param1==0.0) return(pt1); |
1804 | return(pt2); |
1805 | } |
1806 | else if(typeres==IntAna_Point) { |
1807 | if(n==1) return(pt1); |
1808 | return(pt2); |
1809 | } |
1810 | |
1811 | // WNT (what can you expect from MicroSoft ?) |
1812 | return gp_Pnt(0,0,0); |
1813 | } |
1814 | //======================================================================= |
1815 | //function : Line |
1816 | //purpose : Returns a Line |
1817 | //======================================================================= |
1818 | gp_Lin IntAna_QuadQuadGeo::Line(const Standard_Integer n) const |
1819 | { |
1820 | if(!done) { StdFail_NotDone::Raise(); } |
1821 | if((n>nbint) || (n<1) || (typeres!=IntAna_Line)) { |
1822 | Standard_DomainError::Raise(); |
1823 | } |
1824 | if(n==1) { return(gp_Lin(pt1,dir1)); } |
1825 | else { return(gp_Lin(pt2,dir2)); } |
1826 | } |
1827 | //======================================================================= |
1828 | //function : Circle |
1829 | //purpose : Returns a Circle |
1830 | //======================================================================= |
1831 | gp_Circ IntAna_QuadQuadGeo::Circle(const Standard_Integer n) const |
1832 | { |
1833 | if(!done) { StdFail_NotDone::Raise(); } |
1834 | if(typeres==IntAna_PointAndCircle) { |
1835 | if(n!=1) { Standard_DomainError::Raise(); } |
1836 | if(param2==0.0) return(gp_Circ(DirToAx2(pt1,dir1),param1)); |
1837 | return(gp_Circ(DirToAx2(pt2,dir2),param2)); |
1838 | } |
1839 | else if((n>nbint) || (n<1) || (typeres!=IntAna_Circle)) { |
1840 | Standard_DomainError::Raise(); |
1841 | } |
1842 | if(n==1) { return(gp_Circ(DirToAx2(pt1,dir1),param1)); } |
1843 | else { return(gp_Circ(DirToAx2(pt2,dir2),param2)); } |
1844 | } |
1845 | |
1846 | //======================================================================= |
1847 | //function : Ellipse |
1848 | //purpose : Returns a Elips |
1849 | //======================================================================= |
1850 | gp_Elips IntAna_QuadQuadGeo::Ellipse(const Standard_Integer n) const |
1851 | { |
1852 | if(!done) { StdFail_NotDone::Raise(); } |
1853 | if((n>nbint) || (n<1) || (typeres!=IntAna_Ellipse)) { |
1854 | Standard_DomainError::Raise(); |
1855 | } |
1856 | |
1857 | if(n==1) { |
1858 | Standard_Real R1=param1, R2=param1bis, aTmp; |
1859 | if (R1<R2) { |
1860 | aTmp=R1; R1=R2; R2=aTmp; |
1861 | } |
1862 | gp_Ax2 anAx2(pt1, dir1 ,dir2); |
1863 | gp_Elips anElips (anAx2, R1, R2); |
1864 | return anElips; |
1865 | } |
1866 | else { |
1867 | Standard_Real R1=param2, R2=param2bis, aTmp; |
1868 | if (R1<R2) { |
1869 | aTmp=R1; R1=R2; R2=aTmp; |
1870 | } |
1871 | gp_Ax2 anAx2(pt2, dir2 ,dir1); |
1872 | gp_Elips anElips (anAx2, R1, R2); |
1873 | return anElips; |
1874 | } |
1875 | } |
1876 | //======================================================================= |
1877 | //function : Parabola |
1878 | //purpose : Returns a Parabola |
1879 | //======================================================================= |
1880 | gp_Parab IntAna_QuadQuadGeo::Parabola(const Standard_Integer n) const |
1881 | { |
1882 | if(!done) { |
1883 | StdFail_NotDone::Raise(); |
1884 | } |
1885 | if (typeres!=IntAna_Parabola) { |
1886 | Standard_DomainError::Raise(); |
1887 | } |
1888 | if((n>nbint) || (n!=1)) { |
1889 | Standard_OutOfRange::Raise(); |
1890 | } |
1891 | return(gp_Parab(gp_Ax2( pt1 |
1892 | ,dir1 |
1893 | ,dir2) |
1894 | ,param1)); |
1895 | } |
1896 | //======================================================================= |
1897 | //function : Hyperbola |
1898 | //purpose : Returns a Hyperbola |
1899 | //======================================================================= |
1900 | gp_Hypr IntAna_QuadQuadGeo::Hyperbola(const Standard_Integer n) const |
1901 | { |
1902 | if(!done) { |
1903 | StdFail_NotDone::Raise(); |
1904 | } |
1905 | if((n>nbint) || (n<1) || (typeres!=IntAna_Hyperbola)) { |
1906 | Standard_DomainError::Raise(); |
1907 | } |
1908 | if(n==1) { |
1909 | return(gp_Hypr(gp_Ax2( pt1 |
1910 | ,dir1 |
1911 | ,dir2) |
1912 | ,param1,param1bis)); |
1913 | } |
1914 | else { |
1915 | return(gp_Hypr(gp_Ax2( pt2 |
1916 | ,dir1 |
1917 | ,dir2.Reversed()) |
1918 | ,param2,param2bis)); |
1919 | } |
1920 | } |
1921 | |
1922 | //======================================================================= |
1923 | //function : HasCommonGen |
1924 | //purpose : |
1925 | //======================================================================= |
1926 | |
1927 | Standard_Boolean IntAna_QuadQuadGeo::HasCommonGen() const |
1928 | { |
1929 | return myCommonGen; |
1930 | } |
1931 | |
1932 | //======================================================================= |
1933 | //function : PChar |
1934 | //purpose : |
1935 | //======================================================================= |
1936 | |
1937 | const gp_Pnt& IntAna_QuadQuadGeo::PChar() const |
1938 | { |
1939 | return myPChar; |
1940 | } |
1941 | |
1942 | |
1943 | |
1944 | |