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1 | // Created on: 1995-11-20 |
2 | // Created by: Laurent BOURESCHE |
3 | // Copyright (c) 1995-1999 Matra Datavision |
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4 | // Copyright (c) 1999-2014 OPEN CASCADE SAS |
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5 | // |
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6 | // This file is part of Open CASCADE Technology software library. |
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7 | // |
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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 |
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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. |
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13 | // |
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14 | // Alternatively, this file may be used under the terms of Open CASCADE |
15 | // commercial license or contractual agreement. |
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16 | |
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17 | |
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18 | #include <Adaptor3d_Curve.hxx> |
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19 | #include <BSplCLib.hxx> |
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20 | #include <gp_Pnt.hxx> |
21 | #include <Law.hxx> |
22 | #include <Law_BSpFunc.hxx> |
23 | #include <Law_BSpline.hxx> |
24 | #include <Law_Interpolate.hxx> |
25 | #include <Law_Linear.hxx> |
26 | #include <TColStd_Array1OfBoolean.hxx> |
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27 | #include <TColStd_Array1OfReal.hxx> |
28 | #include <TColStd_HArray1OfBoolean.hxx> |
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29 | #include <TColStd_HArray1OfReal.hxx> |
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30 | |
31 | Handle(Law_BSpFunc) Law::MixBnd(const Handle(Law_Linear)& Lin) |
32 | { |
33 | Standard_Real f,l; |
34 | Lin->Bounds(f,l); |
35 | TColStd_Array1OfReal Knots(1,4); |
36 | TColStd_Array1OfInteger Mults(1,4); |
37 | Knots(1) = f; Knots(4) = l; |
38 | Knots(2) = 0.75*f + 0.25*l; Knots(3) = 0.25*f + 0.75*l; |
39 | Mults(1) = Mults(4) = 4; |
40 | Mults(2) = Mults(3) = 1; |
41 | Handle(TColStd_HArray1OfReal) pol = Law::MixBnd(3,Knots,Mults,Lin); |
42 | Handle(Law_BSpline) bs = new Law_BSpline(pol->Array1(),Knots,Mults,3); |
43 | Handle(Law_BSpFunc) bsf = new Law_BSpFunc(); |
44 | bsf->SetCurve(bs); |
45 | return bsf; |
46 | } |
47 | |
48 | Handle(TColStd_HArray1OfReal) Law::MixBnd |
49 | (const Standard_Integer Degree, |
50 | const TColStd_Array1OfReal& Knots, |
51 | const TColStd_Array1OfInteger& Mults, |
52 | const Handle(Law_Linear)& Lin) |
53 | { |
54 | Standard_Integer nbpol = 0, nbfk = 0, i, j, k = 0; |
55 | for(i = Mults.Lower(); i <= Mults.Upper(); i++){ |
56 | nbfk += Mults(i); |
57 | } |
58 | TColStd_Array1OfReal fk(1,nbfk); |
59 | for(i = Mults.Lower(); i <= Mults.Upper(); i++){ |
60 | for(j = 1; j <= Mults(i); j++){ |
61 | fk(++k) = Knots(i); |
62 | } |
63 | } |
64 | nbpol = nbfk - Degree - 1; |
65 | TColStd_Array1OfReal par(1,nbpol); |
66 | BSplCLib::BuildSchoenbergPoints(Degree,fk,par); |
67 | Handle(TColStd_HArray1OfReal) res = new TColStd_HArray1OfReal(1,nbpol); |
68 | TColStd_Array1OfReal& pol = res->ChangeArray1(); |
69 | for(i = 1; i <= nbpol; i++){ |
70 | pol(i) = Lin->Value(par(i)); |
71 | } |
72 | TColStd_Array1OfInteger ord(1,nbpol); |
73 | ord.Init(0); |
74 | BSplCLib::Interpolate(Degree,fk,par,ord,1,pol(1),i); |
75 | if(nbpol >= 4){ |
76 | pol(2) = pol(1); |
77 | pol(nbpol - 1) = pol(nbpol); |
78 | } |
79 | return res; |
80 | } |
81 | |
82 | static Standard_Real eval1(const Standard_Real p, |
83 | const Standard_Real first, |
84 | const Standard_Real last, |
85 | const Standard_Real piv, |
86 | const Standard_Boolean nulr) |
87 | { |
88 | if((nulr && p >= piv) || (!nulr && p <= piv)) return 0.; |
89 | else if(nulr){ |
90 | Standard_Real a = piv - first; |
91 | a *= a; |
92 | a = 1./a; |
93 | Standard_Real b = p - first; |
94 | a *= b; |
95 | b = piv - p; |
96 | a *= b; |
97 | a *= b; |
98 | return a; |
99 | } |
100 | else{ |
101 | Standard_Real a = last - piv; |
102 | a *= a; |
103 | a = 1./a; |
104 | Standard_Real b = last - p; |
105 | a *= b; |
106 | b = p - piv; |
107 | a *= b; |
108 | a *= b; |
109 | return a; |
110 | } |
111 | } |
112 | |
113 | Handle(TColStd_HArray1OfReal) Law::MixTgt |
114 | (const Standard_Integer Degree, |
115 | const TColStd_Array1OfReal& Knots, |
116 | const TColStd_Array1OfInteger& Mults, |
117 | const Standard_Boolean NulOnTheRight, |
118 | const Standard_Integer Index) |
119 | { |
120 | Standard_Real first = Knots(Knots.Lower()); |
121 | Standard_Real last = Knots(Knots.Upper()); |
122 | Standard_Real piv = Knots(Index); |
123 | Standard_Integer nbpol = 0, nbfk = 0, i, j, k = 0; |
124 | for(i = Mults.Lower(); i <= Mults.Upper(); i++){ |
125 | nbfk += Mults(i); |
126 | } |
127 | TColStd_Array1OfReal fk(1,nbfk); |
128 | for(i = Mults.Lower(); i <= Mults.Upper(); i++){ |
129 | for(j = 1; j <= Mults(i); j++){ |
130 | fk(++k) = Knots(i); |
131 | } |
132 | } |
133 | nbpol = nbfk - Degree - 1; |
134 | TColStd_Array1OfReal par(1,nbpol); |
135 | BSplCLib::BuildSchoenbergPoints(Degree,fk,par); |
136 | Handle(TColStd_HArray1OfReal) res = new TColStd_HArray1OfReal(1,nbpol); |
137 | TColStd_Array1OfReal& pol = res->ChangeArray1(); |
138 | for(i = 1; i <= nbpol; i++){ |
139 | pol(i) = eval1(par(i),first,last,piv,NulOnTheRight); |
140 | } |
141 | TColStd_Array1OfInteger ord(1,nbpol); |
142 | ord.Init(0); |
143 | BSplCLib::Interpolate(Degree,fk,par,ord,1,pol(1),i); |
144 | return res; |
145 | } |
146 | |
147 | Handle(Law_BSpline) Law::Reparametrize(const Adaptor3d_Curve& Curve, |
148 | const Standard_Real First, |
149 | const Standard_Real Last, |
150 | const Standard_Boolean HasDF, |
151 | const Standard_Boolean HasDL, |
152 | const Standard_Real DFirst, |
153 | const Standard_Real DLast, |
154 | const Standard_Boolean Rev, |
155 | const Standard_Integer NbPoints) |
156 | { |
157 | // On evalue la longeur approximative de la courbe. |
158 | |
159 | Standard_Integer i; |
160 | Standard_Real DDFirst = DFirst, DDLast = DLast; |
161 | if(HasDF && Rev) DDFirst = -DFirst; |
162 | if(HasDL && Rev) DDLast = -DLast; |
163 | TColStd_Array1OfReal cumdist(1,2*NbPoints); |
164 | TColStd_Array1OfReal ucourbe(1,2*NbPoints); |
165 | gp_Pnt P1,P2; |
166 | Standard_Real U1 = Curve.FirstParameter(); |
167 | Standard_Real U2 = Curve.LastParameter(); |
168 | Standard_Real U, DU, Length = 0.; |
169 | if(!Rev){ |
170 | P1 = Curve.Value(U1); |
171 | U = U1; |
172 | DU = (U2 - U1) / ( 2*NbPoints - 1); |
173 | } |
174 | else{ |
175 | P1 = Curve.Value(U2); |
176 | U = U2; |
177 | DU = (U1 - U2) / ( 2*NbPoints - 1); |
178 | } |
179 | for ( i = 1; i <= 2*NbPoints ; i ++) { |
180 | P2 = Curve.Value(U); |
181 | Length += P2.Distance(P1); |
182 | cumdist(i) = Length; |
183 | ucourbe(i) = U; |
184 | U += DU; |
185 | P1 = P2; |
186 | } |
187 | if(Rev) ucourbe(2*NbPoints) = U1; |
188 | else ucourbe(2*NbPoints) = U2; |
189 | |
190 | Handle(TColStd_HArray1OfReal) point = new TColStd_HArray1OfReal(1,NbPoints); |
191 | Handle(TColStd_HArray1OfReal) param = new TColStd_HArray1OfReal(1,NbPoints); |
192 | |
193 | Standard_Real DCorde = Length / ( NbPoints - 1); |
194 | Standard_Real Corde = DCorde; |
195 | Standard_Integer Index = 1; |
196 | Standard_Real Alpha; |
197 | Standard_Real fac = 1./(NbPoints-1); |
198 | |
199 | point->SetValue(1,ucourbe(1)); |
200 | param->SetValue(1,First); |
201 | point->SetValue(NbPoints,ucourbe(2*NbPoints)); |
202 | param->SetValue(NbPoints,Last); |
203 | |
204 | for ( i = 2; i < NbPoints; i++) { |
205 | while (cumdist(Index) < Corde) Index ++; |
206 | |
207 | Alpha = (Corde - cumdist(Index - 1)) / (cumdist(Index) -cumdist(Index - 1)); |
208 | U = ucourbe(Index-1) + Alpha * (ucourbe(Index) - ucourbe(Index-1)); |
209 | point->SetValue(i,U); |
210 | param->SetValue(i,((NbPoints-i)*First+(i-1)*Last)*fac); |
211 | Corde = i*DCorde; |
212 | } |
213 | Law_Interpolate inter(point,param,0,1.e-9); |
214 | if(HasDF || HasDL){ |
215 | TColStd_Array1OfReal tgt(1,NbPoints); |
216 | Handle(TColStd_HArray1OfBoolean) |
217 | flag = new TColStd_HArray1OfBoolean(1,NbPoints); |
218 | flag->ChangeArray1().Init(0); |
219 | if(HasDF){ flag->SetValue(1,1); tgt.SetValue(1,DDFirst); } |
220 | if(HasDL){ flag->SetValue(NbPoints,1); tgt.SetValue(NbPoints,DDLast); } |
221 | inter.Load(tgt,flag); |
222 | } |
223 | inter.Perform(); |
224 | if(!inter.IsDone()) |
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225 | throw Standard_Failure("Law::Reparametrize echec interpolation"); |
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226 | Handle(Law_BSpline) bs = inter.Curve(); |
227 | return bs; |
228 | } |
229 | |
230 | static Standard_Real eval2(const Standard_Real p, |
231 | // const Standard_Real first, |
232 | const Standard_Real , |
233 | // const Standard_Real last, |
234 | const Standard_Real , |
235 | const Standard_Real mil, |
236 | const Standard_Boolean hasfirst, |
237 | const Standard_Boolean haslast, |
238 | const Handle(Law_BSpline)& bs1, |
239 | const Handle(Law_BSpline)& bs2) |
240 | { |
241 | if(hasfirst && p < mil) return bs1->Value(p); |
242 | else if(haslast && p > mil) return bs2->Value(p); |
243 | else return 1.; |
244 | } |
245 | |
246 | Handle(Law_BSpline) Law::Scale(const Standard_Real First, |
247 | const Standard_Real Last, |
248 | const Standard_Boolean HasF, |
249 | const Standard_Boolean HasL, |
250 | const Standard_Real VFirst, |
251 | const Standard_Real VLast) |
252 | { |
253 | Standard_Integer i; |
254 | Standard_Real Milieu = 0.5*(First+Last); |
255 | TColStd_Array1OfReal knot(1,3); |
256 | TColStd_Array1OfReal fknot(1,10); |
257 | TColStd_Array1OfInteger mult(1,3); |
258 | knot(1) = First; knot(2) = Milieu; knot(3) = Last; |
259 | fknot(1) = fknot(2) = fknot(3) = fknot(4) = First; |
260 | fknot(10) = fknot(9) = fknot(8) = fknot(7) = Last; |
261 | fknot(5) = fknot(6) = Milieu; |
262 | mult(1) = 4; mult(3) = 4; mult(2) = 2; |
263 | |
264 | TColStd_Array1OfReal pbs(1,4); |
265 | TColStd_Array1OfReal kbs(1,2); |
266 | TColStd_Array1OfInteger mbs(1,2); |
267 | mbs(1) = mbs(2) = 4; |
268 | Handle(Law_BSpline) bs1,bs2; |
269 | if(HasF){ |
270 | pbs(1) = pbs(2) = VFirst; |
271 | pbs(3) = pbs(4) = 1.; |
272 | kbs(1) = First; kbs(2) = Milieu; |
273 | bs1 = new Law_BSpline(pbs,kbs,mbs,3); |
274 | } |
275 | if(HasL){ |
276 | pbs(1) = pbs(2) = 1.; |
277 | pbs(3) = pbs(4) = VLast; |
278 | kbs(1) = Milieu; kbs(2) = Last; |
279 | bs2 = new Law_BSpline(pbs,kbs,mbs,3); |
280 | } |
281 | |
282 | TColStd_Array1OfReal pol(1,6); |
283 | TColStd_Array1OfReal par(1,6); |
284 | BSplCLib::BuildSchoenbergPoints(3,fknot,par); |
285 | for(i = 1; i <= 6; i++){ |
286 | pol(i) = eval2(par(i),First,Last,Milieu,HasF,HasL,bs1,bs2); |
287 | } |
288 | TColStd_Array1OfInteger ord(1,6); |
289 | ord.Init(0); |
290 | BSplCLib::Interpolate(3,fknot,par,ord,1,pol(1),i); |
291 | bs1 = new Law_BSpline(pol,knot,mult,3); |
292 | return bs1; |
293 | } |
294 | |
295 | |
296 | Handle(Law_BSpline) Law::ScaleCub(const Standard_Real First, |
297 | const Standard_Real Last, |
298 | const Standard_Boolean HasF, |
299 | const Standard_Boolean HasL, |
300 | const Standard_Real VFirst, |
301 | const Standard_Real VLast) |
302 | { |
303 | //Standard_Integer i; |
304 | Standard_Real Milieu = 0.5*(First+Last); |
305 | TColStd_Array1OfReal pol(1,5); |
306 | TColStd_Array1OfReal knot(1,3); |
307 | TColStd_Array1OfInteger mult(1,3); |
308 | knot(1) = First; knot(2) = Milieu; knot(3) = Last; |
309 | mult(1) = 4; mult(3) = 4; mult(2) = 1; |
310 | |
311 | Handle(Law_BSpline) bs; |
312 | if(HasF){ pol(1) = pol(2) = VFirst;} |
313 | else { pol(1) = pol(2) = 1.; } |
314 | if(HasL){ pol(4) = pol(5) = VLast;} |
315 | else { pol(4) = pol(5) = 1.; } |
316 | |
317 | pol(3) = 1.; |
318 | |
319 | bs = new Law_BSpline(pol,knot,mult,3); |
320 | return bs; |
321 | } |