1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
|
-- File: AppParCurves_Variational.cdl
-- Created: Tue May 14 11:04:08 1996
-- Author: Philippe MANGIN / Jeannine PANCIATICI
-- <pmn@sgi29>
-- Igor FEOKTISTOV - correction 14/12/98
---Copyright: Matra Datavision 1996
generic class Variational from AppParCurves
(MultiLine as any;
ToolLine as any) -- as ToolLine(MultiLine)
---Purpose: This class is used to smooth N points with constraints
-- by minimization of quadratic criterium but also
-- variational criterium in order to obtain " fair Curve "
--
uses Matrix from math,
Vector from math,
HArray1OfReal from TColStd,
Array1OfReal from TColStd,
HArray1OfInteger from TColStd,
Shape from GeomAbs,
HArray1OfConstraintCouple from AppParCurves,
MultiBSpCurve from AppParCurves,
SmoothCriterion from AppParCurves,
Curve from FEmTool,
Assembly from FEmTool,
Base from PLib,
Constraint from AppParCurves
raises OutOfRange from Standard,
DimensionError from Standard,
DomainError from Standard,
ConstructionError from Standard,
NotDone from StdFail,
VectorWithNullMagnitude from gp
class MyCriterion instantiates LinearCriteria from AppParCurves
(MultiLine, ToolLine);
is
Create(SSP: MultiLine;
FirstPoint, LastPoint: Integer;
TheConstraints: HArray1OfConstraintCouple;
MaxDegree: Integer = 14;
MaxSegment: Integer = 100;
Continuity : Shape from GeomAbs = GeomAbs_C2;
WithMinMax : Boolean = Standard_False;
WithCutting: Boolean = Standard_True;
Tolerance : Real = 1.0;
NbIterations: Integer = 2)
---Purpose: Constructor.
-- Initialization of the fields.
-- warning : Nc0 : number of PassagePoint consraints
-- Nc2 : number of TangencyPoint constraints
-- Nc3 : number of CurvaturePoint constraints
-- if
-- ((MaxDegree-Continuity)*MaxSegment -Nc0 - 2*Nc1
-- -3*Nc2)
-- is negative
-- The problem is over-constrained.
--
-- Limitation : The MultiLine has to be composed by
-- only one Line ( Dimension 2 or 3).
returns Variational from AppParCurves;
Approximate(me : in out)
---Purpose: Makes the approximation with the current fields.
raises NotDone from StdFail
is static;
-- ==================== The Selectors ===========================
IsCreated(me)
---Purpose: returns True if the creation is done
-- and correspond to the current fields.
returns Boolean
is static;
IsDone(me)
---Purpose: returns True if the approximation is ok
-- and correspond to the current fields.
returns Boolean
is static;
IsOverConstrained(me)
---Purpose: returns True if the problem is overconstrained
-- in this case, approximation cannot be done.
returns Boolean
is static;
Value(me)
---Purpose: returns all the BSpline curves approximating the
-- MultiLine SSP after minimization of the parameter.
returns MultiBSpCurve from AppParCurves
raises NotDone from StdFail
is static;
MaxError(me)
---Purpose: returns the maximum of the distances between
-- the points of the multiline and the approximation
-- curves.
returns Real
raises NotDone from StdFail
is static;
MaxErrorIndex(me)
---Purpose: returns the index of the MultiPoint of ErrorMax
returns Integer
raises NotDone from StdFail
is static;
QuadraticError(me)
---Purpose: returns the quadratic average of the distances between
-- the points of the multiline and the approximation
-- curves.
returns Real
raises NotDone from StdFail
is static;
Distance(me : in out ; mat : out Matrix from math)
---Purpose: returns the distances between the points of the
-- multiline and the approximation curves.
raises NotDone from StdFail
is static;
AverageError(me)
---Purpose: returns the average error between
-- the MultiLine and the approximation.
returns Real
raises NotDone from StdFail
is static;
Parameters(me)
---Purpose: returns the parameters uses to the approximations
---C++: return const&
returns HArray1OfReal
raises NotDone from StdFail
is static;
Knots(me)
---Purpose: returns the knots uses to the approximations
---C++: return const&
returns HArray1OfReal
raises NotDone from StdFail
is static;
Criterium(me; VFirstOrder,
VSecondOrder,
VThirdOrder : out Real)
---Purpose: returns the values of the quality criterium.
raises NotDone from StdFail
is static;
CriteriumWeight(me ;
Percent1, Percent2, Percent3 : out Real)
---Purpose: returns the Weights (as percent) associed to the criterium used in
-- the optimization.
is static;
MaxDegree(me)
---Purpose: returns the Maximum Degree used in the approximation
returns Integer
is static;
MaxSegment(me)
---Purpose: returns the Maximum of segment used in the approximation
returns Integer
is static;
Continuity(me)
---Purpose: returns the Continuity used in the approximation
returns Shape from GeomAbs
is static;
WithMinMax(me)
---Purpose: returns if the approximation search to minimize the
-- maximum Error or not.
returns Boolean
is static;
WithCutting(me)
---Purpose: returns if the approximation can insert new Knots or not.
returns Boolean
is static;
Tolerance(me)
---Purpose: returns the tolerance used in the approximation.
returns Real
is static;
NbIterations(me)
---Purpose: returns the number of iterations used in the approximation.
returns Integer
is static;
Dump(me ; o : in out OStream)
---Purpose: Prints on the stream o information on the current state
-- of the object.
-- MaxError,MaxErrorIndex,AverageError,QuadraticError,Criterium
-- Distances,Degre,Nombre de poles, parametres, noeuds
is static;
SetConstraints(me:in out; aConstrainst:HArray1OfConstraintCouple)
---Purpose: Define the constraints to approximate
-- If this value is incompatible with the others fields
-- this method modify nothing and returns false
returns Boolean
is static;
SetParameters(me:in out; param : HArray1OfReal)
---Purpose: Defines the parameters used by the approximations.
raises DimensionError
is static;
SetKnots(me:in out; knots : HArray1OfReal)
---Purpose: Defines the knots used by the approximations
-- If this value is incompatible with the others fields
-- this method modify nothing and returns false
returns Boolean
raises DimensionError,
DomainError
is static;
SetMaxDegree(me: in out; Degree : Integer)
---Purpose: Define the Maximum Degree used in the approximation
-- If this value is incompatible with the others fields
-- this method modify nothing and returns false
returns Boolean
is static;
SetMaxSegment(me: in out; NbSegment : Integer)
---Purpose: Define the maximum number of segments used in the approximation
-- If this value is incompatible with the others fields
-- this method modify nothing and returns false
returns Boolean
is static;
SetContinuity(me: in out; C : Shape from GeomAbs)
---Purpose: Define the Continuity used in the approximation
-- If this value is incompatible with the others fields
-- this method modify nothing and returns false
returns Boolean
raises ConstructionError from Standard
is static;
SetWithMinMax(me: in out; MinMax : Boolean)
---Purpose: Define if the approximation search to minimize the
-- maximum Error or not.
is static;
SetWithCutting(me : in out; Cutting : Boolean )
---Purpose: Define if the approximation can insert new Knots or not.
-- If this value is incompatible with the others fields
-- this method modify nothing and returns false
returns Boolean
is static;
SetCriteriumWeight(me : in out;
Percent1, Percent2, Percent3 : Real)
---Purpose: define the Weights (as percent) associed to the criterium used in
-- the optimization.
--
raises DomainError -- if Percent <= 0
is static;
SetCriteriumWeight(me : in out;
Order : Integer;
Percent : Real)
---Purpose: define the Weight (as percent) associed to the
-- criterium Order used in the optimization : Others
-- weights are updated.
raises DomainError, -- if Percent < 0
OutOfRange -- if Order < 1 or Order > 3
is static;
SetTolerance(me:in out; Tol : Real)
---Purpose: define the tolerance used in the approximation.
is static;
SetNbIterations(me:in out; Iter : Integer)
---Purpose: define the number of iterations used in the approximation.
raises DomainError -- if Iter < 1
is static;
-- ====================== The Private methods ======================
TheMotor(me : in out;
J : in out SmoothCriterion from AppParCurves;
WQuadratic, WQuality : Real;
TheCurve : in out Curve from FEmTool;
Ecarts : out Array1OfReal from TColStd) is private;
Adjusting(me : in out;
J : in out SmoothCriterion from AppParCurves;
WQuadratic, WQuality : in out Real;
TheCurve : in out Curve from FEmTool;
Ecarts : out Array1OfReal from TColStd) is private;
Optimization(me;
J : in out SmoothCriterion from AppParCurves;
A : in out Assembly from FEmTool;
ToAssemble : in Boolean;
EpsDeg : Real;
Curve : out Curve from FEmTool;
Parameters : Array1OfReal from TColStd) is private;
Project(me; C : Curve from FEmTool;
Ti : Array1OfReal from TColStd;
ProjTi : out Array1OfReal from TColStd;
Distance : out Array1OfReal from TColStd;
NumPoints : out Integer;
MaxErr, QuaErr, AveErr : out Real;
NbIterations: Integer=2) is private;
ACR(me; Curve : in out Curve from FEmTool;
Ti : in out Array1OfReal from TColStd;
Decima: Integer) is private;
SplitCurve(me; InCurve : Curve from FEmTool;
Ti : Array1OfReal from TColStd;
CurveTol: Real;
OutCurve: out Curve from FEmTool;
iscut : out Boolean) is private;
Init(me : in out)
raises NotDone from StdFail,
ConstructionError from Standard,
DimensionError from Standard
is private;
InitSmoothCriterion(me : in out)
is private;
InitParameters(me : in out; Length : out Real)
raises ConstructionError from Standard
is private;
InitCriterionEstimations(me; Length : Real; J1, J2, J3 : out Real)
is private;
EstTangent(me; ipnt : Integer; VTang : out Vector from math)
is private;
EstSecnd(me; ipnt : Integer; VTang1, VTang2 : Vector from math;
Length : Real; VScnd : out Vector from math)
is private;
InitCutting(me; aBase : Base from PLib; CurvTol : Real;
aCurve : out Curve from FEmTool)
raises ConstructionError from Standard
is private;
AssemblingConstraints(me; Curve : Curve from FEmTool;
Parameters : Array1OfReal from TColStd;
CBLONG : Real from Standard;
A : out Assembly from FEmTool)
is private;
InitTthetaF(me : in out; ndimen : Integer from Standard;
typcon : Constraint from AppParCurves;
begin : Integer from Standard;
jndex : Integer from Standard)
returns Boolean
is private;
fields
-- Description of the points to smooth and the constraints
mySSP : MultiLine;
myNbP3d : Integer;
myNbP2d : Integer;
myDimension : Integer;
myFirstPoint : Integer;
myLastPoint : Integer;
myNbPoints : Integer;
myTabPoints : HArray1OfReal;
myConstraints : HArray1OfConstraintCouple;
myNbConstraints : Integer;
myTabConstraints : HArray1OfReal;
myNbPassPoints : Integer;
myNbTangPoints : Integer;
myNbCurvPoints : Integer;
myTypConstraints : HArray1OfInteger;
myTtheta : HArray1OfReal;
myTfthet : HArray1OfReal;
-- Context parameters
myMaxDegree : Integer;
myMaxSegment : Integer;
myNbIterations: Integer;
myTolerance : Real;
-- Options
myContinuity : Shape from GeomAbs;
myNivCont : Integer;
myWithMinMax : Boolean;
myWithCutting: Boolean;
myPercent : Real[3];
myCriterium : Real[4];
mySmoothCriterion : SmoothCriterion from AppParCurves;
-- output
myParameters : HArray1OfReal;
myKnots : HArray1OfReal;
myMBSpCurve : MultiBSpCurve;
myMaxError : Real;
myMaxErrorIndex: Integer;
myAverageError : Real;
myIsCreated : Boolean;
myIsDone : Boolean;
myIsOverConstr : Boolean;
end Variational;
|
