1 // Created on: 1993-03-09
3 // Copyright (c) 1993-1999 Matra Datavision
4 // Copyright (c) 1999-2014 OPEN CASCADE SAS
6 // This file is part of Open CASCADE Technology software library.
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.
14 // Alternatively, this file may be used under the terms of Open CASCADE
15 // commercial license or contractual agreement.
17 #ifndef _Geom_BSplineSurface_HeaderFile
18 #define _Geom_BSplineSurface_HeaderFile
20 #include <Standard.hxx>
21 #include <Standard_Type.hxx>
23 #include <Precision.hxx>
24 #include <Standard_Boolean.hxx>
25 #include <GeomAbs_BSplKnotDistribution.hxx>
26 #include <GeomAbs_Shape.hxx>
27 #include <Standard_Integer.hxx>
28 #include <TColgp_HArray2OfPnt.hxx>
29 #include <TColStd_HArray2OfReal.hxx>
30 #include <TColStd_HArray1OfReal.hxx>
31 #include <TColStd_HArray1OfInteger.hxx>
32 #include <Standard_Real.hxx>
33 #include <Geom_BoundedSurface.hxx>
34 #include <TColgp_Array2OfPnt.hxx>
35 #include <TColStd_Array1OfReal.hxx>
36 #include <TColStd_Array1OfInteger.hxx>
37 #include <TColStd_Array2OfReal.hxx>
38 #include <TColgp_Array1OfPnt.hxx>
39 class Standard_ConstructionError;
40 class Standard_DimensionError;
41 class Standard_DomainError;
42 class Standard_OutOfRange;
43 class Standard_NoSuchObject;
44 class Standard_RangeError;
45 class Geom_UndefinedDerivative;
53 class Geom_BSplineSurface;
54 DEFINE_STANDARD_HANDLE(Geom_BSplineSurface, Geom_BoundedSurface)
56 //! Describes a BSpline surface.
57 //! In each parametric direction, a BSpline surface can be:
58 //! - uniform or non-uniform,
59 //! - rational or non-rational,
60 //! - periodic or non-periodic.
61 //! A BSpline surface is defined by:
62 //! - its degrees, in the u and v parametric directions,
63 //! - its periodic characteristic, in the u and v parametric directions,
64 //! - a table of poles, also called control points (together
65 //! with the associated weights if the surface is rational), and
66 //! - a table of knots, together with the associated multiplicities.
67 //! The degree of a Geom_BSplineSurface is limited to
68 //! a value (25) which is defined and controlled by the
69 //! system. This value is returned by the function MaxDegree.
71 //! Poles and Weights are manipulated using two associative double arrays:
72 //! - the poles table, which is a double array of gp_Pnt points, and
73 //! - the weights table, which is a double array of reals.
74 //! The bounds of the poles and weights arrays are:
75 //! - 1 and NbUPoles for the row bounds (provided
76 //! that the BSpline surface is not periodic in the u
77 //! parametric direction), where NbUPoles is the
78 //! number of poles of the surface in the u parametric direction, and
79 //! - 1 and NbVPoles for the column bounds (provided
80 //! that the BSpline surface is not periodic in the v
81 //! parametric direction), where NbVPoles is the
82 //! number of poles of the surface in the v parametric direction.
83 //! The poles of the surface are the points used to shape
84 //! and reshape the surface. They comprise a rectangular network.
85 //! If the surface is not periodic:
86 //! - The points (1, 1), (NbUPoles, 1), (1,
87 //! NbVPoles), and (NbUPoles, NbVPoles)
88 //! are the four parametric "corners" of the surface.
89 //! - The first column of poles and the last column of
90 //! poles define two BSpline curves which delimit the
91 //! surface in the v parametric direction. These are the
92 //! v isoparametric curves corresponding to the two
93 //! bounds of the v parameter.
94 //! - The first row of poles and the last row of poles
95 //! define two BSpline curves which delimit the surface
96 //! in the u parametric direction. These are the u
97 //! isoparametric curves corresponding to the two bounds of the u parameter.
98 //! If the surface is periodic, these geometric properties are not verified.
99 //! It is more difficult to define a geometrical significance
100 //! for the weights. However they are useful for
101 //! representing a quadric surface precisely. Moreover, if
102 //! the weights of all the poles are equal, the surface has
103 //! a polynomial equation, and hence is a "non-rational surface".
104 //! The non-rational surface is a special, but frequently
105 //! used, case, where all poles have identical weights.
106 //! The weights are defined and used only in the case of
107 //! a rational surface. The rational characteristic is
108 //! defined in each parametric direction. A surface can be
109 //! rational in the u parametric direction, and
110 //! non-rational in the v parametric direction.
111 //! Knots and Multiplicities
112 //! For a Geom_BSplineSurface the table of knots is
113 //! made up of two increasing sequences of reals, without
114 //! repetition, one for each parametric direction. The
115 //! multiplicities define the repetition of the knots.
116 //! A BSpline surface comprises multiple contiguous
117 //! patches, which are themselves polynomial or rational
118 //! surfaces. The knots are the parameters of the
119 //! isoparametric curves which limit these contiguous
120 //! patches. The multiplicity of a knot on a BSpline
121 //! surface (in a given parametric direction) is related to
122 //! the degree of continuity of the surface at that knot in
123 //! that parametric direction:
124 //! Degree of continuity at knot(i) = Degree - Multi(i) where:
125 //! - Degree is the degree of the BSpline surface in
126 //! the given parametric direction, and
127 //! - Multi(i) is the multiplicity of knot number i in
128 //! the given parametric direction.
129 //! There are some special cases, where the knots are
130 //! regularly spaced in one parametric direction (i.e. the
131 //! difference between two consecutive knots is a constant).
132 //! - "Uniform": all the multiplicities are equal to 1.
133 //! - "Quasi-uniform": all the multiplicities are equal to 1,
134 //! except for the first and last knots in this parametric
135 //! direction, and these are equal to Degree + 1.
136 //! - "Piecewise Bezier": all the multiplicities are equal to
137 //! Degree except for the first and last knots, which
138 //! are equal to Degree + 1. This surface is a
139 //! concatenation of Bezier patches in the given
140 //! parametric direction.
141 //! If the BSpline surface is not periodic in a given
142 //! parametric direction, the bounds of the knots and
143 //! multiplicities tables are 1 and NbKnots, where
144 //! NbKnots is the number of knots of the BSpline
145 //! surface in that parametric direction.
146 //! If the BSpline surface is periodic in a given parametric
147 //! direction, and there are k periodic knots and p
148 //! periodic poles in that parametric direction:
149 //! - the period is such that:
150 //! period = Knot(k+1) - Knot(1), and
151 //! - the poles and knots tables in that parametric
152 //! direction can be considered as infinite tables, such that:
153 //! Knot(i+k) = Knot(i) + period, and
154 //! Pole(i+p) = Pole(i)
155 //! Note: The data structure tables for a periodic BSpline
156 //! surface are more complex than those of a non-periodic one.
158 //! . A survey of curve and surface methods in CADG Wolfgang BOHM
160 //! . On de Boor-like algorithms and blossoming Wolfgang BOEHM
162 //! . Blossoming and knot insertion algorithms for B-spline curves
163 //! Ronald N. GOLDMAN
164 //! . Modelisation des surfaces en CAO, Henri GIAUME Peugeot SA
165 //! . Curves and Surfaces for Computer Aided Geometric Design,
166 //! a practical guide Gerald Farin
167 class Geom_BSplineSurface : public Geom_BoundedSurface
173 //! Creates a non-rational b-spline surface (weights
174 //! default value is 1.).
175 //! The following conditions must be verified.
176 //! 0 < UDegree <= MaxDegree.
177 //! UKnots.Length() == UMults.Length() >= 2
178 //! UKnots(i) < UKnots(i+1) (Knots are increasing)
179 //! 1 <= UMults(i) <= UDegree
180 //! On a non uperiodic surface the first and last
181 //! umultiplicities may be UDegree+1 (this is even
182 //! recommended if you want the curve to start and finish on
183 //! the first and last pole).
184 //! On a uperiodic surface the first and the last
185 //! umultiplicities must be the same.
186 //! on non-uperiodic surfaces
187 //! Poles.ColLength() == Sum(UMults(i)) - UDegree - 1 >= 2
188 //! on uperiodic surfaces
189 //! Poles.ColLength() == Sum(UMults(i)) except the first or last
190 //! The previous conditions for U holds also for V, with the
191 //! RowLength of the poles.
192 Standard_EXPORT Geom_BSplineSurface(const TColgp_Array2OfPnt& Poles, const TColStd_Array1OfReal& UKnots, const TColStd_Array1OfReal& VKnots, const TColStd_Array1OfInteger& UMults, const TColStd_Array1OfInteger& VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean UPeriodic = Standard_False, const Standard_Boolean VPeriodic = Standard_False);
194 //! Creates a non-rational b-spline surface (weights
195 //! default value is 1.).
197 //! The following conditions must be verified.
198 //! 0 < UDegree <= MaxDegree.
200 //! UKnots.Length() == UMults.Length() >= 2
202 //! UKnots(i) < UKnots(i+1) (Knots are increasing)
203 //! 1 <= UMults(i) <= UDegree
205 //! On a non uperiodic surface the first and last
206 //! umultiplicities may be UDegree+1 (this is even
207 //! recommended if you want the curve to start and finish on
208 //! the first and last pole).
210 //! On a uperiodic surface the first and the last
211 //! umultiplicities must be the same.
213 //! on non-uperiodic surfaces
215 //! Poles.ColLength() == Sum(UMults(i)) - UDegree - 1 >= 2
217 //! on uperiodic surfaces
219 //! Poles.ColLength() == Sum(UMults(i)) except the first or
222 //! The previous conditions for U holds also for V, with the
223 //! RowLength of the poles.
224 Standard_EXPORT Geom_BSplineSurface(const TColgp_Array2OfPnt& Poles, const TColStd_Array2OfReal& Weights, const TColStd_Array1OfReal& UKnots, const TColStd_Array1OfReal& VKnots, const TColStd_Array1OfInteger& UMults, const TColStd_Array1OfInteger& VMults, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Boolean UPeriodic = Standard_False, const Standard_Boolean VPeriodic = Standard_False);
226 //! Exchanges the u and v parametric directions on
227 //! this BSpline surface.
228 //! As a consequence:
229 //! - the poles and weights tables are transposed,
230 //! - the knots and multiplicities tables are exchanged,
231 //! - degrees of continuity, and rational, periodic and
232 //! uniform characteristics are exchanged, and
233 //! - the orientation of the surface is inverted.
234 Standard_EXPORT void ExchangeUV();
236 //! Sets the surface U periodic.
237 //! Modifies this surface to be periodic in the U
238 //! parametric direction.
239 //! To become periodic in a given parametric direction a
240 //! surface must be closed in that parametric direction,
241 //! and the knot sequence relative to that direction must be periodic.
242 //! To generate this periodic sequence of knots, the
243 //! functions FirstUKnotIndex and LastUKnotIndex are used to
244 //! compute I1 and I2. These are the indexes, in the
245 //! knot array associated with the given parametric
246 //! direction, of the knots that correspond to the first and
247 //! last parameters of this BSpline surface in the given
248 //! parametric direction. Hence the period is:
249 //! Knots(I1) - Knots(I2)
250 //! As a result, the knots and poles tables are modified.
252 //! Standard_ConstructionError if the surface is not
253 //! closed in the given parametric direction.
254 Standard_EXPORT void SetUPeriodic();
256 //! Sets the surface V periodic.
257 //! Modifies this surface to be periodic in the V
258 //! parametric direction.
259 //! To become periodic in a given parametric direction a
260 //! surface must be closed in that parametric direction,
261 //! and the knot sequence relative to that direction must be periodic.
262 //! To generate this periodic sequence of knots, the
263 //! functions FirstVKnotIndex and LastVKnotIndex are used to
264 //! compute I1 and I2. These are the indexes, in the
265 //! knot array associated with the given parametric
266 //! direction, of the knots that correspond to the first and
267 //! last parameters of this BSpline surface in the given
268 //! parametric direction. Hence the period is:
269 //! Knots(I1) - Knots(I2)
270 //! As a result, the knots and poles tables are modified.
272 //! Standard_ConstructionError if the surface is not
273 //! closed in the given parametric direction.
274 Standard_EXPORT void SetVPeriodic();
276 //! returns the parameter normalized within
277 //! the period if the surface is periodic : otherwise
278 //! does not do anything
279 Standard_EXPORT void PeriodicNormalization (Standard_Real& U, Standard_Real& V) const;
281 //! Assigns the knot of index Index in the knots table in
282 //! the corresponding parametric direction to be the
283 //! origin of this periodic BSpline surface. As a
284 //! consequence, the knots and poles tables are modified.
286 //! Standard_NoSuchObject if this BSpline surface is
287 //! not periodic in the given parametric direction.
288 //! Standard_DomainError if Index is outside the
289 //! bounds of the knots table in the given parametric direction.
290 Standard_EXPORT void SetUOrigin (const Standard_Integer Index);
292 //! Assigns the knot of index Index in the knots table in
293 //! the corresponding parametric direction to be the
294 //! origin of this periodic BSpline surface. As a
295 //! consequence, the knots and poles tables are modified.
297 //! Standard_NoSuchObject if this BSpline surface is
298 //! not periodic in the given parametric direction.
299 //! Standard_DomainError if Index is outside the
300 //! bounds of the knots table in the given parametric direction.
301 Standard_EXPORT void SetVOrigin (const Standard_Integer Index);
303 //! Sets the surface U not periodic.
304 //! Changes this BSpline surface into a non-periodic
305 //! surface along U direction.
306 //! If this surface is already non-periodic, it is not modified.
307 //! Note: the poles and knots tables are modified.
308 Standard_EXPORT void SetUNotPeriodic();
310 //! Sets the surface V not periodic.
311 //! Changes this BSpline surface into a non-periodic
312 //! surface along V direction.
313 //! If this surface is already non-periodic, it is not modified.
314 //! Note: the poles and knots tables are modified.
315 Standard_EXPORT void SetVNotPeriodic();
317 //! Changes the orientation of this BSpline surface in the
318 //! U parametric direction. The bounds of the
319 //! surface are not changed but the given parametric
320 //! direction is reversed. Hence the orientation of the
321 //! surface is reversed.
322 //! The knots and poles tables are modified.
323 Standard_EXPORT void UReverse() Standard_OVERRIDE;
325 //! Changes the orientation of this BSpline surface in the
326 //! V parametric direction. The bounds of the
327 //! surface are not changed but the given parametric
328 //! direction is reversed. Hence the orientation of the
329 //! surface is reversed.
330 //! The knots and poles tables are modified.
331 Standard_EXPORT void VReverse() Standard_OVERRIDE;
333 //! Computes the u parameter on the modified
334 //! surface, produced by reversing its U parametric
335 //! direction, for the point of u parameter U, on this BSpline surface.
336 //! For a BSpline surface, these functions return respectively:
337 //! - UFirst + ULast - U,
338 //! where UFirst, ULast are
339 //! the values of the first and last parameters of this
340 //! BSpline surface, in the u parametric directions.
341 Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
343 //! Computes the v parameter on the modified
344 //! surface, produced by reversing its V parametric
345 //! direction, for the point of v parameter V on this BSpline surface.
346 //! For a BSpline surface, these functions return respectively:
347 //! - VFirst + VLast - V,
348 //! VFirst and VLast are
349 //! the values of the first and last parameters of this
350 //! BSpline surface, in the v pametric directions.
351 Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real V) const Standard_OVERRIDE;
353 //! Increases the degrees of this BSpline surface to
354 //! UDegree and VDegree in the u and v parametric
355 //! directions respectively. As a result, the tables of poles,
356 //! weights and multiplicities are modified. The tables of
357 //! knots is not changed.
358 //! Note: Nothing is done if the given degree is less than
359 //! or equal to the current degree in the corresponding
360 //! parametric direction.
362 //! Standard_ConstructionError if UDegree or
363 //! VDegree is greater than
364 //! Geom_BSplineSurface::MaxDegree().
365 Standard_EXPORT void IncreaseDegree (const Standard_Integer UDegree, const Standard_Integer VDegree);
367 //! Inserts into the knots table for the U
368 //! parametric direction of this BSpline surface:
369 //! - the values of the array Knots, with their respective
370 //! multiplicities, Mults.
371 //! If the knot value to insert already exists in the table, its multiplicity is:
372 //! - increased by M, if Add is true (the default), or
373 //! - increased to M, if Add is false.
374 //! The tolerance criterion used to check the equality of
375 //! the knots is the larger of the values ParametricTolerance and
376 //! Standard_Real::Epsilon(val), where val is the knot value to be inserted.
378 //! - If a given multiplicity coefficient is null, or negative, nothing is done.
379 //! - The new multiplicity of a knot is limited to the degree of this BSpline surface in the
380 //! corresponding parametric direction.
382 //! Standard_ConstructionError if a knot value to
383 //! insert is outside the bounds of this BSpline surface in
384 //! the specified parametric direction. The comparison
385 //! uses the precision criterion ParametricTolerance.
386 Standard_EXPORT void InsertUKnots (const TColStd_Array1OfReal& Knots, const TColStd_Array1OfInteger& Mults, const Standard_Real ParametricTolerance = 0.0, const Standard_Boolean Add = Standard_True);
388 //! Inserts into the knots table for the V
389 //! parametric direction of this BSpline surface:
390 //! - the values of the array Knots, with their respective
391 //! multiplicities, Mults.
392 //! If the knot value to insert already exists in the table, its multiplicity is:
393 //! - increased by M, if Add is true (the default), or
394 //! - increased to M, if Add is false.
395 //! The tolerance criterion used to check the equality of
396 //! the knots is the larger of the values ParametricTolerance and
397 //! Standard_Real::Epsilon(val), where val is the knot value to be inserted.
399 //! - If a given multiplicity coefficient is null, or negative, nothing is done.
400 //! - The new multiplicity of a knot is limited to the degree of this BSpline surface in the
401 //! corresponding parametric direction.
403 //! Standard_ConstructionError if a knot value to
404 //! insert is outside the bounds of this BSpline surface in
405 //! the specified parametric direction. The comparison
406 //! uses the precision criterion ParametricTolerance.
407 Standard_EXPORT void InsertVKnots (const TColStd_Array1OfReal& Knots, const TColStd_Array1OfInteger& Mults, const Standard_Real ParametricTolerance = 0.0, const Standard_Boolean Add = Standard_True);
409 //! Reduces to M the multiplicity of the knot of index
410 //! Index in the U parametric direction. If M is 0, the knot is removed.
411 //! With a modification of this type, the table of poles is also modified.
412 //! Two different algorithms are used systematically to
413 //! compute the new poles of the surface. For each
414 //! pole, the distance between the pole calculated
415 //! using the first algorithm and the same pole
416 //! calculated using the second algorithm, is checked. If
417 //! this distance is less than Tolerance it ensures that
418 //! the surface is not modified by more than Tolerance.
419 //! Under these conditions, the function returns true;
420 //! otherwise, it returns false.
421 //! A low tolerance prevents modification of the
422 //! surface. A high tolerance "smoothes" the surface.
424 //! Standard_OutOfRange if Index is outside the
425 //! bounds of the knots table of this BSpline surface.
426 Standard_EXPORT Standard_Boolean RemoveUKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance);
428 //! Reduces to M the multiplicity of the knot of index
429 //! Index in the V parametric direction. If M is 0, the knot is removed.
430 //! With a modification of this type, the table of poles is also modified.
431 //! Two different algorithms are used systematically to
432 //! compute the new poles of the surface. For each
433 //! pole, the distance between the pole calculated
434 //! using the first algorithm and the same pole
435 //! calculated using the second algorithm, is checked. If
436 //! this distance is less than Tolerance it ensures that
437 //! the surface is not modified by more than Tolerance.
438 //! Under these conditions, the function returns true;
439 //! otherwise, it returns false.
440 //! A low tolerance prevents modification of the
441 //! surface. A high tolerance "smoothes" the surface.
443 //! Standard_OutOfRange if Index is outside the
444 //! bounds of the knots table of this BSpline surface.
445 Standard_EXPORT Standard_Boolean RemoveVKnot (const Standard_Integer Index, const Standard_Integer M, const Standard_Real Tolerance);
448 //! Increases the multiplicity of the knot of range UIndex
449 //! in the UKnots sequence.
450 //! M is the new multiplicity. M must be greater than the
451 //! previous multiplicity and lower or equal to the degree
452 //! of the surface in the U parametric direction.
453 //! Raised if M is not in the range [1, UDegree]
455 //! Raised if UIndex is not in the range [FirstUKnotIndex,
456 //! LastUKnotIndex] given by the methods with the same name.
457 Standard_EXPORT void IncreaseUMultiplicity (const Standard_Integer UIndex, const Standard_Integer M);
460 //! Increases until order M the multiplicity of the set of knots
461 //! FromI1,...., ToI2 in the U direction. This method can be used
462 //! to make a B_spline surface into a PiecewiseBezier B_spline
464 //! If <me> was uniform, it can become non uniform.
466 //! Raised if FromI1 or ToI2 is out of the range [FirstUKnotIndex,
469 //! M should be greater than the previous multiplicity of the
470 //! all the knots FromI1,..., ToI2 and lower or equal to the
471 //! Degree of the surface in the U parametric direction.
472 Standard_EXPORT void IncreaseUMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer M);
475 //! Increments the multiplicity of the consecutives uknots FromI1..ToI2
476 //! by step. The multiplicity of each knot FromI1,.....,ToI2 must be
477 //! lower or equal to the UDegree of the B_spline.
479 //! Raised if FromI1 or ToI2 is not in the range
480 //! [FirstUKnotIndex, LastUKnotIndex]
482 //! Raised if one knot has a multiplicity greater than UDegree.
483 Standard_EXPORT void IncrementUMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer Step);
486 //! Increases the multiplicity of a knot in the V direction.
487 //! M is the new multiplicity.
489 //! M should be greater than the previous multiplicity and lower
490 //! than the degree of the surface in the V parametric direction.
492 //! Raised if VIndex is not in the range [FirstVKnotIndex,
493 //! LastVKnotIndex] given by the methods with the same name.
494 Standard_EXPORT void IncreaseVMultiplicity (const Standard_Integer VIndex, const Standard_Integer M);
497 //! Increases until order M the multiplicity of the set of knots
498 //! FromI1,...., ToI2 in the V direction. This method can be used to
499 //! make a BSplineSurface into a PiecewiseBezier B_spline
500 //! surface. If <me> was uniform, it can become non-uniform.
502 //! Raised if FromI1 or ToI2 is out of the range [FirstVKnotIndex,
503 //! LastVKnotIndex] given by the methods with the same name.
505 //! M should be greater than the previous multiplicity of the
506 //! all the knots FromI1,..., ToI2 and lower or equal to the
507 //! Degree of the surface in the V parametric direction.
508 Standard_EXPORT void IncreaseVMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer M);
511 //! Increments the multiplicity of the consecutives vknots FromI1..ToI2
512 //! by step. The multiplicity of each knot FromI1,.....,ToI2 must be
513 //! lower or equal to the VDegree of the B_spline.
515 //! Raised if FromI1 or ToI2 is not in the range
516 //! [FirstVKnotIndex, LastVKnotIndex]
518 //! Raised if one knot has a multiplicity greater than VDegree.
519 Standard_EXPORT void IncrementVMultiplicity (const Standard_Integer FromI1, const Standard_Integer ToI2, const Standard_Integer Step);
522 //! Inserts a knot value in the sequence of UKnots. If U is a knot
523 //! value this method increases the multiplicity of the knot if the
524 //! previous multiplicity was lower than M else it does nothing. The
525 //! tolerance criterion is ParametricTolerance. ParametricTolerance
526 //! should be greater or equal than Resolution from package gp.
528 //! Raised if U is out of the bounds [U1, U2] given by the methods
529 //! Bounds, the criterion ParametricTolerance is used.
530 //! Raised if M is not in the range [1, UDegree].
531 Standard_EXPORT void InsertUKnot (const Standard_Real U, const Standard_Integer M, const Standard_Real ParametricTolerance, const Standard_Boolean Add = Standard_True);
534 //! Inserts a knot value in the sequence of VKnots. If V is a knot
535 //! value this method increases the multiplicity of the knot if the
536 //! previous multiplicity was lower than M otherwise it does nothing.
537 //! The tolerance criterion is ParametricTolerance.
538 //! ParametricTolerance should be greater or equal than Resolution
541 //! raises if V is out of the Bounds [V1, V2] given by the methods
542 //! Bounds, the criterion ParametricTolerance is used.
543 //! raises if M is not in the range [1, VDegree].
544 Standard_EXPORT void InsertVKnot (const Standard_Real V, const Standard_Integer M, const Standard_Real ParametricTolerance, const Standard_Boolean Add = Standard_True);
547 //! Segments the surface between U1 and U2 in the U-Direction.
548 //! between V1 and V2 in the V-Direction.
549 //! The control points are modified, the first and the last point
550 //! are not the same.
552 //! Parameters theUTolerance, theVTolerance define the possible proximity along the corresponding
553 //! direction of the segment boundaries and B-spline knots to treat them as equal.
556 //! Even if <me> is not closed it can become closed after the
557 //! segmentation for example if U1 or U2 are out of the bounds
558 //! of the surface <me> or if the surface makes loop.
559 //! raises if U2 < U1 or V2 < V1.
560 //! Standard_DomainError if U2 - U1 exceeds the uperiod for uperiodic surfaces.
561 //! i.e. ((U2 - U1) - UPeriod) > Precision::PConfusion().
562 //! Standard_DomainError if V2 - V1 exceeds the vperiod for vperiodic surfaces.
563 //! i.e. ((V2 - V1) - VPeriod) > Precision::PConfusion()).
564 Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2,
565 const Standard_Real theUTolerance = Precision::PConfusion(),
566 const Standard_Real theVTolerance = Precision::PConfusion());
569 //! Segments the surface between U1 and U2 in the U-Direction.
570 //! between V1 and V2 in the V-Direction.
572 //! same as Segment but do nothing if U1 and U2 (resp. V1 and V2) are
573 //! equal to the bounds in U (resp. in V) of <me>.
574 //! For example, if <me> is periodic in V, it will be always periodic
575 //! in V after the segmentation if the bounds in V are unchanged
577 //! Parameters theUTolerance, theVTolerance define the possible proximity along the corresponding
578 //! direction of the segment boundaries and B-spline knots to treat them as equal.
581 //! Even if <me> is not closed it can become closed after the
582 //! segmentation for example if U1 or U2 are out of the bounds
583 //! of the surface <me> or if the surface makes loop.
584 //! raises if U2 < U1 or V2 < V1.
585 //! Standard_DomainError if U2 - U1 exceeds the uperiod for uperiodic surfaces.
586 //! i.e. ((U2 - U1) - UPeriod) > Precision::PConfusion().
587 //! Standard_DomainError if V2 - V1 exceeds the vperiod for vperiodic surfaces.
588 //! i.e. ((V2 - V1) - VPeriod) > Precision::PConfusion()).
589 Standard_EXPORT void CheckAndSegment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2,
590 const Standard_Real theUTolerance = Precision::PConfusion(),
591 const Standard_Real theVTolerance = Precision::PConfusion());
593 //! Substitutes the UKnots of range UIndex with K.
595 //! Raised if UIndex < 1 or UIndex > NbUKnots
597 //! Raised if K >= UKnots(UIndex+1) or K <= UKnots(UIndex-1)
598 Standard_EXPORT void SetUKnot (const Standard_Integer UIndex, const Standard_Real K);
600 //! Changes all the U-knots of the surface.
601 //! The multiplicity of the knots are not modified.
603 //! Raised if there is an index such that UK (Index+1) <= UK (Index).
605 //! Raised if UK.Lower() < 1 or UK.Upper() > NbUKnots
606 Standard_EXPORT void SetUKnots (const TColStd_Array1OfReal& UK);
609 //! Changes the value of the UKnots of range UIndex and
610 //! increases its multiplicity.
612 //! Raised if UIndex is not in the range [FirstUKnotIndex,
613 //! LastUKnotIndex] given by the methods with the same name.
615 //! Raised if K >= UKnots(UIndex+1) or K <= UKnots(UIndex-1)
616 //! M must be lower than UDegree and greater than the previous
617 //! multiplicity of the knot of range UIndex.
618 Standard_EXPORT void SetUKnot (const Standard_Integer UIndex, const Standard_Real K, const Standard_Integer M);
620 //! Substitutes the VKnots of range VIndex with K.
622 //! Raised if VIndex < 1 or VIndex > NbVKnots
624 //! Raised if K >= VKnots(VIndex+1) or K <= VKnots(VIndex-1)
625 Standard_EXPORT void SetVKnot (const Standard_Integer VIndex, const Standard_Real K);
627 //! Changes all the V-knots of the surface.
628 //! The multiplicity of the knots are not modified.
630 //! Raised if there is an index such that VK (Index+1) <= VK (Index).
632 //! Raised if VK.Lower() < 1 or VK.Upper() > NbVKnots
633 Standard_EXPORT void SetVKnots (const TColStd_Array1OfReal& VK);
636 //! Changes the value of the VKnots of range VIndex and increases
637 //! its multiplicity.
639 //! Raised if VIndex is not in the range [FirstVKnotIndex,
640 //! LastVKnotIndex] given by the methods with the same name.
642 //! Raised if K >= VKnots(VIndex+1) or K <= VKnots(VIndex-1)
643 //! M must be lower than VDegree and greater than the previous
644 //! multiplicity of the knot of range VIndex.
645 Standard_EXPORT void SetVKnot (const Standard_Integer VIndex, const Standard_Real K, const Standard_Integer M);
648 //! Locates the parametric value U in the sequence of UKnots.
649 //! If "WithKnotRepetition" is True we consider the knot's
650 //! representation with repetition of multiple knot value,
651 //! otherwise we consider the knot's representation with
652 //! no repetition of multiple knot values.
653 //! UKnots (I1) <= U <= UKnots (I2)
654 //! . if I1 = I2 U is a knot value (the tolerance criterion
655 //! ParametricTolerance is used).
656 //! . if I1 < 1 => U < UKnots(1) - Abs(ParametricTolerance)
657 //! . if I2 > NbUKnots => U > UKnots(NbUKnots)+Abs(ParametricTolerance)
658 Standard_EXPORT void LocateU (const Standard_Real U, const Standard_Real ParametricTolerance, Standard_Integer& I1, Standard_Integer& I2, const Standard_Boolean WithKnotRepetition = Standard_False) const;
661 //! Locates the parametric value V in the sequence of knots.
662 //! If "WithKnotRepetition" is True we consider the knot's
663 //! representation with repetition of multiple knot value,
664 //! otherwise we consider the knot's representation with
665 //! no repetition of multiple knot values.
666 //! VKnots (I1) <= V <= VKnots (I2)
667 //! . if I1 = I2 V is a knot value (the tolerance criterion
668 //! ParametricTolerance is used).
669 //! . if I1 < 1 => V < VKnots(1) - Abs(ParametricTolerance)
670 //! . if I2 > NbVKnots => V > VKnots(NbVKnots)+Abs(ParametricTolerance)
671 //! poles insertion and removing
672 //! The following methods are available only if the surface
673 //! is Uniform or QuasiUniform in the considered direction
674 //! The knot repartition is modified.
675 Standard_EXPORT void LocateV (const Standard_Real V, const Standard_Real ParametricTolerance, Standard_Integer& I1, Standard_Integer& I2, const Standard_Boolean WithKnotRepetition = Standard_False) const;
678 //! Substitutes the pole of range (UIndex, VIndex) with P.
679 //! If the surface is rational the weight of range (UIndex, VIndex)
682 //! Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or
683 //! VIndex > NbVPoles.
684 Standard_EXPORT void SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt& P);
687 //! Substitutes the pole and the weight of range (UIndex, VIndex)
690 //! Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or
691 //! VIndex > NbVPoles.
692 //! Raised if Weight <= Resolution from package gp.
693 Standard_EXPORT void SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt& P, const Standard_Real Weight);
696 //! Changes a column of poles or a part of this column.
697 //! Raised if Vindex < 1 or VIndex > NbVPoles.
699 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles.
700 Standard_EXPORT void SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles);
703 //! Changes a column of poles or a part of this column with the
704 //! corresponding weights. If the surface was rational it can
705 //! become non rational. If the surface was non rational it can
707 //! Raised if Vindex < 1 or VIndex > NbVPoles.
709 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles
710 //! Raised if the bounds of CPoleWeights are not the same as the
711 //! bounds of CPoles.
712 //! Raised if one of the weight value of CPoleWeights is lower or
713 //! equal to Resolution from package gp.
714 Standard_EXPORT void SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
717 //! Changes a row of poles or a part of this row with the
718 //! corresponding weights. If the surface was rational it can
719 //! become non rational. If the surface was non rational it can
721 //! Raised if Uindex < 1 or UIndex > NbUPoles.
723 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles
724 //! raises if the bounds of CPoleWeights are not the same as the
725 //! bounds of CPoles.
726 //! Raised if one of the weight value of CPoleWeights is lower or
727 //! equal to Resolution from package gp.
728 Standard_EXPORT void SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
731 //! Changes a row of poles or a part of this row.
732 //! Raised if Uindex < 1 or UIndex > NbUPoles.
734 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles.
735 Standard_EXPORT void SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles);
738 //! Changes the weight of the pole of range UIndex, VIndex.
739 //! If the surface was non rational it can become rational.
740 //! If the surface was rational it can become non rational.
742 //! Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or
743 //! VIndex > NbVPoles
745 //! Raised if weight is lower or equal to Resolution from
747 Standard_EXPORT void SetWeight (const Standard_Integer UIndex, const Standard_Integer VIndex, const Standard_Real Weight);
750 //! Changes a column of weights of a part of this column.
752 //! Raised if VIndex < 1 or VIndex > NbVPoles
754 //! Raised if CPoleWeights.Lower() < 1 or
755 //! CPoleWeights.Upper() > NbUPoles.
756 //! Raised if a weight value is lower or equal to Resolution
758 Standard_EXPORT void SetWeightCol (const Standard_Integer VIndex, const TColStd_Array1OfReal& CPoleWeights);
761 //! Changes a row of weights or a part of this row.
763 //! Raised if UIndex < 1 or UIndex > NbUPoles
765 //! Raised if CPoleWeights.Lower() < 1 or
766 //! CPoleWeights.Upper() > NbVPoles.
767 //! Raised if a weight value is lower or equal to Resolution
769 Standard_EXPORT void SetWeightRow (const Standard_Integer UIndex, const TColStd_Array1OfReal& CPoleWeights);
771 //! Move a point with parameter U and V to P.
772 //! given u,v as parameters) to reach a new position
773 //! UIndex1, UIndex2, VIndex1, VIndex2:
774 //! indicates the poles which can be moved
775 //! if Problem in BSplineBasis calculation, no change
776 //! for the curve and
777 //! UFirstIndex, VLastIndex = 0
778 //! VFirstIndex, VLastIndex = 0
780 //! Raised if UIndex1 < UIndex2 or VIndex1 < VIndex2 or
781 //! UIndex1 < 1 || UIndex1 > NbUPoles or
782 //! UIndex2 < 1 || UIndex2 > NbUPoles
783 //! VIndex1 < 1 || VIndex1 > NbVPoles or
784 //! VIndex2 < 1 || VIndex2 > NbVPoles
785 //! characteristics of the surface
786 Standard_EXPORT void MovePoint (const Standard_Real U, const Standard_Real V, const gp_Pnt& P, const Standard_Integer UIndex1, const Standard_Integer UIndex2, const Standard_Integer VIndex1, const Standard_Integer VIndex2, Standard_Integer& UFirstIndex, Standard_Integer& ULastIndex, Standard_Integer& VFirstIndex, Standard_Integer& VLastIndex);
789 //! Returns true if the first control points row and the last
790 //! control points row are identical. The tolerance criterion
791 //! is Resolution from package gp.
792 Standard_EXPORT Standard_Boolean IsUClosed() const Standard_OVERRIDE;
795 //! Returns true if the first control points column and the
796 //! last last control points column are identical.
797 //! The tolerance criterion is Resolution from package gp.
798 Standard_EXPORT Standard_Boolean IsVClosed() const Standard_OVERRIDE;
801 //! Returns True if the order of continuity of the surface in the
802 //! U direction is N.
804 Standard_EXPORT Standard_Boolean IsCNu (const Standard_Integer N) const Standard_OVERRIDE;
807 //! Returns True if the order of continuity of the surface
808 //! in the V direction is N.
810 Standard_EXPORT Standard_Boolean IsCNv (const Standard_Integer N) const Standard_OVERRIDE;
813 //! Returns True if the surface is closed in the U direction
814 //! and if the B-spline has been turned into a periodic surface
815 //! using the function SetUPeriodic.
816 Standard_EXPORT Standard_Boolean IsUPeriodic() const Standard_OVERRIDE;
819 //! Returns False if for each row of weights all the weights
821 //! The tolerance criterion is resolution from package gp.
824 //! if Weights = |0.5, 0.5, 0.5| returns False
826 Standard_EXPORT Standard_Boolean IsURational() const;
829 //! Returns True if the surface is closed in the V direction
830 //! and if the B-spline has been turned into a periodic
831 //! surface using the function SetVPeriodic.
832 Standard_EXPORT Standard_Boolean IsVPeriodic() const Standard_OVERRIDE;
835 //! Returns False if for each column of weights all the weights
837 //! The tolerance criterion is resolution from package gp.
840 //! if Weights = |1.0, 2.0, 0.5| returns False
842 Standard_EXPORT Standard_Boolean IsVRational() const;
845 //! Returns the parametric bounds of the surface.
847 //! These parametric values are the bounds of the array of
848 //! knots UKnots and VKnots only if the first knots and the
849 //! last knots have a multiplicity equal to UDegree + 1 or
851 Standard_EXPORT void Bounds (Standard_Real& U1, Standard_Real& U2, Standard_Real& V1, Standard_Real& V2) const Standard_OVERRIDE;
854 //! Returns the continuity of the surface :
855 //! C0 : only geometric continuity,
856 //! C1 : continuity of the first derivative all along the Surface,
857 //! C2 : continuity of the second derivative all along the Surface,
858 //! C3 : continuity of the third derivative all along the Surface,
859 //! CN : the order of continuity is infinite.
860 //! A B-spline surface is infinitely continuously differentiable
861 //! for the couple of parameters U, V such that U != UKnots(i)
862 //! and V != VKnots(i). The continuity of the surface at a knot
863 //! value depends on the multiplicity of this knot.
865 //! If the surface is C1 in the V direction and C2 in the U
866 //! direction this function returns Shape = C1.
867 Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE;
870 //! Computes the Index of the UKnots which gives the first
871 //! parametric value of the surface in the U direction.
872 //! The UIso curve corresponding to this value is a
873 //! boundary curve of the surface.
874 Standard_EXPORT Standard_Integer FirstUKnotIndex() const;
877 //! Computes the Index of the VKnots which gives the
878 //! first parametric value of the surface in the V direction.
879 //! The VIso curve corresponding to this knot is a boundary
880 //! curve of the surface.
881 Standard_EXPORT Standard_Integer FirstVKnotIndex() const;
884 //! Computes the Index of the UKnots which gives the
885 //! last parametric value of the surface in the U direction.
886 //! The UIso curve corresponding to this knot is a boundary
887 //! curve of the surface.
888 Standard_EXPORT Standard_Integer LastUKnotIndex() const;
891 //! Computes the Index of the VKnots which gives the
892 //! last parametric value of the surface in the V direction.
893 //! The VIso curve corresponding to this knot is a
894 //! boundary curve of the surface.
895 Standard_EXPORT Standard_Integer LastVKnotIndex() const;
897 //! Returns the number of knots in the U direction.
898 Standard_EXPORT Standard_Integer NbUKnots() const;
900 //! Returns number of poles in the U direction.
901 Standard_EXPORT Standard_Integer NbUPoles() const;
903 //! Returns the number of knots in the V direction.
904 Standard_EXPORT Standard_Integer NbVKnots() const;
906 //! Returns the number of poles in the V direction.
907 Standard_EXPORT Standard_Integer NbVPoles() const;
910 //! Returns the pole of range (UIndex, VIndex).
912 //! Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or
913 //! VIndex > NbVPoles.
914 Standard_EXPORT const gp_Pnt& Pole(const Standard_Integer UIndex, const Standard_Integer VIndex) const;
916 //! Returns the poles of the B-spline surface.
918 //! Raised if the length of P in the U and V direction
919 //! is not equal to NbUpoles and NbVPoles.
920 Standard_EXPORT void Poles (TColgp_Array2OfPnt& P) const;
922 //! Returns the poles of the B-spline surface.
923 Standard_EXPORT const TColgp_Array2OfPnt& Poles() const;
926 //! Returns the degree of the normalized B-splines Ni,n in the U
928 Standard_EXPORT Standard_Integer UDegree() const;
931 //! Returns the Knot value of range UIndex.
932 //! Raised if UIndex < 1 or UIndex > NbUKnots
933 Standard_EXPORT Standard_Real UKnot (const Standard_Integer UIndex) const;
936 //! Returns NonUniform or Uniform or QuasiUniform or
937 //! PiecewiseBezier. If all the knots differ by a
938 //! positive constant from the preceding knot in the U
939 //! direction the B-spline surface can be :
940 //! - Uniform if all the knots are of multiplicity 1,
941 //! - QuasiUniform if all the knots are of multiplicity 1
942 //! except for the first and last knot which are of
943 //! multiplicity Degree + 1,
944 //! - PiecewiseBezier if the first and last knots have
945 //! multiplicity Degree + 1 and if interior knots have
946 //! multiplicity Degree
947 //! otherwise the surface is non uniform in the U direction
948 //! The tolerance criterion is Resolution from package gp.
949 Standard_EXPORT GeomAbs_BSplKnotDistribution UKnotDistribution() const;
951 //! Returns the knots in the U direction.
953 //! Raised if the length of Ku is not equal to the number of knots
954 //! in the U direction.
955 Standard_EXPORT void UKnots (TColStd_Array1OfReal& Ku) const;
957 //! Returns the knots in the U direction.
958 Standard_EXPORT const TColStd_Array1OfReal& UKnots() const;
960 //! Returns the uknots sequence.
961 //! In this sequence the knots with a multiplicity greater than 1
964 //! Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}
966 //! Raised if the length of Ku is not equal to NbUPoles + UDegree + 1
967 Standard_EXPORT void UKnotSequence (TColStd_Array1OfReal& Ku) const;
969 //! Returns the uknots sequence.
970 //! In this sequence the knots with a multiplicity greater than 1
973 //! Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}
974 Standard_EXPORT const TColStd_Array1OfReal& UKnotSequence() const;
977 //! Returns the multiplicity value of knot of range UIndex in
979 //! Raised if UIndex < 1 or UIndex > NbUKnots.
980 Standard_EXPORT Standard_Integer UMultiplicity (const Standard_Integer UIndex) const;
983 //! Returns the multiplicities of the knots in the U direction.
985 //! Raised if the length of Mu is not equal to the number of
986 //! knots in the U direction.
987 Standard_EXPORT void UMultiplicities (TColStd_Array1OfInteger& Mu) const;
989 //! Returns the multiplicities of the knots in the U direction.
990 Standard_EXPORT const TColStd_Array1OfInteger& UMultiplicities() const;
993 //! Returns the degree of the normalized B-splines Ni,d in the
995 Standard_EXPORT Standard_Integer VDegree() const;
997 //! Returns the Knot value of range VIndex.
998 //! Raised if VIndex < 1 or VIndex > NbVKnots
999 Standard_EXPORT Standard_Real VKnot (const Standard_Integer VIndex) const;
1002 //! Returns NonUniform or Uniform or QuasiUniform or
1003 //! PiecewiseBezier. If all the knots differ by a positive
1004 //! constant from the preceding knot in the V direction the
1005 //! B-spline surface can be :
1006 //! - Uniform if all the knots are of multiplicity 1,
1007 //! - QuasiUniform if all the knots are of multiplicity 1
1008 //! except for the first and last knot which are of
1009 //! multiplicity Degree + 1,
1010 //! - PiecewiseBezier if the first and last knots have
1011 //! multiplicity Degree + 1 and if interior knots have
1012 //! multiplicity Degree
1013 //! otherwise the surface is non uniform in the V direction.
1014 //! The tolerance criterion is Resolution from package gp.
1015 Standard_EXPORT GeomAbs_BSplKnotDistribution VKnotDistribution() const;
1017 //! Returns the knots in the V direction.
1019 //! Raised if the length of Kv is not equal to the number of
1020 //! knots in the V direction.
1021 Standard_EXPORT void VKnots (TColStd_Array1OfReal& Kv) const;
1023 //! Returns the knots in the V direction.
1024 Standard_EXPORT const TColStd_Array1OfReal& VKnots() const;
1026 //! Returns the vknots sequence.
1027 //! In this sequence the knots with a multiplicity greater than 1
1030 //! Kv = {k1, k1, k1, k2, k3, k3, k4, k4, k4}
1032 //! Raised if the length of Kv is not equal to NbVPoles + VDegree + 1
1033 Standard_EXPORT void VKnotSequence (TColStd_Array1OfReal& Kv) const;
1035 //! Returns the vknots sequence.
1036 //! In this sequence the knots with a multiplicity greater than 1
1039 //! Ku = {k1, k1, k1, k2, k3, k3, k4, k4, k4}
1040 Standard_EXPORT const TColStd_Array1OfReal& VKnotSequence() const;
1043 //! Returns the multiplicity value of knot of range VIndex in
1044 //! the v direction.
1045 //! Raised if VIndex < 1 or VIndex > NbVKnots
1046 Standard_EXPORT Standard_Integer VMultiplicity (const Standard_Integer VIndex) const;
1049 //! Returns the multiplicities of the knots in the V direction.
1051 //! Raised if the length of Mv is not equal to the number of
1052 //! knots in the V direction.
1053 Standard_EXPORT void VMultiplicities (TColStd_Array1OfInteger& Mv) const;
1055 //! Returns the multiplicities of the knots in the V direction.
1056 Standard_EXPORT const TColStd_Array1OfInteger& VMultiplicities() const;
1058 //! Returns the weight value of range UIndex, VIndex.
1060 //! Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1
1061 //! or VIndex > NbVPoles.
1062 Standard_EXPORT Standard_Real Weight (const Standard_Integer UIndex, const Standard_Integer VIndex) const;
1064 //! Returns the weights of the B-spline surface.
1066 //! Raised if the length of W in the U and V direction is
1067 //! not equal to NbUPoles and NbVPoles.
1068 Standard_EXPORT void Weights (TColStd_Array2OfReal& W) const;
1070 //! Returns the weights of the B-spline surface.
1071 //! value and derivatives computation
1072 Standard_EXPORT const TColStd_Array2OfReal* Weights() const;
1074 Standard_EXPORT void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt& P) const Standard_OVERRIDE;
1076 //! Raised if the continuity of the surface is not C1.
1077 Standard_EXPORT void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V) const Standard_OVERRIDE;
1079 //! Raised if the continuity of the surface is not C2.
1080 Standard_EXPORT void D2 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V, gp_Vec& D2U, gp_Vec& D2V, gp_Vec& D2UV) const Standard_OVERRIDE;
1082 //! Raised if the continuity of the surface is not C3.
1083 Standard_EXPORT void D3 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V, gp_Vec& D2U, gp_Vec& D2V, gp_Vec& D2UV, gp_Vec& D3U, gp_Vec& D3V, gp_Vec& D3UUV, gp_Vec& D3UVV) const Standard_OVERRIDE;
1086 //! Nu is the order of derivation in the U parametric direction and
1087 //! Nv is the order of derivation in the V parametric direction.
1089 //! Raised if the continuity of the surface is not CNu in the U
1090 //! direction and CNv in the V direction.
1092 //! Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
1094 //! The following functions computes the point for the
1095 //! parametric values (U, V) and the derivatives at
1096 //! this point on the B-spline surface patch delimited
1097 //! with the knots FromUK1, FromVK1 and the knots ToUK2,
1098 //! ToVK2. (U, V) can be out of these parametric bounds
1099 //! but for the computation we only use the definition
1100 //! of the surface between these knots. This method is
1101 //! useful to compute local derivative, if the order of
1102 //! continuity of the whole surface is not greater enough.
1103 //! Inside the parametric knot's domain previously defined
1104 //! the evaluations are the same as if we consider the whole
1105 //! definition of the surface. Of course the evaluations are
1106 //! different outside this parametric domain.
1107 Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const Standard_OVERRIDE;
1109 //! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
1110 Standard_EXPORT void LocalD0 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, gp_Pnt& P) const;
1113 //! Raised if the local continuity of the surface is not C1
1114 //! between the knots FromUK1, ToUK2 and FromVK1, ToVK2.
1115 //! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
1116 Standard_EXPORT void LocalD1 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V) const;
1119 //! Raised if the local continuity of the surface is not C2
1120 //! between the knots FromUK1, ToUK2 and FromVK1, ToVK2.
1121 //! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
1122 Standard_EXPORT void LocalD2 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V, gp_Vec& D2U, gp_Vec& D2V, gp_Vec& D2UV) const;
1125 //! Raised if the local continuity of the surface is not C3
1126 //! between the knots FromUK1, ToUK2 and FromVK1, ToVK2.
1127 //! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
1128 Standard_EXPORT void LocalD3 (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V, gp_Vec& D2U, gp_Vec& D2V, gp_Vec& D2UV, gp_Vec& D3U, gp_Vec& D3V, gp_Vec& D3UUV, gp_Vec& D3UVV) const;
1131 //! Raised if the local continuity of the surface is not CNu
1132 //! between the knots FromUK1, ToUK2 and CNv between the knots
1134 //! Raised if FromUK1 = ToUK2 or FromVK1 = ToVK2.
1135 Standard_EXPORT gp_Vec LocalDN (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2, const Standard_Integer Nu, const Standard_Integer Nv) const;
1138 //! Computes the point of parameter U, V on the BSpline surface patch
1139 //! defines between the knots UK1 UK2, VK1, VK2. U can be out of the
1140 //! bounds [Knot UK1, Knot UK2] and V can be outof the bounds
1141 //! [Knot VK1, Knot VK2] but for the computation we only use the
1142 //! definition of the surface between these knot values.
1143 //! Raises if FromUK1 = ToUK2 or FromVK1 = ToVK2.
1144 Standard_EXPORT gp_Pnt LocalValue (const Standard_Real U, const Standard_Real V, const Standard_Integer FromUK1, const Standard_Integer ToUK2, const Standard_Integer FromVK1, const Standard_Integer ToVK2) const;
1147 //! Computes the U isoparametric curve.
1148 //! A B-spline curve is returned.
1149 Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U) const Standard_OVERRIDE;
1152 //! Computes the V isoparametric curve.
1153 //! A B-spline curve is returned.
1154 Standard_EXPORT Handle(Geom_Curve) VIso (const Standard_Real V) const Standard_OVERRIDE;
1157 //! Computes the U isoparametric curve.
1158 //! If CheckRational=False, no try to make it non-rational.
1159 //! A B-spline curve is returned.
1160 Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U, const Standard_Boolean CheckRational) const;
1163 //! Computes the V isoparametric curve.
1164 //! If CheckRational=False, no try to make it non-rational.
1165 //! A B-spline curve is returned.
1167 Standard_EXPORT Handle(Geom_Curve) VIso (const Standard_Real V, const Standard_Boolean CheckRational) const;
1169 //! Applies the transformation T to this BSpline surface.
1170 Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE;
1173 //! Returns the value of the maximum degree of the normalized
1174 //! B-spline basis functions in the u and v directions.
1175 Standard_EXPORT static Standard_Integer MaxDegree();
1177 //! Computes two tolerance values for this BSpline
1178 //! surface, based on the given tolerance in 3D space
1179 //! Tolerance3D. The tolerances computed are:
1180 //! - UTolerance in the u parametric direction, and
1181 //! - VTolerance in the v parametric direction.
1182 //! If f(u,v) is the equation of this BSpline surface,
1183 //! UTolerance and VTolerance guarantee that :
1184 //! | u1 - u0 | < UTolerance and
1185 //! | v1 - v0 | < VTolerance
1186 //! ====> |f (u1,v1) - f (u0,v0)| < Tolerance3D
1187 Standard_EXPORT void Resolution (const Standard_Real Tolerance3D, Standard_Real& UTolerance, Standard_Real& VTolerance);
1189 //! Creates a new object which is a copy of this BSpline surface.
1190 Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE;
1192 //! Dumps the content of me into the stream
1193 Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE;
1198 DEFINE_STANDARD_RTTIEXT(Geom_BSplineSurface,Geom_BoundedSurface)
1202 //! Segments the surface between U1 and U2 in the U-Direction.
1203 //! between V1 and V2 in the V-Direction.
1204 //! The control points are modified, the first and the last point
1205 //! are not the same.
1207 //! Parameters EpsU, EpsV define the proximity along U-Direction and V-Direction respectively.
1208 void segment(const Standard_Real U1, const Standard_Real U2,
1209 const Standard_Real V1, const Standard_Real V2,
1210 const Standard_Real EpsU, const Standard_Real EpsV,
1211 const Standard_Boolean SegmentInU, const Standard_Boolean SegmentInV);
1217 //! Recompute the flatknots, the knotsdistribution, the
1218 //! continuity for U.
1219 Standard_EXPORT void UpdateUKnots();
1221 //! Recompute the flatknots, the knotsdistribution, the
1222 //! continuity for V.
1223 Standard_EXPORT void UpdateVKnots();
1225 Standard_Boolean urational;
1226 Standard_Boolean vrational;
1227 Standard_Boolean uperiodic;
1228 Standard_Boolean vperiodic;
1229 GeomAbs_BSplKnotDistribution uknotSet;
1230 GeomAbs_BSplKnotDistribution vknotSet;
1231 GeomAbs_Shape Usmooth;
1232 GeomAbs_Shape Vsmooth;
1233 Standard_Integer udeg;
1234 Standard_Integer vdeg;
1235 Handle(TColgp_HArray2OfPnt) poles;
1236 Handle(TColStd_HArray2OfReal) weights;
1237 Handle(TColStd_HArray1OfReal) ufknots;
1238 Handle(TColStd_HArray1OfReal) vfknots;
1239 Handle(TColStd_HArray1OfReal) uknots;
1240 Handle(TColStd_HArray1OfReal) vknots;
1241 Handle(TColStd_HArray1OfInteger) umults;
1242 Handle(TColStd_HArray1OfInteger) vmults;
1243 Standard_Real umaxderivinv;
1244 Standard_Real vmaxderivinv;
1245 Standard_Boolean maxderivinvok;
1256 #endif // _Geom_BSplineSurface_HeaderFile