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_BezierSurface_HeaderFile
18 #define _Geom_BezierSurface_HeaderFile
20 #include <Standard.hxx>
21 #include <Standard_Type.hxx>
23 #include <TColgp_HArray2OfPnt.hxx>
24 #include <TColStd_HArray2OfReal.hxx>
25 #include <Standard_Integer.hxx>
26 #include <Geom_BoundedSurface.hxx>
27 #include <TColgp_Array2OfPnt.hxx>
28 #include <TColStd_Array2OfReal.hxx>
29 #include <TColgp_Array1OfPnt.hxx>
30 #include <TColStd_Array1OfReal.hxx>
31 #include <GeomAbs_Shape.hxx>
32 #include <BSplSLib.hxx>
41 class Geom_BezierSurface;
42 DEFINE_STANDARD_HANDLE(Geom_BezierSurface, Geom_BoundedSurface)
44 //! Describes a rational or non-rational Bezier surface.
45 //! - A non-rational Bezier surface is defined by a table
46 //! of poles (also known as control points).
47 //! - A rational Bezier surface is defined by a table of
48 //! poles with varying associated weights.
49 //! This data is manipulated using two associative 2D arrays:
50 //! - the poles table, which is a 2D array of gp_Pnt, and
51 //! - the weights table, which is a 2D array of reals.
52 //! The bounds of these arrays are:
53 //! - 1 and NbUPoles for the row bounds, where
54 //! NbUPoles is the number of poles of the surface
55 //! in the u parametric direction, and
56 //! - 1 and NbVPoles for the column bounds, where
57 //! NbVPoles is the number of poles of the surface
58 //! in the v parametric direction.
59 //! The poles of the surface, the "control points", are the
60 //! points used to shape and reshape the surface. They
61 //! comprise a rectangular network of points:
62 //! - The points (1, 1), (NbUPoles, 1), (1,
63 //! NbVPoles) and (NbUPoles, NbVPoles)
64 //! are the four parametric "corners" of the surface.
65 //! - The first column of poles and the last column of
66 //! poles define two Bezier curves which delimit the
67 //! surface in the v parametric direction. These are
68 //! the v isoparametric curves corresponding to
69 //! values 0 and 1 of the v parameter.
70 //! - The first row of poles and the last row of poles
71 //! define two Bezier curves which delimit the surface
72 //! in the u parametric direction. These are the u
73 //! isoparametric curves corresponding to values 0
74 //! and 1 of the u parameter.
75 //! It is more difficult to define a geometrical significance
76 //! for the weights. However they are useful for
77 //! representing a quadric surface precisely. Moreover, if
78 //! the weights of all the poles are equal, the surface has
79 //! a polynomial equation, and hence is a "non-rational surface".
80 //! The non-rational surface is a special, but frequently
81 //! used, case, where all poles have identical weights.
82 //! The weights are defined and used only in the case of
83 //! a rational surface. This rational characteristic is
84 //! defined in each parametric direction. Hence, a
85 //! surface can be rational in the u parametric direction,
86 //! and non-rational in the v parametric direction.
87 //! Likewise, the degree of a surface is defined in each
88 //! parametric direction. The degree of a Bezier surface
89 //! in a given parametric direction is equal to the number
90 //! of poles of the surface in that parametric direction,
91 //! minus 1. This must be greater than or equal to 1.
92 //! However, the degree for a Geom_BezierSurface is
93 //! limited to a value of (25) which is defined and
94 //! controlled by the system. This value is returned by the
95 //! function MaxDegree.
96 //! The parameter range for a Bezier surface is [ 0, 1 ]
97 //! in the two parametric directions.
98 //! A Bezier surface can also be closed, or open, in each
99 //! parametric direction. If the first row of poles is
100 //! identical to the last row of poles, the surface is closed
101 //! in the u parametric direction. If the first column of
102 //! poles is identical to the last column of poles, the
103 //! surface is closed in the v parametric direction.
104 //! The continuity of a Bezier surface is infinite in the u
105 //! parametric direction and the in v parametric direction.
106 //! Note: It is not possible to build a Bezier surface with
107 //! negative weights. Any weight value that is less than,
108 //! or equal to, gp::Resolution() is considered
109 //! to be zero. Two weight values, W1 and W2, are
110 //! considered equal if: |W2-W1| <= gp::Resolution()
111 class Geom_BezierSurface : public Geom_BoundedSurface
118 //! Creates a non-rational Bezier surface with a set of poles.
119 //! Control points representation :
120 //! SPoles(Uorigin,Vorigin) ...................SPoles(Uorigin,Vend)
123 //! SPoles(Uend, Vorigin) .....................SPoles(Uend, Vend)
124 //! For the double array the row indice corresponds to the parametric
125 //! U direction and the columns indice corresponds to the parametric
127 //! The weights are defaulted to all being 1.
129 //! Raised if the number of poles of the surface is lower than 2
130 //! or greater than MaxDegree + 1 in one of the two directions
132 Standard_EXPORT Geom_BezierSurface(const TColgp_Array2OfPnt& SurfacePoles);
135 //! Creates a rational Bezier surface with a set of poles and a
137 //! For the double array the row indice corresponds to the parametric
138 //! U direction and the columns indice corresponds to the parametric
140 //! If all the weights are identical the surface is considered as
141 //! non-rational (the tolerance criterion is Resolution from package
144 //! Raised if SurfacePoles and PoleWeights have not the same
145 //! Rowlength or have not the same ColLength.
146 //! Raised if PoleWeights (i, j) <= Resolution from gp;
147 //! Raised if the number of poles of the surface is lower than 2
148 //! or greater than MaxDegree + 1 in one of the two directions U or V.
149 Standard_EXPORT Geom_BezierSurface(const TColgp_Array2OfPnt& SurfacePoles, const TColStd_Array2OfReal& PoleWeights);
151 //! Exchanges the direction U and V on a Bezier surface
152 //! As a consequence:
153 //! - the poles and weights tables are transposed,
154 //! - degrees, rational characteristics and so on are
155 //! exchanged between the two parametric directions, and
156 //! - the orientation of the surface is reversed.
157 Standard_EXPORT void ExchangeUV();
159 //! Increases the degree of this Bezier surface in the two parametric directions.
161 //! Raised if UDegree < UDegree <me> or VDegree < VDegree <me>
162 //! Raised if the degree of the surface is greater than MaxDegree
163 //! in one of the two directions U or V.
164 Standard_EXPORT void Increase (const Standard_Integer UDeg, const Standard_Integer VDeg);
167 //! Inserts a column of poles. If the surface is rational the weights
168 //! values associated with CPoles are equal defaulted to 1.
170 //! Raised if Vindex < 1 or VIndex > NbVPoles.
172 //! raises if VDegree is greater than MaxDegree.
173 //! raises if the Length of CPoles is not equal to NbUPoles
174 Standard_EXPORT void InsertPoleColAfter (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles);
177 //! Inserts a column of poles and weights.
178 //! If the surface was non-rational it can become rational.
180 //! Raised if Vindex < 1 or VIndex > NbVPoles.
182 //! . VDegree is greater than MaxDegree.
183 //! . the Length of CPoles is not equal to NbUPoles
184 //! . a weight value is lower or equal to Resolution from
186 Standard_EXPORT void InsertPoleColAfter (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
189 //! Inserts a column of poles. If the surface is rational the weights
190 //! values associated with CPoles are equal defaulted to 1.
192 //! Raised if Vindex < 1 or VIndex > NbVPoles.
194 //! Raised if VDegree is greater than MaxDegree.
195 //! Raised if the Length of CPoles is not equal to NbUPoles
196 Standard_EXPORT void InsertPoleColBefore (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles);
199 //! Inserts a column of poles and weights.
200 //! If the surface was non-rational it can become rational.
202 //! Raised if Vindex < 1 or VIndex > NbVPoles.
204 //! . VDegree is greater than MaxDegree.
205 //! . the Length of CPoles is not equal to NbUPoles
206 //! . a weight value is lower or equal to Resolution from
208 Standard_EXPORT void InsertPoleColBefore (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
211 //! Inserts a row of poles. If the surface is rational the weights
212 //! values associated with CPoles are equal defaulted to 1.
214 //! Raised if Uindex < 1 or UIndex > NbUPoles.
216 //! Raised if UDegree is greater than MaxDegree.
217 //! Raised if the Length of CPoles is not equal to NbVPoles
218 Standard_EXPORT void InsertPoleRowAfter (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles);
221 //! Inserts a row of poles and weights.
222 //! If the surface was non-rational it can become rational.
224 //! Raised if Uindex < 1 or UIndex > NbUPoles.
226 //! . UDegree is greater than MaxDegree.
227 //! . the Length of CPoles is not equal to NbVPoles
228 //! . a weight value is lower or equal to Resolution from
230 Standard_EXPORT void InsertPoleRowAfter (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
233 //! Inserts a row of poles. If the surface is rational the weights
234 //! values associated with CPoles are equal defaulted to 1.
236 //! Raised if Uindex < 1 or UIndex > NbUPoles.
238 //! Raised if UDegree is greater than MaxDegree.
239 //! Raised if the Length of CPoles is not equal to NbVPoles
240 Standard_EXPORT void InsertPoleRowBefore (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles);
243 //! Inserts a row of poles and weights.
244 //! If the surface was non-rational it can become rational.
246 //! Raised if Uindex < 1 or UIndex > NbUPoles.
248 //! . UDegree is greater than MaxDegree.
249 //! . the Length of CPoles is not equal to NbVPoles
250 //! . a weight value is lower or equal to Resolution from
252 Standard_EXPORT void InsertPoleRowBefore (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
254 //! Removes a column of poles.
255 //! If the surface was rational it can become non-rational.
257 //! Raised if NbVPoles <= 2 after removing, a Bezier surface
258 //! must have at least two columns of poles.
259 //! Raised if Vindex < 1 or VIndex > NbVPoles
260 Standard_EXPORT void RemovePoleCol (const Standard_Integer VIndex);
262 //! Removes a row of poles.
263 //! If the surface was rational it can become non-rational.
265 //! Raised if NbUPoles <= 2 after removing, a Bezier surface
266 //! must have at least two rows of poles.
267 //! Raised if Uindex < 1 or UIndex > NbUPoles
268 Standard_EXPORT void RemovePoleRow (const Standard_Integer UIndex);
270 //! Modifies this Bezier surface by segmenting it
271 //! between U1 and U2 in the u parametric direction,
272 //! and between V1 and V2 in the v parametric
273 //! direction. U1, U2, V1, and V2 can be outside the
274 //! bounds of this surface.
275 //! - U1 and U2 isoparametric Bezier curves,
276 //! segmented between V1 and V2, become the two
277 //! bounds of the surface in the v parametric
278 //! direction (0. and 1. u isoparametric curves).
279 //! - V1 and V2 isoparametric Bezier curves,
280 //! segmented between U1 and U2, become the two
281 //! bounds of the surface in the u parametric
282 //! direction (0. and 1. v isoparametric curves).
283 //! The poles and weights tables are modified, but the
284 //! degree of this surface in the u and v parametric
285 //! directions does not change.
286 //! U1 can be greater than U2, and V1 can be greater
287 //! than V2. In these cases, the corresponding
288 //! parametric direction is inverted. The orientation of
289 //! the surface is inverted if one (and only one)
290 //! parametric direction is inverted.
291 Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2);
293 //! Modifies a pole value.
294 //! If the surface is rational the weight of range (UIndex, VIndex)
297 //! Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1
298 //! or VIndex > NbVPoles.
299 Standard_EXPORT void SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt& P);
302 //! Substitutes the pole and the weight of range UIndex, VIndex.
303 //! If the surface <me> is not rational it can become rational.
304 //! if the surface was rational it can become non-rational.
306 //! raises if UIndex < 1 or UIndex > NbUPoles or VIndex < 1
307 //! or VIndex > NbVPoles.
308 //! Raised if Weight <= Resolution from package gp.
309 Standard_EXPORT void SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt& P, const Standard_Real Weight);
311 //! Modifies a column of poles.
312 //! The length of CPoles can be lower but not greater than NbUPoles
313 //! so you can modify just a part of the column.
314 //! Raised if VIndex < 1 or VIndex > NbVPoles
316 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles
317 Standard_EXPORT void SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles);
319 //! Modifies a column of poles.
320 //! If the surface was rational it can become non-rational
321 //! If the surface was non-rational it can become rational.
322 //! The length of CPoles can be lower but not greater than NbUPoles
323 //! so you can modify just a part of the column.
324 //! Raised if VIndex < 1 or VIndex > NbVPoles
326 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles
327 //! Raised if CPoleWeights and CPoles have not the same bounds.
328 //! Raised if one of the weight value CPoleWeights (i) is lower
329 //! or equal to Resolution from package gp.
330 Standard_EXPORT void SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
332 //! Modifies a row of poles.
333 //! The length of CPoles can be lower but not greater than NbVPoles
334 //! so you can modify just a part of the row.
335 //! Raised if UIndex < 1 or UIndex > NbUPoles
337 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles
338 Standard_EXPORT void SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles);
340 //! Modifies a row of poles and weights.
341 //! If the surface was rational it can become non-rational.
342 //! If the surface was non-rational it can become rational.
343 //! The length of CPoles can be lower but not greater than NbVPoles
344 //! so you can modify just a part of the row.
345 //! Raised if UIndex < 1 or UIndex > NbUPoles
347 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles
348 //! Raised if CPoleWeights and CPoles have not the same bounds.
349 //! Raised if one of the weight value CPoleWeights (i) is lower
350 //! or equal to Resolution from gp.
351 Standard_EXPORT void SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
354 //! Modifies the weight of the pole of range UIndex, VIndex.
355 //! If the surface was non-rational it can become rational.
356 //! If the surface was rational it can become non-rational.
358 //! Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or
359 //! VIndex > NbVPoles.
360 //! Raised if Weight <= Resolution from package gp.
361 Standard_EXPORT void SetWeight (const Standard_Integer UIndex, const Standard_Integer VIndex, const Standard_Real Weight);
363 //! Modifies a column of weights.
364 //! If the surface was rational it can become non-rational.
365 //! If the surface was non-rational it can become rational.
366 //! The length of CPoleWeights can be lower but not greater than
368 //! Raised if VIndex < 1 or VIndex > NbVPoles
370 //! Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() >
372 //! Raised if one of the weight value CPoleWeights (i) is lower
373 //! or equal to Resolution from package gp.
374 Standard_EXPORT void SetWeightCol (const Standard_Integer VIndex, const TColStd_Array1OfReal& CPoleWeights);
376 //! Modifies a row of weights.
377 //! If the surface was rational it can become non-rational.
378 //! If the surface was non-rational it can become rational.
379 //! The length of CPoleWeights can be lower but not greater than
381 //! Raised if UIndex < 1 or UIndex > NbUPoles
383 //! Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() >
385 //! Raised if one of the weight value CPoleWeights (i) is lower
386 //! or equal to Resolution from package gp.
387 Standard_EXPORT void SetWeightRow (const Standard_Integer UIndex, const TColStd_Array1OfReal& CPoleWeights);
389 //! Changes the orientation of this Bezier surface in the
390 //! u parametric direction. The bounds of the
391 //! surface are not changed, but the given parametric
392 //! direction is reversed. Hence, the orientation of the surface is reversed.
393 Standard_EXPORT void UReverse() Standard_OVERRIDE;
395 //! Computes the u (or v) parameter on the modified
396 //! surface, produced by reversing its u (or v) parametric
397 //! direction, for any point of u parameter U (or of v
398 //! parameter V) on this Bezier surface.
399 //! In the case of a Bezier surface, these functions return respectively:
401 Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
403 //! Changes the orientation of this Bezier surface in the
404 //! v parametric direction. The bounds of the
405 //! surface are not changed, but the given parametric
406 //! direction is reversed. Hence, the orientation of the
407 //! surface is reversed.
408 Standard_EXPORT void VReverse() Standard_OVERRIDE;
410 //! Computes the u (or v) parameter on the modified
411 //! surface, produced by reversing its u (or v) parametric
412 //! direction, for any point of u parameter U (or of v
413 //! parameter V) on this Bezier surface.
414 //! In the case of a Bezier surface, these functions return respectively:
416 Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real V) const Standard_OVERRIDE;
418 //! Returns the parametric bounds U1, U2, V1 and V2 of
419 //! this Bezier surface.
420 //! In the case of a Bezier surface, this function returns
421 //! U1 = 0, V1 = 0, U2 = 1, V2 = 1.
422 Standard_EXPORT void Bounds (Standard_Real& U1, Standard_Real& U2, Standard_Real& V1, Standard_Real& V2) const Standard_OVERRIDE;
425 //! Returns the continuity of the surface CN : the order of
426 //! continuity is infinite.
427 Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE;
429 Standard_EXPORT void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt& P) const Standard_OVERRIDE;
431 Standard_EXPORT void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V) const Standard_OVERRIDE;
433 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;
435 //! Computes P, the point of parameters (U, V) of this Bezier surface, and
436 //! - one or more of the following sets of vectors:
437 //! - D1U and D1V, the first derivative vectors at this point,
438 //! - D2U, D2V and D2UV, the second derivative
439 //! vectors at this point,
440 //! - D3U, D3V, D3UUV and D3UVV, the third
441 //! derivative vectors at this point.
442 //! Note: The parameters U and V can be outside the bounds of the surface.
443 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;
445 //! Computes the derivative of order Nu in the u
446 //! parametric direction, and Nv in the v parametric
447 //! direction, at the point of parameters (U, V) of this Bezier surface.
448 //! Note: The parameters U and V can be outside the bounds of the surface.
450 //! Standard_RangeError if:
451 //! - Nu + Nv is less than 1, or Nu or Nv is negative.
452 Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const Standard_OVERRIDE;
454 //! Returns the number of poles in the U direction.
455 Standard_EXPORT Standard_Integer NbUPoles() const;
457 //! Returns the number of poles in the V direction.
458 Standard_EXPORT Standard_Integer NbVPoles() const;
460 //! Returns the pole of range UIndex, VIndex
461 //! Raised if UIndex < 1 or UIndex > NbUPoles, or
462 //! VIndex < 1 or VIndex > NbVPoles.
463 Standard_EXPORT const gp_Pnt& Pole(const Standard_Integer UIndex, const Standard_Integer VIndex) const;
465 //! Returns the poles of the Bezier surface.
467 //! Raised if the length of P in the U an V direction is not equal to
468 //! NbUPoles and NbVPoles.
469 Standard_EXPORT void Poles (TColgp_Array2OfPnt& P) const;
471 //! Returns the poles of the Bezier surface.
472 const TColgp_Array2OfPnt& Poles() const
474 return poles->Array2();
477 //! Returns the degree of the surface in the U direction it is
479 Standard_EXPORT Standard_Integer UDegree() const;
482 //! Computes the U isoparametric curve. For a Bezier surface the
483 //! UIso curve is a Bezier curve.
484 Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U) const Standard_OVERRIDE;
487 //! Returns the degree of the surface in the V direction it is
489 Standard_EXPORT Standard_Integer VDegree() const;
492 //! Computes the V isoparametric curve. For a Bezier surface the
493 //! VIso curve is a Bezier curve.
494 Standard_EXPORT Handle(Geom_Curve) VIso (const Standard_Real V) const Standard_OVERRIDE;
496 //! Returns the weight of range UIndex, VIndex
498 //! Raised if UIndex < 1 or UIndex > NbUPoles, or
499 //! VIndex < 1 or VIndex > NbVPoles.
500 Standard_EXPORT Standard_Real Weight (const Standard_Integer UIndex, const Standard_Integer VIndex) const;
502 //! Returns the weights of the Bezier surface.
504 //! Raised if the length of W in the U an V direction is not
505 //! equal to NbUPoles and NbVPoles.
506 Standard_EXPORT void Weights (TColStd_Array2OfReal& W) const;
508 //! Returns the weights of the Bezier surface.
509 const TColStd_Array2OfReal* Weights() const
511 if (!weights.IsNull())
512 return &weights->Array2();
513 return BSplSLib::NoWeights();
516 //! Returns True if the first control points row and the
517 //! last control points row are identical. The tolerance
518 //! criterion is Resolution from package gp.
519 Standard_EXPORT Standard_Boolean IsUClosed() const Standard_OVERRIDE;
522 //! Returns True if the first control points column
523 //! and the last control points column are identical.
524 //! The tolerance criterion is Resolution from package gp.
525 Standard_EXPORT Standard_Boolean IsVClosed() const Standard_OVERRIDE;
527 //! Returns True, a Bezier surface is always CN
528 Standard_EXPORT Standard_Boolean IsCNu (const Standard_Integer N) const Standard_OVERRIDE;
530 //! Returns True, a BezierSurface is always CN
531 Standard_EXPORT Standard_Boolean IsCNv (const Standard_Integer N) const Standard_OVERRIDE;
534 Standard_EXPORT Standard_Boolean IsUPeriodic() const Standard_OVERRIDE;
537 Standard_EXPORT Standard_Boolean IsVPeriodic() const Standard_OVERRIDE;
540 //! Returns False if the weights are identical in the U direction,
541 //! The tolerance criterion is Resolution from package gp.
544 //! if Weights = |0.5, 0.5, 0.5| returns False
546 Standard_EXPORT Standard_Boolean IsURational() const;
549 //! Returns False if the weights are identical in the V direction,
550 //! The tolerance criterion is Resolution from package gp.
553 //! if Weights = |1.0, 2.0, 0.5| returns False
555 Standard_EXPORT Standard_Boolean IsVRational() const;
557 //! Applies the transformation T to this Bezier surface.
558 Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE;
561 //! Returns the value of the maximum polynomial degree of a
562 //! Bezier surface. This value is 25.
563 Standard_EXPORT static Standard_Integer MaxDegree();
565 //! Computes two tolerance values for this Bezier
566 //! surface, based on the given tolerance in 3D space
567 //! Tolerance3D. The tolerances computed are:
568 //! - UTolerance in the u parametric direction, and
569 //! - VTolerance in the v parametric direction.
570 //! If f(u,v) is the equation of this Bezier surface,
571 //! UTolerance and VTolerance guarantee that:
572 //! | u1 - u0 | < UTolerance and
573 //! | v1 - v0 | < VTolerance
574 //! ====> |f (u1,v1) - f (u0,v0)| < Tolerance3D
575 Standard_EXPORT void Resolution (const Standard_Real Tolerance3D, Standard_Real& UTolerance, Standard_Real& VTolerance);
577 //! Creates a new object which is a copy of this Bezier surface.
578 Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE;
580 //! Dumps the content of me into the stream
581 Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE;
586 DEFINE_STANDARD_RTTIEXT(Geom_BezierSurface,Geom_BoundedSurface)
596 Geom_BezierSurface(const Handle(TColgp_HArray2OfPnt)& SurfacePoles, const Handle(TColStd_HArray2OfReal)& PoleWeights, const Standard_Boolean IsURational, const Standard_Boolean IsVRational);
598 //! Set poles to Poles, weights to Weights (not
600 //! Create the arrays of coefficients. Poles
601 //! and Weights are assumed to have the first
604 //! if nbpoles < 2 or nbpoles > MaDegree
605 void Init (const Handle(TColgp_HArray2OfPnt)& Poles, const Handle(TColStd_HArray2OfReal)& Weights);
608 Standard_Boolean urational;
609 Standard_Boolean vrational;
610 Handle(TColgp_HArray2OfPnt) poles;
611 Handle(TColStd_HArray2OfReal) weights;
612 Standard_Real umaxderivinv;
613 Standard_Real vmaxderivinv;
614 Standard_Boolean maxderivinvok;
625 #endif // _Geom_BezierSurface_HeaderFile