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 <Standard_Boolean.hxx>
24 #include <TColgp_HArray2OfPnt.hxx>
25 #include <TColStd_HArray2OfReal.hxx>
26 #include <Standard_Real.hxx>
27 #include <Standard_Integer.hxx>
28 #include <Geom_BoundedSurface.hxx>
29 #include <TColgp_Array2OfPnt.hxx>
30 #include <TColStd_Array2OfReal.hxx>
31 #include <TColgp_Array1OfPnt.hxx>
32 #include <TColStd_Array1OfReal.hxx>
33 #include <GeomAbs_Shape.hxx>
34 class Standard_ConstructionError;
35 class Standard_DimensionError;
36 class Standard_RangeError;
37 class Standard_OutOfRange;
45 class Geom_BezierSurface;
46 DEFINE_STANDARD_HANDLE(Geom_BezierSurface, Geom_BoundedSurface)
48 //! Describes a rational or non-rational Bezier surface.
49 //! - A non-rational Bezier surface is defined by a table
50 //! of poles (also known as control points).
51 //! - A rational Bezier surface is defined by a table of
52 //! poles with varying associated weights.
53 //! This data is manipulated using two associative 2D arrays:
54 //! - the poles table, which is a 2D array of gp_Pnt, and
55 //! - the weights table, which is a 2D array of reals.
56 //! The bounds of these arrays are:
57 //! - 1 and NbUPoles for the row bounds, where
58 //! NbUPoles is the number of poles of the surface
59 //! in the u parametric direction, and
60 //! - 1 and NbVPoles for the column bounds, where
61 //! NbVPoles is the number of poles of the surface
62 //! in the v parametric direction.
63 //! The poles of the surface, the "control points", are the
64 //! points used to shape and reshape the surface. They
65 //! comprise a rectangular network of points:
66 //! - The points (1, 1), (NbUPoles, 1), (1,
67 //! NbVPoles) and (NbUPoles, NbVPoles)
68 //! are the four parametric "corners" of the surface.
69 //! - The first column of poles and the last column of
70 //! poles define two Bezier curves which delimit the
71 //! surface in the v parametric direction. These are
72 //! the v isoparametric curves corresponding to
73 //! values 0 and 1 of the v parameter.
74 //! - The first row of poles and the last row of poles
75 //! define two Bezier curves which delimit the surface
76 //! in the u parametric direction. These are the u
77 //! isoparametric curves corresponding to values 0
78 //! and 1 of the u parameter.
79 //! It is more difficult to define a geometrical significance
80 //! for the weights. However they are useful for
81 //! representing a quadric surface precisely. Moreover, if
82 //! the weights of all the poles are equal, the surface has
83 //! a polynomial equation, and hence is a "non-rational surface".
84 //! The non-rational surface is a special, but frequently
85 //! used, case, where all poles have identical weights.
86 //! The weights are defined and used only in the case of
87 //! a rational surface. This rational characteristic is
88 //! defined in each parametric direction. Hence, a
89 //! surface can be rational in the u parametric direction,
90 //! and non-rational in the v parametric direction.
91 //! Likewise, the degree of a surface is defined in each
92 //! parametric direction. The degree of a Bezier surface
93 //! in a given parametric direction is equal to the number
94 //! of poles of the surface in that parametric direction,
95 //! minus 1. This must be greater than or equal to 1.
96 //! However, the degree for a Geom_BezierSurface is
97 //! limited to a value of (25) which is defined and
98 //! controlled by the system. This value is returned by the
99 //! function MaxDegree.
100 //! The parameter range for a Bezier surface is [ 0, 1 ]
101 //! in the two parametric directions.
102 //! A Bezier surface can also be closed, or open, in each
103 //! parametric direction. If the first row of poles is
104 //! identical to the last row of poles, the surface is closed
105 //! in the u parametric direction. If the first column of
106 //! poles is identical to the last column of poles, the
107 //! surface is closed in the v parametric direction.
108 //! The continuity of a Bezier surface is infinite in the u
109 //! parametric direction and the in v parametric direction.
110 //! Note: It is not possible to build a Bezier surface with
111 //! negative weights. Any weight value that is less than,
112 //! or equal to, gp::Resolution() is considered
113 //! to be zero. Two weight values, W1 and W2, are
114 //! considered equal if: |W2-W1| <= gp::Resolution()
115 class Geom_BezierSurface : public Geom_BoundedSurface
122 //! Creates a non-rational Bezier surface with a set of poles.
123 //! Control points representation :
124 //! SPoles(Uorigin,Vorigin) ...................SPoles(Uorigin,Vend)
127 //! SPoles(Uend, Vorigin) .....................SPoles(Uend, Vend)
128 //! For the double array the row indice corresponds to the parametric
129 //! U direction and the columns indice corresponds to the parametric
131 //! The weights are defaulted to all being 1.
133 //! Raised if the number of poles of the surface is lower than 2
134 //! or greater than MaxDegree + 1 in one of the two directions
136 Standard_EXPORT Geom_BezierSurface(const TColgp_Array2OfPnt& SurfacePoles);
139 //! Creates a rational Bezier surface with a set of poles and a
141 //! For the double array the row indice corresponds to the parametric
142 //! U direction and the columns indice corresponds to the parametric
144 //! If all the weights are identical the surface is considered as
145 //! non-rational (the tolerance criterion is Resolution from package
148 //! Raised if SurfacePoles and PoleWeights have not the same
149 //! Rowlength or have not the same ColLength.
150 //! Raised if PoleWeights (i, j) <= Resolution from gp;
151 //! Raised if the number of poles of the surface is lower than 2
152 //! or greater than MaxDegree + 1 in one of the two directions U or V.
153 Standard_EXPORT Geom_BezierSurface(const TColgp_Array2OfPnt& SurfacePoles, const TColStd_Array2OfReal& PoleWeights);
155 //! Exchanges the direction U and V on a Bezier surface
156 //! As a consequence:
157 //! - the poles and weights tables are transposed,
158 //! - degrees, rational characteristics and so on are
159 //! exchanged between the two parametric directions, and
160 //! - the orientation of the surface is reversed.
161 Standard_EXPORT void ExchangeUV();
163 //! Increases the degree of this Bezier surface in the two parametric directions.
165 //! Raised if UDegree < UDegree <me> or VDegree < VDegree <me>
166 //! Raised if the degree of the surface is greater than MaxDegree
167 //! in one of the two directions U or V.
168 Standard_EXPORT void Increase (const Standard_Integer UDeg, const Standard_Integer VDeg);
171 //! Inserts a column of poles. If the surface is rational the weights
172 //! values associated with CPoles are equal defaulted to 1.
174 //! Raised if Vindex < 1 or VIndex > NbVPoles.
176 //! raises if VDegree is greater than MaxDegree.
177 //! raises if the Length of CPoles is not equal to NbUPoles
178 Standard_EXPORT void InsertPoleColAfter (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles);
181 //! Inserts a column of poles and weights.
182 //! If the surface was non-rational it can become rational.
184 //! Raised if Vindex < 1 or VIndex > NbVPoles.
186 //! . VDegree is greater than MaxDegree.
187 //! . the Length of CPoles is not equal to NbUPoles
188 //! . a weight value is lower or equal to Resolution from
190 Standard_EXPORT void InsertPoleColAfter (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
193 //! Inserts a column of poles. If the surface is rational the weights
194 //! values associated with CPoles are equal defaulted to 1.
196 //! Raised if Vindex < 1 or VIndex > NbVPoles.
198 //! Raised if VDegree is greater than MaxDegree.
199 //! Raised if the Length of CPoles is not equal to NbUPoles
200 Standard_EXPORT void InsertPoleColBefore (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles);
203 //! Inserts a column of poles and weights.
204 //! If the surface was non-rational it can become rational.
206 //! Raised if Vindex < 1 or VIndex > NbVPoles.
208 //! . VDegree is greater than MaxDegree.
209 //! . the Length of CPoles is not equal to NbUPoles
210 //! . a weight value is lower or equal to Resolution from
212 Standard_EXPORT void InsertPoleColBefore (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
215 //! Inserts a row of poles. If the surface is rational the weights
216 //! values associated with CPoles are equal defaulted to 1.
218 //! Raised if Uindex < 1 or UIndex > NbUPoles.
220 //! Raised if UDegree is greater than MaxDegree.
221 //! Raised if the Length of CPoles is not equal to NbVPoles
222 Standard_EXPORT void InsertPoleRowAfter (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles);
225 //! Inserts a row of poles and weights.
226 //! If the surface was non-rational it can become rational.
228 //! Raised if Uindex < 1 or UIndex > NbUPoles.
230 //! . UDegree is greater than MaxDegree.
231 //! . the Length of CPoles is not equal to NbVPoles
232 //! . a weight value is lower or equal to Resolution from
234 Standard_EXPORT void InsertPoleRowAfter (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
237 //! Inserts a row of poles. If the surface is rational the weights
238 //! values associated with CPoles are equal defaulted to 1.
240 //! Raised if Uindex < 1 or UIndex > NbUPoles.
242 //! Raised if UDegree is greater than MaxDegree.
243 //! Raised if the Length of CPoles is not equal to NbVPoles
244 Standard_EXPORT void InsertPoleRowBefore (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles);
247 //! Inserts a row of poles and weights.
248 //! If the surface was non-rational it can become rational.
250 //! Raised if Uindex < 1 or UIndex > NbUPoles.
252 //! . UDegree is greater than MaxDegree.
253 //! . the Length of CPoles is not equal to NbVPoles
254 //! . a weight value is lower or equal to Resolution from
256 Standard_EXPORT void InsertPoleRowBefore (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
258 //! Removes a column of poles.
259 //! If the surface was rational it can become non-rational.
261 //! Raised if NbVPoles <= 2 after removing, a Bezier surface
262 //! must have at least two columns of poles.
263 //! Raised if Vindex < 1 or VIndex > NbVPoles
264 Standard_EXPORT void RemovePoleCol (const Standard_Integer VIndex);
266 //! Removes a row of poles.
267 //! If the surface was rational it can become non-rational.
269 //! Raised if NbUPoles <= 2 after removing, a Bezier surface
270 //! must have at least two rows of poles.
271 //! Raised if Uindex < 1 or UIndex > NbUPoles
272 Standard_EXPORT void RemovePoleRow (const Standard_Integer UIndex);
274 //! Modifies this Bezier surface by segmenting it
275 //! between U1 and U2 in the u parametric direction,
276 //! and between V1 and V2 in the v parametric
277 //! direction. U1, U2, V1, and V2 can be outside the
278 //! bounds of this surface.
279 //! - U1 and U2 isoparametric Bezier curves,
280 //! segmented between V1 and V2, become the two
281 //! bounds of the surface in the v parametric
282 //! direction (0. and 1. u isoparametric curves).
283 //! - V1 and V2 isoparametric Bezier curves,
284 //! segmented between U1 and U2, become the two
285 //! bounds of the surface in the u parametric
286 //! direction (0. and 1. v isoparametric curves).
287 //! The poles and weights tables are modified, but the
288 //! degree of this surface in the u and v parametric
289 //! directions does not change.
290 //! U1 can be greater than U2, and V1 can be greater
291 //! than V2. In these cases, the corresponding
292 //! parametric direction is inverted. The orientation of
293 //! the surface is inverted if one (and only one)
294 //! parametric direction is inverted.
295 Standard_EXPORT void Segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2);
297 //! Modifies a pole value.
298 //! If the surface is rational the weight of range (UIndex, VIndex)
301 //! Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1
302 //! or VIndex > NbVPoles.
303 Standard_EXPORT void SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt& P);
306 //! Substitutes the pole and the weight of range UIndex, VIndex.
307 //! If the surface <me> is not rational it can become rational.
308 //! if the surface was rational it can become non-rational.
310 //! raises if UIndex < 1 or UIndex > NbUPoles or VIndex < 1
311 //! or VIndex > NbVPoles.
312 //! Raised if Weight <= Resolution from package gp.
313 Standard_EXPORT void SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt& P, const Standard_Real Weight);
315 //! Modifies a column of poles.
316 //! The length of CPoles can be lower but not greater than NbUPoles
317 //! so you can modify just a part of the column.
318 //! Raised if VIndex < 1 or VIndex > NbVPoles
320 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles
321 Standard_EXPORT void SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles);
323 //! Modifies a column of poles.
324 //! If the surface was rational it can become non-rational
325 //! If the surface was non-rational it can become rational.
326 //! The length of CPoles can be lower but not greater than NbUPoles
327 //! so you can modify just a part of the column.
328 //! Raised if VIndex < 1 or VIndex > NbVPoles
330 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles
331 //! Raised if CPoleWeights and CPoles have not the same bounds.
332 //! Raised if one of the weight value CPoleWeights (i) is lower
333 //! or equal to Resolution from package gp.
334 Standard_EXPORT void SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
336 //! Modifies a row of poles.
337 //! The length of CPoles can be lower but not greater than NbVPoles
338 //! so you can modify just a part of the row.
339 //! Raised if UIndex < 1 or UIndex > NbUPoles
341 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles
342 Standard_EXPORT void SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles);
344 //! Modifies a row of poles and weights.
345 //! If the surface was rational it can become non-rational.
346 //! If the surface was non-rational it can become rational.
347 //! The length of CPoles can be lower but not greater than NbVPoles
348 //! so you can modify just a part of the row.
349 //! Raised if UIndex < 1 or UIndex > NbUPoles
351 //! Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles
352 //! Raised if CPoleWeights and CPoles have not the same bounds.
353 //! Raised if one of the weight value CPoleWeights (i) is lower
354 //! or equal to Resolution from gp.
355 Standard_EXPORT void SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt& CPoles, const TColStd_Array1OfReal& CPoleWeights);
358 //! Modifies the weight of the pole of range UIndex, VIndex.
359 //! If the surface was non-rational it can become rational.
360 //! If the surface was rational it can become non-rational.
362 //! Raised if UIndex < 1 or UIndex > NbUPoles or VIndex < 1 or
363 //! VIndex > NbVPoles.
364 //! Raised if Weight <= Resolution from package gp.
365 Standard_EXPORT void SetWeight (const Standard_Integer UIndex, const Standard_Integer VIndex, const Standard_Real Weight);
367 //! Modifies a column of weights.
368 //! If the surface was rational it can become non-rational.
369 //! If the surface was non-rational it can become rational.
370 //! The length of CPoleWeights can be lower but not greater than
372 //! Raised if VIndex < 1 or VIndex > NbVPoles
374 //! Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() >
376 //! Raised if one of the weight value CPoleWeights (i) is lower
377 //! or equal to Resolution from package gp.
378 Standard_EXPORT void SetWeightCol (const Standard_Integer VIndex, const TColStd_Array1OfReal& CPoleWeights);
380 //! Modifies a row of weights.
381 //! If the surface was rational it can become non-rational.
382 //! If the surface was non-rational it can become rational.
383 //! The length of CPoleWeights can be lower but not greater than
385 //! Raised if UIndex < 1 or UIndex > NbUPoles
387 //! Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() >
389 //! Raised if one of the weight value CPoleWeights (i) is lower
390 //! or equal to Resolution from package gp.
391 Standard_EXPORT void SetWeightRow (const Standard_Integer UIndex, const TColStd_Array1OfReal& CPoleWeights);
393 //! Changes the orientation of this Bezier surface in the
394 //! u parametric direction. The bounds of the
395 //! surface are not changed, but the given parametric
396 //! direction is reversed. Hence, the orientation of the surface is reversed.
397 Standard_EXPORT void UReverse() Standard_OVERRIDE;
399 //! Computes the u (or v) parameter on the modified
400 //! surface, produced by reversing its u (or v) parametric
401 //! direction, for any point of u parameter U (or of v
402 //! parameter V) on this Bezier surface.
403 //! In the case of a Bezier surface, these functions return respectively:
405 Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const Standard_OVERRIDE;
407 //! Changes the orientation of this Bezier surface in the
408 //! v parametric direction. The bounds of the
409 //! surface are not changed, but the given parametric
410 //! direction is reversed. Hence, the orientation of the
411 //! surface is reversed.
412 Standard_EXPORT void VReverse() Standard_OVERRIDE;
414 //! Computes the u (or v) parameter on the modified
415 //! surface, produced by reversing its u (or v) parametric
416 //! direction, for any point of u parameter U (or of v
417 //! parameter V) on this Bezier surface.
418 //! In the case of a Bezier surface, these functions return respectively:
420 Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real V) const Standard_OVERRIDE;
422 //! Returns the parametric bounds U1, U2, V1 and V2 of
423 //! this Bezier surface.
424 //! In the case of a Bezier surface, this function returns
425 //! U1 = 0, V1 = 0, U2 = 1, V2 = 1.
426 Standard_EXPORT void Bounds (Standard_Real& U1, Standard_Real& U2, Standard_Real& V1, Standard_Real& V2) const Standard_OVERRIDE;
429 //! Returns the continuity of the surface CN : the order of
430 //! continuity is infinite.
431 Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE;
433 Standard_EXPORT void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt& P) const Standard_OVERRIDE;
435 Standard_EXPORT void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V) const Standard_OVERRIDE;
437 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;
439 //! Computes P, the point of parameters (U, V) of this Bezier surface, and
440 //! - one or more of the following sets of vectors:
441 //! - D1U and D1V, the first derivative vectors at this point,
442 //! - D2U, D2V and D2UV, the second derivative
443 //! vectors at this point,
444 //! - D3U, D3V, D3UUV and D3UVV, the third
445 //! derivative vectors at this point.
446 //! Note: The parameters U and V can be outside the bounds of the surface.
447 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;
449 //! Computes the derivative of order Nu in the u
450 //! parametric direction, and Nv in the v parametric
451 //! direction, at the point of parameters (U, V) of this Bezier surface.
452 //! Note: The parameters U and V can be outside the bounds of the surface.
454 //! Standard_RangeError if:
455 //! - Nu + Nv is less than 1, or Nu or Nv is negative.
456 Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const Standard_OVERRIDE;
458 //! Returns the number of poles in the U direction.
459 Standard_EXPORT Standard_Integer NbUPoles() const;
461 //! Returns the number of poles in the V direction.
462 Standard_EXPORT Standard_Integer NbVPoles() const;
464 //! Returns the pole of range UIndex, VIndex
465 //! Raised if UIndex < 1 or UIndex > NbUPoles, or
466 //! VIndex < 1 or VIndex > NbVPoles.
467 Standard_EXPORT gp_Pnt Pole (const Standard_Integer UIndex, const Standard_Integer VIndex) const;
469 //! Returns the poles of the Bezier surface.
471 //! Raised if the length of P in the U an V direction is not equal to
472 //! NbUPoles and NbVPoles.
473 Standard_EXPORT void Poles (TColgp_Array2OfPnt& P) const;
476 //! Returns the degree of the surface in the U direction it is
478 Standard_EXPORT Standard_Integer UDegree() const;
481 //! Computes the U isoparametric curve. For a Bezier surface the
482 //! UIso curve is a Bezier curve.
483 Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U) const Standard_OVERRIDE;
486 //! Returns the degree of the surface in the V direction it is
488 Standard_EXPORT Standard_Integer VDegree() const;
491 //! Computes the V isoparametric curve. For a Bezier surface the
492 //! VIso curve is a Bezier curve.
493 Standard_EXPORT Handle(Geom_Curve) VIso (const Standard_Real V) const Standard_OVERRIDE;
495 //! Returns the weight of range UIndex, VIndex
497 //! Raised if UIndex < 1 or UIndex > NbUPoles, or
498 //! VIndex < 1 or VIndex > NbVPoles.
499 Standard_EXPORT Standard_Real Weight (const Standard_Integer UIndex, const Standard_Integer VIndex) const;
501 //! Returns the weights of the Bezier surface.
503 //! Raised if the length of W in the U an V direction is not
504 //! equal to NbUPoles and NbVPoles.
505 Standard_EXPORT void Weights (TColStd_Array2OfReal& W) const;
508 //! Returns True if the first control points row and the
509 //! last control points row are identical. The tolerance
510 //! criterion is Resolution from package gp.
511 Standard_EXPORT Standard_Boolean IsUClosed() const Standard_OVERRIDE;
514 //! Returns True if the first control points column
515 //! and the last control points column are identical.
516 //! The tolerance criterion is Resolution from package gp.
517 Standard_EXPORT Standard_Boolean IsVClosed() const Standard_OVERRIDE;
519 //! Returns True, a Bezier surface is always CN
520 Standard_EXPORT Standard_Boolean IsCNu (const Standard_Integer N) const Standard_OVERRIDE;
522 //! Returns True, a BezierSurface is always CN
523 Standard_EXPORT Standard_Boolean IsCNv (const Standard_Integer N) const Standard_OVERRIDE;
526 Standard_EXPORT Standard_Boolean IsUPeriodic() const Standard_OVERRIDE;
529 Standard_EXPORT Standard_Boolean IsVPeriodic() const Standard_OVERRIDE;
532 //! Returns False if the weights are identical in the U direction,
533 //! The tolerance criterion is Resolution from package gp.
536 //! if Weights = |0.5, 0.5, 0.5| returns False
538 Standard_EXPORT Standard_Boolean IsURational() const;
541 //! Returns False if the weights are identical in the V direction,
542 //! The tolerance criterion is Resolution from package gp.
545 //! if Weights = |1.0, 2.0, 0.5| returns False
547 Standard_EXPORT Standard_Boolean IsVRational() const;
549 //! Applies the transformation T to this Bezier surface.
550 Standard_EXPORT void Transform (const gp_Trsf& T) Standard_OVERRIDE;
553 //! Returns the value of the maximum polynomial degree of a
554 //! Bezier surface. This value is 25.
555 Standard_EXPORT static Standard_Integer MaxDegree();
557 //! Computes two tolerance values for this Bezier
558 //! surface, based on the given tolerance in 3D space
559 //! Tolerance3D. The tolerances computed are:
560 //! - UTolerance in the u parametric direction, and
561 //! - VTolerance in the v parametric direction.
562 //! If f(u,v) is the equation of this Bezier surface,
563 //! UTolerance and VTolerance guarantee that:
564 //! | u1 - u0 | < UTolerance and
565 //! | v1 - v0 | < VTolerance
566 //! ====> |f (u1,v1) - f (u0,v0)| < Tolerance3D
567 Standard_EXPORT void Resolution (const Standard_Real Tolerance3D, Standard_Real& UTolerance, Standard_Real& VTolerance);
569 //! Creates a new object which is a copy of this Bezier surface.
570 Standard_EXPORT Handle(Geom_Geometry) Copy() const Standard_OVERRIDE;
575 DEFINE_STANDARD_RTTI(Geom_BezierSurface,Geom_BoundedSurface)
585 Standard_EXPORT Geom_BezierSurface(const Handle(TColgp_HArray2OfPnt)& SurfacePoles, const Handle(TColgp_HArray2OfPnt)& SurfaceCoefficients, const Handle(TColStd_HArray2OfReal)& PoleWeights, const Handle(TColStd_HArray2OfReal)& CoefficientWeights, const Standard_Boolean IsURational, const Standard_Boolean IsVRational);
587 //! Set poles to Poles, weights to Weights (not
589 //! Create the arrays of coefficients. Poles
590 //! and Weights are assumed to have the first
593 //! if nbpoles < 2 or nbpoles > MaDegree
594 Standard_EXPORT void Init (const Handle(TColgp_HArray2OfPnt)& Poles, const Handle(TColStd_HArray2OfReal)& Weights);
596 //! Recompute the coeficients.
597 Standard_EXPORT void UpdateCoefficients (const Standard_Real U = 0.0, const Standard_Real V = 0.0);
599 Standard_Boolean urational;
600 Standard_Boolean vrational;
601 Handle(TColgp_HArray2OfPnt) poles;
602 Handle(TColStd_HArray2OfReal) weights;
603 Handle(TColgp_HArray2OfPnt) coeffs;
604 Handle(TColStd_HArray2OfReal) wcoeffs;
605 Standard_Real ucacheparameter;
606 Standard_Real vcacheparameter;
607 Standard_Real ucachespanlenght;
608 Standard_Real vcachespanlenght;
609 Standard_Integer validcache;
610 Standard_Real umaxderivinv;
611 Standard_Real vmaxderivinv;
612 Standard_Boolean maxderivinvok;
623 #endif // _Geom_BezierSurface_HeaderFile