1 // Created on: 1993-03-24
2 // Created by: Philippe DAUTRY
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 _Geom2d_OffsetCurve_HeaderFile
18 #define _Geom2d_OffsetCurve_HeaderFile
20 #include <Standard.hxx>
21 #include <Standard_Type.hxx>
23 #include <Standard_Real.hxx>
24 #include <GeomAbs_Shape.hxx>
25 #include <Geom2d_Curve.hxx>
26 #include <Standard_Boolean.hxx>
27 #include <Standard_Integer.hxx>
29 class Standard_ConstructionError;
30 class Standard_RangeError;
31 class Standard_NoSuchObject;
32 class Geom2d_UndefinedDerivative;
33 class Geom2d_UndefinedValue;
34 class Standard_NotImplemented;
38 class Geom2d_Geometry;
41 class Geom2d_OffsetCurve;
42 DEFINE_STANDARD_HANDLE(Geom2d_OffsetCurve, Geom2d_Curve)
45 //! This class implements the basis services for the creation,
46 //! edition, modification and evaluation of planar offset curve.
47 //! The offset curve is obtained by offsetting by distance along
48 //! the normal to a basis curve defined in 2D space.
49 //! The offset curve in this package can be a self intersecting
50 //! curve even if the basis curve does not self-intersect.
51 //! The self intersecting portions are not deleted at the
52 //! construction time.
53 //! An offset curve is a curve at constant distance (Offset) from a
54 //! basis curve and the offset curve takes its parametrization from
55 //! the basis curve. The Offset curve is in the direction of the
56 //! normal to the basis curve N.
57 //! The distance offset may be positive or negative to indicate the
58 //! preferred side of the curve :
59 //! . distance offset >0 => the curve is in the direction of N
60 //! . distance offset >0 => the curve is in the direction of - N
61 //! On the Offset curve :
62 //! Value(u) = BasisCurve.Value(U) + (Offset * (T ^ Z)) / ||T ^ Z||
63 //! where T is the tangent vector to the basis curve and Z the
64 //! direction of the normal vector to the plane of the curve,
65 //! N = T ^ Z defines the offset direction and should not have
69 //! In this package we suppose that the continuity of the offset
70 //! curve is one degree less than the continuity of the
71 //! basis curve and we don't check that at any point ||T^Z|| != 0.0
73 //! So to evaluate the curve it is better to check that the offset
74 //! curve is well defined at any point because an exception could
75 //! be raised. The check is not done in this package at the creation
76 //! of the offset curve because the control needs the use of an
77 //! algorithm which cannot be implemented in this package.
78 //! The OffsetCurve is closed if the first point and the last point
79 //! are the same (The distance between these two points is lower or
80 //! equal to the Resolution sea package gp) . The OffsetCurve can be
81 //! closed even if the basis curve is not closed.
82 class Geom2d_OffsetCurve : public Geom2d_Curve
88 //! Constructs a curve offset from the basis curve C,
89 //! where Offset is the distance between the offset
90 //! curve and the basis curve at any point.
91 //! A point on the offset curve is built by measuring the
92 //! offset value along a normal vector at a point on C.
93 //! This normal vector is obtained by rotating the
94 //! vector tangential to C at 90 degrees in the
95 //! anti-trigonometric sense. The side of C on which
96 //! the offset value is measured is indicated by this
97 //! normal vector if Offset is positive, or in the inverse
98 //! sense if Offset is negative.
99 //! If isNotCheckC0 = TRUE checking if basis curve has C0-continuity
102 //! In this package the entities are not shared. The OffsetCurve is
103 //! built with a copy of the curve C. So when C is modified the
104 //! OffsetCurve is not modified
105 //! Warning! if isNotCheckC0 = false,
106 //! ConstructionError raised if the basis curve C is not at least C1.
107 //! No check is done to know if ||V^Z|| != 0.0 at any point.
108 Standard_EXPORT Geom2d_OffsetCurve(const Handle(Geom2d_Curve)& C, const Standard_Real Offset, const Standard_Boolean isNotCheckC0 = Standard_False);
110 //! Changes the direction of parametrization of <me>.
112 //! - the basis curve is reversed,
113 //! - the start point of the initial curve becomes the end
114 //! point of the reversed curve,
115 //! - the end point of the initial curve becomes the start
116 //! point of the reversed curve, and
117 //! - the first and last parameters are recomputed.
118 Standard_EXPORT void Reverse();
120 //! Computes the parameter on the reversed curve for
121 //! the point of parameter U on this offset curve.
122 Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const;
124 //! Changes this offset curve by assigning C as the
125 //! basis curve from which it is built.
126 //! If isNotCheckC0 = TRUE checking if basis curve has C0-continuity
129 //! if isNotCheckC0 = false,
130 //! Standard_ConstructionError if the curve C is not at least "C1" continuous.
131 Standard_EXPORT void SetBasisCurve (const Handle(Geom2d_Curve)& C, const Standard_Boolean isNotCheckC0 = Standard_False);
133 //! Changes this offset curve by assigning D as the offset value.
134 Standard_EXPORT void SetOffsetValue (const Standard_Real D);
136 //! Returns the basis curve of this offset curve. The basis curve can be an offset curve.
137 Standard_EXPORT Handle(Geom2d_Curve) BasisCurve() const;
140 //! Continuity of the Offset curve :
141 //! C0 : only geometric continuity,
142 //! C1 : continuity of the first derivative all along the Curve,
143 //! C2 : continuity of the second derivative all along the Curve,
144 //! C3 : continuity of the third derivative all along the Curve,
145 //! G1 : tangency continuity all along the Curve,
146 //! G2 : curvature continuity all along the Curve,
147 //! CN : the order of continuity is infinite.
149 //! Returns the continuity of the basis curve - 1.
150 //! The offset curve must have a unique normal direction defined
152 //! Value and derivatives
155 //! The exception UndefinedValue or UndefinedDerivative is
156 //! raised if it is not possible to compute a unique offset
158 //! If T is the first derivative with not null length and
159 //! Z the direction normal to the plane of the curve, the
160 //! relation ||T(U) ^ Z|| != 0 must be satisfied to evaluate
161 //! the offset curve.
162 //! No check is done at the creation time and we suppose
163 //! in this package that the offset curve is well defined.
164 Standard_EXPORT GeomAbs_Shape Continuity() const;
166 //! Warning! this should not be called
167 //! if the basis curve is not at least C1. Nevertheless
168 //! if used on portion where the curve is C1, it is OK
169 Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt2d& P) const;
171 //! Warning! this should not be called
172 //! if the continuity of the basis curve is not C2.
173 //! Nevertheless, it's OK to use it on portion
174 //! where the curve is C2
175 Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const;
177 //! Warning! This should not be called
178 //! if the continuity of the basis curve is not C3.
179 //! Nevertheless, it's OK to use it on portion
180 //! where the curve is C3
181 Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const;
183 //! Warning! This should not be called
184 //! if the continuity of the basis curve is not C4.
185 //! Nevertheless, it's OK to use it on portion
186 //! where the curve is C4
187 Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const;
189 //! The returned vector gives the value of the derivative
190 //! for the order of derivation N.
191 //! Warning! this should not be called
192 //! raises UndefunedDerivative if the continuity of the basis curve is not CN+1.
193 //! Nevertheless, it's OK to use it on portion
194 //! where the curve is CN+1
195 //! raises RangeError if N < 1.
196 //! raises NotImplemented if N > 3.
197 //! The following functions compute the value and derivatives
198 //! on the offset curve and returns the derivatives on the
200 //! The computation of the value and derivatives on the basis
201 //! curve are used to evaluate the offset curve
203 //! The exception UndefinedValue or UndefinedDerivative is
204 //! raised if it is not possible to compute a unique offset direction.
205 Standard_EXPORT gp_Vec2d DN (const Standard_Real U, const Standard_Integer N) const;
207 //! Warning! this should not be called
208 //! if the basis curve is not at least C1. Nevertheless
209 //! if used on portion where the curve is C1, it is OK
210 Standard_EXPORT void Value (const Standard_Real U, gp_Pnt2d& P, gp_Pnt2d& Pbasis, gp_Vec2d& V1basis) const;
212 //! Warning! this should not be called
213 //! if the continuity of the basis curve is not C1.
214 //! Nevertheless, it's OK to use it on portion
215 //! where the curve is C1
216 Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Pnt2d& Pbasis, gp_Vec2d& V1, gp_Vec2d& V1basis, gp_Vec2d& V2basis) const;
218 //! Warning! this should not be called
219 //! if the continuity of the basis curve is not C3.
220 //! Nevertheless, it's OK to use it on portion
221 //! where the curve is C3
222 Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Pnt2d& Pbasis, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V1basis, gp_Vec2d& V2basis, gp_Vec2d& V3basis) const;
224 Standard_EXPORT Standard_Real FirstParameter() const;
226 //! Returns the value of the first or last parameter of this
227 //! offset curve. The first parameter corresponds to the
228 //! start point of the curve. The last parameter
229 //! corresponds to the end point.
230 //! Note: the first and last parameters of this offset curve
231 //! are also the ones of its basis curve.
232 Standard_EXPORT Standard_Real LastParameter() const;
234 //! Returns the offset value of this offset curve.
235 Standard_EXPORT Standard_Real Offset() const;
238 //! Returns True if the distance between the start point
239 //! and the end point of the curve is lower or equal to
240 //! Resolution from package gp.
241 Standard_EXPORT Standard_Boolean IsClosed() const;
243 //! Is the order of continuity of the curve N ?
245 //! This method answer True if the continuity of the basis curve
246 //! is N + 1. We suppose in this class that a normal direction
247 //! to the basis curve (used to compute the offset curve) is
248 //! defined at any point on the basis curve.
250 Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const;
252 //! Is the parametrization of a curve is periodic ?
253 //! If the basis curve is a circle or an ellipse the corresponding
254 //! OffsetCurve is periodic. If the basis curve can't be periodic
255 //! (for example BezierCurve) the OffsetCurve can't be periodic.
256 Standard_EXPORT Standard_Boolean IsPeriodic() const;
258 //! Returns the period of this offset curve, i.e. the period
259 //! of the basis curve of this offset curve.
261 //! Standard_NoSuchObject if the basis curve is not periodic.
262 Standard_EXPORT virtual Standard_Real Period() const Standard_OVERRIDE;
264 //! Applies the transformation T to this offset curve.
265 //! Note: the basis curve is also modified.
266 Standard_EXPORT void Transform (const gp_Trsf2d& T);
268 //! Returns the parameter on the transformed curve for
269 //! the transform of the point of parameter U on <me>.
271 //! me->Transformed(T)->Value(me->TransformedParameter(U,T))
273 //! is the same point as
275 //! me->Value(U).Transformed(T)
277 //! This methods calls the basis curve method.
278 Standard_EXPORT virtual Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf2d& T) const Standard_OVERRIDE;
280 //! Returns a coefficient to compute the parameter on
281 //! the transformed curve for the transform of the
284 //! Transformed(T)->Value(U * ParametricTransformation(T))
286 //! is the same point as
288 //! Value(U).Transformed(T)
290 //! This methods calls the basis curve method.
291 Standard_EXPORT virtual Standard_Real ParametricTransformation (const gp_Trsf2d& T) const Standard_OVERRIDE;
293 //! Creates a new object, which is a copy of this offset curve.
294 Standard_EXPORT Handle(Geom2d_Geometry) Copy() const;
296 //! Returns continuity of the basis curve.
297 Standard_EXPORT GeomAbs_Shape GetBasisCurveContinuity() const;
302 DEFINE_STANDARD_RTTI(Geom2d_OffsetCurve,Geom2d_Curve)
312 Handle(Geom2d_Curve) basisCurve;
313 Standard_Real offsetValue;
314 GeomAbs_Shape myBasisCurveContinuity;
325 #endif // _Geom2d_OffsetCurve_HeaderFile