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e2e0498b17
The root of the problem is incorrect processing of cases when intersection line goes through the apex(es) of sphere. The fix improves this situation. The algorithm is taken from DecomposeResult(...) function (see IntPatch_ImpPrmIntersection.cxx file). Before the fix, faltering steps were done to solve this problem. As result, it worked in some particular cases. Now, its possibilities have been extended significantly. Following changes have been made in the fix: 1. Class IntPatch_ALineToWLine has been rewritten cardinally. It touches as interfaces of existing methods as adding/removing some methods/fields. Correction touches both cases: going through seam of Cone/Sphere and through pole(s) of sphere. Old interface did not allow making some actions with analytical line (ALine), e.g. splitting it on several Walking-lines (WLine). 2. Restriction-line support has been removed from Implicit-Implicit intersection result (see IntPatch_Intersection::GeomGeomPerfom(...) method). It connects with the fact that the intersection algorithm itself returns precise intersection line in analytical cases (in compare with parametric intersector). Therefore, we do not need in additional (restriction) line. 3. New class IntPatch_SpecialPoints has been added. This class contains methods to add some special points (such as apex of cone, pole of sphere, point on surface boundary etc.) in intersection line (IntPatch_PointLine). It is based on the static functions, which already exist in IntPatch_ImpPrmIntersection.cxx file (these functions have been moved to the new class). 4. Method IntPatch_WLineTool::ExtendTwoWlinesToEachOther(...) has been renamed to IntPatch_WLineTool::ExtendTwoWLines(...). It is connected with changing main idea of the method. Now it allows extending WLine to the surface boundary or to the singular point (if it is possible): cone apex, sphere pole etc. Interface of this method has been corrected, too. At that, old functionality (extending to each other) has been kept. For implementation of this algorithm, new enumeration "IntPatchWT_WLsConnectionType" has been created. 5. Method IntPatch_PointLine::CurvatureRadiusOfIntersLine(...) has been added. See IntPatch_PointLine.hxx for detail information. It allows correct step computing depended on the local curvature of the intersection line. This method uses geometrical properties of intersected surfaces to compute local curvature. Therefore, it can be applied in wide range of cases even if the intersection curve is not represented in explicit form (e.g. in case of param-param-intersection). 6. Method IntSurf::SetPeriod(...) has been created. 7. Additional check has been added in Draft_Modification::Perform() method for better choice of correct fragment of intersection line for processing DRAFT operation. 8. New overload method IntPatch_Point::SetValue() has been added. 9. Some refactoring of the code has been made. Creation of test case for issue #27431. --------------------------------------------------------------------------------------------- Some test cases have been adjusted according to their new behavior. tests\bugs\modalg_4\bug62 It is really IMPROVEMENT (but fortuitous). tests\bugs\modalg_5\bug25838 The behavior of this test has been reverted to the state before fixing the issue #27341. Main problem has not been fixed in #27341. It was fortuitous improvement. tests\bugs\moddata_2\bug565 Quality of intersection curve was not checked. And the curve is bad on both MASTER and FIX. Input data are really wrong: plane-like-cone. However, on the MASTER, four intersection curves (the quality is insignificant) are expected. On the fix, not empty intersection result is expected simply. tests\boolean\volumemaker\A8 Differences in images and CPU is expected. Difference in images is expected to be fixed in the issue #26020. Now, we should apply this behavior. Much CPU time is spent by IntTools_FaceFace::ComputeTolReached3d(...) and GeomInt_IntSS::BuildPCurves(...) methods calling. These methods are not touched by the algorithm. It is the result of change of intersection curve(s) form. However, the new Curve(s) seems to be valid and can be applied. As result, new behavior can be applied, too. tests\boolean\volumemaker\F8 tests\boolean\volumemaker\F9 tests\boolean\volumemaker\G5 tests\boolean\volumemaker\G6 CPU difference is expected. Much CPU time is spent by IntPatch_PointLine::CurvatureRadiusOfIntersLine(...) method calling. This method is really new (it does not exist on the MASTER) and is really useful. Therefore, we should apply new behavior. tests\boolean\volumemaker\G1 CPU difference is expected. Much CPU time is spent by IntTools_WLineTool::DecompositionOfWLine(...) and IntTools_FaceFace::ComputeTolReached3d(...) methods calling. These methods are not touched by the algorithm. It is the result of change of intersection curve(s) form. However, the new Curve(s) seems to be valid and can be applied. As result, new behavior can be applied, too. tests\bugs\modalg_6\bug26619 Differences in images is expected. The test keeps its BAD status on the FIX. But the result on the fix is nearer to expected than on the MASTER. Issue #27014 is still actual. As before, it is not clear, why the number of entities is different. The number of section curves has not been changed. Interfered entities are the same as on the MASTER. tests\bugs\modalg_5\bug25319_1(2) The reason is described in the issue #27896. Small correction in the test case
476 lines
22 KiB
C++
476 lines
22 KiB
C++
// Created on: 1991-09-10
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// Created by: Michel Chauvat
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// Copyright (c) 1991-1999 Matra Datavision
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// Copyright (c) 1999-2014 OPEN CASCADE SAS
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//
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// This file is part of Open CASCADE Technology software library.
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//
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// This library is free software; you can redistribute it and/or modify it under
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// the terms of the GNU Lesser General Public License version 2.1 as published
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// by the Free Software Foundation, with special exception defined in the file
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// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
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// distribution for complete text of the license and disclaimer of any warranty.
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//
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// Alternatively, this file may be used under the terms of Open CASCADE
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// commercial license or contractual agreement.
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#ifndef _ElCLib_HeaderFile
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#define _ElCLib_HeaderFile
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#include <Standard.hxx>
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#include <Standard_DefineAlloc.hxx>
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#include <Standard_Handle.hxx>
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#include <Standard_Real.hxx>
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#include <gp_Pnt.hxx>
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#include <Standard_Integer.hxx>
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#include <gp_Vec.hxx>
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#include <gp_Pnt2d.hxx>
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#include <gp_Vec2d.hxx>
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class gp_Pnt;
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class gp_Lin;
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class gp_Circ;
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class gp_Elips;
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class gp_Hypr;
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class gp_Parab;
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class gp_Vec;
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class gp_Lin2d;
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class gp_Circ2d;
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class gp_Elips2d;
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class gp_Hypr2d;
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class gp_Parab2d;
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class gp_Pnt2d;
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class gp_Vec2d;
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class gp_Ax1;
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class gp_Ax2;
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class gp_Ax2d;
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class gp_Ax22d;
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class gp_Dir;
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class gp_Dir2d;
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//! Provides functions for basic geometric computations on
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//! elementary curves such as conics and lines in 2D and 3D space.
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//! This includes:
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//! - calculation of a point or derived vector on a 2D or
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//! 3D curve where:
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//! - the curve is provided by the gp package, or
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//! defined in reference form (as in the gp package),
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//! and
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//! - the point is defined by a parameter,
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//! - evaluation of the parameter corresponding to a point
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//! on a 2D or 3D curve from gp,
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//! - various elementary computations which allow you to
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//! position parameterized values within the period of a curve.
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//! Notes:
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//! - ElCLib stands for Elementary Curves Library.
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//! - If the curves provided by the gp package are not
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//! explicitly parameterized, they still have an implicit
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//! parameterization, analogous to that which they infer
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//! for the equivalent Geom or Geom2d curves.
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class ElCLib
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{
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public:
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DEFINE_STANDARD_ALLOC
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//! Return a value in the range <UFirst, ULast> by
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//! adding or removing the period <ULast - UFirst> to
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//! <U>.
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//! ATTENTION!!!
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//! It is expected but not checked that (ULast > UFirst)
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Standard_EXPORT static Standard_Real InPeriod (const Standard_Real U, const Standard_Real UFirst, const Standard_Real ULast);
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//! Adjust U1 and U2 in the parametric range UFirst
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//! Ulast of a periodic curve, where ULast -
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//! UFirst is its period. To do this, this function:
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//! - sets U1 in the range [ UFirst, ULast ] by
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//! adding/removing the period to/from the value U1, then
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//! - sets U2 in the range [ U1, U1 + period ] by
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//! adding/removing the period to/from the value U2.
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//! Precision is used to test the equalities.
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Standard_EXPORT static void AdjustPeriodic (const Standard_Real UFirst, const Standard_Real ULast, const Standard_Real Precision, Standard_Real& U1, Standard_Real& U2);
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//! For elementary curves (lines, circles and conics) from
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//! the gp package, computes the point of parameter U.
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//! The result is either:
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//! - a gp_Pnt point for a curve in 3D space, or
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//! - a gp_Pnt2d point for a curve in 2D space.
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Standard_EXPORT static gp_Pnt Value (const Standard_Real U, const gp_Lin& L);
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static gp_Pnt Value (const Standard_Real U, const gp_Circ& C);
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static gp_Pnt Value (const Standard_Real U, const gp_Elips& E);
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static gp_Pnt Value (const Standard_Real U, const gp_Hypr& H);
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static gp_Pnt Value (const Standard_Real U, const gp_Parab& Prb);
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//! For elementary curves (lines, circles and conics) from the
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//! gp package, computes:
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//! - the point P of parameter U, and
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//! - the first derivative vector V1 at this point.
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//! The results P and V1 are either:
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//! - a gp_Pnt point and a gp_Vec vector, for a curve in 3D space, or
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//! - a gp_Pnt2d point and a gp_Vec2d vector, for a curve in 2D space.
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Standard_EXPORT static void D1 (const Standard_Real U, const gp_Lin& L, gp_Pnt& P, gp_Vec& V1);
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static void D1 (const Standard_Real U, const gp_Circ& C, gp_Pnt& P, gp_Vec& V1);
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static void D1 (const Standard_Real U, const gp_Elips& E, gp_Pnt& P, gp_Vec& V1);
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static void D1 (const Standard_Real U, const gp_Hypr& H, gp_Pnt& P, gp_Vec& V1);
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static void D1 (const Standard_Real U, const gp_Parab& Prb, gp_Pnt& P, gp_Vec& V1);
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//! For elementary curves (circles and conics) from the gp
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//! package, computes:
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//! - the point P of parameter U, and
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//! - the first and second derivative vectors V1 and V2 at this point.
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//! The results, P, V1 and V2, are either:
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//! - a gp_Pnt point and two gp_Vec vectors, for a curve in 3D space, or
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//! - a gp_Pnt2d point and two gp_Vec2d vectors, for a curve in 2D space.
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Standard_EXPORT static void D2 (const Standard_Real U, const gp_Circ& C, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2);
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static void D2 (const Standard_Real U, const gp_Elips& E, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2);
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static void D2 (const Standard_Real U, const gp_Hypr& H, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2);
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static void D2 (const Standard_Real U, const gp_Parab& Prb, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2);
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//! For elementary curves (circles, ellipses and hyperbolae)
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//! from the gp package, computes:
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//! - the point P of parameter U, and
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//! - the first, second and third derivative vectors V1, V2
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//! and V3 at this point.
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//! The results, P, V1, V2 and V3, are either:
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//! - a gp_Pnt point and three gp_Vec vectors, for a curve in 3D space, or
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//! - a gp_Pnt2d point and three gp_Vec2d vectors, for a curve in 2D space.
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Standard_EXPORT static void D3 (const Standard_Real U, const gp_Circ& C, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3);
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static void D3 (const Standard_Real U, const gp_Elips& E, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3);
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Standard_EXPORT static void D3 (const Standard_Real U, const gp_Hypr& H, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3);
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//! For elementary curves (lines, circles and conics) from
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//! the gp package, computes the vector corresponding to
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//! the Nth derivative at the point of parameter U. The result is either:
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//! - a gp_Vec vector for a curve in 3D space, or
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//! - a gp_Vec2d vector for a curve in 2D space.
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//! In the following functions N is the order of derivation
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//! and should be greater than 0
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Standard_EXPORT static gp_Vec DN (const Standard_Real U, const gp_Lin& L, const Standard_Integer N);
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static gp_Vec DN (const Standard_Real U, const gp_Circ& C, const Standard_Integer N);
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static gp_Vec DN (const Standard_Real U, const gp_Elips& E, const Standard_Integer N);
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static gp_Vec DN (const Standard_Real U, const gp_Hypr& H, const Standard_Integer N);
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static gp_Vec DN (const Standard_Real U, const gp_Parab& Prb, const Standard_Integer N);
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static gp_Pnt2d Value (const Standard_Real U, const gp_Lin2d& L);
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static gp_Pnt2d Value (const Standard_Real U, const gp_Circ2d& C);
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static gp_Pnt2d Value (const Standard_Real U, const gp_Elips2d& E);
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static gp_Pnt2d Value (const Standard_Real U, const gp_Hypr2d& H);
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static gp_Pnt2d Value (const Standard_Real U, const gp_Parab2d& Prb);
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static void D1 (const Standard_Real U, const gp_Lin2d& L, gp_Pnt2d& P, gp_Vec2d& V1);
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static void D1 (const Standard_Real U, const gp_Circ2d& C, gp_Pnt2d& P, gp_Vec2d& V1);
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static void D1 (const Standard_Real U, const gp_Elips2d& E, gp_Pnt2d& P, gp_Vec2d& V1);
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static void D1 (const Standard_Real U, const gp_Hypr2d& H, gp_Pnt2d& P, gp_Vec2d& V1);
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static void D1 (const Standard_Real U, const gp_Parab2d& Prb, gp_Pnt2d& P, gp_Vec2d& V1);
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static void D2 (const Standard_Real U, const gp_Circ2d& C, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2);
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static void D2 (const Standard_Real U, const gp_Elips2d& E, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2);
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static void D2 (const Standard_Real U, const gp_Hypr2d& H, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2);
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static void D2 (const Standard_Real U, const gp_Parab2d& Prb, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2);
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static void D3 (const Standard_Real U, const gp_Circ2d& C, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3);
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static void D3 (const Standard_Real U, const gp_Elips2d& E, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3);
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//! In the following functions N is the order of derivation
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//! and should be greater than 0
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static void D3 (const Standard_Real U, const gp_Hypr2d& H, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3);
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static gp_Vec2d DN (const Standard_Real U, const gp_Lin2d& L, const Standard_Integer N);
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static gp_Vec2d DN (const Standard_Real U, const gp_Circ2d& C, const Standard_Integer N);
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static gp_Vec2d DN (const Standard_Real U, const gp_Elips2d& E, const Standard_Integer N);
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static gp_Vec2d DN (const Standard_Real U, const gp_Hypr2d& H, const Standard_Integer N);
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static gp_Vec2d DN (const Standard_Real U, const gp_Parab2d& Prb, const Standard_Integer N);
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//! Curve evaluation
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//! The following basis functions compute the derivatives on
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//! elementary curves defined by their geometric characteristics.
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//! These functions can be called without constructing a conic
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//! from package gp. They are called by the previous functions.
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//! Example :
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//! A circle is defined by its position and its radius.
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Standard_EXPORT static gp_Pnt LineValue (const Standard_Real U, const gp_Ax1& Pos);
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Standard_EXPORT static gp_Pnt CircleValue (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real Radius);
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Standard_EXPORT static gp_Pnt EllipseValue (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius);
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Standard_EXPORT static gp_Pnt HyperbolaValue (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius);
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Standard_EXPORT static gp_Pnt ParabolaValue (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real Focal);
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Standard_EXPORT static void LineD1 (const Standard_Real U, const gp_Ax1& Pos, gp_Pnt& P, gp_Vec& V1);
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Standard_EXPORT static void CircleD1 (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& V1);
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Standard_EXPORT static void EllipseD1 (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& V1);
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Standard_EXPORT static void HyperbolaD1 (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& V1);
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Standard_EXPORT static void ParabolaD1 (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real Focal, gp_Pnt& P, gp_Vec& V1);
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Standard_EXPORT static void CircleD2 (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2);
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Standard_EXPORT static void EllipseD2 (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2);
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Standard_EXPORT static void HyperbolaD2 (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2);
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Standard_EXPORT static void ParabolaD2 (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real Focal, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2);
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Standard_EXPORT static void CircleD3 (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real Radius, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3);
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Standard_EXPORT static void EllipseD3 (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3);
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Standard_EXPORT static void HyperbolaD3 (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3);
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//! In the following functions N is the order of derivation
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//! and should be greater than 0
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Standard_EXPORT static gp_Vec LineDN (const Standard_Real U, const gp_Ax1& Pos, const Standard_Integer N);
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Standard_EXPORT static gp_Vec CircleDN (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real Radius, const Standard_Integer N);
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Standard_EXPORT static gp_Vec EllipseDN (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N);
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Standard_EXPORT static gp_Vec HyperbolaDN (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N);
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Standard_EXPORT static gp_Vec ParabolaDN (const Standard_Real U, const gp_Ax2& Pos, const Standard_Real Focal, const Standard_Integer N);
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Standard_EXPORT static gp_Pnt2d LineValue (const Standard_Real U, const gp_Ax2d& Pos);
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Standard_EXPORT static gp_Pnt2d CircleValue (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real Radius);
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Standard_EXPORT static gp_Pnt2d EllipseValue (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius);
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Standard_EXPORT static gp_Pnt2d HyperbolaValue (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius);
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Standard_EXPORT static gp_Pnt2d ParabolaValue (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real Focal);
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Standard_EXPORT static void LineD1 (const Standard_Real U, const gp_Ax2d& Pos, gp_Pnt2d& P, gp_Vec2d& V1);
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Standard_EXPORT static void CircleD1 (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real Radius, gp_Pnt2d& P, gp_Vec2d& V1);
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Standard_EXPORT static void EllipseD1 (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d& P, gp_Vec2d& V1);
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Standard_EXPORT static void HyperbolaD1 (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d& P, gp_Vec2d& V1);
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Standard_EXPORT static void ParabolaD1 (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real Focal, gp_Pnt2d& P, gp_Vec2d& V1);
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Standard_EXPORT static void CircleD2 (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real Radius, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2);
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Standard_EXPORT static void EllipseD2 (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2);
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Standard_EXPORT static void HyperbolaD2 (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2);
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Standard_EXPORT static void ParabolaD2 (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real Focal, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2);
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Standard_EXPORT static void CircleD3 (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real Radius, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3);
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Standard_EXPORT static void EllipseD3 (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3);
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//! In the following functions N is the order of derivation
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//! and should be greater than 0
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Standard_EXPORT static void HyperbolaD3 (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3);
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Standard_EXPORT static gp_Vec2d LineDN (const Standard_Real U, const gp_Ax2d& Pos, const Standard_Integer N);
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Standard_EXPORT static gp_Vec2d CircleDN (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real Radius, const Standard_Integer N);
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Standard_EXPORT static gp_Vec2d EllipseDN (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N);
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Standard_EXPORT static gp_Vec2d HyperbolaDN (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N);
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//! The following functions compute the parametric value corresponding
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//! to a given point on a elementary curve. The point should be on the
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//! curve.
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Standard_EXPORT static gp_Vec2d ParabolaDN (const Standard_Real U, const gp_Ax22d& Pos, const Standard_Real Focal, const Standard_Integer N);
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//! Computes the parameter value of the point P on the given curve.
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//! Note: In its local coordinate system, the parametric
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//! equation of the curve is given by the following:
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//! - for the line L: P(U) = Po + U*Vo
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//! where Po is the origin and Vo the unit vector of its positioning axis.
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//! - for the circle C: X(U) = Radius*Cos(U), Y(U) = Radius*Sin(U)
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//! - for the ellipse E: X(U) = MajorRadius*Cos(U). Y(U) = MinorRadius*Sin(U)
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//! - for the hyperbola H: X(U) = MajorRadius*Ch(U), Y(U) = MinorRadius*Sh(U)
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//! - for the parabola Prb:
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//! X(U) = U**2 / (2*p)
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//! Y(U) = U
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//! where p is the distance between the focus and the directrix.
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//! Warning
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//! The point P must be on the curve. These functions are
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//! not protected, however, and if point P is not on the
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//! curve, an exception may be raised.
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static Standard_Real Parameter (const gp_Lin& L, const gp_Pnt& P);
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//! parametrization
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//! P (U) = L.Location() + U * L.Direction()
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static Standard_Real Parameter (const gp_Lin2d& L, const gp_Pnt2d& P);
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static Standard_Real Parameter (const gp_Circ& C, const gp_Pnt& P);
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//! parametrization
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//! In the local coordinate system of the circle
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//! X (U) = Radius * Cos (U)
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//! Y (U) = Radius * Sin (U)
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static Standard_Real Parameter (const gp_Circ2d& C, const gp_Pnt2d& P);
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static Standard_Real Parameter (const gp_Elips& E, const gp_Pnt& P);
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//! parametrization
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//! In the local coordinate system of the Ellipse
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//! X (U) = MajorRadius * Cos (U)
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//! Y (U) = MinorRadius * Sin (U)
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static Standard_Real Parameter (const gp_Elips2d& E, const gp_Pnt2d& P);
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static Standard_Real Parameter (const gp_Hypr& H, const gp_Pnt& P);
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//! parametrization
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//! In the local coordinate system of the Hyperbola
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//! X (U) = MajorRadius * Ch (U)
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//! Y (U) = MinorRadius * Sh (U)
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static Standard_Real Parameter (const gp_Hypr2d& H, const gp_Pnt2d& P);
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static Standard_Real Parameter (const gp_Parab& Prb, const gp_Pnt& P);
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//! parametrization
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//! In the local coordinate system of the parabola
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//! Y**2 = (2*P) * X where P is the distance between the focus
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//! and the directrix.
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static Standard_Real Parameter (const gp_Parab2d& Prb, const gp_Pnt2d& P);
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Standard_EXPORT static Standard_Real LineParameter (const gp_Ax1& Pos, const gp_Pnt& P);
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//! parametrization
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//! P (U) = L.Location() + U * L.Direction()
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Standard_EXPORT static Standard_Real LineParameter (const gp_Ax2d& Pos, const gp_Pnt2d& P);
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Standard_EXPORT static Standard_Real CircleParameter (const gp_Ax2& Pos, const gp_Pnt& P);
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//! Pos is the Axis of the Circle
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//! parametrization
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//! In the local coordinate system of the circle
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//! X (U) = Radius * Cos (U)
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//! Y (U) = Radius * Sin (U)
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Standard_EXPORT static Standard_Real CircleParameter (const gp_Ax22d& Pos, const gp_Pnt2d& P);
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Standard_EXPORT static Standard_Real EllipseParameter (const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt& P);
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//! Pos is the Axis of the Ellipse
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//! parametrization
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//! In the local coordinate system of the Ellipse
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//! X (U) = MajorRadius * Cos (U)
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//! Y (U) = MinorRadius * Sin (U)
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Standard_EXPORT static Standard_Real EllipseParameter (const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt2d& P);
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Standard_EXPORT static Standard_Real HyperbolaParameter (const gp_Ax2& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt& P);
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//! Pos is the Axis of the Hyperbola
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//! parametrization
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//! In the local coordinate system of the Hyperbola
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//! X (U) = MajorRadius * Ch (U)
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//! Y (U) = MinorRadius * Sh (U)
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Standard_EXPORT static Standard_Real HyperbolaParameter (const gp_Ax22d& Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt2d& P);
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Standard_EXPORT static Standard_Real ParabolaParameter (const gp_Ax2& Pos, const gp_Pnt& P);
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//! Pos is the mirror axis of the parabola
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//! parametrization
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//! In the local coordinate system of the parabola
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//! Y**2 = (2*P) * X where P is the distance between the focus
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//! and the directrix.
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//! The following functions build a 3d curve from a
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//! 2d curve at a given position defined with an Ax2.
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Standard_EXPORT static Standard_Real ParabolaParameter (const gp_Ax22d& Pos, const gp_Pnt2d& P);
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Standard_EXPORT static gp_Pnt To3d (const gp_Ax2& Pos, const gp_Pnt2d& P);
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Standard_EXPORT static gp_Vec To3d (const gp_Ax2& Pos, const gp_Vec2d& V);
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Standard_EXPORT static gp_Dir To3d (const gp_Ax2& Pos, const gp_Dir2d& V);
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Standard_EXPORT static gp_Ax1 To3d (const gp_Ax2& Pos, const gp_Ax2d& A);
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Standard_EXPORT static gp_Ax2 To3d (const gp_Ax2& Pos, const gp_Ax22d& A);
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Standard_EXPORT static gp_Lin To3d (const gp_Ax2& Pos, const gp_Lin2d& L);
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Standard_EXPORT static gp_Circ To3d (const gp_Ax2& Pos, const gp_Circ2d& C);
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Standard_EXPORT static gp_Elips To3d (const gp_Ax2& Pos, const gp_Elips2d& E);
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Standard_EXPORT static gp_Hypr To3d (const gp_Ax2& Pos, const gp_Hypr2d& H);
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//! These functions build a 3D geometric entity from a 2D geometric entity.
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//! The "X Axis" and the "Y Axis" of the global coordinate
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//! system (i.e. 2D space) are lined up respectively with the
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//! "X Axis" and "Y Axis" of the 3D coordinate system, Pos.
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Standard_EXPORT static gp_Parab To3d (const gp_Ax2& Pos, const gp_Parab2d& Prb);
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protected:
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private:
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};
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#include <ElCLib.lxx>
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#endif // _ElCLib_HeaderFile
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