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7bd071edb1
Removed tight connections between data structures, auxiliary tools and algorithms in order to create extensible solution, easy for maintenance and improvements; Code is separated on several functional units responsible for specific operation for the sake of simplification of debugging and readability; Introduced new data structures enabling possibility to manipulate discrete model of particular entity (edge, wire, face) in order to perform computations locally instead of processing an entire model. The workflow of updated component can be divided on six parts: * Creation of model data structure: source TopoDS_Shape passed to algorithm is analyzed and exploded on faces and edges. For each topological entity corresponding reflection is created in data model. Note that underlying algorithms use data model as input and access it via common interface which allows user to create custom data model with necessary dependencies between particular entities; * Discretize edges 3D & 2D curves: 3D curve as well as associated set of 2D curves of each model edge is discretized in order to create coherent skeleton used as a base in faces meshing process. In case if some edge of source shape already contains polygonal data which suites specified parameters, it is extracted from shape and stored to the model as is. Each edge is processed separately, adjacency is not taken into account; * Heal discrete model: source TopoDS_Shape can contain problems, such as open-wire or self-intersections, introduced during design, exchange or modification of model. In addition, some problems like self-intersections can be introduced by roughly discretized edges. This stage is responsible for analysis of discrete model in order to detect and repair faced problems or refuse model’s part for further processing in case if problem cannot be solved; * Preprocess discrete model: defines actions specific for implemented approach to be performed before meshing of faces. By default, iterates over model faces and checks consistency of existing triangulations. Cleans topological faces and its adjacent edges from polygonal data in case of inconsistency or marks face of discrete model as not required for computation; * Discretize faces: represents core part performing mesh generation for particular face based on 2D discrete data related to processing face. Caches polygonal data associated with face’s edges in data model for further processing and stores generated mesh to TopoDS_Face; * Postprocess discrete model: defines actions specific for implemented approach to be performed after meshing of faces. By default, stores polygonal data obtained on previous stage to TopoDS_Edge objects of source model. Component is now spread over IMeshData, IMeshTools, BRepMeshData and BRepMesh units. <!break> 1. Extend "tricheck" DRAW-command in order to find degenerated triangles. 2. Class BRepMesh_FastDiscret::Parameters has been declared as deprecated. 3. NURBS range splitter: do not split intervals without necessity. Intervals are split only in case if it is impossible to compute normals directly on intervals. 4. Default value of IMeshTools_Parameters::MinSize has been changed. New value is equal to 0.1*Deflection. 5. Correction of test scripts: 1) perf mesh bug27119: requested deflection is increased from 1e-6 to 1e-5 to keep reasonable performance (but still reproducing original issue) 2) bugs mesh bug26692_1, 2: make snapshot of triangulation instead of wireframe (irrelevant) Correction in upgrade guide.
1620 lines
46 KiB
C++
1620 lines
46 KiB
C++
// Created on: 1991-09-09
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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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// Evolutions JCV Dec 1991 ajout de calculs de derivees et traitement
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// d'entites 2d
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// JCV Mars 1992 ajout method SetLinearForm
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#define No_Standard_OutOfRange
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#include <ElCLib.hxx>
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#include <gp.hxx>
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#include <gp_Ax1.hxx>
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#include <gp_Ax2.hxx>
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#include <gp_Ax2d.hxx>
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#include <gp_Ax22d.hxx>
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#include <gp_Circ.hxx>
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#include <gp_Circ2d.hxx>
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#include <gp_Dir.hxx>
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#include <gp_Dir2d.hxx>
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#include <gp_Elips.hxx>
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#include <gp_Elips2d.hxx>
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#include <gp_Hypr.hxx>
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#include <gp_Hypr2d.hxx>
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#include <gp_Lin.hxx>
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#include <gp_Lin2d.hxx>
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#include <gp_Parab.hxx>
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#include <gp_Parab2d.hxx>
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#include <gp_Pnt.hxx>
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#include <gp_Pnt2d.hxx>
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#include <gp_Vec.hxx>
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#include <gp_Vec2d.hxx>
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static Standard_Real PIPI = M_PI + M_PI;
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//=======================================================================
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//function : InPeriod
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//purpose : Value theULast is never returned.
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// Example of some case (checked on WIN64 platform)
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// with some surface having period 2*PI = 6.2831853071795862.
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// Let theUFirst be equal to 6.1645624650899675. Then,
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// theULast must be equal to
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// 6.1645624650899675+6.2831853071795862=12.4477477722695537.
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//
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// However, real result is 12.447747772269555.
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// Therefore, new period value to adjust will be equal to
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// 12.447747772269555-6.1645624650899675=6.2831853071795871.
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//
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// As we can see, (6.2831853071795871 != 6.2831853071795862).
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//
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// According to above said, this method should be used carefully.
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// In order to increase reliability of this method, input arguments
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// needs to be replaced with following:
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// (theU, theUFirst, thePeriod). theULast parameter is excess.
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//=======================================================================
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Standard_Real ElCLib::InPeriod(const Standard_Real theU,
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const Standard_Real theUFirst,
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const Standard_Real theULast)
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{
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if( Precision::IsInfinite(theU) ||
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Precision::IsInfinite(theUFirst) ||
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Precision::IsInfinite(theULast))
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{//In order to avoid FLT_Overflow exception
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return theU;
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}
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const Standard_Real aPeriod = theULast - theUFirst;
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if(aPeriod < Epsilon(theULast))
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return theU;
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return Max(theUFirst, theU + aPeriod*Ceiling((theUFirst-theU)/aPeriod));
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}
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//=======================================================================
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//function : AdjustPeriodic
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//purpose :
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//=======================================================================
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void ElCLib::AdjustPeriodic(const Standard_Real UFirst,
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const Standard_Real ULast,
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const Standard_Real Preci,
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Standard_Real& U1,
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Standard_Real& U2)
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{
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if (Precision::IsInfinite(UFirst) ||
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Precision::IsInfinite(ULast))
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{
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U1 = UFirst;
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U2 = ULast;
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return;
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}
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Standard_Real period = ULast - UFirst;
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if (period < Epsilon(ULast))
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{
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// In order to avoid FLT_Overflow exception
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// (test bugs moddata_1 bug22757)
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U1 = UFirst;
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U2 = ULast;
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return;
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}
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U1 -= Floor((U1-UFirst)/period) * period;
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if (ULast - U1 < Preci) U1 -= period;
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U2 -= Floor((U2-U1)/period) * period;
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if (U2 - U1 < Preci) U2 += period;
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}
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//=======================================================================
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//function : LineValue
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//purpose :
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//=======================================================================
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gp_Pnt ElCLib::LineValue (const Standard_Real U,
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const gp_Ax1& Pos)
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{
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const gp_XYZ& ZDir = Pos.Direction().XYZ();
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const gp_XYZ& PLoc = Pos.Location ().XYZ();
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return gp_Pnt(U * ZDir.X() + PLoc.X(),
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U * ZDir.Y() + PLoc.Y(),
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U * ZDir.Z() + PLoc.Z());
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}
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//=======================================================================
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//function : CircleValue
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//purpose :
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//=======================================================================
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gp_Pnt ElCLib::CircleValue (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real Radius)
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{
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const gp_XYZ& XDir = Pos.XDirection().XYZ();
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const gp_XYZ& YDir = Pos.YDirection().XYZ();
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const gp_XYZ& PLoc = Pos.Location ().XYZ();
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Standard_Real A1 = Radius * cos(U);
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Standard_Real A2 = Radius * sin(U);
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return gp_Pnt(A1 * XDir.X() + A2 * YDir.X() + PLoc.X(),
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A1 * XDir.Y() + A2 * YDir.Y() + PLoc.Y(),
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A1 * XDir.Z() + A2 * YDir.Z() + PLoc.Z());
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}
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//=======================================================================
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//function : EllipseValue
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//purpose :
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//=======================================================================
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gp_Pnt ElCLib::EllipseValue (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real MajorRadius,
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const Standard_Real MinorRadius)
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{
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const gp_XYZ& XDir = Pos.XDirection().XYZ();
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const gp_XYZ& YDir = Pos.YDirection().XYZ();
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const gp_XYZ& PLoc = Pos.Location ().XYZ();
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Standard_Real A1 = MajorRadius * cos(U);
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Standard_Real A2 = MinorRadius * sin(U);
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return gp_Pnt(A1 * XDir.X() + A2 * YDir.X() + PLoc.X(),
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A1 * XDir.Y() + A2 * YDir.Y() + PLoc.Y(),
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A1 * XDir.Z() + A2 * YDir.Z() + PLoc.Z());
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}
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//=======================================================================
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//function : HyperbolaValue
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//purpose :
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//=======================================================================
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gp_Pnt ElCLib::HyperbolaValue (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real MajorRadius,
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const Standard_Real MinorRadius)
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{
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const gp_XYZ& XDir = Pos.XDirection().XYZ();
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const gp_XYZ& YDir = Pos.YDirection().XYZ();
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const gp_XYZ& PLoc = Pos.Location ().XYZ();
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Standard_Real A1 = MajorRadius * Cosh(U);
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Standard_Real A2 = MinorRadius * Sinh(U);
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return gp_Pnt(A1 * XDir.X() + A2 * YDir.X() + PLoc.X(),
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A1 * XDir.Y() + A2 * YDir.Y() + PLoc.Y(),
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A1 * XDir.Z() + A2 * YDir.Z() + PLoc.Z());
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}
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//=======================================================================
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//function : ParabolaValue
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//purpose :
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//=======================================================================
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gp_Pnt ElCLib::ParabolaValue (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real Focal)
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{
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if (Focal == 0.0) {
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const gp_XYZ& XDir = Pos.XDirection().XYZ();
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const gp_XYZ& PLoc = Pos.Location ().XYZ();
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return gp_Pnt(U * XDir.X() + PLoc.X(),
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U * XDir.Y() + PLoc.Y(),
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U * XDir.Z() + PLoc.Z());
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}
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const gp_XYZ& XDir = Pos.XDirection().XYZ();
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const gp_XYZ& YDir = Pos.YDirection().XYZ();
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const gp_XYZ& PLoc = Pos.Location ().XYZ();
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Standard_Real A1 = U * U / (4.0 * Focal);
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return gp_Pnt(A1 * XDir.X() + U * YDir.X() + PLoc.X(),
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A1 * XDir.Y() + U * YDir.Y() + PLoc.Y(),
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A1 * XDir.Z() + U * YDir.Z() + PLoc.Z());
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}
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//=======================================================================
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//function : LineD1
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//purpose :
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//=======================================================================
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void ElCLib::LineD1 (const Standard_Real U,
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const gp_Ax1& Pos,
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gp_Pnt& P,
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gp_Vec& V1)
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{
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gp_XYZ Coord = Pos.Direction().XYZ();
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V1.SetXYZ (Coord);
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Coord.SetLinearForm (U, Coord, Pos.Location().XYZ());
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P.SetXYZ (Coord);
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}
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//=======================================================================
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//function : CircleD1
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//purpose :
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//=======================================================================
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void ElCLib::CircleD1 (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real Radius,
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gp_Pnt& P,
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gp_Vec& V1)
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{
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Standard_Real Xc = Radius * Cos (U);
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Standard_Real Yc = Radius * Sin (U);
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gp_XYZ Coord0;
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gp_XYZ Coord1 (Pos.XDirection().XYZ());
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gp_XYZ Coord2 (Pos.YDirection().XYZ());
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//Point courant :
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Coord0.SetLinearForm (Xc, Coord1, Yc, Coord2, Pos.Location().XYZ());
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P.SetXYZ (Coord0);
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//D1 :
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Coord0.SetLinearForm (-Yc, Coord1, Xc, Coord2);
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V1.SetXYZ (Coord0);
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}
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//=======================================================================
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//function : EllipseD1
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//purpose :
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//=======================================================================
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void ElCLib::EllipseD1 (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real MajorRadius,
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const Standard_Real MinorRadius,
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gp_Pnt& P,
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gp_Vec& V1)
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{
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Standard_Real Xc = Cos (U);
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Standard_Real Yc = Sin (U);
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gp_XYZ Coord0;
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gp_XYZ Coord1 (Pos.XDirection().XYZ());
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gp_XYZ Coord2 (Pos.YDirection().XYZ());
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//Point courant :
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Coord0.SetLinearForm (Xc*MajorRadius, Coord1,
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Yc*MinorRadius, Coord2,
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Pos.Location().XYZ());
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P.SetXYZ (Coord0);
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//D1 :
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Coord0.SetLinearForm (-Yc*MajorRadius, Coord1, Xc*MinorRadius, Coord2);
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V1.SetXYZ (Coord0);
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}
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//=======================================================================
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//function : HyperbolaD1
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//purpose :
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//=======================================================================
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void ElCLib::HyperbolaD1 (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real MajorRadius,
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const Standard_Real MinorRadius,
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gp_Pnt& P,
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gp_Vec& V1)
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{
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Standard_Real Xc = Cosh (U);
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Standard_Real Yc = Sinh (U);
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gp_XYZ Coord0;
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gp_XYZ Coord1 (Pos.XDirection().XYZ());
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gp_XYZ Coord2 (Pos.YDirection().XYZ());
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//Point courant :
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Coord0.SetLinearForm (Xc*MajorRadius, Coord1,
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Yc*MinorRadius, Coord2,
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Pos.Location().XYZ());
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P.SetXYZ (Coord0);
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//D1 :
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Coord0.SetLinearForm (Yc*MajorRadius, Coord1, Xc*MinorRadius, Coord2);
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V1.SetXYZ (Coord0);
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}
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//=======================================================================
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//function : ParabolaD1
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//purpose :
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//=======================================================================
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void ElCLib::ParabolaD1 (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real Focal,
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gp_Pnt& P,
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gp_Vec& V1)
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{
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gp_XYZ Coord0;
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gp_XYZ Coord1 (Pos.XDirection().XYZ());
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if (Focal == 0.0) { //Parabole degenere en une droite
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V1.SetXYZ (Coord1);
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Coord1.Multiply (U);
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Coord1.Add (Pos.Location().XYZ());
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P.SetXYZ (Coord1);
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}
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else {
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gp_XYZ Coord2 (Pos.YDirection().XYZ());
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Coord0.SetLinearForm (U / (2.0 * Focal), Coord1, Coord2);
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V1.SetXYZ (Coord0);
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Coord0.SetLinearForm ((U * U) / (4.0 * Focal), Coord1,
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U, Coord2,
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Pos.Location().XYZ());
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P.SetXYZ (Coord0);
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}
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}
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//=======================================================================
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//function : CircleD2
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//purpose :
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//=======================================================================
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void ElCLib::CircleD2 (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real Radius,
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gp_Pnt& P,
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gp_Vec& V1,
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gp_Vec& V2)
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{
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Standard_Real Xc = Radius * cos(U);
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Standard_Real Yc = Radius * sin(U);
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gp_XYZ Coord0;
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gp_XYZ Coord1 (Pos.XDirection().XYZ());
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gp_XYZ Coord2 (Pos.YDirection().XYZ());
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//Point courant :
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Coord0.SetLinearForm (Xc, Coord1, Yc, Coord2, Pos.Location().XYZ());
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P.SetXYZ (Coord0);
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//D1 :
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Coord0.SetLinearForm (-Yc, Coord1, Xc, Coord2);
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V1.SetXYZ (Coord0);
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//D2 :
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Coord0.SetLinearForm (-Xc, Coord1, -Yc, Coord2);
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V2.SetXYZ (Coord0);
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}
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//=======================================================================
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//function : EllipseD2
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//purpose :
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//=======================================================================
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void ElCLib::EllipseD2 (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real MajorRadius,
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const Standard_Real MinorRadius,
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gp_Pnt& P,
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gp_Vec& V1,
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gp_Vec& V2)
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{
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Standard_Real Xc = cos(U);
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Standard_Real Yc = sin(U);
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gp_XYZ Coord0;
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gp_XYZ Coord1 (Pos.XDirection().XYZ());
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gp_XYZ Coord2 (Pos.YDirection().XYZ());
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//Point courant :
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Coord0.SetLinearForm (Xc*MajorRadius, Coord1,
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Yc*MinorRadius, Coord2,
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Pos.Location().XYZ());
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P.SetXYZ (Coord0);
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//D1 :
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Coord0.SetLinearForm (-Yc*MajorRadius, Coord1, Xc*MinorRadius, Coord2);
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V1.SetXYZ (Coord0);
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//D2 :
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Coord0.SetLinearForm (-Xc*MajorRadius, Coord1, -Yc*MinorRadius, Coord2);
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V2.SetXYZ (Coord0);
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}
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//=======================================================================
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//function : HyperbolaD2
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//purpose :
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//=======================================================================
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void ElCLib::HyperbolaD2 (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real MajorRadius,
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const Standard_Real MinorRadius,
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gp_Pnt& P,
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gp_Vec& V1,
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gp_Vec& V2)
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{
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Standard_Real Xc = Cosh(U);
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Standard_Real Yc = Sinh(U);
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gp_XYZ Coord0;
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gp_XYZ Coord1 (Pos.XDirection().XYZ());
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gp_XYZ Coord2 (Pos.YDirection().XYZ());
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//Point courant et D2:
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Coord0.SetLinearForm (Xc*MajorRadius, Coord1, Yc*MinorRadius, Coord2);
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V2.SetXYZ (Coord0);
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Coord0.Add (Pos.Location().XYZ());
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P.SetXYZ (Coord0);
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//D1 :
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Coord0.SetLinearForm (Yc*MajorRadius, Coord1, Xc*MinorRadius, Coord2);
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V1.SetXYZ (Coord0);
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}
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//=======================================================================
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//function : ParabolaD2
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//purpose :
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//=======================================================================
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void ElCLib::ParabolaD2 (const Standard_Real U,
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const gp_Ax2& Pos,
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const Standard_Real Focal,
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gp_Pnt& P,
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gp_Vec& V1,
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gp_Vec& V2)
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{
|
|
gp_XYZ Coord0(0.0, 0.0, 0.0);
|
|
gp_XYZ Coord1 (Pos.XDirection().XYZ());
|
|
if (Focal == 0.0) {
|
|
V2.SetCoord (0.0, 0.0, 0.0);
|
|
V1.SetXYZ (Coord1);
|
|
Coord1.Multiply (U);
|
|
Coord1.Add (Pos.Location().XYZ());
|
|
P.SetXYZ (Coord1);//was: P.SetXYZ (Coord0);
|
|
|
|
}
|
|
else {
|
|
gp_XYZ Coord2 (Pos.YDirection().XYZ());
|
|
Coord0.SetLinearForm ((U * U) / (4.0 * Focal), Coord1,
|
|
U, Coord2,
|
|
Pos.Location().XYZ());
|
|
P.SetXYZ (Coord0);
|
|
Coord0.SetLinearForm (U / (2.0 * Focal), Coord1, Coord2);
|
|
V1.SetXYZ (Coord0);
|
|
Coord1.Multiply (1.0 / (2.0 * Focal));
|
|
V2.SetXYZ (Coord1);
|
|
}
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CircleD3
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::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)
|
|
{
|
|
Standard_Real Xc = Radius * cos(U);
|
|
Standard_Real Yc = Radius * sin(U);
|
|
gp_XYZ Coord0;
|
|
gp_XYZ Coord1 (Pos.XDirection().XYZ());
|
|
gp_XYZ Coord2 (Pos.YDirection().XYZ());
|
|
//Point Courant :
|
|
Coord0.SetLinearForm (Xc, Coord1, Yc, Coord2, Pos.Location().XYZ());
|
|
P.SetXYZ (Coord0);
|
|
//D1 :
|
|
Coord0.SetLinearForm (-Yc, Coord1, Xc, Coord2);
|
|
V1.SetXYZ (Coord0);
|
|
//D2 :
|
|
Coord0.SetLinearForm (-Xc, Coord1, -Yc, Coord2);
|
|
V2.SetXYZ (Coord0);
|
|
//D3 :
|
|
Coord0.SetLinearForm (Yc, Coord1, -Xc, Coord2);
|
|
V3.SetXYZ (Coord0);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : EllipseD3
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::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)
|
|
{
|
|
Standard_Real Xc = cos(U);
|
|
Standard_Real Yc = sin(U);
|
|
gp_XYZ Coord0;
|
|
gp_XYZ Coord1 (Pos.XDirection().XYZ());
|
|
gp_XYZ Coord2 (Pos.YDirection().XYZ());
|
|
//Point Courant :
|
|
Coord0.SetLinearForm (Xc*MajorRadius, Coord1,
|
|
Yc*MinorRadius, Coord2,
|
|
Pos.Location().XYZ());
|
|
P.SetXYZ (Coord0);
|
|
//D1 :
|
|
Coord0.SetLinearForm (-Yc*MajorRadius, Coord1, Xc*MinorRadius, Coord2);
|
|
V1.SetXYZ (Coord0);
|
|
//D2 :
|
|
Coord0.SetLinearForm (-Xc*MajorRadius, Coord1, -Yc*MinorRadius, Coord2);
|
|
V2.SetXYZ (Coord0);
|
|
//D3
|
|
Coord0.SetLinearForm (Yc*MajorRadius, Coord1, -Xc*MinorRadius, Coord2);
|
|
V3.SetXYZ (Coord0);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : HyperbolaD3
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::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)
|
|
{
|
|
Standard_Real Xc = Cosh(U);
|
|
Standard_Real Yc = Sinh(U);
|
|
gp_XYZ Coord0;
|
|
gp_XYZ Coord1 (Pos.XDirection().XYZ());
|
|
gp_XYZ Coord2 (Pos.YDirection().XYZ());
|
|
//Point courant et D2 :
|
|
Coord0.SetLinearForm (Xc*MajorRadius, Coord1, Yc*MinorRadius, Coord2);
|
|
V2.SetXYZ (Coord0);
|
|
Coord0.Add (Pos.Location().XYZ());
|
|
P.SetXYZ (Coord0);
|
|
//D1 et D3 :
|
|
Coord0.SetLinearForm (Yc*MajorRadius, Coord1, Xc*MinorRadius, Coord2);
|
|
V1.SetXYZ (Coord0);
|
|
V3.SetXYZ (Coord0);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : LineValue
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Pnt2d ElCLib::LineValue (const Standard_Real U,
|
|
const gp_Ax2d& Pos)
|
|
{
|
|
const gp_XY& ZDir = Pos.Direction().XY();
|
|
const gp_XY& PLoc = Pos.Location ().XY();
|
|
return gp_Pnt2d(U * ZDir.X() + PLoc.X(),
|
|
U * ZDir.Y() + PLoc.Y());
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CircleValue
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Pnt2d ElCLib::CircleValue (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real Radius)
|
|
{
|
|
const gp_XY& XDir = Pos.XDirection().XY();
|
|
const gp_XY& YDir = Pos.YDirection().XY();
|
|
const gp_XY& PLoc = Pos.Location ().XY();
|
|
Standard_Real A1 = Radius * cos(U);
|
|
Standard_Real A2 = Radius * sin(U);
|
|
return gp_Pnt2d(A1 * XDir.X() + A2 * YDir.X() + PLoc.X(),
|
|
A1 * XDir.Y() + A2 * YDir.Y() + PLoc.Y());
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : EllipseValue
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Pnt2d ElCLib::EllipseValue (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real MajorRadius,
|
|
const Standard_Real MinorRadius)
|
|
{
|
|
const gp_XY& XDir = Pos.XDirection().XY();
|
|
const gp_XY& YDir = Pos.YDirection().XY();
|
|
const gp_XY& PLoc = Pos.Location ().XY();
|
|
Standard_Real A1 = MajorRadius * cos(U);
|
|
Standard_Real A2 = MinorRadius * sin(U);
|
|
return gp_Pnt2d(A1 * XDir.X() + A2 * YDir.X() + PLoc.X(),
|
|
A1 * XDir.Y() + A2 * YDir.Y() + PLoc.Y());
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : HyperbolaValue
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Pnt2d ElCLib::HyperbolaValue (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real MajorRadius,
|
|
const Standard_Real MinorRadius)
|
|
{
|
|
const gp_XY& XDir = Pos.XDirection().XY();
|
|
const gp_XY& YDir = Pos.YDirection().XY();
|
|
const gp_XY& PLoc = Pos.Location ().XY();
|
|
Standard_Real A1 = MajorRadius * Cosh(U);
|
|
Standard_Real A2 = MinorRadius * Sinh(U);
|
|
return gp_Pnt2d(A1 * XDir.X() + A2 * YDir.X() + PLoc.X(),
|
|
A1 * XDir.Y() + A2 * YDir.Y() + PLoc.Y());
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : ParabolaValue
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Pnt2d ElCLib::ParabolaValue (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real Focal)
|
|
{
|
|
if (Focal == 0.0) {
|
|
const gp_XY& XDir = Pos.XDirection().XY();
|
|
const gp_XY& PLoc = Pos.Location ().XY();
|
|
return gp_Pnt2d(U * XDir.X() + PLoc.X(),
|
|
U * XDir.Y() + PLoc.Y());
|
|
}
|
|
const gp_XY& XDir = Pos.XDirection().XY();
|
|
const gp_XY& YDir = Pos.YDirection().XY();
|
|
const gp_XY& PLoc = Pos.Location ().XY();
|
|
Standard_Real A1 = U * U / (4.0 * Focal);
|
|
return gp_Pnt2d(A1 * XDir.X() + U * YDir.X() + PLoc.X(),
|
|
A1 * XDir.Y() + U * YDir.Y() + PLoc.Y());
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : LineD1
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::LineD1(const Standard_Real U,
|
|
const gp_Ax2d& Pos,
|
|
gp_Pnt2d& P,
|
|
gp_Vec2d& V1)
|
|
{
|
|
gp_XY Coord = Pos.Direction().XY();
|
|
V1.SetXY (Coord);
|
|
Coord.SetLinearForm (U, Coord, Pos.Location().XY());
|
|
P.SetXY (Coord);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CircleD1
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::CircleD1 (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real Radius,
|
|
gp_Pnt2d& P,
|
|
gp_Vec2d& V1)
|
|
{
|
|
gp_XY Vxy;
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Standard_Real Xc = Radius * cos(U);
|
|
Standard_Real Yc = Radius * sin(U);
|
|
//Point courant :
|
|
Vxy.SetLinearForm (Xc, Xdir, Yc, Ydir, Pos.Location().XY());
|
|
P.SetXY (Vxy);
|
|
//V1 :
|
|
Vxy.SetLinearForm (-Yc, Xdir, Xc, Ydir);
|
|
V1.SetXY (Vxy);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : EllipseD1
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::EllipseD1 (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real MajorRadius,
|
|
const Standard_Real MinorRadius,
|
|
gp_Pnt2d& P,
|
|
gp_Vec2d& V1)
|
|
{
|
|
gp_XY Vxy;
|
|
gp_XY Xdir ((Pos.XDirection()).XY());
|
|
gp_XY Ydir ((Pos.YDirection()).XY());
|
|
Standard_Real Xc = cos(U);
|
|
Standard_Real Yc = sin(U);
|
|
//Point courant :
|
|
Vxy.SetLinearForm (Xc*MajorRadius, Xdir,
|
|
Yc*MinorRadius, Ydir,
|
|
Pos.Location().XY());
|
|
P.SetXY (Vxy);
|
|
|
|
//V1 :
|
|
Vxy.SetLinearForm (-Yc*MajorRadius, Xdir, Xc*MinorRadius, Ydir);
|
|
V1.SetXY (Vxy);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : HyperbolaD1
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::HyperbolaD1 (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real MajorRadius,
|
|
const Standard_Real MinorRadius,
|
|
gp_Pnt2d& P,
|
|
gp_Vec2d& V1)
|
|
{
|
|
gp_XY Vxy;
|
|
gp_XY Xdir ((Pos.XDirection()).XY());
|
|
gp_XY Ydir ((Pos.YDirection()).XY());
|
|
Standard_Real Xc = Cosh(U);
|
|
Standard_Real Yc = Sinh(U);
|
|
//Point courant :
|
|
Vxy.SetLinearForm (Xc*MajorRadius, Xdir,
|
|
Yc*MinorRadius, Ydir,
|
|
Pos.Location().XY());
|
|
P.SetXY (Vxy);
|
|
|
|
//V1 :
|
|
Vxy.SetLinearForm (Yc*MajorRadius, Xdir, Xc*MinorRadius, Ydir);
|
|
V1.SetXY (Vxy);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : ParabolaD1
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::ParabolaD1 (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real Focal,
|
|
gp_Pnt2d& P,
|
|
gp_Vec2d& V1)
|
|
{
|
|
gp_XY Vxy;
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
if (Focal == 0.0) { //Parabole degenere en une droite
|
|
V1.SetXY (Xdir);
|
|
Vxy.SetLinearForm (U, Xdir, Pos.Location().XY());
|
|
}
|
|
else {
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Vxy.SetLinearForm (U / (2.0 * Focal), Xdir, Ydir);
|
|
V1.SetXY (Vxy);
|
|
Vxy.SetLinearForm ((U * U) / (4.0 * Focal), Xdir,
|
|
U, Ydir,
|
|
Pos.Location().XY());
|
|
}
|
|
P.SetXY (Vxy);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CircleD2
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::CircleD2 (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real Radius,
|
|
gp_Pnt2d& P,
|
|
gp_Vec2d& V1,
|
|
gp_Vec2d& V2)
|
|
{
|
|
gp_XY Vxy;
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Standard_Real Xc = Radius * cos(U);
|
|
Standard_Real Yc = Radius * sin(U);
|
|
//V2 :
|
|
Vxy.SetLinearForm (Xc, Xdir, Yc, Ydir);
|
|
V2.SetXY (Vxy);
|
|
V2.Reverse();
|
|
Vxy.Add (Pos.Location().XY());
|
|
P.SetXY (Vxy);
|
|
|
|
//V1 :
|
|
Vxy.SetLinearForm (-Yc, Xdir, Xc, Ydir);
|
|
V1.SetXY (Vxy);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : EllipseD2
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::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)
|
|
{
|
|
gp_XY Vxy;
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Standard_Real Xc = cos(U);
|
|
Standard_Real Yc = sin(U);
|
|
|
|
//V2 :
|
|
Vxy.SetLinearForm (Xc*MajorRadius, Xdir, Yc*MinorRadius, Ydir);
|
|
V2.SetXY (Vxy);
|
|
V2.Reverse ();
|
|
|
|
//Point courant :
|
|
Vxy.Add (Pos.Location().XY());
|
|
P.SetXY (Vxy);
|
|
|
|
//V1 :
|
|
Vxy.SetLinearForm (-Yc*MajorRadius, Xdir, Xc*MinorRadius, Ydir);
|
|
V1.SetXY (Vxy);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : HyperbolaD2
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::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)
|
|
{
|
|
gp_XY Vxy;
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Standard_Real Xc = Cosh(U);
|
|
Standard_Real Yc = Sinh(U);
|
|
|
|
//V2 :
|
|
Vxy.SetLinearForm (Xc*MajorRadius, Xdir, Yc*MinorRadius, Ydir);
|
|
V2.SetXY (Vxy);
|
|
|
|
//Point courant :
|
|
Vxy.Add (Pos.Location().XY());
|
|
P.SetXY (Vxy);
|
|
|
|
//V1 :
|
|
Vxy.SetLinearForm (Yc*MajorRadius, Xdir, Xc*MinorRadius, Ydir);
|
|
V1.SetXY (Vxy);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : ParabolaD2
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::ParabolaD2 (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real Focal,
|
|
gp_Pnt2d& P,
|
|
gp_Vec2d& V1,
|
|
gp_Vec2d& V2)
|
|
{
|
|
gp_XY Vxy;
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
if (Focal == 0.0) {
|
|
V2.SetCoord (0.0, 0.0);
|
|
V1.SetXY (Xdir);
|
|
Vxy.SetLinearForm (U, Xdir, Pos.Location().XY());
|
|
}
|
|
else {
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Vxy = Xdir.Multiplied (1.0 / (2.0 * Focal));
|
|
V2.SetXY (Vxy);
|
|
Vxy.SetLinearForm (U, Vxy, Ydir);
|
|
V1.SetXY (Vxy);
|
|
Vxy.SetLinearForm (U * U / (4.0 * Focal), Xdir, U, Ydir);
|
|
Vxy.Add (Pos.Location().XY());
|
|
}
|
|
P.SetXY (Vxy);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CircleD3
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::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)
|
|
{
|
|
gp_XY Vxy;
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Standard_Real Xc = Radius * cos(U);
|
|
Standard_Real Yc = Radius * sin(U);
|
|
|
|
//V2 :
|
|
Vxy.SetLinearForm (Xc, Xdir, Yc, Ydir);
|
|
V2.SetXY (Vxy);
|
|
V2.Reverse();
|
|
|
|
//Point courant :
|
|
Vxy.Add (Pos.Location().XY());
|
|
P.SetXY (Vxy);
|
|
|
|
//V1 :
|
|
Vxy.SetLinearForm (-Yc, Xdir, Xc, Ydir);
|
|
V1.SetXY (Vxy);
|
|
|
|
//V3 :
|
|
V3.SetXY (Vxy);
|
|
V3.Reverse ();
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : EllipseD3
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::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)
|
|
{
|
|
gp_XY Vxy;
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Standard_Real Xc = cos(U);
|
|
Standard_Real Yc = sin(U);
|
|
|
|
//V2 :
|
|
Vxy.SetLinearForm (Xc*MajorRadius, Xdir, Yc*MinorRadius, Ydir);
|
|
V2.SetXY (Vxy);
|
|
V2.Reverse ();
|
|
|
|
//Point courant :
|
|
Vxy.Add (Pos.Location().XY());
|
|
P.SetXY (Vxy);
|
|
|
|
//V1 :
|
|
Vxy.SetLinearForm (-Yc*MajorRadius, Xdir, Xc*MinorRadius, Ydir);
|
|
V1.SetXY (Vxy);
|
|
|
|
//V3 :
|
|
V3.SetXY (Vxy);
|
|
V3.Reverse ();
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : HyperbolaD3
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
void ElCLib::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)
|
|
{
|
|
gp_XY Vxy;
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Standard_Real Xc = Cosh(U);
|
|
Standard_Real Yc = Sinh(U);
|
|
|
|
//V2 :
|
|
Vxy.SetLinearForm (Xc*MajorRadius, Xdir, Yc*MinorRadius, Ydir);
|
|
V2.SetXY (Vxy);
|
|
|
|
//Point courant :
|
|
Vxy.Add (Pos.Location().XY());
|
|
P.SetXY (Vxy);
|
|
|
|
//V1 :
|
|
Vxy.SetLinearForm (Yc*MajorRadius, Xdir, Xc*MinorRadius, Ydir);
|
|
V1.SetXY (Vxy);
|
|
|
|
//V3 :
|
|
V3.SetXY (Vxy);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : LineDN
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Vec ElCLib::LineDN (const Standard_Real,
|
|
const gp_Ax1& Pos,
|
|
const Standard_Integer N)
|
|
{
|
|
if (N == 1) { return gp_Vec(Pos.Direction()); }
|
|
return gp_Vec (0., 0., 0.);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CircleDN
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Vec ElCLib::CircleDN (const Standard_Real U,
|
|
const gp_Ax2& Pos,
|
|
const Standard_Real Radius,
|
|
const Standard_Integer N)
|
|
{
|
|
Standard_Real Xc=0, Yc=0;
|
|
if (N == 1) {
|
|
Xc = Radius * -sin(U);
|
|
Yc = Radius * cos(U);
|
|
}
|
|
else if ((N + 2) % 4 == 0) {
|
|
Xc = Radius * -cos(U);
|
|
Yc = Radius * -sin(U);
|
|
}
|
|
else if ((N + 1) % 4 == 0) {
|
|
Xc = Radius * sin(U);
|
|
Yc = Radius * -cos(U);
|
|
}
|
|
else if (N % 4 == 0) {
|
|
Xc = Radius * cos(U);
|
|
Yc = Radius * sin(U);
|
|
}
|
|
else if ((N-1) % 4 == 0) {
|
|
Xc = Radius * -sin(U);
|
|
Yc = Radius * cos(U);
|
|
}
|
|
gp_XYZ Coord1 (Pos.XDirection().XYZ());
|
|
Coord1.SetLinearForm (Xc, Coord1, Yc, Pos.YDirection().XYZ());
|
|
return gp_Vec (Coord1);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : EllipseDN
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Vec ElCLib::EllipseDN (const Standard_Real U,
|
|
const gp_Ax2& Pos,
|
|
const Standard_Real MajorRadius,
|
|
const Standard_Real MinorRadius,
|
|
const Standard_Integer N)
|
|
{
|
|
Standard_Real Xc=0, Yc=0;
|
|
if (N == 1) {
|
|
Xc = MajorRadius * -sin(U);
|
|
Yc = MinorRadius * cos(U);
|
|
}
|
|
else if ((N + 2) % 4 == 0) {
|
|
Xc = MajorRadius * -cos(U);
|
|
Yc = MinorRadius * -sin(U);
|
|
}
|
|
else if ((N + 1) % 4 == 0) {
|
|
Xc = MajorRadius * sin(U);
|
|
Yc = MinorRadius * -cos(U);
|
|
}
|
|
else if (N % 4 == 0) {
|
|
Xc = MajorRadius * cos(U);
|
|
Yc = MinorRadius * sin(U);
|
|
}
|
|
else if ((N-1) % 4 == 0) {
|
|
Xc = MajorRadius * -sin(U);
|
|
Yc = MinorRadius * cos(U);
|
|
}
|
|
gp_XYZ Coord1 (Pos.XDirection().XYZ());
|
|
Coord1.SetLinearForm (Xc, Coord1, Yc, Pos.YDirection().XYZ());
|
|
return gp_Vec (Coord1);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : HyperbolaDN
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Vec ElCLib::HyperbolaDN (const Standard_Real U,
|
|
const gp_Ax2& Pos,
|
|
const Standard_Real MajorRadius,
|
|
const Standard_Real MinorRadius,
|
|
const Standard_Integer N)
|
|
{
|
|
Standard_Real Xc=0, Yc=0;
|
|
if (IsOdd (N)) {
|
|
Xc = MajorRadius * Sinh(U);
|
|
Yc = MinorRadius * Cosh(U);
|
|
}
|
|
else if (IsEven (N)) {
|
|
Xc = MajorRadius * Cosh(U);
|
|
Yc = MinorRadius * Sinh(U);
|
|
}
|
|
gp_XYZ Coord1 (Pos.XDirection().XYZ());
|
|
Coord1.SetLinearForm (Xc, Coord1, Yc, Pos.YDirection().XYZ());
|
|
return gp_Vec (Coord1);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : ParabolaDN
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Vec ElCLib::ParabolaDN (const Standard_Real U,
|
|
const gp_Ax2& Pos,
|
|
const Standard_Real Focal,
|
|
const Standard_Integer N)
|
|
{
|
|
if (N <= 2) {
|
|
gp_XYZ Coord1 (Pos.XDirection().XYZ());
|
|
if (N == 1) {
|
|
if (Focal == 0.0) {
|
|
return gp_Vec(Coord1);
|
|
}
|
|
else {
|
|
Coord1.SetLinearForm
|
|
(U / (2.0 * Focal), Coord1, Pos.YDirection().XYZ());
|
|
return gp_Vec (Coord1);
|
|
}
|
|
}
|
|
else if (N == 2) {
|
|
if (Focal == 0.0) {
|
|
return gp_Vec(0.0, 0.0, 0.0);
|
|
}
|
|
else {
|
|
Coord1.Multiply ( 1.0 / (2.0 * Focal));
|
|
return gp_Vec (Coord1);
|
|
}
|
|
}
|
|
}
|
|
return gp_Vec (0.,0.,0.);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : LineDN
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Vec2d ElCLib::LineDN (const Standard_Real,
|
|
const gp_Ax2d& Pos,
|
|
const Standard_Integer N)
|
|
{
|
|
if (N == 1) { return gp_Vec2d (Pos.Direction ()); }
|
|
return gp_Vec2d (0.0, 0.0);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CircleDN
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Vec2d ElCLib::CircleDN (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real Radius,
|
|
const Standard_Integer N)
|
|
{
|
|
Standard_Real Xc=0, Yc=0;
|
|
if (N == 1) {
|
|
Xc = Radius * -sin(U);
|
|
Yc = Radius * cos(U);
|
|
}
|
|
else if ((N + 2) % 4 == 0) {
|
|
Xc = Radius * -cos(U);
|
|
Yc = Radius * -sin(U);
|
|
}
|
|
else if ((N + 1) % 4 == 0) {
|
|
Xc = Radius * sin(U);
|
|
Yc = Radius * -cos(U);
|
|
}
|
|
else if (N % 4 == 0) {
|
|
Xc = Radius * cos(U);
|
|
Yc = Radius * sin(U);
|
|
}
|
|
else if ((N-1) % 4 == 0) {
|
|
Xc = Radius * -sin(U);
|
|
Yc = Radius * cos(U);
|
|
}
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Xdir.SetLinearForm (Xc, Xdir, Yc, Ydir);
|
|
return gp_Vec2d (Xdir);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : EllipseDN
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Vec2d ElCLib::EllipseDN (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real MajorRadius,
|
|
const Standard_Real MinorRadius,
|
|
const Standard_Integer N)
|
|
{
|
|
Standard_Real Xc=0, Yc=0;
|
|
if (N == 1) {
|
|
Xc = MajorRadius * -sin(U);
|
|
Yc = MinorRadius * cos(U);
|
|
}
|
|
else if ((N + 2) % 4 == 0) {
|
|
Xc = MajorRadius * -cos(U);
|
|
Yc = MinorRadius * -sin(U);
|
|
}
|
|
else if ((N + 1) % 4 == 0) {
|
|
Xc = MajorRadius * sin(U);
|
|
Yc = MinorRadius * -cos(U);
|
|
}
|
|
else if (N % 4 == 0) {
|
|
Xc = MajorRadius * cos(U);
|
|
Yc = MinorRadius * sin(U);
|
|
}
|
|
else if ((N-1) % 4 == 0) {
|
|
Xc = MajorRadius * -sin(U);
|
|
Yc = MinorRadius * cos(U);
|
|
}
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Xdir.SetLinearForm (Xc, Xdir, Yc, Ydir);
|
|
return gp_Vec2d (Xdir);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : HyperbolaDN
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Vec2d ElCLib::HyperbolaDN (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real MajorRadius,
|
|
const Standard_Real MinorRadius,
|
|
const Standard_Integer N)
|
|
{
|
|
Standard_Real Xc=0, Yc=0;
|
|
if (IsOdd (N)) {
|
|
Xc = MajorRadius * Sinh(U);
|
|
Yc = MinorRadius * Cosh(U);
|
|
}
|
|
else if (IsEven (N)) {
|
|
Xc = MajorRadius * Cosh(U);
|
|
Yc = MinorRadius * Sinh(U);
|
|
}
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Xdir.SetLinearForm (Xc, Xdir, Yc, Ydir);
|
|
return gp_Vec2d (Xdir);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : ParabolaDN
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Vec2d ElCLib::ParabolaDN (const Standard_Real U,
|
|
const gp_Ax22d& Pos,
|
|
const Standard_Real Focal,
|
|
const Standard_Integer N)
|
|
{
|
|
if (N <= 2) {
|
|
gp_XY Xdir (Pos.XDirection().XY());
|
|
if (N == 1) {
|
|
if (Focal == 0.0) {
|
|
return gp_Vec2d (Xdir);
|
|
}
|
|
else {
|
|
gp_XY Ydir (Pos.YDirection().XY());
|
|
Xdir.SetLinearForm (U / (2.0 * Focal), Xdir, Ydir);
|
|
return gp_Vec2d (Xdir);
|
|
}
|
|
}
|
|
else if (N == 2) {
|
|
if (Focal == 0.0) {
|
|
return gp_Vec2d (0.0, 0.0);
|
|
}
|
|
else {
|
|
Xdir.Multiply ( 1.0 / (2.0 * Focal));
|
|
return gp_Vec2d (Xdir);
|
|
}
|
|
}
|
|
}
|
|
return gp_Vec2d (0.0, 0.0);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : LineParameter
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
Standard_Real ElCLib::LineParameter (const gp_Ax1& L, const gp_Pnt& P)
|
|
{
|
|
return (P.XYZ() - L.Location().XYZ()).Dot (L.Direction().XYZ());
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CircleParameter
|
|
//purpose :
|
|
//=======================================================================
|
|
Standard_Real ElCLib::CircleParameter(const gp_Ax2& Pos,
|
|
const gp_Pnt& P)
|
|
{
|
|
gp_Vec aVec(Pos.Location(), P);
|
|
if (aVec.SquareMagnitude() < gp::Resolution())
|
|
// coinciding points -> infinite number of parameters
|
|
return 0.0;
|
|
|
|
const gp_Dir& dir = Pos.Direction();
|
|
// Project vector on circle's plane
|
|
gp_XYZ aVProj = dir.XYZ().CrossCrossed(aVec.XYZ(), dir.XYZ());
|
|
|
|
if (aVProj.SquareModulus() < gp::Resolution())
|
|
return 0.0;
|
|
|
|
// Angle between X direction and projected vector
|
|
Standard_Real Teta = (Pos.XDirection()).AngleWithRef(aVProj, dir);
|
|
|
|
if (Teta < -1.e-16) Teta += PIPI;
|
|
else if (Teta < 0) Teta = 0;
|
|
return Teta;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : EllipseParameter
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
Standard_Real ElCLib::EllipseParameter (const gp_Ax2& Pos,
|
|
const Standard_Real MajorRadius,
|
|
const Standard_Real MinorRadius,
|
|
const gp_Pnt& P)
|
|
{
|
|
gp_XYZ OP = P.XYZ()-Pos.Location().XYZ();
|
|
gp_XYZ xaxis = Pos.XDirection().XYZ();
|
|
gp_XYZ yaxis = Pos.YDirection().XYZ();
|
|
Standard_Real NY = OP.Dot(yaxis);
|
|
Standard_Real NX = OP.Dot(xaxis);
|
|
|
|
if( (Abs(NX) <= gp::Resolution())
|
|
&&(Abs(NY) <= gp::Resolution()))
|
|
//-- The point P is on the Axis of the Ellipse.
|
|
return(0.0);
|
|
|
|
yaxis.Multiply (NY * (MajorRadius/MinorRadius));
|
|
gp_XYZ Om = xaxis.Multiplied (NX);
|
|
Om.Add (yaxis);
|
|
Standard_Real Teta = gp_Vec(xaxis).AngleWithRef
|
|
(gp_Vec(Om), gp_Vec(Pos.Direction()));
|
|
if (Teta < -1.e-16) Teta += PIPI;
|
|
else if (Teta < 0) Teta = 0;
|
|
return Teta;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : HyperbolaParameter
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
Standard_Real ElCLib::HyperbolaParameter (const gp_Ax2& Pos,
|
|
const Standard_Real,
|
|
const Standard_Real MinorRadius,
|
|
const gp_Pnt& P)
|
|
{
|
|
Standard_Real sht =
|
|
gp_Vec(Pos.Location (), P).Dot
|
|
(gp_Vec (Pos.YDirection())) / MinorRadius;
|
|
|
|
#if __QNX__
|
|
return std::asinh(sht);
|
|
#else
|
|
return asinh(sht);
|
|
#endif
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : ParabolaParameter
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
Standard_Real ElCLib::ParabolaParameter (const gp_Ax2& Pos,
|
|
const gp_Pnt& P)
|
|
{
|
|
return gp_Vec(Pos.Location(),P).Dot(gp_Vec(Pos.YDirection()));
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : LineParameter
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
Standard_Real ElCLib::LineParameter (const gp_Ax2d& L,
|
|
const gp_Pnt2d& P)
|
|
{
|
|
gp_XY Coord = P.XY();
|
|
Coord.Subtract (L.Location().XY());
|
|
return Coord.Dot (L.Direction().XY());
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : CircleParameter
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
Standard_Real ElCLib::CircleParameter (const gp_Ax22d& Pos,
|
|
const gp_Pnt2d& P)
|
|
{
|
|
Standard_Real Teta = (Pos.XDirection()).Angle
|
|
(gp_Vec2d (Pos.Location(),P));
|
|
Teta = ((Pos.XDirection() ^ Pos.YDirection()) >= 0.0) ? Teta: -Teta;
|
|
if (Teta < -1.e-16) Teta += PIPI;
|
|
else if (Teta < 0) Teta = 0;
|
|
return Teta;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : EllipseParameter
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
Standard_Real ElCLib::EllipseParameter (const gp_Ax22d& Pos,
|
|
const Standard_Real MajorRadius,
|
|
const Standard_Real MinorRadius,
|
|
const gp_Pnt2d& P)
|
|
{
|
|
gp_XY OP = P.XY();
|
|
OP.Subtract (Pos.Location().XY());
|
|
gp_XY xaxis = Pos.XDirection().XY();
|
|
gp_XY yaxis = Pos.YDirection().XY();
|
|
gp_XY Om = xaxis.Multiplied (OP.Dot(xaxis));
|
|
yaxis.Multiply ( (OP.Dot(yaxis)) * (MajorRadius/MinorRadius) );
|
|
Om.Add (yaxis);
|
|
Standard_Real Teta = gp_Vec2d(xaxis).Angle (gp_Vec2d(Om));
|
|
Teta = ((Pos.XDirection() ^ Pos.YDirection()) >= 0.0) ? Teta: -Teta;
|
|
if (Teta < -1.e-16) Teta += PIPI;
|
|
else if (Teta < 0) Teta = 0;
|
|
return Teta;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : HyperbolaParameter
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
Standard_Real ElCLib::HyperbolaParameter (const gp_Ax22d& Pos,
|
|
const Standard_Real,
|
|
const Standard_Real MinorRadius,
|
|
const gp_Pnt2d& P)
|
|
{
|
|
gp_Vec2d V (Pos.YDirection().XY());
|
|
Standard_Real sht = gp_Vec2d(Pos.Location(),P).Dot(V) /MinorRadius;
|
|
#if __QNX__
|
|
return std::asinh(sht);
|
|
#else
|
|
return asinh(sht);
|
|
#endif
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : ParabolaParameter
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
Standard_Real ElCLib::ParabolaParameter (const gp_Ax22d& Pos,
|
|
const gp_Pnt2d& P)
|
|
{
|
|
gp_Vec2d Directrix (Pos.YDirection().XY());
|
|
return gp_Vec2d(Pos.Location(),P).Dot(Directrix);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : To3d
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Pnt ElCLib::To3d (const gp_Ax2& Pos, const gp_Pnt2d& P)
|
|
{
|
|
gp_XYZ Vxy = Pos.XDirection().XYZ();
|
|
Vxy.SetLinearForm (P.X(), Vxy, P.Y(), Pos.YDirection().XYZ(),
|
|
Pos.Location().XYZ());
|
|
return gp_Pnt (Vxy);
|
|
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : To3d
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Dir ElCLib::To3d (const gp_Ax2& Pos, const gp_Dir2d& V)
|
|
{
|
|
gp_Vec Vx = Pos.XDirection();
|
|
gp_Vec Vy = Pos.YDirection();
|
|
Vx.Multiply (V.X());
|
|
Vy.Multiply (V.Y());
|
|
Vx.Add(Vy);
|
|
return gp_Dir (Vx);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : To3d
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Vec ElCLib::To3d (const gp_Ax2& Pos, const gp_Vec2d& V)
|
|
{
|
|
gp_Vec Vx = Pos.XDirection();
|
|
gp_Vec Vy = Pos.YDirection();
|
|
Vx.Multiply (V.X());
|
|
Vy.Multiply (V.Y());
|
|
Vx.Add(Vy);
|
|
return Vx;
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : To3d
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Ax1 ElCLib::To3d (const gp_Ax2& Pos, const gp_Ax2d& A)
|
|
{
|
|
gp_Pnt P = ElCLib::To3d (Pos, A.Location());
|
|
gp_Vec V = ElCLib::To3d (Pos, A.Direction());
|
|
return gp_Ax1 (P, V);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : To3d
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Ax2 ElCLib::To3d (const gp_Ax2& Pos, const gp_Ax22d& A)
|
|
{
|
|
gp_Pnt P = ElCLib::To3d (Pos, A.Location());
|
|
gp_Vec VX = ElCLib::To3d (Pos, A.XDirection());
|
|
gp_Vec VY = ElCLib::To3d (Pos, A.YDirection());
|
|
return gp_Ax2 (P, VX.Crossed(VY), VX);
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : To3d
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Lin ElCLib::To3d (const gp_Ax2& Pos, const gp_Lin2d& L)
|
|
{
|
|
return gp_Lin (ElCLib::To3d (Pos, L.Position()));
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : To3d
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Circ ElCLib::To3d (const gp_Ax2& Pos, const gp_Circ2d& C)
|
|
{
|
|
return gp_Circ (ElCLib::To3d (Pos, C.Axis()), C.Radius());
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : To3d
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Elips ElCLib::To3d (const gp_Ax2& Pos, const gp_Elips2d& E)
|
|
{
|
|
return gp_Elips (ElCLib::To3d (Pos, E.Axis ()), E.MajorRadius (),
|
|
E.MinorRadius ());
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : To3d
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Hypr ElCLib::To3d (const gp_Ax2& Pos, const gp_Hypr2d& H)
|
|
{
|
|
return gp_Hypr (ElCLib::To3d (Pos, H.Axis ()), H.MajorRadius (),
|
|
H.MinorRadius ());
|
|
}
|
|
|
|
//=======================================================================
|
|
//function : To3d
|
|
//purpose :
|
|
//=======================================================================
|
|
|
|
gp_Parab ElCLib::To3d (const gp_Ax2& Pos, const gp_Parab2d& Prb)
|
|
{
|
|
return gp_Parab ( ElCLib::To3d (Pos, Prb.Axis ()), Prb.Focal ());
|
|
}
|
|
|