--- /dev/null
+// Created on: 2015-09-21
+// Copyright (c) 2015 OPEN CASCADE SAS
+//
+// This file is part of Open CASCADE Technology software library.
+//
+// This library is free software; you can redistribute it and/or modify it under
+// the terms of the GNU Lesser General Public License version 2.1 as published
+// by the Free Software Foundation, with special exception defined in the file
+// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
+// distribution for complete text of the license and disclaimer of any warranty.
+//
+// Alternatively, this file may be used under the terms of Open CASCADE
+// commercial license or contractual agreement.
+
+#include <Geom2dEvaluator.hxx>
+#include <gp_Pnt2d.hxx>
+#include <gp_Vec2d.hxx>
+#include <gp_XY.hxx>
+#include <Standard_NullValue.hxx>
+
+//=======================================================================
+//function : CalculateD0
+//purpose :
+//=======================================================================
+void Geom2dEvaluator::CalculateD0( gp_Pnt2d& theValue,
+ const gp_Vec2d& theD1, const Standard_Real theOffset)
+{
+ if (theD1.SquareMagnitude() <= gp::Resolution())
+ throw Standard_NullValue("Geom2dEvaluator: Undefined normal vector "
+ "because tangent vector has zero-magnitude!");
+
+ gp_Dir2d aNormal(theD1.Y(), -theD1.X());
+ theValue.ChangeCoord().Add(aNormal.XY() * theOffset);
+}
+
+//=======================================================================
+//function : CalculateD1
+//purpose :
+//=======================================================================
+void Geom2dEvaluator::CalculateD1(gp_Pnt2d& theValue,
+ gp_Vec2d& theD1,
+ const gp_Vec2d& theD2, const Standard_Real theOffset)
+{
+ // P(u) = p(u) + Offset * Ndir / R
+ // with R = || p' ^ Z|| and Ndir = P' ^ Z
+
+ // P'(u) = p'(u) + (Offset / R**2) * (DNdir/DU * R - Ndir * (DR/R))
+
+ gp_XY Ndir(theD1.Y(), -theD1.X());
+ gp_XY DNdir(theD2.Y(), -theD2.X());
+ Standard_Real R2 = Ndir.SquareModulus();
+ Standard_Real R = Sqrt(R2);
+ Standard_Real R3 = R * R2;
+ Standard_Real Dr = Ndir.Dot(DNdir);
+ if (R3 <= gp::Resolution())
+ {
+ if (R2 <= gp::Resolution())
+ throw Standard_NullValue("Geom2dEvaluator_OffsetCurve: Null derivative");
+ //We try another computation but the stability is not very good.
+ DNdir.Multiply(R);
+ DNdir.Subtract(Ndir.Multiplied(Dr / R));
+ DNdir.Multiply(theOffset / R2);
+ }
+ else
+ {
+ // Same computation as IICURV in EUCLID-IS because the stability is better
+ DNdir.Multiply(theOffset / R);
+ DNdir.Subtract(Ndir.Multiplied(theOffset * Dr / R3));
+ }
+
+ Ndir.Multiply(theOffset / R);
+ // P(u)
+ theValue.ChangeCoord().Add(Ndir);
+ // P'(u)
+ theD1.Add(gp_Vec2d(DNdir));
+}
+
+//=======================================================================
+//function : CalculateD2
+//purpose :
+//=======================================================================
+void Geom2dEvaluator::CalculateD2( gp_Pnt2d& theValue,
+ gp_Vec2d& theD1,
+ gp_Vec2d& theD2,
+ const gp_Vec2d& theD3,
+ const Standard_Boolean theIsDirChange, const Standard_Real theOffset)
+{
+ // P(u) = p(u) + Offset * Ndir / R
+ // with R = || p' ^ Z|| and Ndir = P' ^ Z
+
+ // P'(u) = p'(u) + (Offset / R**2) * (DNdir/DU * R - Ndir * (DR/R))
+
+ // P"(u) = p"(u) + (Offset / R) * (D2Ndir/DU - DNdir * (2.0 * Dr/ R**2) +
+ // Ndir * ( (3.0 * Dr**2 / R**4) - (D2r / R**2)))
+
+ gp_XY Ndir(theD1.Y(), -theD1.X());
+ gp_XY DNdir(theD2.Y(), -theD2.X());
+ gp_XY D2Ndir(theD3.Y(), -theD3.X());
+ Standard_Real R2 = Ndir.SquareModulus();
+ Standard_Real R = Sqrt(R2);
+ Standard_Real R3 = R2 * R;
+ Standard_Real R4 = R2 * R2;
+ Standard_Real R5 = R3 * R2;
+ Standard_Real Dr = Ndir.Dot(DNdir);
+ Standard_Real D2r = Ndir.Dot(D2Ndir) + DNdir.Dot(DNdir);
+ if (R5 <= gp::Resolution())
+ {
+ if (R4 <= gp::Resolution())
+ throw Standard_NullValue("Geom2dEvaluator: Null derivative");
+ //We try another computation but the stability is not very good dixit ISG.
+ // V2 = P" (U) :
+ D2Ndir.Subtract(DNdir.Multiplied(2.0 * Dr / R2));
+ D2Ndir.Add(Ndir.Multiplied(((3.0 * Dr * Dr) / R4) - (D2r / R2)));
+ D2Ndir.Multiply(theOffset / R);
+
+ // V1 = P' (U) :
+ DNdir.Multiply(R);
+ DNdir.Subtract(Ndir.Multiplied(Dr / R));
+ DNdir.Multiply(theOffset / R2);
+ }
+ else
+ {
+ // Same computation as IICURV in EUCLID-IS because the stability is better.
+ // V2 = P" (U) :
+ D2Ndir.Multiply(theOffset / R);
+ D2Ndir.Subtract(DNdir.Multiplied(2.0 * theOffset * Dr / R3));
+ D2Ndir.Add(Ndir.Multiplied(theOffset * (((3.0 * Dr * Dr) / R5) - (D2r / R3))));
+
+ // V1 = P' (U)
+ DNdir.Multiply(theOffset / R);
+ DNdir.Subtract(Ndir.Multiplied(theOffset * Dr / R3));
+ }
+
+ Ndir.Multiply(theOffset / R);
+ // P(u)
+ theValue.ChangeCoord().Add(Ndir);
+ // P'(u) :
+ theD1.Add(gp_Vec2d(DNdir));
+ // P"(u) :
+ if (theIsDirChange)
+ theD2.Reverse();
+ theD2.Add(gp_Vec2d(D2Ndir));
+}
+
+//=======================================================================
+//function : CalculateD3
+//purpose :
+//=======================================================================
+void Geom2dEvaluator::CalculateD3( gp_Pnt2d& theValue,
+ gp_Vec2d& theD1,
+ gp_Vec2d& theD2,
+ gp_Vec2d& theD3,
+ const gp_Vec2d& theD4,
+ const Standard_Boolean theIsDirChange, const Standard_Real theOffset)
+{
+ // P(u) = p(u) + Offset * Ndir / R
+ // with R = || p' ^ Z|| and Ndir = P' ^ Z
+
+ // P'(u) = p'(u) + (Offset / R**2) * (DNdir/DU * R - Ndir * (DR/R))
+
+ // P"(u) = p"(u) + (Offset / R) * (D2Ndir/DU - DNdir * (2.0 * Dr/ R**2) +
+ // Ndir * ( (3.0 * Dr**2 / R**4) - (D2r / R**2)))
+
+ // P"'(u) = p"'(u) + (Offset / R) * (D3Ndir - (3.0 * Dr/R**2 ) * D2Ndir -
+ // (3.0 * D2r / R2) * DNdir) + (3.0 * Dr * Dr / R4) * DNdir -
+ // (D3r/R2) * Ndir + (6.0 * Dr * Dr / R4) * Ndir +
+ // (6.0 * Dr * D2r / R4) * Ndir - (15.0 * Dr* Dr* Dr /R6) * Ndir
+
+ gp_XY Ndir(theD1.Y(), -theD1.X());
+ gp_XY DNdir(theD2.Y(), -theD2.X());
+ gp_XY D2Ndir(theD3.Y(), -theD3.X());
+ gp_XY D3Ndir(theD4.Y(), -theD4.X());
+ Standard_Real R2 = Ndir.SquareModulus();
+ Standard_Real R = Sqrt(R2);
+ Standard_Real R3 = R2 * R;
+ Standard_Real R4 = R2 * R2;
+ Standard_Real R5 = R3 * R2;
+ Standard_Real R6 = R3 * R3;
+ Standard_Real R7 = R5 * R2;
+ Standard_Real Dr = Ndir.Dot(DNdir);
+ Standard_Real D2r = Ndir.Dot(D2Ndir) + DNdir.Dot(DNdir);
+ Standard_Real D3r = Ndir.Dot(D3Ndir) + 3.0 * DNdir.Dot(D2Ndir);
+
+ if (R7 <= gp::Resolution())
+ {
+ if (R6 <= gp::Resolution())
+ throw Standard_NullValue("Geom2dEvaluator: Null derivative");
+ //We try another computation but the stability is not very good dixit ISG.
+ // V3 = P"' (U) :
+ D3Ndir.Subtract(D2Ndir.Multiplied(3.0 * theOffset * Dr / R2));
+ D3Ndir.Subtract(
+ (DNdir.Multiplied((3.0 * theOffset) * ((D2r / R2) + (Dr*Dr) / R4))));
+ D3Ndir.Add(Ndir.Multiplied(
+ (theOffset * (6.0*Dr*Dr / R4 + 6.0*Dr*D2r / R4 - 15.0*Dr*Dr*Dr / R6 - D3r))));
+ D3Ndir.Multiply(theOffset / R);
+ // V2 = P" (U) :
+ R4 = R2 * R2;
+ D2Ndir.Subtract(DNdir.Multiplied(2.0 * Dr / R2));
+ D2Ndir.Subtract(Ndir.Multiplied(((3.0 * Dr * Dr) / R4) - (D2r / R2)));
+ D2Ndir.Multiply(theOffset / R);
+ // V1 = P' (U) :
+ DNdir.Multiply(R);
+ DNdir.Subtract(Ndir.Multiplied(Dr / R));
+ DNdir.Multiply(theOffset / R2);
+ }
+ else
+ {
+ // Same computation as IICURV in EUCLID-IS because the stability is better.
+ // V3 = P"' (U) :
+ D3Ndir.Multiply(theOffset / R);
+ D3Ndir.Subtract(D2Ndir.Multiplied(3.0 * theOffset * Dr / R3));
+ D3Ndir.Subtract(DNdir.Multiplied(
+ ((3.0 * theOffset) * ((D2r / R3) + (Dr*Dr) / R5))));
+ D3Ndir.Add(Ndir.Multiplied(
+ (theOffset * (6.0*Dr*Dr / R5 + 6.0*Dr*D2r / R5 - 15.0*Dr*Dr*Dr / R7 - D3r))));
+ // V2 = P" (U) :
+ D2Ndir.Multiply(theOffset / R);
+ D2Ndir.Subtract(DNdir.Multiplied(2.0 * theOffset * Dr / R3));
+ D2Ndir.Subtract(Ndir.Multiplied(
+ theOffset * (((3.0 * Dr * Dr) / R5) - (D2r / R3))));
+ // V1 = P' (U) :
+ DNdir.Multiply(theOffset / R);
+ DNdir.Subtract(Ndir.Multiplied(theOffset * Dr / R3));
+ }
+
+ Ndir.Multiply(theOffset / R);
+ // P(u)
+ theValue.ChangeCoord().Add(Ndir);
+ // P'(u) :
+ theD1.Add(gp_Vec2d(DNdir));
+ // P"(u)
+ theD2.Add(gp_Vec2d(D2Ndir));
+ // P"'(u)
+ if (theIsDirChange)
+ theD3.Reverse();
+ theD3.Add(gp_Vec2d(D2Ndir));
+}
+
+
projects / occt.git / blobdiff