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153 lines
6.3 KiB
C++
153 lines
6.3 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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#ifndef _CSLib_HeaderFile
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#define _CSLib_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 <CSLib_DerivativeStatus.hxx>
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#include <Standard_Boolean.hxx>
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#include <CSLib_NormalStatus.hxx>
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#include <Standard_Integer.hxx>
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#include <TColgp_Array2OfVec.hxx>
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class gp_Vec;
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class gp_Dir;
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class CSLib_Class2d;
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class CSLib_NormalPolyDef;
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//! This package implements functions for basis geometric
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//! computation on curves and surfaces.
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//! The tolerance criterions used in this package are
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//! Resolution from package gp and RealEpsilon from class
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//! Real of package Standard.
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class CSLib
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{
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public:
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DEFINE_STANDARD_ALLOC
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//! The following functions computes the normal to a surface
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//! inherits FunctionWithDerivative from math
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//!
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//! Computes the normal direction of a surface as the cross product
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//! between D1U and D1V.
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//! If D1U has null length or D1V has null length or D1U and D1V are
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//! parallel the normal is undefined.
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//! To check that D1U and D1V are colinear the sinus of the angle
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//! between D1U and D1V is computed and compared with SinTol.
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//! The normal is computed if theStatus == Done else the theStatus gives the
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//! reason why the computation has failed.
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Standard_EXPORT static void Normal (const gp_Vec& D1U, const gp_Vec& D1V, const Standard_Real SinTol, CSLib_DerivativeStatus& theStatus, gp_Dir& Normal);
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//! If there is a singularity on the surface the previous method
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//! cannot compute the local normal.
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//! This method computes an approached normal direction of a surface.
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//! It does a limited development and needs the second derivatives
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//! on the surface as input data.
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//! It computes the normal as follow :
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//! N(u, v) = D1U ^ D1V
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//! N(u0+du,v0+dv) = N0 + DN/du(u0,v0) * du + DN/dv(u0,v0) * dv + Eps
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//! with Eps->0 so we can have the equivalence N ~ dN/du + dN/dv.
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//! DNu = ||DN/du|| and DNv = ||DN/dv||
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//!
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//! . if DNu IsNull (DNu <= Resolution from gp) the answer Done = True
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//! the normal direction is given by DN/dv
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//! . if DNv IsNull (DNv <= Resolution from gp) the answer Done = True
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//! the normal direction is given by DN/du
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//! . if the two directions DN/du and DN/dv are parallel Done = True
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//! the normal direction is given either by DN/du or DN/dv.
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//! To check that the two directions are colinear the sinus of the
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//! angle between these directions is computed and compared with
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//! SinTol.
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//! . if DNu/DNv or DNv/DNu is lower or equal than Real Epsilon
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//! Done = False, the normal is undefined
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//! . if DNu IsNull and DNv is Null Done = False, there is an
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//! indetermination and we should do a limited development at
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//! order 2 (it means that we cannot omit Eps).
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//! . if DNu Is not Null and DNv Is not Null Done = False, there are
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//! an infinity of normals at the considered point on the surface.
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Standard_EXPORT static void Normal (const gp_Vec& D1U, const gp_Vec& D1V, const gp_Vec& D2U, const gp_Vec& D2V, const gp_Vec& D2UV, const Standard_Real SinTol, Standard_Boolean& Done, CSLib_NormalStatus& theStatus, gp_Dir& Normal);
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//! Computes the normal direction of a surface as the cross product
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//! between D1U and D1V.
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Standard_EXPORT static void Normal (const gp_Vec& D1U, const gp_Vec& D1V, const Standard_Real MagTol, CSLib_NormalStatus& theStatus, gp_Dir& Normal);
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//! find the first order k0 of deriviative of NUV
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//! where: foreach order < k0 all the derivatives of NUV are
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//! null all the derivatives of NUV corresponding to the order
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//! k0 are collinear and have the same sens.
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//! In this case, normal at U,V is unique.
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Standard_EXPORT static void Normal (const Standard_Integer MaxOrder, const TColgp_Array2OfVec& DerNUV, const Standard_Real MagTol, const Standard_Real U, const Standard_Real V, const Standard_Real Umin, const Standard_Real Umax, const Standard_Real Vmin, const Standard_Real Vmax, CSLib_NormalStatus& theStatus, gp_Dir& Normal, Standard_Integer& OrderU, Standard_Integer& OrderV);
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//! -- Computes the derivative of order Nu in the --
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//! direction U and Nv in the direction V of the not --
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//! normalized normal vector at the point P(U,V) The
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//! array DerSurf contain the derivative (i,j) of the surface
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//! for i=0,Nu+1 ; j=0,Nv+1
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Standard_EXPORT static gp_Vec DNNUV (const Standard_Integer Nu, const Standard_Integer Nv, const TColgp_Array2OfVec& DerSurf);
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//! Computes the derivatives of order Nu in the direction Nu
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//! and Nv in the direction Nv of the not normalized vector
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//! N(u,v) = dS1/du * dS2/dv (cases where we use an osculating surface)
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//! DerSurf1 are the derivatives of S1
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Standard_EXPORT static gp_Vec DNNUV (const Standard_Integer Nu, const Standard_Integer Nv, const TColgp_Array2OfVec& DerSurf1, const TColgp_Array2OfVec& DerSurf2);
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//! -- Computes the derivative of order Nu in the --
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//! direction U and Nv in the direction V of the
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//! normalized normal vector at the point P(U,V) array
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//! DerNUV contain the derivative (i+Iduref,j+Idvref)
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//! of D1U ^ D1V for i=0,Nu ; j=0,Nv Iduref and Idvref
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//! correspond to a derivative of D1U ^ D1V which can
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//! be used to compute the normalized normal vector.
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//! In the regular cases , Iduref=Idvref=0.
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Standard_EXPORT static gp_Vec DNNormal (const Standard_Integer Nu, const Standard_Integer Nv, const TColgp_Array2OfVec& DerNUV, const Standard_Integer Iduref = 0, const Standard_Integer Idvref = 0);
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protected:
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private:
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friend class CSLib_Class2d;
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friend class CSLib_NormalPolyDef;
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};
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#endif // _CSLib_HeaderFile
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