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 // Created on: 1991-09-09
 // Created by: Michel Chauvat
 // Copyright (c) 1991-1999 Matra Datavision
 // Copyright (c) 1999-2014 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.
 
 #ifndef _CSLib_HeaderFile
 #define _CSLib_HeaderFile
 
 #include <Standard.hxx>
 #include <Standard_DefineAlloc.hxx>
 #include <Standard_Handle.hxx>
 
 #include <CSLib_DerivativeStatus.hxx>
 #include <Standard_Boolean.hxx>
 #include <CSLib_NormalStatus.hxx>
 #include <TColgp_Array2OfVec.hxx>
 class gp_Vec;
 class gp_Dir;
 
 //! This package implements functions for basis geometric
 //! computation on curves and surfaces.
 //! The tolerance criterions used in this package are
 //! Resolution from package gp and RealEpsilon from class
 //! Real of package Standard.
 class CSLib
 {
 public:
   DEFINE_STANDARD_ALLOC
 
   //! The following functions computes the normal to a surface
   //! inherits FunctionWithDerivative from math
   //!
   //! Computes the normal direction of a surface as the cross product
   //! between D1U and D1V.
   //! If D1U has null length or D1V has null length or D1U and D1V are
   //! parallel the normal is undefined.
   //! To check that D1U and D1V are colinear the sinus of the angle
   //! between D1U and D1V is computed and compared with SinTol.
   //! The normal is computed if theStatus == Done else the theStatus gives the
   //! reason why the computation has failed.
   Standard_EXPORT static void Normal(const gp_Vec&           D1U,
                                      const gp_Vec&           D1V,
                                      const Standard_Real     SinTol,
                                      CSLib_DerivativeStatus& theStatus,
                                      gp_Dir&                 Normal);
 
   //! If there is a singularity on the surface  the previous method
   //! cannot compute the local normal.
   //! This method computes an approached normal direction of a surface.
   //! It does a limited development and needs the second derivatives
   //! on the surface as input data.
   //! It computes the normal as follow :
   //! N(u, v) = D1U ^ D1V
   //! N(u0+du,v0+dv) = N0 + DN/du(u0,v0) * du + DN/dv(u0,v0) * dv + Eps
   //! with Eps->0 so we can have the equivalence N ~ dN/du + dN/dv.
   //! DNu = ||DN/du|| and DNv = ||DN/dv||
   //!
   //! . if DNu IsNull (DNu <= Resolution from gp) the answer Done = True
   //! the normal direction is given by DN/dv
   //! . if DNv IsNull (DNv <= Resolution from gp) the answer Done = True
   //! the normal direction is given by DN/du
   //! . if the two directions DN/du and DN/dv are parallel Done = True
   //! the normal direction is given either by DN/du or DN/dv.
   //! To check that the two directions are colinear the sinus of the
   //! angle between these directions is computed and compared with
   //! SinTol.
   //! . if DNu/DNv or DNv/DNu is lower or equal than Real Epsilon
   //! Done = False, the normal is undefined
   //! . if DNu IsNull and DNv is Null Done = False, there is an
   //! indetermination and we should do a limited development at
   //! order 2 (it means that we cannot omit Eps).
   //! . if DNu Is not Null and DNv Is not Null Done = False, there are
   //! an infinity of normals at the considered point on the surface.
   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);
 
   //! Computes the normal direction of a surface as the cross product
   //! between D1U and D1V.
   Standard_EXPORT static void Normal(const gp_Vec&       D1U,
                                      const gp_Vec&       D1V,
                                      const Standard_Real MagTol,
                                      CSLib_NormalStatus& theStatus,
                                      gp_Dir&             Normal);
 
   //! find the first  order k0  of deriviative of NUV
   //! where: foreach order < k0  all the derivatives of NUV  are
   //! null all the derivatives of NUV corresponding to the order
   //! k0 are collinear and have the same sens.
   //! In this case, normal at U,V is unique.
   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);
 
   //! -- Computes the derivative  of order Nu in the --
   //! direction U and Nv in the direction V of the not --
   //! normalized  normal vector at  the point  P(U,V) The
   //! array DerSurf contain the derivative (i,j) of the surface
   //! for i=0,Nu+1 ; j=0,Nv+1
   Standard_EXPORT static gp_Vec DNNUV(const Standard_Integer    Nu,
                                       const Standard_Integer    Nv,
                                       const TColgp_Array2OfVec& DerSurf);
 
   //! Computes the derivatives of order Nu in the direction Nu
   //! and Nv in the direction Nv of the not normalized vector
   //! N(u,v) = dS1/du * dS2/dv (cases where we use an osculating surface)
   //! DerSurf1 are the derivatives of S1
   Standard_EXPORT static gp_Vec DNNUV(const Standard_Integer    Nu,
                                       const Standard_Integer    Nv,
                                       const TColgp_Array2OfVec& DerSurf1,
                                       const TColgp_Array2OfVec& DerSurf2);
 
   //! -- Computes the derivative  of order Nu in the --
   //! direction   U and  Nv in the  direction  V  of the
   //! normalized normal vector  at the point P(U,V) array
   //! DerNUV contain the  derivative  (i+Iduref,j+Idvref)
   //! of D1U ^ D1V for i=0,Nu  ; j=0,Nv Iduref and Idvref
   //! correspond to a derivative  of D1U ^ D1V  which can
   //! be used to compute the normalized normal vector.
   //! In the regular cases , Iduref=Idvref=0.
   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);
 };
 
 #endif // _CSLib_HeaderFile

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