// 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 #include #include #include #include #include #include #include #include class gp_Vec; class gp_Dir; class CSLib_Class2d; class CSLib_NormalPolyDef; //! 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 approched 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 developpement 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); protected: private: friend class CSLib_Class2d; friend class CSLib_NormalPolyDef; }; #endif // _CSLib_HeaderFile