// 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