Open CASCADE Technology
7.7.0.dev

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. More...
#include <CSLib.hxx>
Static Public Member Functions  
static void  Normal (const gp_Vec &D1U, const gp_Vec &D1V, const Standard_Real SinTol, CSLib_DerivativeStatus &theStatus, gp_Dir &Normal) 
The following functions computes the normal to a surface inherits FunctionWithDerivative from math. More...  
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) 
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. More...  
static void  Normal (const gp_Vec &D1U, const gp_Vec &D1V, const Standard_Real MagTol, CSLib_NormalStatus &theStatus, gp_Dir &Normal) 
Computes the normal direction of a surface as the cross product between D1U and D1V. More...  
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) 
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. More...  
static gp_Vec  DNNUV (const Standard_Integer Nu, const Standard_Integer Nv, const TColgp_Array2OfVec &DerSurf) 
– 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 More...  
static gp_Vec  DNNUV (const Standard_Integer Nu, const Standard_Integer Nv, const TColgp_Array2OfVec &DerSurf1, const TColgp_Array2OfVec &DerSurf2) 
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. More...  
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) 
– 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. More...  
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.

static 
– 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.

static 
– 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

static 
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.

static 
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.

static 
Computes the normal direction of a surface as the cross product between D1U and D1V.

static 
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.

static 
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.