# FoundationClasses
TKMath
CSLib

# CSLib Class Reference

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.
.

`#include <CSLib.hxx>`

## Public Member Functions

void * | operator new (size_t, void *anAddress)
void * | operator new (size_t size)
void | operator delete (void *anAddress)

## Static Public Member Functions

static Standard_EXPORT void | Normal (const gp_Vec &D1U, const gp_Vec &D1V, const Standard_Real SinTol, CSLib_DerivativeStatus &Status, gp_Dir &Normal)

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 Status == Done else the Status gives the
reason why the computation has failed.
.

static Standard_EXPORT 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 &Status, 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.
.

static Standard_EXPORT void | Normal (const gp_Vec &D1U, const gp_Vec &D1V, const Standard_Real MagTol, CSLib_NormalStatus &Status, gp_Dir &Normal)
| Computes the normal direction of a surface as the cross product between D1U and D1V. .
static Standard_EXPORT 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 &Status, 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.
static Standard_EXPORT 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
static Standard_EXPORT 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 .
static Standard_EXPORT 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.

## Member Function Documentation

static Standard_EXPORT gp_Vec CSLib::DNNormal | ( | const Standard_Integer | Nu,
|  | const Standard_Integer | Nv,
|  | const TColgp_Array2OfVec & | DerNUV,
|  | const Standard_Integer | Iduref = `0`,
|  | const Standard_Integer | Idvref = `0`
| ) | `[static]`

static Standard_EXPORT gp_Vec CSLib::DNNUV | ( | const Standard_Integer | Nu,
|  | const Standard_Integer | Nv,
|  | const TColgp_Array2OfVec & | DerSurf1,
|  | const TColgp_Array2OfVec & | DerSurf2
| ) | `[static]`

static Standard_EXPORT gp_Vec CSLib::DNNUV | ( | const Standard_Integer | Nu,
|  | const Standard_Integer | Nv,
|  | const TColgp_Array2OfVec & | DerSurf
| ) | `[static]`

static Standard_EXPORT void CSLib::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 & | Status,
|  | gp_Dir & | Normal,
|  | Standard_Integer & | OrderU,
|  | Standard_Integer & | OrderV
| ) | `[static]`

static Standard_EXPORT void CSLib::Normal | ( | const gp_Vec & | D1U,
|  | const gp_Vec & | D1V,
|  | const Standard_Real | MagTol,
|  | CSLib_NormalStatus & | Status,
|  | gp_Dir & | Normal
| ) | `[static]`

static Standard_EXPORT void CSLib::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 & | Status,
|  | gp_Dir & | Normal
| ) | `[static]`

static Standard_EXPORT void CSLib::Normal | ( | const gp_Vec & | D1U,
|  | const gp_Vec & | D1V,
|  | const Standard_Real | SinTol,
|  | CSLib_DerivativeStatus & | Status,
|  | gp_Dir & | Normal
| ) | `[static]`

void CSLib::operator delete | ( | void * | anAddress | ) | `[inline]`

void* CSLib::operator new | ( | size_t | size | ) | `[inline]`

void* CSLib::operator new | ( | size_t | ,
|  | void * | anAddress
| ) | `[inline]`

The documentation for this class was generated from the following file:

- CSLib.hxx