Provides functions for basic geometric computation on curves and surfaces. More...

#include <CSLib.hxx>

Static Public Member Functions
static void	Normal (const gp_Vec &theD1U, const gp_Vec &theD1V, double theSinTol, CSLib_DerivativeStatus &theStatus, gp_Dir &theNormal)
	Computes the normal direction of a surface as the cross product D1U ^ D1V.

static void	Normal (const gp_Vec &theD1U, const gp_Vec &theD1V, const gp_Vec &theD2U, const gp_Vec &theD2V, const gp_Vec &theD2UV, double theSinTol, bool &theDone, CSLib_NormalStatus &theStatus, gp_Dir &theNormal)
	Computes an approximate normal direction at a singular point using second derivatives.

static void	Normal (const gp_Vec &theD1U, const gp_Vec &theD1V, double theMagTol, CSLib_NormalStatus &theStatus, gp_Dir &theNormal)
	Computes the normal direction using magnitude tolerance.

static void	Normal (int theMaxOrder, const NCollection_Array2< gp_Vec > &theDerNUV, double theMagTol, double theU, double theV, double theUmin, double theUmax, double theVmin, double theVmax, CSLib_NormalStatus &theStatus, gp_Dir &theNormal, int &theOrderU, int &theOrderV)
	Computes the normal at a singular point using higher-order derivatives.

static gp_Vec	DNNUV (int theNu, int theNv, const NCollection_Array2< gp_Vec > &theDerSurf)
	Computes the derivative of order (theNu, theNv) of the non-normalized normal vector.

static gp_Vec	DNNUV (int theNu, int theNv, const NCollection_Array2< gp_Vec > &theDerSurf1, const NCollection_Array2< gp_Vec > &theDerSurf2)
	Computes the derivative of the non-normalized vector N = dS1/du ^ dS2/dv.

static gp_Vec	DNNormal (int theNu, int theNv, const NCollection_Array2< gp_Vec > &theDerNUV, int theIduref=0, int theIdvref=0)
	Computes the derivative of order (theNu, theNv) of the normalized normal vector.

Detailed Description

Provides functions for basic geometric computation on curves and surfaces.

This package implements functions for computing surface normals and their derivatives at parametric points. The tolerance criteria used are Resolution from gp and RealEpsilon from double.

Key functionality:

Normal computation from surface first derivatives (D1U, D1V)
Approximate normal in singular cases using second derivatives
Derivatives of the non-normalized and normalized normal vectors

Member Function Documentation

◆ DNNormal()

static gp_Vec CSLib::DNNormal	(	int	theNu,
		int	theNv,
		const NCollection_Array2< gp_Vec > &	theDerNUV,
		int	theIduref = 0,
		int	theIdvref = 0 )

static

Computes the derivative of order (theNu, theNv) of the normalized normal vector.

Parameters

[in]	theNu	Derivative order in U direction
[in]	theNv	Derivative order in V direction
[in]	theDerNUV	Array of derivatives of the non-normalized normal. Contains derivatives d^(i+j)(D1U^D1V)/(du^i * dv^j) for i = theIduref..theNu+theIduref, j = theIdvref..theNv+theIdvref
[in]	theIduref	Reference index offset in U (default 0 for regular cases)
[in]	theIdvref	Reference index offset in V (default 0 for regular cases)

Returns: The derivative of the normalized normal vector

◆ DNNUV() [1/2]

static gp_Vec CSLib::DNNUV	(	int	theNu,
		int	theNv,
		const NCollection_Array2< gp_Vec > &	theDerSurf )

static

Computes the derivative of order (theNu, theNv) of the non-normalized normal vector.

The non-normalized normal is N = dS/du ^ dS/dv. This function computes d^(Nu+Nv)N / (du^Nu * dv^Nv).

Parameters

[in]	theNu	Derivative order in U direction
[in]	theNv	Derivative order in V direction
[in]	theDerSurf	Surface derivatives array where theDerSurf(i,j) = d^(i+j)S/(du^i * dv^j) for i = 0..theNu+1, j = 0..theNv+1

Returns: The derivative vector d^(Nu+Nv)N / (du^Nu * dv^Nv)

◆ DNNUV() [2/2]

static gp_Vec CSLib::DNNUV	(	int	theNu,
		int	theNv,
		const NCollection_Array2< gp_Vec > &	theDerSurf1,
		const NCollection_Array2< gp_Vec > &	theDerSurf2 )

static

Computes the derivative of the non-normalized vector N = dS1/du ^ dS2/dv.

This variant is used for osculating surfaces where the normal is computed from derivatives of two different surfaces.

Parameters

[in]	theNu	Derivative order in U direction
[in]	theNv	Derivative order in V direction
[in]	theDerSurf1	Derivatives of the first surface S1
[in]	theDerSurf2	Derivatives of the second surface S2

Returns: The derivative vector

◆ Normal() [1/4]

static void CSLib::Normal	(	const gp_Vec &	theD1U,
		const gp_Vec &	theD1V,
		const gp_Vec &	theD2U,
		const gp_Vec &	theD2V,
		const gp_Vec &	theD2UV,
		double	theSinTol,
		bool &	theDone,
		CSLib_NormalStatus &	theStatus,
		gp_Dir &	theNormal )

static

Computes an approximate normal direction at a singular point using second derivatives.

When the standard method cannot compute the normal (D1U ^ D1V is null or too small), this method uses a limited Taylor expansion: N(u0+du, v0+dv) = N0 + dN/du * du + dN/dv * dv + O(du^2, dv^2)

The normal is approximated from dN/du and dN/dv where N = D1U ^ D1V.

Parameters

[in]	theD1U	First derivative in U direction
[in]	theD1V	First derivative in V direction
[in]	theD2U	Second derivative in U direction (d^2S/du^2)
[in]	theD2V	Second derivative in V direction (d^2S/dv^2)
[in]	theD2UV	Mixed second derivative (d^2S/dudv)
[in]	theSinTol	Sine tolerance for parallelism check
[out]	theDone	True if normal was successfully computed
[out]	theStatus	Result status with detailed information
[out]	theNormal	Computed normal direction (valid only if theDone is true)

◆ Normal() [2/4]

static void CSLib::Normal	(	const gp_Vec &	theD1U,
		const gp_Vec &	theD1V,
		double	theMagTol,
		CSLib_NormalStatus &	theStatus,
		gp_Dir &	theNormal )

static

Computes the normal direction using magnitude tolerance.

A simpler version that checks if the cross product magnitude and derivative magnitudes exceed the given tolerance.

Parameters

[in]	theD1U	First derivative in U direction
[in]	theD1V	First derivative in V direction
[in]	theMagTol	Magnitude tolerance for singularity detection
[out]	theStatus	Result status (CSLib_Defined or CSLib_Singular)
[out]	theNormal	Computed normal direction (valid only if theStatus == CSLib_Defined)

◆ Normal() [3/4]

static void CSLib::Normal	(	const gp_Vec &	theD1U,
		const gp_Vec &	theD1V,
		double	theSinTol,
		CSLib_DerivativeStatus &	theStatus,
		gp_Dir &	theNormal )

static

Computes the normal direction of a surface as the cross product D1U ^ D1V.

The normal is undefined if:

D1U has null length, or
D1V has null length, or
D1U and D1V are parallel.

To check parallelism, the sine of the angle between D1U and D1V is computed and compared with theSinTol.

Parameters

[in]	theD1U	First derivative in U direction
[in]	theD1V	First derivative in V direction
[in]	theSinTol	Sine tolerance for parallelism check
[out]	theStatus	Result status indicating success or failure reason
[out]	theNormal	Computed normal direction (valid only if theStatus == CSLib_Done)

◆ Normal() [4/4]

static void CSLib::Normal	(	int	theMaxOrder,
		const NCollection_Array2< gp_Vec > &	theDerNUV,
		double	theMagTol,
		double	theU,
		double	theV,
		double	theUmin,
		double	theUmax,
		double	theVmin,
		double	theVmax,
		CSLib_NormalStatus &	theStatus,
		gp_Dir &	theNormal,
		int &	theOrderU,
		int &	theOrderV )

static

Computes the normal at a singular point using higher-order derivatives.

Finds the first order k0 where the derivatives of N = D1U ^ D1V become non-null and collinear, ensuring a unique normal direction.

Parameters

[in]	theMaxOrder	Maximum derivative order to examine
[in]	theDerNUV	Array of derivatives of N (indices correspond to derivative orders)
[in]	theMagTol	Magnitude tolerance
[in]	theU,theV	Current parameter values
[in]	theUmin,theUmax,theVmin,theVmax	Parameter bounds
[out]	theStatus	Result status
[out]	theNormal	Computed normal direction
[out]	theOrderU,theOrderV	Orders of the first non-null derivative used

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

CSLib.hxx

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ DNNormal()

◆ DNNUV() [1/2]

◆ DNNUV() [2/2]

◆ Normal() [1/4]

◆ Normal() [2/4]

◆ Normal() [3/4]

◆ Normal() [4/4]