ElSLib Class Reference

Provides functions for basic geometric computation on elementary surfaces. This includes: More...

#include <ElSLib.hxx>

Static Public Member Functions
static gp_Pnt	Value (const Standard_Real U, const Standard_Real V, const gp_Pln &Pl)
	For elementary surfaces from the gp package (planes, cones, cylinders, spheres and tori), computes the point of parameters (U, V). More...
static gp_Pnt	Value (const Standard_Real U, const Standard_Real V, const gp_Cone &C)
static gp_Pnt	Value (const Standard_Real U, const Standard_Real V, const gp_Cylinder &C)
static gp_Pnt	Value (const Standard_Real U, const Standard_Real V, const gp_Sphere &S)
static gp_Pnt	Value (const Standard_Real U, const Standard_Real V, const gp_Torus &T)
static gp_Vec	DN (const Standard_Real U, const Standard_Real V, const gp_Pln &Pl, const Standard_Integer Nu, const Standard_Integer Nv)
	For elementary surfaces from the gp package (planes, cones, cylinders, spheres and tori), computes the derivative vector of order Nu and Nv in the u and v parametric directions respectively, at the point of parameters (U, V). More...
static gp_Vec	DN (const Standard_Real U, const Standard_Real V, const gp_Cone &C, const Standard_Integer Nu, const Standard_Integer Nv)
static gp_Vec	DN (const Standard_Real U, const Standard_Real V, const gp_Cylinder &C, const Standard_Integer Nu, const Standard_Integer Nv)
static gp_Vec	DN (const Standard_Real U, const Standard_Real V, const gp_Sphere &S, const Standard_Integer Nu, const Standard_Integer Nv)
static gp_Vec	DN (const Standard_Real U, const Standard_Real V, const gp_Torus &T, const Standard_Integer Nu, const Standard_Integer Nv)
static void	D0 (const Standard_Real U, const Standard_Real V, const gp_Pln &Pl, gp_Pnt &P)
	For elementary surfaces from the gp package (planes, cones, cylinders, spheres and tori), computes the point P of parameters (U, V).inline. More...
static void	D0 (const Standard_Real U, const Standard_Real V, const gp_Cone &C, gp_Pnt &P)
static void	D0 (const Standard_Real U, const Standard_Real V, const gp_Cylinder &C, gp_Pnt &P)
static void	D0 (const Standard_Real U, const Standard_Real V, const gp_Sphere &S, gp_Pnt &P)
static void	D0 (const Standard_Real U, const Standard_Real V, const gp_Torus &T, gp_Pnt &P)
static void	D1 (const Standard_Real U, const Standard_Real V, const gp_Pln &Pl, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
	For elementary surfaces from the gp package (planes, cones, cylinders, spheres and tori), computes: More...
static void	D1 (const Standard_Real U, const Standard_Real V, const gp_Cone &C, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
static void	D1 (const Standard_Real U, const Standard_Real V, const gp_Cylinder &C, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
static void	D1 (const Standard_Real U, const Standard_Real V, const gp_Sphere &S, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
static void	D1 (const Standard_Real U, const Standard_Real V, const gp_Torus &T, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
static void	D2 (const Standard_Real U, const Standard_Real V, const gp_Cone &C, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv)
	For elementary surfaces from the gp package (cones, cylinders, spheres and tori), computes: More...
static void	D2 (const Standard_Real U, const Standard_Real V, const gp_Cylinder &C, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv)
static void	D2 (const Standard_Real U, const Standard_Real V, const gp_Sphere &S, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv)
static void	D2 (const Standard_Real U, const Standard_Real V, const gp_Torus &T, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv)
static void	D3 (const Standard_Real U, const Standard_Real V, const gp_Cone &C, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv, gp_Vec &Vuuu, gp_Vec &Vvvv, gp_Vec &Vuuv, gp_Vec &Vuvv)
	For elementary surfaces from the gp package (cones, cylinders, spheres and tori), computes: More...
static void	D3 (const Standard_Real U, const Standard_Real V, const gp_Cylinder &C, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv, gp_Vec &Vuuu, gp_Vec &Vvvv, gp_Vec &Vuuv, gp_Vec &Vuvv)
static void	D3 (const Standard_Real U, const Standard_Real V, const gp_Sphere &S, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv, gp_Vec &Vuuu, gp_Vec &Vvvv, gp_Vec &Vuuv, gp_Vec &Vuvv)
static void	D3 (const Standard_Real U, const Standard_Real V, const gp_Torus &T, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv, gp_Vec &Vuuu, gp_Vec &Vvvv, gp_Vec &Vuuv, gp_Vec &Vuvv)
	Surface evaluation The following functions compute the point and the derivatives on elementary surfaces defined with their geometric characterisitics. You don't need to create the surface to use these functions. These functions are called by the previous ones. Example : A cylinder is defined with its position and its radius. More...
static gp_Pnt	PlaneValue (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos)
static gp_Pnt	CylinderValue (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius)
static gp_Pnt	ConeValue (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real SAngle)
static gp_Pnt	SphereValue (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius)
static gp_Pnt	TorusValue (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius)
static gp_Vec	PlaneDN (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Integer Nu, const Standard_Integer Nv)
static gp_Vec	CylinderDN (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Integer Nu, const Standard_Integer Nv)
static gp_Vec	ConeDN (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real SAngle, const Standard_Integer Nu, const Standard_Integer Nv)
static gp_Vec	SphereDN (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Integer Nu, const Standard_Integer Nv)
static gp_Vec	TorusDN (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer Nu, const Standard_Integer Nv)
static void	PlaneD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, gp_Pnt &P)
static void	ConeD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt &P)
static void	CylinderD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, gp_Pnt &P)
static void	SphereD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, gp_Pnt &P)
static void	TorusD0 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt &P)
static void	PlaneD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
static void	ConeD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
static void	CylinderD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
static void	SphereD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
static void	TorusD1 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv)
static void	ConeD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv)
static void	CylinderD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv)
static void	SphereD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv)
static void	TorusD2 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv)
static void	ConeD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real SAngle, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv, gp_Vec &Vuuu, gp_Vec &Vvvv, gp_Vec &Vuuv, gp_Vec &Vuvv)
static void	CylinderD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv, gp_Vec &Vuuu, gp_Vec &Vvvv, gp_Vec &Vuuv, gp_Vec &Vuvv)
static void	SphereD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real Radius, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv, gp_Vec &Vuuu, gp_Vec &Vvvv, gp_Vec &Vuuv, gp_Vec &Vuvv)
static void	TorusD3 (const Standard_Real U, const Standard_Real V, const gp_Ax3 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt &P, gp_Vec &Vu, gp_Vec &Vv, gp_Vec &Vuu, gp_Vec &Vvv, gp_Vec &Vuv, gp_Vec &Vuuu, gp_Vec &Vvvv, gp_Vec &Vuuv, gp_Vec &Vuvv)
	The following functions compute the parametric values corresponding to a given point on a elementary surface. The point should be on the surface. More...
static void	Parameters (const gp_Pln &Pl, const gp_Pnt &P, Standard_Real &U, Standard_Real &V)
	parametrization P (U, V) = Pl.Location() + U * Pl.XDirection() + V * Pl.YDirection() More...
static void	Parameters (const gp_Cylinder &C, const gp_Pnt &P, Standard_Real &U, Standard_Real &V)
	parametrization P (U, V) = Location + V * ZDirection + Radius * (Cos(U) * XDirection + Sin (U) * YDirection) More...
static void	Parameters (const gp_Cone &C, const gp_Pnt &P, Standard_Real &U, Standard_Real &V)
	parametrization P (U, V) = Location + V * ZDirection + (Radius + V * Tan (SemiAngle)) * (Cos(U) * XDirection + Sin(U) * YDirection) More...
static void	Parameters (const gp_Sphere &S, const gp_Pnt &P, Standard_Real &U, Standard_Real &V)
	parametrization P (U, V) = Location + Radius * Cos (V) * (Cos (U) * XDirection + Sin (U) * YDirection) + Radius * Sin (V) * ZDirection More...
static void	Parameters (const gp_Torus &T, const gp_Pnt &P, Standard_Real &U, Standard_Real &V)
	parametrization P (U, V) = Location + (MajorRadius + MinorRadius * Cos(U)) * (Cos(V) * XDirection - Sin(V) * YDirection) + MinorRadius * Sin(U) * ZDirection More...
static void	PlaneParameters (const gp_Ax3 &Pos, const gp_Pnt &P, Standard_Real &U, Standard_Real &V)
	parametrization P (U, V) = Pl.Location() + U * Pl.XDirection() + V * Pl.YDirection() More...
static void	CylinderParameters (const gp_Ax3 &Pos, const Standard_Real Radius, const gp_Pnt &P, Standard_Real &U, Standard_Real &V)
	parametrization P (U, V) = Location + V * ZDirection + Radius * (Cos(U) * XDirection + Sin (U) * YDirection) More...
static void	ConeParameters (const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real SAngle, const gp_Pnt &P, Standard_Real &U, Standard_Real &V)
	parametrization P (U, V) = Location + V * ZDirection + (Radius + V * Tan (SemiAngle)) * (Cos(U) * XDirection + Sin(U) * YDirection) More...
static void	SphereParameters (const gp_Ax3 &Pos, const Standard_Real Radius, const gp_Pnt &P, Standard_Real &U, Standard_Real &V)
	parametrization P (U, V) = Location + Radius * Cos (V) * (Cos (U) * XDirection + Sin (U) * YDirection) + Radius * Sin (V) * ZDirection More...
static void	TorusParameters (const gp_Ax3 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt &P, Standard_Real &U, Standard_Real &V)
	parametrization P (U, V) = Location + (MajorRadius + MinorRadius * Cos(U)) * (Cos(V) * XDirection - Sin(V) * YDirection) + MinorRadius * Sin(U) * ZDirection More...
static gp_Lin	PlaneUIso (const gp_Ax3 &Pos, const Standard_Real U)
	compute the U Isoparametric gp_Lin of the plane. More...
static gp_Lin	CylinderUIso (const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real U)
	compute the U Isoparametric gp_Lin of the cylinder. More...
static gp_Lin	ConeUIso (const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real SAngle, const Standard_Real U)
	compute the U Isoparametric gp_Lin of the cone. More...
static gp_Circ	SphereUIso (const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real U)
	compute the U Isoparametric gp_Circ of the sphere, (the meridian is not trimmed). More...
static gp_Circ	TorusUIso (const gp_Ax3 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Real U)
	compute the U Isoparametric gp_Circ of the torus. More...
static gp_Lin	PlaneVIso (const gp_Ax3 &Pos, const Standard_Real V)
	compute the V Isoparametric gp_Lin of the plane. More...
static gp_Circ	CylinderVIso (const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real V)
	compute the V Isoparametric gp_Circ of the cylinder. More...
static gp_Circ	ConeVIso (const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real SAngle, const Standard_Real V)
	compute the V Isoparametric gp_Circ of the cone. More...
static gp_Circ	SphereVIso (const gp_Ax3 &Pos, const Standard_Real Radius, const Standard_Real V)
	compute the V Isoparametric gp_Circ of the sphere, (the meridian is not trimmed). More...
static gp_Circ	TorusVIso (const gp_Ax3 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Real V)
	compute the V Isoparametric gp_Circ of the torus. More...

Detailed Description

Provides functions for basic geometric computation on elementary surfaces. This includes:

• calculation of a point or derived vector on a surface where the surface is provided by the gp package, or defined in canonical form (as in the gp package), and the point is defined with a parameter,
• evaluation of the parameters corresponding to a point on an elementary surface from gp,
• calculation of isoparametric curves on an elementary surface defined in canonical form (as in the gp package). Notes:
• ElSLib stands for Elementary Surfaces Library.
• If the surfaces provided by the gp package are not explicitly parameterized, they still have an implicit parameterization, similar to that which they infer on the equivalent Geom surfaces. Note: ElSLib stands for Elementary Surfaces Library.

Member Function Documentation

ConeD0()

static void ElSLib::ConeD0 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  SAngle, gp_Pnt &  P  )

static

ConeD1()

static void ElSLib::ConeD1 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  SAngle, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv  )

static

ConeD2()

static void ElSLib::ConeD2 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  SAngle, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv  )

static

ConeD3()

static void ElSLib::ConeD3 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  SAngle, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv, gp_Vec &  Vuuu, gp_Vec &  Vvvv, gp_Vec &  Vuuv, gp_Vec &  Vuvv  )

static

ConeDN()

static gp_Vec ElSLib::ConeDN ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  SAngle, const Standard_Integer  Nu, const Standard_Integer  Nv  )

static

ConeParameters()

static void ElSLib::ConeParameters ( const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  SAngle, const gp_Pnt &  P, Standard_Real &  U, Standard_Real &  V  )

static

parametrization P (U, V) = Location + V * ZDirection + (Radius + V * Tan (SemiAngle)) * (Cos(U) * XDirection + Sin(U) * YDirection)

ConeUIso()

static gp_Lin ElSLib::ConeUIso ( const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  SAngle, const Standard_Real  U  )

static

compute the U Isoparametric gp_Lin of the cone.

ConeValue()

static gp_Pnt ElSLib::ConeValue ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  SAngle  )

static

ConeVIso()

static gp_Circ ElSLib::ConeVIso ( const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  SAngle, const Standard_Real  V  )

static

compute the V Isoparametric gp_Circ of the cone.

CylinderD0()

static void ElSLib::CylinderD0 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, gp_Pnt &  P  )

static

CylinderD1()

static void ElSLib::CylinderD1 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv  )

static

CylinderD2()

static void ElSLib::CylinderD2 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv  )

static

CylinderD3()

static void ElSLib::CylinderD3 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv, gp_Vec &  Vuuu, gp_Vec &  Vvvv, gp_Vec &  Vuuv, gp_Vec &  Vuvv  )

static

CylinderDN()

static gp_Vec ElSLib::CylinderDN ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Integer  Nu, const Standard_Integer  Nv  )

static

CylinderParameters()

static void ElSLib::CylinderParameters ( const gp_Ax3 &  Pos, const Standard_Real  Radius, const gp_Pnt &  P, Standard_Real &  U, Standard_Real &  V  )

static

parametrization P (U, V) = Location + V * ZDirection + Radius * (Cos(U) * XDirection + Sin (U) * YDirection)

CylinderUIso()

static gp_Lin ElSLib::CylinderUIso ( const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  U  )

static

compute the U Isoparametric gp_Lin of the cylinder.

CylinderValue()

static gp_Pnt ElSLib::CylinderValue ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius  )

static

CylinderVIso()

static gp_Circ ElSLib::CylinderVIso ( const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  V  )

static

compute the V Isoparametric gp_Circ of the cylinder.

D0() [1/5]

static void ElSLib::D0 ( const Standard_Real  U, const Standard_Real  V, const gp_Pln &  Pl, gp_Pnt &  P  )

static

For elementary surfaces from the gp package (planes, cones, cylinders, spheres and tori), computes the point P of parameters (U, V).inline.

D0() [2/5]

static void ElSLib::D0 ( const Standard_Real  U, const Standard_Real  V, const gp_Cone &  C, gp_Pnt &  P  )

static

D0() [3/5]

static void ElSLib::D0 ( const Standard_Real  U, const Standard_Real  V, const gp_Cylinder &  C, gp_Pnt &  P  )

static

D0() [4/5]

static void ElSLib::D0 ( const Standard_Real  U, const Standard_Real  V, const gp_Sphere &  S, gp_Pnt &  P  )

static

D0() [5/5]

static void ElSLib::D0 ( const Standard_Real  U, const Standard_Real  V, const gp_Torus &  T, gp_Pnt &  P  )

static

D1() [1/5]

static void ElSLib::D1 ( const Standard_Real  U, const Standard_Real  V, const gp_Pln &  Pl, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv  )

static

For elementary surfaces from the gp package (planes, cones, cylinders, spheres and tori), computes:

• the point P of parameters (U, V), and
• the first derivative vectors Vu and Vv at this point in the u and v parametric directions respectively.

D1() [2/5]

static void ElSLib::D1 ( const Standard_Real  U, const Standard_Real  V, const gp_Cone &  C, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv  )

static

D1() [3/5]

static void ElSLib::D1 ( const Standard_Real  U, const Standard_Real  V, const gp_Cylinder &  C, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv  )

static

D1() [4/5]

static void ElSLib::D1 ( const Standard_Real  U, const Standard_Real  V, const gp_Sphere &  S, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv  )

static

D1() [5/5]

static void ElSLib::D1 ( const Standard_Real  U, const Standard_Real  V, const gp_Torus &  T, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv  )

static

D2() [1/4]

static void ElSLib::D2 ( const Standard_Real  U, const Standard_Real  V, const gp_Cone &  C, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv  )

static

For elementary surfaces from the gp package (cones, cylinders, spheres and tori), computes:

• the point P of parameters (U, V), and
• the first derivative vectors Vu and Vv at this point in the u and v parametric directions respectively, and
• the second derivative vectors Vuu, Vvv and Vuv at this point.

D2() [2/4]

static void ElSLib::D2 ( const Standard_Real  U, const Standard_Real  V, const gp_Cylinder &  C, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv  )

static

D2() [3/4]

static void ElSLib::D2 ( const Standard_Real  U, const Standard_Real  V, const gp_Sphere &  S, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv  )

static

D2() [4/4]

static void ElSLib::D2 ( const Standard_Real  U, const Standard_Real  V, const gp_Torus &  T, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv  )

static

D3() [1/4]

static void ElSLib::D3 ( const Standard_Real  U, const Standard_Real  V, const gp_Cone &  C, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv, gp_Vec &  Vuuu, gp_Vec &  Vvvv, gp_Vec &  Vuuv, gp_Vec &  Vuvv  )

static

For elementary surfaces from the gp package (cones, cylinders, spheres and tori), computes:

• the point P of parameters (U,V), and
• the first derivative vectors Vu and Vv at this point in the u and v parametric directions respectively, and
• the second derivative vectors Vuu, Vvv and Vuv at this point, and
• the third derivative vectors Vuuu, Vvvv, Vuuv and Vuvv at this point.

D3() [2/4]

static void ElSLib::D3 ( const Standard_Real  U, const Standard_Real  V, const gp_Cylinder &  C, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv, gp_Vec &  Vuuu, gp_Vec &  Vvvv, gp_Vec &  Vuuv, gp_Vec &  Vuvv  )

static

D3() [3/4]

static void ElSLib::D3 ( const Standard_Real  U, const Standard_Real  V, const gp_Sphere &  S, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv, gp_Vec &  Vuuu, gp_Vec &  Vvvv, gp_Vec &  Vuuv, gp_Vec &  Vuvv  )

static

D3() [4/4]

static void ElSLib::D3 ( const Standard_Real  U, const Standard_Real  V, const gp_Torus &  T, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv, gp_Vec &  Vuuu, gp_Vec &  Vvvv, gp_Vec &  Vuuv, gp_Vec &  Vuvv  )

static

Surface evaluation The following functions compute the point and the derivatives on elementary surfaces defined with their geometric characterisitics. You don't need to create the surface to use these functions. These functions are called by the previous ones. Example : A cylinder is defined with its position and its radius.

DN() [1/5]

static gp_Vec ElSLib::DN ( const Standard_Real  U, const Standard_Real  V, const gp_Pln &  Pl, const Standard_Integer  Nu, const Standard_Integer  Nv  )

static

For elementary surfaces from the gp package (planes, cones, cylinders, spheres and tori), computes the derivative vector of order Nu and Nv in the u and v parametric directions respectively, at the point of parameters (U, V).

DN() [2/5]

static gp_Vec ElSLib::DN ( const Standard_Real  U, const Standard_Real  V, const gp_Cone &  C, const Standard_Integer  Nu, const Standard_Integer  Nv  )

static

DN() [3/5]

static gp_Vec ElSLib::DN ( const Standard_Real  U, const Standard_Real  V, const gp_Cylinder &  C, const Standard_Integer  Nu, const Standard_Integer  Nv  )

static

DN() [4/5]

static gp_Vec ElSLib::DN ( const Standard_Real  U, const Standard_Real  V, const gp_Sphere &  S, const Standard_Integer  Nu, const Standard_Integer  Nv  )

static

DN() [5/5]

static gp_Vec ElSLib::DN ( const Standard_Real  U, const Standard_Real  V, const gp_Torus &  T, const Standard_Integer  Nu, const Standard_Integer  Nv  )

static

Parameters() [1/5]

static void ElSLib::Parameters ( const gp_Pln &  Pl, const gp_Pnt &  P, Standard_Real &  U, Standard_Real &  V  )

static

parametrization P (U, V) = Pl.Location() + U * Pl.XDirection() + V * Pl.YDirection()

Parameters() [2/5]

static void ElSLib::Parameters ( const gp_Cylinder &  C, const gp_Pnt &  P, Standard_Real &  U, Standard_Real &  V  )

static

parametrization P (U, V) = Location + V * ZDirection + Radius * (Cos(U) * XDirection + Sin (U) * YDirection)

Parameters() [3/5]

static void ElSLib::Parameters ( const gp_Cone &  C, const gp_Pnt &  P, Standard_Real &  U, Standard_Real &  V  )

static

parametrization P (U, V) = Location + V * ZDirection + (Radius + V * Tan (SemiAngle)) * (Cos(U) * XDirection + Sin(U) * YDirection)

Parameters() [4/5]

static void ElSLib::Parameters ( const gp_Sphere &  S, const gp_Pnt &  P, Standard_Real &  U, Standard_Real &  V  )

static

parametrization P (U, V) = Location + Radius * Cos (V) * (Cos (U) * XDirection + Sin (U) * YDirection) + Radius * Sin (V) * ZDirection

Parameters() [5/5]

static void ElSLib::Parameters ( const gp_Torus &  T, const gp_Pnt &  P, Standard_Real &  U, Standard_Real &  V  )

static

parametrization P (U, V) = Location + (MajorRadius + MinorRadius * Cos(U)) * (Cos(V) * XDirection - Sin(V) * YDirection) + MinorRadius * Sin(U) * ZDirection

PlaneD0()

static void ElSLib::PlaneD0 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, gp_Pnt &  P  )

static

PlaneD1()

static void ElSLib::PlaneD1 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv  )

static

PlaneDN()

static gp_Vec ElSLib::PlaneDN ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Integer  Nu, const Standard_Integer  Nv  )

static

PlaneParameters()

static void ElSLib::PlaneParameters ( const gp_Ax3 &  Pos, const gp_Pnt &  P, Standard_Real &  U, Standard_Real &  V  )

static

parametrization P (U, V) = Pl.Location() + U * Pl.XDirection() + V * Pl.YDirection()

PlaneUIso()

static gp_Lin ElSLib::PlaneUIso ( const gp_Ax3 &  Pos, const Standard_Real  U  )

static

compute the U Isoparametric gp_Lin of the plane.

PlaneValue()

static gp_Pnt ElSLib::PlaneValue ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos  )

static

PlaneVIso()

static gp_Lin ElSLib::PlaneVIso ( const gp_Ax3 &  Pos, const Standard_Real  V  )

static

compute the V Isoparametric gp_Lin of the plane.

SphereD0()

static void ElSLib::SphereD0 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, gp_Pnt &  P  )

static

SphereD1()

static void ElSLib::SphereD1 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv  )

static

SphereD2()

static void ElSLib::SphereD2 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv  )

static

SphereD3()

static void ElSLib::SphereD3 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv, gp_Vec &  Vuuu, gp_Vec &  Vvvv, gp_Vec &  Vuuv, gp_Vec &  Vuvv  )

static

SphereDN()

static gp_Vec ElSLib::SphereDN ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Integer  Nu, const Standard_Integer  Nv  )

static

SphereParameters()

static void ElSLib::SphereParameters ( const gp_Ax3 &  Pos, const Standard_Real  Radius, const gp_Pnt &  P, Standard_Real &  U, Standard_Real &  V  )

static

parametrization P (U, V) = Location + Radius * Cos (V) * (Cos (U) * XDirection + Sin (U) * YDirection) + Radius * Sin (V) * ZDirection

SphereUIso()

static gp_Circ ElSLib::SphereUIso ( const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  U  )

static

compute the U Isoparametric gp_Circ of the sphere, (the meridian is not trimmed).

SphereValue()

static gp_Pnt ElSLib::SphereValue ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  Radius  )

static

SphereVIso()

static gp_Circ ElSLib::SphereVIso ( const gp_Ax3 &  Pos, const Standard_Real  Radius, const Standard_Real  V  )

static

compute the V Isoparametric gp_Circ of the sphere, (the meridian is not trimmed).

TorusD0()

static void ElSLib::TorusD0 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  MajorRadius, const Standard_Real  MinorRadius, gp_Pnt &  P  )

static

TorusD1()

static void ElSLib::TorusD1 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  MajorRadius, const Standard_Real  MinorRadius, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv  )

static

TorusD2()

static void ElSLib::TorusD2 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  MajorRadius, const Standard_Real  MinorRadius, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv  )

static

TorusD3()

static void ElSLib::TorusD3 ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  MajorRadius, const Standard_Real  MinorRadius, gp_Pnt &  P, gp_Vec &  Vu, gp_Vec &  Vv, gp_Vec &  Vuu, gp_Vec &  Vvv, gp_Vec &  Vuv, gp_Vec &  Vuuu, gp_Vec &  Vvvv, gp_Vec &  Vuuv, gp_Vec &  Vuvv  )

static

The following functions compute the parametric values corresponding to a given point on a elementary surface. The point should be on the surface.

TorusDN()

static gp_Vec ElSLib::TorusDN ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  MajorRadius, const Standard_Real  MinorRadius, const Standard_Integer  Nu, const Standard_Integer  Nv  )

static

TorusParameters()

static void ElSLib::TorusParameters ( const gp_Ax3 &  Pos, const Standard_Real  MajorRadius, const Standard_Real  MinorRadius, const gp_Pnt &  P, Standard_Real &  U, Standard_Real &  V  )

static

parametrization P (U, V) = Location + (MajorRadius + MinorRadius * Cos(U)) * (Cos(V) * XDirection - Sin(V) * YDirection) + MinorRadius * Sin(U) * ZDirection

TorusUIso()

static gp_Circ ElSLib::TorusUIso ( const gp_Ax3 &  Pos, const Standard_Real  MajorRadius, const Standard_Real  MinorRadius, const Standard_Real  U  )

static

compute the U Isoparametric gp_Circ of the torus.

TorusValue()

static gp_Pnt ElSLib::TorusValue ( const Standard_Real  U, const Standard_Real  V, const gp_Ax3 &  Pos, const Standard_Real  MajorRadius, const Standard_Real  MinorRadius  )

static

TorusVIso()

static gp_Circ ElSLib::TorusVIso ( const gp_Ax3 &  Pos, const Standard_Real  MajorRadius, const Standard_Real  MinorRadius, const Standard_Real  V  )

static

compute the V Isoparametric gp_Circ of the torus.

Value() [1/5]

static gp_Pnt ElSLib::Value ( const Standard_Real  U, const Standard_Real  V, const gp_Pln &  Pl  )

static

For elementary surfaces from the gp package (planes, cones, cylinders, spheres and tori), computes the point of parameters (U, V).

Value() [2/5]

static gp_Pnt ElSLib::Value ( const Standard_Real  U, const Standard_Real  V, const gp_Cone &  C  )

static

Value() [3/5]

static gp_Pnt ElSLib::Value ( const Standard_Real  U, const Standard_Real  V, const gp_Cylinder &  C  )

static

Value() [4/5]

static gp_Pnt ElSLib::Value ( const Standard_Real  U, const Standard_Real  V, const gp_Sphere &  S  )

static

Value() [5/5]

static gp_Pnt ElSLib::Value ( const Standard_Real  U, const Standard_Real  V, const gp_Torus &  T  )

static

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

• ElSLib.hxx