Open CASCADE Technology  7.7.0.dev
Static Public Member Functions

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 characteristics. 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:

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_Cone C,
gp_Pnt P 
)
static

◆ D0() [2/5]

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

◆ D0() [3/5]

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() [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_Cone C,
gp_Pnt P,
gp_Vec Vu,
gp_Vec Vv 
)
static

◆ D1() [2/5]

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() [3/5]

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() [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 characteristics. 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_Cone C,
const Standard_Integer  Nu,
const Standard_Integer  Nv 
)
static

◆ DN() [2/5]

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() [3/5]

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() [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_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() [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_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() [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_Cone C 
)
static

◆ Value() [2/5]

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

◆ Value() [3/5]

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() [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

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