Open CASCADE Technology  7.1.0.beta
ElCLib Class Reference

Provides functions for basic geometric computations on elementary curves such as conics and lines in 2D and 3D space. This includes: More...

`#include <ElCLib.hxx>`

## Static Public Member Functions

static Standard_Real InPeriod (const Standard_Real U, const Standard_Real UFirst, const Standard_Real ULast)
Return a value in the range <UFirst, ULast> by adding or removing the period <ULast - UFirst> to <U>. ATTENTION!!! It is expected but not checked that (ULast > UFirst) More...

static void AdjustPeriodic (const Standard_Real UFirst, const Standard_Real ULast, const Standard_Real Precision, Standard_Real &U1, Standard_Real &U2)
Adjust U1 and U2 in the parametric range UFirst Ulast of a periodic curve, where ULast - UFirst is its period. To do this, this function: More...

static gp_Pnt Value (const Standard_Real U, const gp_Lin &L)
For elementary curves (lines, circles and conics) from the gp package, computes the point of parameter U. The result is either: More...

static gp_Pnt Value (const Standard_Real U, const gp_Circ &C)

static gp_Pnt Value (const Standard_Real U, const gp_Elips &E)

static gp_Pnt Value (const Standard_Real U, const gp_Hypr &H)

static gp_Pnt Value (const Standard_Real U, const gp_Parab &Prb)

static void D1 (const Standard_Real U, const gp_Lin &L, gp_Pnt &P, gp_Vec &V1)
For elementary curves (lines, circles and conics) from the gp package, computes: More...

static void D1 (const Standard_Real U, const gp_Circ &C, gp_Pnt &P, gp_Vec &V1)

static void D1 (const Standard_Real U, const gp_Elips &E, gp_Pnt &P, gp_Vec &V1)

static void D1 (const Standard_Real U, const gp_Hypr &H, gp_Pnt &P, gp_Vec &V1)

static void D1 (const Standard_Real U, const gp_Parab &Prb, gp_Pnt &P, gp_Vec &V1)

static void D2 (const Standard_Real U, const gp_Circ &C, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)
For elementary curves (circles and conics) from the gp package, computes: More...

static void D2 (const Standard_Real U, const gp_Elips &E, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)

static void D2 (const Standard_Real U, const gp_Hypr &H, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)

static void D2 (const Standard_Real U, const gp_Parab &Prb, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)

static void D3 (const Standard_Real U, const gp_Circ &C, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3)
For elementary curves (circles, ellipses and hyperbolae) from the gp package, computes: More...

static void D3 (const Standard_Real U, const gp_Elips &E, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3)

static void D3 (const Standard_Real U, const gp_Hypr &H, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3)

static gp_Vec DN (const Standard_Real U, const gp_Lin &L, const Standard_Integer N)
For elementary curves (lines, circles and conics) from the gp package, computes the vector corresponding to the Nth derivative at the point of parameter U. The result is either: More...

static gp_Vec DN (const Standard_Real U, const gp_Circ &C, const Standard_Integer N)

static gp_Vec DN (const Standard_Real U, const gp_Elips &E, const Standard_Integer N)

static gp_Vec DN (const Standard_Real U, const gp_Hypr &H, const Standard_Integer N)

static gp_Vec DN (const Standard_Real U, const gp_Parab &Prb, const Standard_Integer N)

static gp_Pnt2d Value (const Standard_Real U, const gp_Lin2d &L)

static gp_Pnt2d Value (const Standard_Real U, const gp_Circ2d &C)

static gp_Pnt2d Value (const Standard_Real U, const gp_Elips2d &E)

static gp_Pnt2d Value (const Standard_Real U, const gp_Hypr2d &H)

static gp_Pnt2d Value (const Standard_Real U, const gp_Parab2d &Prb)

static void D1 (const Standard_Real U, const gp_Lin2d &L, gp_Pnt2d &P, gp_Vec2d &V1)

static void D1 (const Standard_Real U, const gp_Circ2d &C, gp_Pnt2d &P, gp_Vec2d &V1)

static void D1 (const Standard_Real U, const gp_Elips2d &E, gp_Pnt2d &P, gp_Vec2d &V1)

static void D1 (const Standard_Real U, const gp_Hypr2d &H, gp_Pnt2d &P, gp_Vec2d &V1)

static void D1 (const Standard_Real U, const gp_Parab2d &Prb, gp_Pnt2d &P, gp_Vec2d &V1)

static void D2 (const Standard_Real U, const gp_Circ2d &C, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)

static void D2 (const Standard_Real U, const gp_Elips2d &E, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)

static void D2 (const Standard_Real U, const gp_Hypr2d &H, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)

static void D2 (const Standard_Real U, const gp_Parab2d &Prb, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)

static void D3 (const Standard_Real U, const gp_Circ2d &C, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3)

static void D3 (const Standard_Real U, const gp_Elips2d &E, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3)

static void D3 (const Standard_Real U, const gp_Hypr2d &H, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3)
In the following functions N is the order of derivation and should be greater than 0. More...

static gp_Vec2d DN (const Standard_Real U, const gp_Lin2d &L, const Standard_Integer N)

static gp_Vec2d DN (const Standard_Real U, const gp_Circ2d &C, const Standard_Integer N)

static gp_Vec2d DN (const Standard_Real U, const gp_Elips2d &E, const Standard_Integer N)

static gp_Vec2d DN (const Standard_Real U, const gp_Hypr2d &H, const Standard_Integer N)

static gp_Vec2d DN (const Standard_Real U, const gp_Parab2d &Prb, const Standard_Integer N)

static gp_Pnt LineValue (const Standard_Real U, const gp_Ax1 &Pos)
Curve evaluation The following basis functions compute the derivatives on elementary curves defined by their geometric characteristics. These functions can be called without constructing a conic from package gp. They are called by the previous functions. Example : A circle is defined by its position and its radius. More...

static gp_Pnt CircleValue (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Radius)

static gp_Pnt EllipseValue (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius)

static gp_Pnt HyperbolaValue (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius)

static gp_Pnt ParabolaValue (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Focal)

static void LineD1 (const Standard_Real U, const gp_Ax1 &Pos, gp_Pnt &P, gp_Vec &V1)

static void CircleD1 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Radius, gp_Pnt &P, gp_Vec &V1)

static void EllipseD1 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt &P, gp_Vec &V1)

static void HyperbolaD1 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt &P, gp_Vec &V1)

static void ParabolaD1 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Focal, gp_Pnt &P, gp_Vec &V1)

static void CircleD2 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Radius, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)

static void EllipseD2 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)

static void HyperbolaD2 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)

static void ParabolaD2 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Focal, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2)

static void CircleD3 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Radius, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3)

static void EllipseD3 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3)

static void HyperbolaD3 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3)

static gp_Vec LineDN (const Standard_Real U, const gp_Ax1 &Pos, const Standard_Integer N)
In the following functions N is the order of derivation and should be greater than 0. More...

static gp_Vec CircleDN (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Radius, const Standard_Integer N)

static gp_Vec EllipseDN (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N)

static gp_Vec HyperbolaDN (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N)

static gp_Vec ParabolaDN (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Focal, const Standard_Integer N)

static gp_Pnt2d LineValue (const Standard_Real U, const gp_Ax2d &Pos)

static gp_Pnt2d CircleValue (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Radius)

static gp_Pnt2d EllipseValue (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius)

static gp_Pnt2d HyperbolaValue (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius)

static gp_Pnt2d ParabolaValue (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Focal)

static void LineD1 (const Standard_Real U, const gp_Ax2d &Pos, gp_Pnt2d &P, gp_Vec2d &V1)

static void CircleD1 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Radius, gp_Pnt2d &P, gp_Vec2d &V1)

static void EllipseD1 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d &P, gp_Vec2d &V1)

static void HyperbolaD1 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d &P, gp_Vec2d &V1)

static void ParabolaD1 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Focal, gp_Pnt2d &P, gp_Vec2d &V1)

static void CircleD2 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Radius, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)

static void EllipseD2 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)

static void HyperbolaD2 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)

static void ParabolaD2 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Focal, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2)

static void CircleD3 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Radius, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3)

static void EllipseD3 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3)

static void HyperbolaD3 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3)
In the following functions N is the order of derivation and should be greater than 0. More...

static gp_Vec2d LineDN (const Standard_Real U, const gp_Ax2d &Pos, const Standard_Integer N)

static gp_Vec2d CircleDN (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Radius, const Standard_Integer N)

static gp_Vec2d EllipseDN (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N)

static gp_Vec2d HyperbolaDN (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N)

static gp_Vec2d ParabolaDN (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Focal, const Standard_Integer N)
The following functions compute the parametric value corresponding to a given point on a elementary curve. The point should be on the curve. More...

static Standard_Real Parameter (const gp_Lin &L, const gp_Pnt &P)
Computes the parameter value of the point P on the given curve. Note: In its local coordinate system, the parametric equation of the curve is given by the following: More...

static Standard_Real Parameter (const gp_Lin2d &L, const gp_Pnt2d &P)
parametrization P (U) = L.Location() + U * L.Direction() More...

static Standard_Real Parameter (const gp_Circ &C, const gp_Pnt &P)

static Standard_Real Parameter (const gp_Circ2d &C, const gp_Pnt2d &P)
parametrization In the local coordinate system of the circle X (U) = Radius * Cos (U) Y (U) = Radius * Sin (U) More...

static Standard_Real Parameter (const gp_Elips &E, const gp_Pnt &P)

static Standard_Real Parameter (const gp_Elips2d &E, const gp_Pnt2d &P)
parametrization In the local coordinate system of the Ellipse X (U) = MajorRadius * Cos (U) Y (U) = MinorRadius * Sin (U) More...

static Standard_Real Parameter (const gp_Hypr &H, const gp_Pnt &P)

static Standard_Real Parameter (const gp_Hypr2d &H, const gp_Pnt2d &P)
parametrization In the local coordinate system of the Hyperbola X (U) = MajorRadius * Ch (U) Y (U) = MinorRadius * Sh (U) More...

static Standard_Real Parameter (const gp_Parab &Prb, const gp_Pnt &P)

static Standard_Real Parameter (const gp_Parab2d &Prb, const gp_Pnt2d &P)
parametrization In the local coordinate system of the parabola Y**2 = (2*P) * X where P is the distance between the focus and the directrix. More...

static Standard_Real LineParameter (const gp_Ax1 &Pos, const gp_Pnt &P)

static Standard_Real LineParameter (const gp_Ax2d &Pos, const gp_Pnt2d &P)
parametrization P (U) = L.Location() + U * L.Direction() More...

static Standard_Real CircleParameter (const gp_Ax2 &Pos, const gp_Pnt &P)

static Standard_Real CircleParameter (const gp_Ax22d &Pos, const gp_Pnt2d &P)
Pos is the Axis of the Circle parametrization In the local coordinate system of the circle X (U) = Radius * Cos (U) Y (U) = Radius * Sin (U) More...

static Standard_Real EllipseParameter (const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt &P)

static Standard_Real EllipseParameter (const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt2d &P)
Pos is the Axis of the Ellipse parametrization In the local coordinate system of the Ellipse X (U) = MajorRadius * Cos (U) Y (U) = MinorRadius * Sin (U) More...

static Standard_Real HyperbolaParameter (const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt &P)

static Standard_Real HyperbolaParameter (const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt2d &P)
Pos is the Axis of the Hyperbola parametrization In the local coordinate system of the Hyperbola X (U) = MajorRadius * Ch (U) Y (U) = MinorRadius * Sh (U) More...

static Standard_Real ParabolaParameter (const gp_Ax2 &Pos, const gp_Pnt &P)

static Standard_Real ParabolaParameter (const gp_Ax22d &Pos, const gp_Pnt2d &P)
Pos is the mirror axis of the parabola parametrization In the local coordinate system of the parabola Y**2 = (2*P) * X where P is the distance between the focus and the directrix. The following functions build a 3d curve from a 2d curve at a given position defined with an Ax2. More...

static gp_Pnt To3d (const gp_Ax2 &Pos, const gp_Pnt2d &P)

static gp_Vec To3d (const gp_Ax2 &Pos, const gp_Vec2d &V)

static gp_Dir To3d (const gp_Ax2 &Pos, const gp_Dir2d &V)

static gp_Ax1 To3d (const gp_Ax2 &Pos, const gp_Ax2d &A)

static gp_Ax2 To3d (const gp_Ax2 &Pos, const gp_Ax22d &A)

static gp_Lin To3d (const gp_Ax2 &Pos, const gp_Lin2d &L)

static gp_Circ To3d (const gp_Ax2 &Pos, const gp_Circ2d &C)

static gp_Elips To3d (const gp_Ax2 &Pos, const gp_Elips2d &E)

static gp_Hypr To3d (const gp_Ax2 &Pos, const gp_Hypr2d &H)

static gp_Parab To3d (const gp_Ax2 &Pos, const gp_Parab2d &Prb)
These functions build a 3D geometric entity from a 2D geometric entity. The "X Axis" and the "Y Axis" of the global coordinate system (i.e. 2D space) are lined up respectively with the "X Axis" and "Y Axis" of the 3D coordinate system, Pos. More...

## Detailed Description

Provides functions for basic geometric computations on elementary curves such as conics and lines in 2D and 3D space. This includes:

• calculation of a point or derived vector on a 2D or 3D curve where:
• the curve is provided by the gp package, or defined in reference form (as in the gp package), and
• the point is defined by a parameter,
• evaluation of the parameter corresponding to a point on a 2D or 3D curve from gp,
• various elementary computations which allow you to position parameterized values within the period of a curve. Notes:
• ElCLib stands for Elementary Curves Library.
• If the curves provided by the gp package are not explicitly parameterized, they still have an implicit parameterization, analogous to that which they infer for the equivalent Geom or Geom2d curves.

## Member Function Documentation

 static void ElCLib::AdjustPeriodic ( const Standard_Real UFirst, const Standard_Real ULast, const Standard_Real Precision, Standard_Real & U1, Standard_Real & U2 )
static

Adjust U1 and U2 in the parametric range UFirst Ulast of a periodic curve, where ULast - UFirst is its period. To do this, this function:

• sets U1 in the range [ UFirst, ULast ] by adding/removing the period to/from the value U1, then
• sets U2 in the range [ U1, U1 + period ] by adding/removing the period to/from the value U2. Precision is used to test the equalities.
 static void ElCLib::CircleD1 ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real Radius, gp_Pnt & P, gp_Vec & V1 )
static
 static void ElCLib::CircleD1 ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real Radius, gp_Pnt2d & P, gp_Vec2d & V1 )
static
 static void ElCLib::CircleD2 ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real Radius, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 )
static
 static void ElCLib::CircleD2 ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real Radius, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 )
static
 static void ElCLib::CircleD3 ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real Radius, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2, gp_Vec & V3 )
static
 static void ElCLib::CircleD3 ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real Radius, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2, gp_Vec2d & V3 )
static
 static gp_Vec ElCLib::CircleDN ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real Radius, const Standard_Integer N )
static
 static gp_Vec2d ElCLib::CircleDN ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real Radius, const Standard_Integer N )
static
 static Standard_Real ElCLib::CircleParameter ( const gp_Ax2 & Pos, const gp_Pnt & P )
static
 static Standard_Real ElCLib::CircleParameter ( const gp_Ax22d & Pos, const gp_Pnt2d & P )
static

Pos is the Axis of the Circle parametrization In the local coordinate system of the circle X (U) = Radius * Cos (U) Y (U) = Radius * Sin (U)

 static gp_Pnt ElCLib::CircleValue ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real Radius )
static
 static gp_Pnt2d ElCLib::CircleValue ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real Radius )
static
 static void ElCLib::D1 ( const Standard_Real U, const gp_Lin & L, gp_Pnt & P, gp_Vec & V1 )
static

For elementary curves (lines, circles and conics) from the gp package, computes:

• the point P of parameter U, and
• the first derivative vector V1 at this point. The results P and V1 are either:
• a gp_Pnt point and a gp_Vec vector, for a curve in 3D space, or
• a gp_Pnt2d point and a gp_Vec2d vector, for a curve in 2D space.
 static void ElCLib::D1 ( const Standard_Real U, const gp_Circ & C, gp_Pnt & P, gp_Vec & V1 )
static
 static void ElCLib::D1 ( const Standard_Real U, const gp_Elips & E, gp_Pnt & P, gp_Vec & V1 )
static
 static void ElCLib::D1 ( const Standard_Real U, const gp_Hypr & H, gp_Pnt & P, gp_Vec & V1 )
static
 static void ElCLib::D1 ( const Standard_Real U, const gp_Parab & Prb, gp_Pnt & P, gp_Vec & V1 )
static
 static void ElCLib::D1 ( const Standard_Real U, const gp_Lin2d & L, gp_Pnt2d & P, gp_Vec2d & V1 )
static
 static void ElCLib::D1 ( const Standard_Real U, const gp_Circ2d & C, gp_Pnt2d & P, gp_Vec2d & V1 )
static
 static void ElCLib::D1 ( const Standard_Real U, const gp_Elips2d & E, gp_Pnt2d & P, gp_Vec2d & V1 )
static
 static void ElCLib::D1 ( const Standard_Real U, const gp_Hypr2d & H, gp_Pnt2d & P, gp_Vec2d & V1 )
static
 static void ElCLib::D1 ( const Standard_Real U, const gp_Parab2d & Prb, gp_Pnt2d & P, gp_Vec2d & V1 )
static
 static void ElCLib::D2 ( const Standard_Real U, const gp_Circ & C, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 )
static

For elementary curves (circles and conics) from the gp package, computes:

• the point P of parameter U, and
• the first and second derivative vectors V1 and V2 at this point. The results, P, V1 and V2, are either:
• a gp_Pnt point and two gp_Vec vectors, for a curve in 3D space, or
• a gp_Pnt2d point and two gp_Vec2d vectors, for a curve in 2D space.
 static void ElCLib::D2 ( const Standard_Real U, const gp_Elips & E, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 )
static
 static void ElCLib::D2 ( const Standard_Real U, const gp_Hypr & H, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 )
static
 static void ElCLib::D2 ( const Standard_Real U, const gp_Parab & Prb, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 )
static
 static void ElCLib::D2 ( const Standard_Real U, const gp_Circ2d & C, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 )
static
 static void ElCLib::D2 ( const Standard_Real U, const gp_Elips2d & E, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 )
static
 static void ElCLib::D2 ( const Standard_Real U, const gp_Hypr2d & H, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 )
static
 static void ElCLib::D2 ( const Standard_Real U, const gp_Parab2d & Prb, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 )
static
 static void ElCLib::D3 ( const Standard_Real U, const gp_Circ & C, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2, gp_Vec & V3 )
static

For elementary curves (circles, ellipses and hyperbolae) from the gp package, computes:

• the point P of parameter U, and
• the first, second and third derivative vectors V1, V2 and V3 at this point. The results, P, V1, V2 and V3, are either:
• a gp_Pnt point and three gp_Vec vectors, for a curve in 3D space, or
• a gp_Pnt2d point and three gp_Vec2d vectors, for a curve in 2D space.
 static void ElCLib::D3 ( const Standard_Real U, const gp_Elips & E, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2, gp_Vec & V3 )
static
 static void ElCLib::D3 ( const Standard_Real U, const gp_Hypr & H, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2, gp_Vec & V3 )
static
 static void ElCLib::D3 ( const Standard_Real U, const gp_Circ2d & C, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2, gp_Vec2d & V3 )
static
 static void ElCLib::D3 ( const Standard_Real U, const gp_Elips2d & E, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2, gp_Vec2d & V3 )
static
 static void ElCLib::D3 ( const Standard_Real U, const gp_Hypr2d & H, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2, gp_Vec2d & V3 )
static

In the following functions N is the order of derivation and should be greater than 0.

 static gp_Vec ElCLib::DN ( const Standard_Real U, const gp_Lin & L, const Standard_Integer N )
static

For elementary curves (lines, circles and conics) from the gp package, computes the vector corresponding to the Nth derivative at the point of parameter U. The result is either:

• a gp_Vec vector for a curve in 3D space, or
• a gp_Vec2d vector for a curve in 2D space. In the following functions N is the order of derivation and should be greater than 0
 static gp_Vec ElCLib::DN ( const Standard_Real U, const gp_Circ & C, const Standard_Integer N )
static
 static gp_Vec ElCLib::DN ( const Standard_Real U, const gp_Elips & E, const Standard_Integer N )
static
 static gp_Vec ElCLib::DN ( const Standard_Real U, const gp_Hypr & H, const Standard_Integer N )
static
 static gp_Vec ElCLib::DN ( const Standard_Real U, const gp_Parab & Prb, const Standard_Integer N )
static
 static gp_Vec2d ElCLib::DN ( const Standard_Real U, const gp_Lin2d & L, const Standard_Integer N )
static
 static gp_Vec2d ElCLib::DN ( const Standard_Real U, const gp_Circ2d & C, const Standard_Integer N )
static
 static gp_Vec2d ElCLib::DN ( const Standard_Real U, const gp_Elips2d & E, const Standard_Integer N )
static
 static gp_Vec2d ElCLib::DN ( const Standard_Real U, const gp_Hypr2d & H, const Standard_Integer N )
static
 static gp_Vec2d ElCLib::DN ( const Standard_Real U, const gp_Parab2d & Prb, const Standard_Integer N )
static
 static void ElCLib::EllipseD1 ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt & P, gp_Vec & V1 )
static
 static void ElCLib::EllipseD1 ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d & P, gp_Vec2d & V1 )
static
 static void ElCLib::EllipseD2 ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 )
static
 static void ElCLib::EllipseD2 ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 )
static
 static void ElCLib::EllipseD3 ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2, gp_Vec & V3 )
static
 static void ElCLib::EllipseD3 ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2, gp_Vec2d & V3 )
static
 static gp_Vec ElCLib::EllipseDN ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N )
static
 static gp_Vec2d ElCLib::EllipseDN ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N )
static
 static Standard_Real ElCLib::EllipseParameter ( const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt & P )
static
 static Standard_Real ElCLib::EllipseParameter ( const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt2d & P )
static

Pos is the Axis of the Ellipse parametrization In the local coordinate system of the Ellipse X (U) = MajorRadius * Cos (U) Y (U) = MinorRadius * Sin (U)

 static gp_Pnt ElCLib::EllipseValue ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius )
static
 static gp_Pnt2d ElCLib::EllipseValue ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius )
static
 static void ElCLib::HyperbolaD1 ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt & P, gp_Vec & V1 )
static
 static void ElCLib::HyperbolaD1 ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d & P, gp_Vec2d & V1 )
static
 static void ElCLib::HyperbolaD2 ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 )
static
 static void ElCLib::HyperbolaD2 ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 )
static
 static void ElCLib::HyperbolaD3 ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2, gp_Vec & V3 )
static
 static void ElCLib::HyperbolaD3 ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2, gp_Vec2d & V3 )
static

In the following functions N is the order of derivation and should be greater than 0.

 static gp_Vec ElCLib::HyperbolaDN ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N )
static
 static gp_Vec2d ElCLib::HyperbolaDN ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N )
static
 static Standard_Real ElCLib::HyperbolaParameter ( const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt & P )
static
 static Standard_Real ElCLib::HyperbolaParameter ( const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt2d & P )
static

Pos is the Axis of the Hyperbola parametrization In the local coordinate system of the Hyperbola X (U) = MajorRadius * Ch (U) Y (U) = MinorRadius * Sh (U)

 static gp_Pnt ElCLib::HyperbolaValue ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius )
static
 static gp_Pnt2d ElCLib::HyperbolaValue ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius )
static
 static Standard_Real ElCLib::InPeriod ( const Standard_Real U, const Standard_Real UFirst, const Standard_Real ULast )
static

Return a value in the range <UFirst, ULast> by adding or removing the period <ULast - UFirst> to <U>. ATTENTION!!! It is expected but not checked that (ULast > UFirst)

 static void ElCLib::LineD1 ( const Standard_Real U, const gp_Ax1 & Pos, gp_Pnt & P, gp_Vec & V1 )
static
 static void ElCLib::LineD1 ( const Standard_Real U, const gp_Ax2d & Pos, gp_Pnt2d & P, gp_Vec2d & V1 )
static
 static gp_Vec ElCLib::LineDN ( const Standard_Real U, const gp_Ax1 & Pos, const Standard_Integer N )
static

In the following functions N is the order of derivation and should be greater than 0.

 static gp_Vec2d ElCLib::LineDN ( const Standard_Real U, const gp_Ax2d & Pos, const Standard_Integer N )
static
 static Standard_Real ElCLib::LineParameter ( const gp_Ax1 & Pos, const gp_Pnt & P )
static
 static Standard_Real ElCLib::LineParameter ( const gp_Ax2d & Pos, const gp_Pnt2d & P )
static

parametrization P (U) = L.Location() + U * L.Direction()

 static gp_Pnt ElCLib::LineValue ( const Standard_Real U, const gp_Ax1 & Pos )
static

Curve evaluation The following basis functions compute the derivatives on elementary curves defined by their geometric characteristics. These functions can be called without constructing a conic from package gp. They are called by the previous functions. Example : A circle is defined by its position and its radius.

 static gp_Pnt2d ElCLib::LineValue ( const Standard_Real U, const gp_Ax2d & Pos )
static
 static void ElCLib::ParabolaD1 ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real Focal, gp_Pnt & P, gp_Vec & V1 )
static
 static void ElCLib::ParabolaD1 ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real Focal, gp_Pnt2d & P, gp_Vec2d & V1 )
static
 static void ElCLib::ParabolaD2 ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real Focal, gp_Pnt & P, gp_Vec & V1, gp_Vec & V2 )
static
 static void ElCLib::ParabolaD2 ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real Focal, gp_Pnt2d & P, gp_Vec2d & V1, gp_Vec2d & V2 )
static
 static gp_Vec ElCLib::ParabolaDN ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real Focal, const Standard_Integer N )
static
 static gp_Vec2d ElCLib::ParabolaDN ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real Focal, const Standard_Integer N )
static

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

 static Standard_Real ElCLib::ParabolaParameter ( const gp_Ax2 & Pos, const gp_Pnt & P )
static
 static Standard_Real ElCLib::ParabolaParameter ( const gp_Ax22d & Pos, const gp_Pnt2d & P )
static

Pos is the mirror axis of the parabola parametrization In the local coordinate system of the parabola Y**2 = (2*P) * X where P is the distance between the focus and the directrix. The following functions build a 3d curve from a 2d curve at a given position defined with an Ax2.

 static gp_Pnt ElCLib::ParabolaValue ( const Standard_Real U, const gp_Ax2 & Pos, const Standard_Real Focal )
static
 static gp_Pnt2d ElCLib::ParabolaValue ( const Standard_Real U, const gp_Ax22d & Pos, const Standard_Real Focal )
static
 static Standard_Real ElCLib::Parameter ( const gp_Lin & L, const gp_Pnt & P )
static

Computes the parameter value of the point P on the given curve. Note: In its local coordinate system, the parametric equation of the curve is given by the following:

• for the line L: P(U) = Po + U*Vo where Po is the origin and Vo the unit vector of its positioning axis.
• for the circle C: X(U) = Radius*Cos(U), Y(U) = Radius*Sin(U)
• for the ellipse E: X(U) = MajorRadius*Cos(U). Y(U) = MinorRadius*Sin(U)
• for the hyperbola H: X(U) = MajorRadius*Ch(U), Y(U) = MinorRadius*Sh(U)
• for the parabola Prb: X(U) = U**2 / (2*p) Y(U) = U where p is the distance between the focus and the directrix. Warning The point P must be on the curve. These functions are not protected, however, and if point P is not on the curve, an exception may be raised.
 static Standard_Real ElCLib::Parameter ( const gp_Lin2d & L, const gp_Pnt2d & P )
static

parametrization P (U) = L.Location() + U * L.Direction()

 static Standard_Real ElCLib::Parameter ( const gp_Circ & C, const gp_Pnt & P )
static
 static Standard_Real ElCLib::Parameter ( const gp_Circ2d & C, const gp_Pnt2d & P )
static

parametrization In the local coordinate system of the circle X (U) = Radius * Cos (U) Y (U) = Radius * Sin (U)

 static Standard_Real ElCLib::Parameter ( const gp_Elips & E, const gp_Pnt & P )
static
 static Standard_Real ElCLib::Parameter ( const gp_Elips2d & E, const gp_Pnt2d & P )
static

parametrization In the local coordinate system of the Ellipse X (U) = MajorRadius * Cos (U) Y (U) = MinorRadius * Sin (U)

 static Standard_Real ElCLib::Parameter ( const gp_Hypr & H, const gp_Pnt & P )
static
 static Standard_Real ElCLib::Parameter ( const gp_Hypr2d & H, const gp_Pnt2d & P )
static

parametrization In the local coordinate system of the Hyperbola X (U) = MajorRadius * Ch (U) Y (U) = MinorRadius * Sh (U)

 static Standard_Real ElCLib::Parameter ( const gp_Parab & Prb, const gp_Pnt & P )
static
 static Standard_Real ElCLib::Parameter ( const gp_Parab2d & Prb, const gp_Pnt2d & P )
static

parametrization In the local coordinate system of the parabola Y**2 = (2*P) * X where P is the distance between the focus and the directrix.

 static gp_Pnt ElCLib::To3d ( const gp_Ax2 & Pos, const gp_Pnt2d & P )
static
 static gp_Vec ElCLib::To3d ( const gp_Ax2 & Pos, const gp_Vec2d & V )
static
 static gp_Dir ElCLib::To3d ( const gp_Ax2 & Pos, const gp_Dir2d & V )
static
 static gp_Ax1 ElCLib::To3d ( const gp_Ax2 & Pos, const gp_Ax2d & A )
static
 static gp_Ax2 ElCLib::To3d ( const gp_Ax2 & Pos, const gp_Ax22d & A )
static
 static gp_Lin ElCLib::To3d ( const gp_Ax2 & Pos, const gp_Lin2d & L )
static
 static gp_Circ ElCLib::To3d ( const gp_Ax2 & Pos, const gp_Circ2d & C )
static
 static gp_Elips ElCLib::To3d ( const gp_Ax2 & Pos, const gp_Elips2d & E )
static
 static gp_Hypr ElCLib::To3d ( const gp_Ax2 & Pos, const gp_Hypr2d & H )
static
 static gp_Parab ElCLib::To3d ( const gp_Ax2 & Pos, const gp_Parab2d & Prb )
static

These functions build a 3D geometric entity from a 2D geometric entity. The "X Axis" and the "Y Axis" of the global coordinate system (i.e. 2D space) are lined up respectively with the "X Axis" and "Y Axis" of the 3D coordinate system, Pos.

 static gp_Pnt ElCLib::Value ( const Standard_Real U, const gp_Lin & L )
static

For elementary curves (lines, circles and conics) from the gp package, computes the point of parameter U. The result is either:

• a gp_Pnt point for a curve in 3D space, or
• a gp_Pnt2d point for a curve in 2D space.
 static gp_Pnt ElCLib::Value ( const Standard_Real U, const gp_Circ & C )
static
 static gp_Pnt ElCLib::Value ( const Standard_Real U, const gp_Elips & E )
static
 static gp_Pnt ElCLib::Value ( const Standard_Real U, const gp_Hypr & H )
static
 static gp_Pnt ElCLib::Value ( const Standard_Real U, const gp_Parab & Prb )
static
 static gp_Pnt2d ElCLib::Value ( const Standard_Real U, const gp_Lin2d & L )
static
 static gp_Pnt2d ElCLib::Value ( const Standard_Real U, const gp_Circ2d & C )
static
 static gp_Pnt2d ElCLib::Value ( const Standard_Real U, const gp_Elips2d & E )
static
 static gp_Pnt2d ElCLib::Value ( const Standard_Real U, const gp_Hypr2d & H )
static
 static gp_Pnt2d ElCLib::Value ( const Standard_Real U, const gp_Parab2d & Prb )
static

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