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Public Member Functions |
void * | operator new (size_t, void *anAddress) |
void * | operator new (size_t size) |
void | operator delete (void *anAddress) |
Static Public Member Functions |
static Standard_EXPORT 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>.
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static Standard_EXPORT 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:
- 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.
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static Standard_EXPORT 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:
- a gp_Pnt point for a curve in 3D space, or
- a gp_Pnt2d point for a curve in 2D space.
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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 Standard_EXPORT 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:
- 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.
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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 Standard_EXPORT 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:
- 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.
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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 Standard_EXPORT 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:
- 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.
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static void | D3 (const Standard_Real U, const gp_Elips &E, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) |
static Standard_EXPORT void | D3 (const Standard_Real U, const gp_Hypr &H, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) |
static Standard_EXPORT 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:
- 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
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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
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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 Standard_EXPORT 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.
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static Standard_EXPORT gp_Pnt | CircleValue (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Radius) |
static Standard_EXPORT gp_Pnt | EllipseValue (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius) |
static Standard_EXPORT gp_Pnt | HyperbolaValue (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius) |
static Standard_EXPORT gp_Pnt | ParabolaValue (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Focal) |
static Standard_EXPORT void | LineD1 (const Standard_Real U, const gp_Ax1 &Pos, gp_Pnt &P, gp_Vec &V1) |
static Standard_EXPORT void | CircleD1 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Radius, gp_Pnt &P, gp_Vec &V1) |
static Standard_EXPORT 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 Standard_EXPORT 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 Standard_EXPORT void | ParabolaD1 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Focal, gp_Pnt &P, gp_Vec &V1) |
static Standard_EXPORT void | CircleD2 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Radius, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) |
static Standard_EXPORT 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 Standard_EXPORT 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 Standard_EXPORT void | ParabolaD2 (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Focal, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) |
static Standard_EXPORT 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 Standard_EXPORT 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 Standard_EXPORT 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 Standard_EXPORT 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
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static Standard_EXPORT gp_Vec | CircleDN (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Radius, const Standard_Integer N) |
static Standard_EXPORT gp_Vec | EllipseDN (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N) |
static Standard_EXPORT gp_Vec | HyperbolaDN (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N) |
static Standard_EXPORT gp_Vec | ParabolaDN (const Standard_Real U, const gp_Ax2 &Pos, const Standard_Real Focal, const Standard_Integer N) |
static Standard_EXPORT gp_Pnt2d | LineValue (const Standard_Real U, const gp_Ax2d &Pos) |
static Standard_EXPORT gp_Pnt2d | CircleValue (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Radius) |
static Standard_EXPORT gp_Pnt2d | EllipseValue (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius) |
static Standard_EXPORT gp_Pnt2d | HyperbolaValue (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius) |
static Standard_EXPORT gp_Pnt2d | ParabolaValue (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Focal) |
static Standard_EXPORT void | LineD1 (const Standard_Real U, const gp_Ax2d &Pos, gp_Pnt2d &P, gp_Vec2d &V1) |
static Standard_EXPORT void | CircleD1 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Radius, gp_Pnt2d &P, gp_Vec2d &V1) |
static Standard_EXPORT 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 Standard_EXPORT 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 Standard_EXPORT void | ParabolaD1 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Focal, gp_Pnt2d &P, gp_Vec2d &V1) |
static Standard_EXPORT void | CircleD2 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Radius, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) |
static Standard_EXPORT 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 Standard_EXPORT 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 Standard_EXPORT void | ParabolaD2 (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Focal, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2) |
static Standard_EXPORT 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 Standard_EXPORT 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 Standard_EXPORT 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
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static Standard_EXPORT gp_Vec2d | LineDN (const Standard_Real U, const gp_Ax2d &Pos, const Standard_Integer N) |
static Standard_EXPORT gp_Vec2d | CircleDN (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real Radius, const Standard_Integer N) |
static Standard_EXPORT gp_Vec2d | EllipseDN (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N) |
static Standard_EXPORT gp_Vec2d | HyperbolaDN (const Standard_Real U, const gp_Ax22d &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const Standard_Integer N) |
static Standard_EXPORT 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.
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static Standard_EXPORT 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:
- 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.
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static Standard_Real | Parameter (const gp_Lin2d &L, const gp_Pnt2d &P) |
| parametrization
P (U) = L.Location() + U * L.Direction()
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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)
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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)
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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)
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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.
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static Standard_EXPORT Standard_Real | LineParameter (const gp_Ax1 &Pos, const gp_Pnt &P) |
static Standard_EXPORT Standard_Real | LineParameter (const gp_Ax2d &Pos, const gp_Pnt2d &P) |
| parametrization
P (U) = L.Location() + U * L.Direction()
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static Standard_EXPORT Standard_Real | CircleParameter (const gp_Ax2 &Pos, const gp_Pnt &P) |
static Standard_EXPORT 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)
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static Standard_EXPORT Standard_Real | EllipseParameter (const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt &P) |
static Standard_EXPORT 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)
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static Standard_EXPORT Standard_Real | HyperbolaParameter (const gp_Ax2 &Pos, const Standard_Real MajorRadius, const Standard_Real MinorRadius, const gp_Pnt &P) |
static Standard_EXPORT 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)
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static Standard_EXPORT Standard_Real | ParabolaParameter (const gp_Ax2 &Pos, const gp_Pnt &P) |
static Standard_EXPORT 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.
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static Standard_EXPORT gp_Pnt | To3d (const gp_Ax2 &Pos, const gp_Pnt2d &P) |
static Standard_EXPORT gp_Vec | To3d (const gp_Ax2 &Pos, const gp_Vec2d &V) |
static Standard_EXPORT gp_Dir | To3d (const gp_Ax2 &Pos, const gp_Dir2d &V) |
static Standard_EXPORT gp_Ax1 | To3d (const gp_Ax2 &Pos, const gp_Ax2d &A) |
static Standard_EXPORT gp_Ax2 | To3d (const gp_Ax2 &Pos, const gp_Ax22d &A) |
static Standard_EXPORT gp_Lin | To3d (const gp_Ax2 &Pos, const gp_Lin2d &L) |
static Standard_EXPORT gp_Circ | To3d (const gp_Ax2 &Pos, const gp_Circ2d &C) |
static Standard_EXPORT gp_Elips | To3d (const gp_Ax2 &Pos, const gp_Elips2d &E) |
static Standard_EXPORT gp_Hypr | To3d (const gp_Ax2 &Pos, const gp_Hypr2d &H) |
static Standard_EXPORT 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.
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