ElCLib

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.

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.

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.

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.

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

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

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.

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

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

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

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) = Radiusstd::cos(U), Y(U) = RadiusSin(U)
• for the ellipse E: X(U) = MajorRadiusstd::cos(U). Y(U) = MinorRadiusSin(U)
• for the hyperbola H: X(U) = MajorRadiusCh(U), Y(U) = MinorRadiusSh(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.

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

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

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

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

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.

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

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).

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).

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).

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.

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.