MbPlaneCurve Plane Curve

The MbPlaneCurve class is declared in the cur_plane_curve.h file.

The MbPlaneCurve plane curve is defined by a local coordinate system MbPlacement3D position and a two-dimensional curve MbCurve curve lying in the XY plane of the local coordinate system.

A plane curve represents a mapping of a curve in the two-dimensional space of the XY plane of the local coordinate system into three-dimensional space.

In the PointOn(double & t, MbCartPoint3D & r) method, the radius vector r of the curve is described by the vector function

\[\mathbf{r}(t) = \mathbf{position.origin} + \bigl(\mathbf{point}.x \cdot \mathbf{position.axisX}\bigr) + \bigl(\mathbf{point}.y \cdot \mathbf{position.axisY}\bigr),\]

where point is a point of the two-dimensional curve computed by the curve-> PointOn(t, point) method.

A plane curve as part of a two-dimensional ellipse and a local coordinate system is shown in the figure:

The domain of the parameters and the periodicity of the plane curve coincide with the parameter domain and periodicity of the two-dimensional curve.