Polyline MbPolyline3D

The MbPolyline3D class is declared in the cur_polyline3d.h file.

The polyline is derived from the MbPolyCurve3D curve. The MbPolyline3D polyline is defined by the number of segments segmentsCount, the set of control points SArray<MbCartPoint3D> pointList and the curve periodicity flag closed.

The curve passes through the set of points pointList[i], i = 0,…, segmentsCount, at parameter values t = 0,…, segmentsCount. If closed = true, then the curve contains a segment connecting the last point of the set pointList[segmentsCount - 1] with the first point pointList[0]. The curve parameter t takes values on the interval 0 ≤ t ≤ segmentsCount.

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

\[\mathbf{r}(t) = \mathbf{pointList}[i] \cdot (1 - w) + \mathbf{pointList}[i + 1] \cdot w,\]

where

\[w = \frac{t - t_{i}}{t_{i+1} - t_{i}},\]

and t_i ≤ t ≤ t_i+1. The polyline is the simplest curve constructed from a set of points. It consists of segments that consecutively connect the control points.

The polyline is shown in the figure:

The curve may be periodic. The period of a periodic curve is equal to segmentsCount. The derivatives of the curve at the control points (for integer parameter values) lose continuity in length and direction. The derivatives of the curve at the control points have a specific direction and length. The polyline has a number of useful properties: it requires a minimum of computations, and the projection of a polyline is also a polyline.