MbSectorSurface Sectorial Surface

Class MbSectorSurface is declared in file surf_sector_surface.h.

Sectorial surface MbSectorSurface belongs to the group of swept surfaces MbSweptSurface. The sectorial surface is defined by a curve MbCurve3D curve and a point MbCartPoint3D origin.

The first parameter of the surface u coincides with the parameter of curve curve. The first parameter of the surface takes values on the segment umin ≤ u ≤ umax, which corresponds to the domain of curve curve. The surface can be periodic in the first parameter if curve curve is periodic.

The second parameter of the surface v takes values on the segment vmin ≤ v ≤ vmax. Value v = vmin corresponds to a point on curve curve, and value v = vmax corresponds to point origin. The surface cannot be periodic in the second parameter.

In method PointOn( double u, double v, MbCartPoint3D & s ) the radius vector of the surface s is described by the vector function

\begin{equation} \mathbf{s}(u, v) = \mathbf{curve}(u) (1 - w) + \mathbf{origin} \, w, \end{equation}

where

\begin{equation} w = \frac{v - \mathit{vmin}}{\mathit{vmax} - \mathit{vmin}}. \end{equation}

The sectorial surface is shown in the figure:

Curves of the surface s(const, v) are straight-line segments. The surface has a pole at point origin for v = vmax. Sectorial surface is a special case of a ruled surface.