.. role:: blue
   :class: blue


MbSectorSurface Sectorial Surface
=================================
.. _MbSectorSurface_Sectorial_Surface_:


.. версия ядра: 1180ХХ


Class :blue:`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 :ref:`MbCurve3D <MbCurve3D_Curve_>` **curve** and a point :ref:`MbCartPoint3D <MbCartPoint3D_Radius_Vector_of_Point_in_3D_Space_>` **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 :blue:`PointOn`\( double *u*, double *v*, :ref:`MbCartPoint3D <MbCartPoint3D_Radius_Vector_of_Point_in_3D_Space_>` & **s** ) the radius vector of the surface **s** is described by the vector function


.. math::
   :nowrap:


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


where


.. math::
   :nowrap:


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


The sectorial surface is shown in the figure:


.. figure:: /MODELER/SURFACES/pictures/O.5.13.1.png
   :width: 12cm
   :align: center


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.