.. role:: blue
   :class: blue


MbRuledSurface Ruled Surface
============================
.. _MbRuledSurface_Ruled_Surface_:

.. версия ядра: 1180ХХ


Class :blue:`MbRuledSurface` is declared in file *surf\_ruled\_surface.h*.

Ruled surface MbRuledSurface belongs to the group of swept surfaces MbSweptSurface. The ruled surface is defined by a curve :ref:`MbCurve3D <MbCurve3D_Curve_>` * **curve**, a curve :ref:`MbCurve3D <MbCurve3D_Curve_>` * **sline**, a flag of the presence of a pole of the surface at the initial value of the first parameter *poleMin*, a flag of the presence of a pole of the surface at the final value of the first parameter *poleMax*, the initial parameter *tmin* of curve **sline**, the derivative *dt* of the parameter of curve **sline** with respect to the parameter of curve **curve**, and the surface shape type *type*. The surface also has some additional data that are not mandatory and are used to speed up the work of the surface methods.

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 derivative *dt* is defined by

.. math::
   :nowrap:


   \begin{equation}
   \mathit{dt} = \frac{\mathit{tmax} - \mathit{tmin}}{\mathit{umax} - \mathit{umin}},
   \end{equation}


where *tmax* is the final parameter of curve **sline**. The surface can be periodic in the first parameter if curves **curve** and **sline** are 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 a point on curve **sline**. 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{sline}(t) \, w,
   \end{equation}


where


.. math::
   :nowrap:


   \begin{equation}
   w = \frac{v - \mathit{vmin}}{\mathit{vmax} - \mathit{vmin}}, \quad
   t = tmin + (u - umin) \cdot dt.
   \end{equation}


The ruled surface is shown in Fig. 1:


.. figure:: /MODELER/SURFACES/pictures/O.5.14.1.png
   :width: 12cm
   :align: center


   Fig. 1


Curves of the surface **s**\ (\ *const*\ , *v*\ ) with parameters *u* = const are straight-line segments. The surface may have a pole if one of the curves **curve** or **sline** is contracted to a point, or if curves **curve** and **sline** coincide at one of the ends.