MbContourOnSurface Contour on Surface

The MbContourOnSurface class is declared in the cur_contour_on_surface.h file.

A contour on surface MbContourOnSurface is defined by a surface MbSurface surface and a two-dimensional contour MbContour contour in the surface parameter space. The curve also contains some additional data that is not mandatory and is used to speed up the work of the curve methods.

A contour on a surface is a composite curve, therefore it may have breaks at the junction points of the segments of the two-dimensional contour. A contour on the surface represents a mapping of a contour from the two-dimensional surface parameter space into three-dimensional space. The two-dimensional contour contour may lie outside the domain of the surface parameters. The parameter domain of the contour on the surface coincides with the parameter domain of the two-dimensional contour contour.

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

\[\mathbf{r}(t) = \mathbf{surface}(\mathbf{point}.x, \mathbf{point}.y),\]

where point is a point of the two-dimensional contour that is calculated by the contour → PointOn( t, point ) method. The x and y coordinates of the two-dimensional point point serve as the u and v parameters of the surface surface( u, v ). A contour on the surface is constructed by introducing a dependence of the surface parameters u and v on a common parameter t: u = u( t ), v = v( t ). This dependence is defined by the two-dimensional contour contour. The derivative of a contour on a surface is computed as a composite function

\[\frac{\mathit{dr}(t)}{\mathit{\text{dt}}} = \frac{\partial\mathbf{\text{surface}}(u,v)}{\partial u}\mathbf{\text{derive}}\text{.}{x + \frac{\partial\mathbf{\text{surface}}(u,v)}{\partial v}}\mathbf{\text{derive}}\text{.}y,\]

where derive is the derivative of the two-dimensional contour that is calculated by the contour → FirstDer( t, derive ) method. The derivative of the contour on the surface lies in the tangent plane of the surface constructed at the point under consideration.

A contour on the surface is shown in the figure:

A contour on a surface can be periodic if the two-dimensional contour contour is periodic or if the surface surface is periodic and the end points of the contour contour are shifted by the corresponding period of the surface that is periodic in the first or second parameter surface.

A periodic contour on a surface is usually used to describe the boundary of this surface.

The surface surface of a contour on a surface can be any surface except for a surface bounded by curves MbCurveBoundedSurface. If a contour on a surface bounded by curves needs to be constructed, then the base surface MbCurveBoundedSurface is used as the surface.