| | Describes a rational or non-rational Bezier surface.
- A non-rational Bezier surface is defined by a table
of poles (also known as control points).
- A rational Bezier surface is defined by a table of
poles with varying associated weights.
This data is manipulated using two associative 2D arrays:
- the poles table, which is a 2D array of gp_Pnt, and
- the weights table, which is a 2D array of reals.
The bounds of these arrays are:
- 1 and NbUPoles for the row bounds, where
NbUPoles is the number of poles of the surface
in the u parametric direction, and
- 1 and NbVPoles for the column bounds, where
NbVPoles is the number of poles of the surface
in the v parametric direction.
The poles of the surface, the "control points", are the
points used to shape and reshape the surface. They
comprise a rectangular network of points:
- The points (1, 1), (NbUPoles, 1), (1,
NbVPoles) and (NbUPoles, NbVPoles)
are the four parametric "corners" of the surface.
- The first column of poles and the last column of
poles define two Bezier curves which delimit the
surface in the v parametric direction. These are
the v isoparametric curves corresponding to
values 0 and 1 of the v parameter.
- The first row of poles and the last row of poles
define two Bezier curves which delimit the surface
in the u parametric direction. These are the u
isoparametric curves corresponding to values 0
and 1 of the u parameter.
It is more difficult to define a geometrical significance
for the weights. However they are useful for
representing a quadric surface precisely. Moreover, if
the weights of all the poles are equal, the surface has
a polynomial equation, and hence is a "non-rational surface".
The non-rational surface is a special, but frequently
used, case, where all poles have identical weights.
The weights are defined and used only in the case of
a rational surface. This rational characteristic is
defined in each parametric direction. Hence, a
surface can be rational in the u parametric direction,
and non-rational in the v parametric direction.
Likewise, the degree of a surface is defined in each
parametric direction. The degree of a Bezier surface
in a given parametric direction is equal to the number
of poles of the surface in that parametric direction,
minus 1. This must be greater than or equal to 1.
However, the degree for a Geom_BezierSurface is
limited to a value of (25) which is defined and
controlled by the system. This value is returned by the
function MaxDegree.
The parameter range for a Bezier surface is [ 0, 1 ]
in the two parametric directions.
A Bezier surface can also be closed, or open, in each
parametric direction. If the first row of poles is
identical to the last row of poles, the surface is closed
in the u parametric direction. If the first column of
poles is identical to the last column of poles, the
surface is closed in the v parametric direction.
The continuity of a Bezier surface is infinite in the u
parametric direction and the in v parametric direction.
Note: It is not possible to build a Bezier surface with
negative weights. Any weight value that is less than,
or equal to, gp::Resolution() is considered
to be zero. Two weight values, W1 and W2, are
considered equal if: |W2-W1| <= gp::Resolution()
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1.6.3