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Interpolation / Fitting /ByControlPts

NURBS are non-uniform rational B-splines.

NUBS is a kind of polynomial piecewise curve, defined by a degree, a control polygon and a knot vector.

The degree is the polynomial degree.

The control points are a set of points that the curve approximates smoothly. Usually the curve pass through the first and last control point.

The knot vector is a vector of increasing real numbers (from 0 to 1 in GiD) that divides the parametric space in the intervals.

A NURBS (with 'R') could also have rational weights, an extra real value by control point. The curve approximate more closely the control points with bigger relative weight values. Rational NURBS are a quotient between two polynomials, this allow to mathematically describing conical curves like circumferences or ellipses in an exact way.

There are three ways of creating a NURBS line from series of points using this command:

Interpolation (default option): the NURBS will be a cubic polynomial calculating the control polygon and knots in such a way that the curve pass through all the user points.

Fitting: Similar to the interpolation case, but the curve will not exactly interpolates the user points, only approximate them by a 'minimum squared' criteria. The degree of the curve must be set before the curve calculation.

ByControlPts: Directly defines NURBS setting its degree and control polygon. The shape of the curve is similar to the control polygon, but it does not interpolate the polygon points.

During the session the selected method become the current one until it is changed again.

All the NURBS creation options are available from the contextual menu during the curve creation or from the Right buttons toolbar

The messages showed in the command line will orientate the user about the required parameters on each case.

When defining interpolating curves, you can choose to explicitly define the tangents to one or both ends (using the Tangents option). These tangents can be customized, in that they can either be defined by picking their direction on the screen or by considering an existing line as a tangent to the NURBS if it follows a previous curve (the option ByLine). The Next option allows only one tangent to be defined.

In this way, it is possible to create a closed NURBS by selecting the initial point as the end one and choosing one of the options 'Tangent', 'Next', or 'ByLine'.

The Undo option undoes the creation of the last point; this can be done all the way back to the first point.

When a NURBS has been created, all the interior points (except the first and last) are temporary points, not really entity points unless they previously existed.

To enter rational weights on the curve, the Edit NURBS line/surface command (see Edit NURBS) can be used.

Surface constant: This option allow the creation of a curve on a parametric surface setting the parameter u or v to a constant value specified by the user.

It is possible to create also NURBS curves from the Copy window, be extrusion of points with a transformation of translation or rotation, this allow the creation of straight lines and arcs respectively.

NURBS line creationCreate NURBS line