As described in Creating NURBS Curves, NURBS curves can be created by interpolation points or control points. Similarly, a NURBS surface can be created by interpolation points. An interpolated surface is a NURBS surface that passes through a two-dimensional array of 3D interpolation points. Regular NURBS surfaces are defined by their control points, which may not lie on the surface and can be difficult to use for reshaping the surface (it is difficult to know how much the control point should be moved in order to reshape the surface by a specific distance). Because interpolation points lie on the surface, it is much easier to modify these points with the Reshape tool or the Object Info palette, and have the surface pass through the points.
An interpolated surface can be created, or an existing untrimmed NURBS surface can be converted to an interpolated surface, for easier reshaping.
When an interpolated surface is used in another operation, such as a Boolean operation or trimming, the surface becomes a control point surface.
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