On a curve, a minimum of 4 CVs are needed to create the curve. Adding more CVs means that the curve can have a more complex shape.
Construction history means that you can modify the shape of a surface by changing the curves it was built from.
Alternatively, you can turn on the CV display for the surface and modify the surface CVs directly to change the surface shape.
The Control Panel can be used to display or hide the CVs of a curve or surface.
It is good practice to turn off the CVs on objects that aren't being modified, to reduce the complexity of the view on the screen.
You have already used CVs to create and shape curves. Surfaces also have CVs which can be used in the same way to directly modify the surface shape.

Modeling Workflow
In this tutorial you will use a modeling technique called overbuilding and trimming. With this technique, you will create simple swept surfaces to define the main shape of the design. You will then combine these surfaces using intersecting and trimming.

A common way to combine NURBS surfaces is to intersect the surfaces and then trim them where the two surfaces cross each other. This is the approach you will take with the upper and lower surfaces of the vacuum cleaner
First, you will intersect the surfaces. When you intersect surfaces, you create curves-on-surface, which are lines that are created on the surfaces where the surfaces intersect. You will then trim the intersecting surfaces along the curves-on-surface, so that the unnecessary surface areas are discarded, and only the necessary surface areas remain.
To create a rounded transition between the two surfaces, you will create a fillet surface using the Surfaces > Surface fillet tool.
The surface fillet tool will create a rounded surface that blends smoothly between two surfaces, or two sets of surfaces. As well as creating the rounded surface, the Surface Fillet tool can also trim back the original surfaces to create a finished continuous form. This trimming is achieved using curves-on-surface which are automatically created by the Surface Fillet tool.
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