# Surfaces: Interpolated, Control Points, Loft, Revolve

The two-dimensional analog to a NurbsCurve is the NurbsSurface, and like the freeform NurbsCurve, NurbsSurfaces can be constructed with two basic methods: inputting a set of base points and having Dynamo interpolate between them, and explicitly specifying the control points of the surface. Also like freeform curves, interpolated surfaces are useful when a designer knows precisely the shape a surface needs to take, or if a design requires the surface to pass through constraint points. On the other hand, Surfaces created by control points can be more useful for exploratory designs across various smoothing levels.

### Interpolated Surface

To create an interpolated surface, simply generate a two-dimensional collection of points approximating the shape of a surface. The collection must be rectangular, that is, not jagged. The method *NurbsSurface.ByPoints* constructs a surface from these points.

### Control Points Surface

Freeform NurbsSurfaces can also be created by specifying underlying control points of a surface. Like NurbsCurves, the control points can be thought of as representing a quadrilateral mesh with straight segments, which, depending on the degree of the surface, is smoothed into the final surface form. To create a NurbsSurface by control points, include two additional parameters to *NurbsSurface.ByPoints*, indicating the degrees of the underlying curves in both directions of the surface.

We can increase the degree of the NurbsSurface to change the resulting surface geometry:

### Loft Surface

Just as Surfaces can be created by interpolating between a set of input points, they can be created by interpolating between a set of base curves. This is called lofting. A lofted curve is created using the *Surface.ByLoft* constructor, with a collection of input curves as the only parameter.

### Revolve Surface

Surfaces of revolution are an additional type of surface created by sweeping a base curve around a central axis. If interpolated surfaces are the two-dimensional analog to interpolated curves, then surfaces of revolution are the two-dimensional analog to circles and arcs.

Surfaces of revolution are specified by a base curve, representing the “edge” of the surface; an axis origin, the base point of the surface; an axis direction, the central “core” direction; a sweep start angle; and a sweep end angle. These are used as the input to the *Surface.Revolve* constructor.

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