# 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.

``````// python_points_1 is a set of Points generated with
// a Python script found in Chapter 12, Section 10

surf = NurbsSurface.ByPoints(python_points_1);``````

### 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.

``````// python_points_1 is a set of Points generated with
// a Python script found in Chapter 12, Section 10

// create a surface of degree 2 with smooth segments
surf = NurbsSurface.ByPoints(python_points_1, 2, 2);``````

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

``````// python_points_1 is a set of Points generated with
// a Python script found in Chapter 12, Section 10

// create a surface of degree 6
surf = NurbsSurface.ByPoints(python_points_1, 6, 6);``````

### 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.

``````// python_points_2, 3, and 4 are generated with
// Python scripts found in Chapter 12, Section 10

c1 = NurbsCurve.ByPoints(python_points_2);
c2 = NurbsCurve.ByPoints(python_points_3);
c3 = NurbsCurve.ByPoints(python_points_4);

loft = Surface.ByLoft([c1, c2, c3]);``````

### 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.

``````pts = {};
pts[0] = Point.ByCoordinates(4, 0, 0);
pts[1] = Point.ByCoordinates(3, 0, 1);
pts[2] = Point.ByCoordinates(4, 0, 2);
pts[3] = Point.ByCoordinates(4, 0, 3);
pts[4] = Point.ByCoordinates(4, 0, 4);
pts[5] = Point.ByCoordinates(5, 0, 5);
pts[6] = Point.ByCoordinates(4, 0, 6);
pts[7] = Point.ByCoordinates(4, 0, 7);

crv = NurbsCurve.ByPoints(pts);

axis_origin = Point.ByCoordinates(0, 0, 0);
axis = Vector.ByCoordinates(0, 0, 1);

surf = Surface.ByRevolve(crv, axis_origin, axis, 0,
360);``````

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