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Manual - Blender 2.40

[edit] Surfaces

Surfaces are actually an extension of NURBS curves but are still a unique object unto themselves. Whereas a curve produces only one-dimensional interpolation, Surfaces have a second extra dimension of interpolation. The first dimension is U, as for curves, and the second dimension is V.

You may ask yourself “but the surface appears to be 3D, why is it only 2D?”. In order to be 3D the object needs to have “Volume” and a surface doesn’t have a volume, it is infinitely thin. If it has a volume the surface would have a thickness. Even though the surface appears to extend in 3D, it has no volume, and hence it only has two interpolation coordinates, U and V. U is the Yellow grid lines and V is the pink grid lines in (Surface).

Many of the concepts from NURBS curves carry directly over to NURBS Surfaces, such as control-points, Order, Weight, Resolution, etc.

For NURBS Surfaces the control-points form a grid and is sometimes called a “Cage”. The grid performs exactly like the control-points of a NURBS curve; they control the boundary of the surface.

To help get started in creating surfaces there are four preset NURBS Surfaces: (Surface), (Tube), (Sphere) and (Donut).

Surface.	Tube.
Sphere.	Donut.

Each preset is accessible from the Add → Surface sub-menu of the Toolbox menu where each is designed as a starting point for creating more complex surfaces, of which the most common starting surface is NURBS Surface.

There are also two preset NURBS Surface Curves: (Curve) and (Circle).

Curve.

Circle.

Although they visually look like NURBS curves they are not. Blender internally treats NURBS Surface Curves and NURBS Curves completely differently. There are several attributes that separate them but the most important is that a NURBS Curve has a single interpolation axis and a NURBS Surface Curve has two interpolation axes.

Visually you can tell which is which by entering Edit mode and looking at the 3D window’s header; either the header shows “Surface” or “Curve” as one of the menu choices. Also, you can Extrude a NURBS Surface Curve to create a surface but you can’t with a NURBS Curve.

Use Surfaces to create and revise fluid curved surfaces. Surfaces can be cyclical in both directions, allowing you to easily create a Donut shape, and they can be drawn as “solids” in Edit mode. This makes working with surfaces quite easy.

[edit] Uniform-Endpoints

Just like with NURBS curves, NURBS Surfaces have a knot vector and the configuration of the knot values are controlled by the Uniform and Endpoint buttons. Each interpolation axis can be independently set to either Uniform or Endpoint.

Endpoint U.

In (Endpoint U), the U interpolation axis is labelled as “U” and the V interpolation axis is labelled as “V”. The U’s interpolation axis has been set to Endpoint and as such the surface now extends to the outer edges from “E1” to “E2” along the U interpolation axis.

To cause the surface to extend to all edges you would set the V’s axis to Endpoint as well.

[edit] Order

As with NURBS Curves, Order specifies how much the control-points are taken into account for calculating the curve of the surface shape. For high Orders, (Order 4 surface), the surface pulls away from the control-points creating a smoother surface – assuming that the Resolution is high enough. For low Orders, (Order 2 surface), the surface follows the control-points creating a surface that tends to follow the grid cage.

Order 2 surface.

Order 4 surface.

For illustration purposes, in both (Order 4 surface) and (Order 2 surface), the knot vectors were set to Endpoint causing the surface to extend to all edges.

[edit] Weight

Surface Weight 100.

Again, as with NURBS Curves, Weight specifies how much each control-point “pulls” on the curve.

In (Surface Weight 100), a single control-point, labelled “C”, has had its Weight set to 100.0 while all others are at their default of 1.0. As you can see that control-point pulls the surface towards it.

If all the control-points have the same Weight then each effectively cancels each other out. It is the difference in the Weights that cause the surface to move towards or away from a control-point.

The Weight of any particular control-point is visible in the Transform Properties panel which is accessed using the N.

See NURBS Curves Weight for further details.

[edit] Preset Weights

A sphere surface.

NURBS can create pure shapes such as circles, cylinders, and spheres (note that a Bézier circle is not a pure circle). To create pure circles, globes, or cylinders, you must set to specific values the weights of the control-points. This is not intuitive, and you should read more on NURBS before trying this.

Basically, to produce a circular arc from a curve with three control-points, the end points must have a unitary weight, while the weight of the central control point must be equal to one-half the cosine of half the angle between the segments joining the points. Lets take an example: if you have three control-points creating a right angle, to get a quadrant, you would set the centre point’s weight to cos(90/2)/2 = cos(45)/2 = sqrt(2)/4 ≃ 0.354. This is the same principle for (A sphere surface) – you’ll note that the four different weights needed for creating a sphere (1.0, 0.707 = sqrt(0.5), 0.354 = sqrt(2)/4, and 0.25) are the four presets available in the Curve Tools panel…

[edit] Resolution

Just like NURBS Curves, Resolution controls the detail of the surface. The higher the Resolution the more detailed and smoother the surface is. The lower the Resolution the rougher the surface.

(Resolution 4×4 surface) is an example of a surface resolution of 4 for both U and V. (Resolution 20×20 surface) is an example of a surface resolution of 20 for both U and V.

Resolution 4×4 surface.

Resolution 20×20 surface.

For illustration purposes the knot vectors where set to Endpoint causing the surface to extend to all edges.

Manual

[edit] Subpages

1. Editing
2. Skinning