Rotational Surfaces

Objects with a circular cross section can be constructed from two NURBS curves: an axis of rotation and a profile curve. We use the classical example of creating a wine glass for the demonstration.

1. Use the NURBS/Curve tool to create a vertical line in the view window. The length of the line does not matter, except that a long line is helpful when drawing the glass profile. Rename it to 'axis curve'.

2. Create another curve representing a suitable wine glass profile. Rename it to 'profile curve'.

3. Multi-select the curves using the Shift key, the axis curve first, and the profile curve next.

An axis curve and a profile curve

4. The control bar now shows you the tools, which can be applied to the selected curves. Select the Rotate tool.

Rotate tool

The Rotate tool takes the first selected curve as an axis of rotation and the second curve as a profile curve.

If you accidentally selected the curves in the wrong order (in which case the tool rotates the axis about the profile curve), simply select the curves in the correct order again. There is no need to restart the tool.

5. The default options are fine for this example - just click 'Accept'.

A wine glass

Editing the construction curves

NURBS mesh construction tools allow you to access the original construction curves and edit them in order to modify the shape of the mesh. For example, let's assume that the profile of the glass is not exactly what you expected and you need to make the wine glass slimmer.

1. In the select window, click the '+' handle of the created NURBS mesh object. You can now see that the NURBS mesh includes two sub objects - the curves you used to create the wine glass in the first place.

The hierarchical structure of the wine glass
Control points of the profile curve modified

2. Select the profile curve and enter the 'Edit' mode (press Space bar) to access the control points of the curve. Modify the profile curve. The shape of the wine glass is updated with the curve.

[Note] Note
In addition to moving points, you can add new points, delete existing points, add sharp edges, and so on. You can even replace the entire profile curve with another curve to rebuild the shape of the glass. If you model wine glasses a lot, you may build a library of profile curves. Just drag & drop the desired profile curve inside a wine glass mesh to get a desired wine glass constructed!

[Note] Note
You might want to control the 'Forced visibility' attribute of the NURBS curves when working with the shaded OpenGL mode. This attribute makes the curves visible even if there they are hidden by the actual surface of the wine glass. The higher the 'forced visibility', the better they can be seen. You can access this option in the property window's 'Wire' tab.

Tutorial project: 'tutorprojects\modeling\nurbs\rotate\wine glass'

Torus

A torus surface can be created by rotating a NURBS circle about an axis.

Tutorial project: 'tutorprojects\modeling\nurbs\torus.r3d'

Rotate a circular curve about an axis to get a torus

Sphere

Rotating a semi circle about an axis creates spheres and ellipsoids.

Tutorial project: 'tutorprojects\modeling\nurbs\rotate\sphere'

Rotate a semi circle about an axis to build a sphere

Interactive Method

The Nurbs Curve tool's Pen option allows you to create rotated surfaces interactively.

1. Create or select a NURBS curve representing an axis. Note: the axis curve does not have to be a straight line. Any curve will do.

2. Activate the NURBS/Curve tool and set the 'Pen' option to 'Rotate'.

Set the Pen option to Rotate

3. Enter points for the curve as usual. New curve points are rotated about the selected 'axis' curve while you enter them.

Tutorial project: 'tutorprojects\modeling\nurbs\rotate\banana'

Create a banana with the Rotate pen

Scale curve

If only two curves are selected, the rotation tool rotates the second curve about the first curve. A third curve can be selected to control the properties of the mesh in its 'v' direction.

A side view of the axis and the profile

For example, to create a vase with a non-circular cross section:

1. Create an axis and a profile curve from the side view.

2. Switch to the top view and create a closed scaling curve.

The axis, the profile and the scale curves created

3. Select the axis, profile and scale curves (in this order) and click the Rotate tool in the control bar. Then click 'Accept' to finish the mesh construction.

Tutorial project: 'tutorprojects\modeling\nurbs\rotate\vase'

A non-circular vase

If the scale curve is open, also the mesh is open in the corresponding direction. By using a 'helix' for the scale curve, one can create screws and other objects with a spiral shape.

Tutorial project: 'tutorprojects\modeling\nurbs\rotate\open scale curve'

A circle arc used as a scale curve

Controlling the order of the surface

Let's create another banana.

1. Create two NURBS curves: a slightly bent axis curve and a profile curve. However, this time, make the profile curve polygonal by setting the 'Order' option of the Nurbs Curve tool to 'Polygonal'.

Rotate a polygonal profile curve
Polygonal curve rotated

2. Select both curves: first the axis curve and then the polygonal profile curve. Activate and accept the Rotate tool.

The result is a mesh, which is polygonal in the 'v' direction and cubic in the 'U' direction.

Tutorial project: 'tutorprojects\modeling\nurbs\rotate\polygonal profile'

We can also create a banana, which is polygonal in its closed direction but smooth in the axis direction. The Rotate tool provides the necessary controls for this.

1. Create two smooth cubic NURBS curves: a bent axis and a profile for the banana.

Rotation controls, which determine mesh properties in the direction of rotation

2. Select the curves and activate the 'Rotate' construction tool as shown above. The control bar now shows you the rotation specific options.

3. Set Order to Polygonal and click Accept.

Polygonal rotation

When using a 'scale' curve, the order of the mesh is fetched from it. For example, the following image demonstrates a combination of a cubic profile curve and a polygonal scale curve.

A cubic profile and a polygonal scale curve. The mesh is polygonal in the direction of the scale curve.