Rational Subdivision Surfaces

Rational subdivision surfaces introduce a new parameter called 'weight'. The higher the weight, the stronger the control point affects the surface.

You can turn any SDS object into its rational version by dragging points, edges or faces with the left mouse button while holding down the Alt key. By moving the mouse up, you can increase the weight. By moving the mouse down, you can decrease the weight.

The following image demonstrates the effect of changing the weight of the apex of a pyramid.

In the next tutorial we create a simple 'jug' object which demonstrates the power of rational SDS surfaces.

Weights from left to right: 0.1, 1, 10, 100

1. Switch to the top view and create a SDS cube of the resolution 2x2x4 (click the SDS/Cube tool and enter U=2, V=2,W=4 through the control bar). Switch to the face mode and subdivide and extrude the top face as shown below. We have created so many cups by now that we don't need to repeat the detailed steps here anymore.

A SDS cube with 2x2x4 control points
The top face subdivided and extruded inside the cube

The first problem is that our jug has a pretty round base and it wouldn't be able to stand on a table. We could subdivide or bevel the bottom face to get it more 'flat'. However, increasing the weight of the bottom face has the same effect.

2. Select the bottom face.

Bottom face weight increased

3. Press down the Alt key and drag the bottom face with the left mouse button. Drag upwards a couple of times until the desired sharpness is achieved.

Let's create a spout for the jug next.

Select one of the top face edges
Weight of an edge increased

4. Switch to the edge mode and select one of the diagonal 'top face' edges.

5. Zoom in so that you can clearly see the edge and drag the edge with the left mouse button while holding down the Alt key. Instead of moving the edge, the weight of the edge is modified. Drag up to increase the weight until the desired sharpness for the spout is achieved.

Defining weights through the property window

You can also make the surface rational by setting the Rational checkbox in the Property Window/Spec tab.

You can then select any of the control points, edges or faces and define the desired weight through the Weight field.

Set the Rational check box in the property window
Weight of the selected point increased

Top face with different weights

Create a propeller

In this tutorial we demonstrate weights by creating a very simple propeller.

1. Create a SDS cube consisting of 6x2x2 control points.

Options for creating a 6x2x2 SDS cube
6x2x2 SDS cube

2. Enter the face editing mode and select two faces as shown in the figure:

3. Subdivide the selected faces (for example, hold down the Ctrl key while dragging an end point handle of a face normal). Then click the Tunnel tool to drill a hole for the screw shaft.

Two opposite faces selected for the 'axis' hole

Subdivide and Tunnel tools applied

4. Switch to the edge mode and select two opposite edges at both ends of the screw. Then open the property window, set 'Rational' check box and enter the value 5 to the 'Weight' field.

5. Repeat the step 4 at the other end of the propeller, but this time use the other edge pair to twist the shape to the opposite direction.

Weights of two opposite edges increased