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.

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

Creating a rational jug

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

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.
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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.

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.

Weight increased for the bottom face

Let's create a spout for the jug next.

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

Select one of the '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.

Weight of an edge increased
 

Defining weights through the property window

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

Set the 'Rational' check box in the property window.

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

Weight of the selected control 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 below:

Two opposite faces selected for the 'axis' hole

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.

 
'Subdivide' and 'Tunnel' 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.

Weights of two opposite edges increased

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.