Not being overly experienced in modelling with nurbs, I went looking for advice/tutorials to model a car tyre. I didn't have a lot of luck. This led me to try things for myself and in the end I came up with the method in this tutorial. The result is a car tyre modelled entyrely with nurbs that isn't too heavy on geometry (early attempts had my reasonably high spec machine struggling).

The focus of this tutorial will be modelling of the tread. Examples will be kept relatively simple with the creation of more elaborate tread patterns left up to the reader. Modelling of the tyre side walls will be given only a very basic treatment.

In order to get the desired result, I had to think about producing a repeatable section of the tread that I could then duplicate over 360 degrees. To get this result, I started by asking myself how many times I wanted to repeat the tread on the tyre and how much groove I wanted between each tread. It's important to choose numbers that divide nicely into 360 degrees here (otherwise you end up with rounding problems when you create the tread section duplicates)

In our example, we'll select 48 treads around the tyre and a groove that's one quarter of the size of the tread. To explain how these numbers work, we consider the following:

     360 degrees / 48 treads+grooves = 7.5 degrees per tread-groove
        (this includes a groove on one side of the tread)

Now out of that 7.5 degrees we have a four to one ratio of tread to groove. In other words, the groove occupies one fifth of the 7.5 degrees and the tread occupies four fifths of the 7.5 degrees.$nbsp;So:

     7.5 degrees * 1/5 = 1.5 degrees per groove

     7.5 degrees * 4/5 = 6 degrees per tread

As you can see, these are nice numbers with no repeating decimals. You want this!

The last part of planning is to decide how tall and wide the tyre will be and how deep the grooves will be. In this example I'm going to choose the following:

     Tyre Radius = 5 units.

     Tyre Width = 4 units.

     Groove depth crossing the tyre = 0.1 units.

     Groove depth around the tyre = 0.2 units.

OK so now we'll start getting down to business. The first step is to lay out some basic geometry that we'll use to create the curves we need for the piece of repeatable tread. Create:

     A nurbs cylinder: axis x, radius 5, height 4, sections 8, spans 1.

     A nurbs cylinder: axis x, radius 4.9, height 4, sections 8, spans 1.

     A nurbs cylinder: axis x, radius 4.8, height 4, sections 8, spans 1.

     A nurbs circle: normal axis y, sweep angle 180, radius 2, section 4.

Assign each one of these to its own layer (just makes it easier).

Rotate the circle 90 degrees around the y-axis and then freeze transformations. You should end up with what I have in this screenshot.

Notice that the largest cylinder is the same radius as we want our tyre and the other cylinders correspond to the groove depths we chose above.

Now we'll want to switch to the top view and change to CV editing for the circle. Using the scale tool, bring in the highlighted CV's to start the shape of the tread pattern:

Still in the top view and with grid snap activated, use the edit point tool to create a single span curve as shown. We'll be duplicating this to create construction for the grooves that run around the tyre:

Move the curve that we just created 0.1 units in the x direction. Next, reset the duplicate tool and then use CTRL+d to duplicate the curve. Translate this duplicate so that it's 0.9 units from the original position of the original curve. Create more duplicates in the same fashion and translate them until there is one at:

     0.1, 0.9, 1.1, 1.9, 2.1, 2.9, 3.1 and 3.9.

The results are shown highlighted here:

Add these curves to the same layer as the circle and then freeze transforms and clear history on everything we've created so far.

Hide the layers that contain the inner and middle cylinders. You should just have the outer cylinder and all of the curves showing.

Select all of the curves (circle included) and then shift+click the cylinder. Make sure you're in the TOP view. In the modelling menu set, select Edit NURBS -> Project curve on surface (make sure the tool has been reset).

The result should be as shown:

Hide the outer cylinder and then repeat these steps for each of the other cylinders.

Hide all the layers except the one for the outer cylinder. Select all of the curves shown and then choose Edit Curve -> Duplicate Surface Curves.

Hide the outer cylinder layer, select all of the remaing curves, delete their history and assign them to their own layer. Hide this layer.

Repeat these steps for the middle and inner cylinders placing the resulting curves on separate layers.

Unhide all of the layers for the curves we just duplicated off our construction surfaces. From the menu choose Display -> Nurbs smoothness -> Fine

Hide the middle and inner curve layers so that only the outer curve layer is displayed. Deselect everything and then select only these curves. From the menu choose Edit Curves -> Cut Curve.

Delete all curves so that you only leave the curves shown in the screenshot (note that the remaining curves is a set of a number of small curves):

Assign these back to the outer curve layer (they get pulled out when you cut them).

Repeat for the middle and inner curves.

Make a duplicate of the inner curves and assign them to the outer curves layer.

Select the original inner curves and assign them to the middle curves layer.

Make only the outer curves layer visible.

Delete curve pieces leaving those shown in the screenshot (inner curves are highlighted and outer curves are not).  Repeat by hiding the outer curves layer and showing the middle curves layer:

Hide the middle curves layer, display the outer curves layer and select all of the curves. From the menu, choose Display -> Nurbs components -> Edit points.

Using the edit point curve tool and point snapping, create a curve that bridges between two of the existing sections:

Repeat bridging sections of curve until you end up with the curves in the screenshot. Also delete the small original curves at the end (we don't need them). Add all of these new curves to the outer curves layer and then repeat for the middle curves layer:

Show the outer curves layer again. Select the first two curves at one end. From the menu, choose Edit Curves -> Attach Curves -> []. Choose Edit -> Reset settings and then switch to Connect mode, select Keep knots and untick Keep Originals. Click Attach.

The new attached curve is selected. Shift+click the next in line and press G to repeat the last command (attach). Continue this way until you've attached all the curves in this layer (see screenshot).

Repeat for the middle layer curves.

Make both the outer layer curves and the middle layer curves layers visible. Select both of the curves and freeze transformations followed by deleting history.

Now we refer back to our planning again. The tread + groove was going to cover 7.5 degrees. Select the outer curve and duplicate it. Rotate the new duplicate around the x-axis by 7.5 degrees,

The groove is going to be 1.5 degrees. We'll set this up at the front as we're looking at it in the perspective view. 7.5 - 1.5 is 6 degrees. Make another duplicate of the original outer curve and rotate it 6 degrees.

So that the final lofted surface preserves the original curve of the cylinder, make another duplicate of the same curve and rotate it by 3 degrees (half way between the back and front of the tread).

We now have 3 duplicates rotated by 7.5, 6 and 3 degrees as well as the original outer curve.

Rotate the middle curve by 6.1 degrees and then make a duplicate rotated to 7.4 degrees (slightly more and less than the edges of the groove).

We're now going to loft 4 separate surfaces from our curves. Clear the selection and then shift+click the back three curves from back to front. From the menu choose Surfaces -> Loft. Create a new layer, assign this surface to the layer and hide it.

Loft another surface for the back of the groove between just two curves - the outer curve at the front of the last selection and the middle curve towards the back. Add this to the hidden surfaces layer.

Repeat to produce the surface at the bottom of the groove (using the two middle curves) and then finally, to produce the front of the groove.

Hide the outer and middle curve layers and show the surfaces layer. It should look something like the following:

Select the rear two surfaces and from the menu choose Edit Nurbs -> Attach Surfaces -> []. Reset the tool and then select the Connect Method, to Remove knots and not to Keep Originals. Click Attach.

Shift+click the surface at the base of the groove and choose Edit Nurbs -> Attach Surfaces. Repeat one last time so that there is just one surface comprised of the original four.

The tread section is complete. All that remains is to duplicate it to form a complete tire and add the side walls

With the tread section still selected, choose Edit -> Duplicate -> []. Set an x-rotation of 7.5 degrees and the number of copies to 47 (360 / 7.5 - 1). Click Duplicate to get the result shown.

Create a side wall by lofting three circles - x-axis normal, 8 sections, the largest with a 4.81 radius. Put a mirrored duplicate on the other side.

Enjoy - MrR