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This was always something that puzzled me when I first started using Bryce, so I thought I would share this information with everyone. The basic Torus and Cylinder primitives always looked like they were just made for linking together to form curves and bends. But it is not immediately apparent just how to get them the same size to make a seamless connection. Now the secret is revealed.

We will start off and create just a basic Torus primitive and leave all the default settings as they are. This will give us a frame of reference later when we resize the Torus and want to create the right sized Cylinder with which to connect.

Here we have the basic Torus. Clicking on the [A] button brings up the Attributes to the primitive. Notice the Z size here, as this will be one of the dimensions needed to make the Cylinder.

Clicking on the [E] button will bring up the information for the internal diameter of the Torus. This diameter is needed to calculate the second part of the Cylinder. The value you want is the internal diameter divided by 50. I know, this isn't all that obvious, so here's a quick example:

256 / 50 = 5.12 Notice that this is the same value as the Z size above? Simple, once you see what the trick is.

Next we will create a basic cylinder and resize it to mate with the Torus. Nothing fancy here, just keeping it simple for now.

Using the values from the Torus, we'll resize the Z value to match the same from the Torus, and resize the X value to be the Torus internal diameter divided by 50.

Positioning the Cylinder to intersect the centerline of the Torus requires a few more simple calculations. For the X offset you take the radius of the Torus and subtract the internal diameter divided by 100.

As shown here, the radius of the Torus is 10.24 (half of the 20.48 diameter. And the internal diameter of 256 divided by 100 is 2.56, and thus 10.24 - 2.56 = 7.68

To calculate the Y offset, you simply take the Y origin value of the Torus, and subtract half of the Cylinder's Y length. 10.24 - (20.48/2) = 0.

A quick render then shows that the Torus and Cylinder are aligned properly and are ready for any additional boolean operations you may wish to apply.

What if you don't want to use the default size of the Torus? Just follow the same steps above and you'll have your primitives joined together in perfect harmony.

Here's a modified Torus to play with.

Remember the Z value of 7.

And we'll calculate the X value as 130 / 50 = 2.60

Plugging in all the numbers we calculated above, we get the right sized Cylinder to mate with the Torus. Calculating the position of the Cylinder follows the same steps as above.

Internal radius divided by 100, then subtracted from the main Torus radius gives us 10.24 - 1.30 = 8.94

And another quick render shows that everything is aligned properly as we expected.

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