There are many choices in dome construction. I chose to build a 3/8 3v dome to keep the complexity low. This is where the 'designed on a computer" part came into play.
First, I used a program called Dome Designer
to play with raw material lengths. It is very useful in calculating the amount of scrap that will be produced, and letting the user experiment with different dome frequencies and sizes. Unfortunately, it has a tendency to stop working, and then needs to be reinstalled in order to start again. Part way through the project, it stopped accepting my license key, and the creator never returned my emails. I wasn't about to spend another $100 on a program that doesn't work, so it was back to the web. In the end, everything I needed was online. The scrap length didn't matter on a dome this size anyway, so it was no loss.
The design tutorial that comes with Dome Designer was actually one of the most useful things I got out of my $100. In it, they point out that most domes are overbuilt. People making a house are used to using 2x12" boards, and think that it should naturally be the same with domes.
This is not the case. The stress that is put on dome struts is actually tension, instead of compression. Picture a drinking straw, standing vertically. Now put a stack of books on the straw. It immediately bends over and drops the load, breaking if it were something like wood. But what if you were to suspend the books from the straw? It could hold them until the end of time. This principle applies to domes, all of the force exerted on the struts is pulling,
That's why I built this dome out of 1" (which is actually 3/4" in the real world) sticks, weak and many cracked. I wanted to see if they could hold up. More on the results of that later.
These are the most useful online tools I used:
Desert Domes has a number of great resources, the Dome Calculator
and Reverse Dome Calculator
being my most used. It is helpful for figuring out the length and number of struts, and number of vertices needed for different frequencies of domes.
Then I used this diagram
Dome frequency is basically the number of triangles that exist in the dome. The higher the frequency, the stronger the dome, and the more complicated and more materials you will need. The one pictured is a 3v (frequency 3) 3/8 dome. The 3/8 means it is 3/8 of a sphere, so you can imagine just cutting the top 3/8 off a baseball, and that's what it will look like.