When I noticed our cats really seemed to like the left over felt from my Kindle and laptop sleeve projects I decided to use it in a cat tree to replace the tiger striped abomination under our living room window.
Step 1: Inspiration
The felt is F-13 from Sutherland Felt. It's great stuff.
Step 2: The pillar
I started by creating a paper pattern and gluing it directly to the plywood close to the edges to conserve wood.
The inside corners were cut with a jigsaw leaving only straight cuts that were handled with the circular saw and a cutting guide. This initial piece serves as a pattern for the other two. Subsequent layers start out as rough cut pieces large enough to screw/glue the original onto with an overhang around all the edges. A flush trim router bit was then used to remove the excess wood.
Step 3: Platform layout
I wanted to make sure they were both directly over each other when assembled.
First I found the platform centers. To help with layout I aligned the platforms to the edge of the workbench. The pillar was positioned making certain the top and bottom edge of the pillar lined up with centerlines of the platforms. Then I just struck a line and used the pillar itself to layout the box where contact would occur.