What is everyone excited for??? More math! Ok, maybe not, but I’ll come back to the electronics projects later (including investigating the Parallax RFID reader, Arduino FIO, and heck, maybe even some more LED fun). In the meantime, let’s get back to math.
What do the volume calculations look like, and how would one go about calculating the center of mass/geometric centroid of a spherical plot? More after the break…
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My current research at Rutgers focuses on identifying the cognitive mechanisms that are employed when perceiving the shape and structure of 3D objects. One of the little problems that I had to overcome was finding out how to calculate the center of mass/gravity of a 3D surface of revolution analytically. Specifically, I needed to calculate the COM for conical frustums with and without an attached part (which was also analytically generated).
Unfortunately, it wasn’t as easy to derive as I assumed, but the steps toward that end are pretty straightforward. After the break you can see the general equation I ultimately derived for calculating the COM in 3D-space.
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So, this project was sidelined until I had to make another BatchPCB purchase. Thankfully it wasn’t too long until I had the opportunity to work on it again! The current setup is basically 4 of the original 4 RGB LED Controller boards and 12 of the updated DR1r3 boards. All 16 are wired in parallel and being controlled by my desktop machine. You can see an extended version of this RGB test sequence after the break and I’m also including the (uncommented, sorry!) Processing 1.1 code that I used to control the boards.