Calculating the COM of a Spherical Plot

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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Calculating the COM of a 3D Surface of Revolution

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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8×8 RGB LED Display

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.



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4 RGB LED Controller Update

I recently began working on a consulting project that required the creation of some PCBs.  Since I have had such great success with BatchPCB.com in the past, I decided to use them again to fab the custom PCBs.  The BatchPCB purchasing system adds a few static fees (set-up, handling, and shipping), so I felt that this was as good a time as any to make some additional of my PIC16F628 4 RGB LED PWM Controller boards with a couple of modifications.

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Life of a Graduate Student

I have been neglecting semifluid.com for sometime now, but fear not! I will post new projects shortly as I try to dig through the comments.  My time has been split between coursework (which is diminishing), research, and teaching.  As I send revisions of papers back and forth with my advisor, I will devote time to updating the site.  In the meantime, here are 3 videos demonstrating aftereffects that I created for my sensation and perception lab:



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PIC16F628 4 RGB LED PWM Controller

I am a big fan of LEDs.  Bright, colorful, flashing LEDs.  So, given my affinity for LEDs, I decided to work on a controller that me and a few of my friends could use as an art project/passive information display.  I have posted videos from the first prototypes (here and here), but it has been tough to dedicate time to further development given my research, so I thought I would post the information so that anyone can take the design and modify it to their liking!

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PIC16F628 Serial 4 LED PWM DR1r6

I’ve been working on a project in my spare time with two friends to create some ambient light controllers, so I thought I’d just post two short videos to demonstrate the current state of the project.  In the current iteration, they can be used as wall-washers or they can be enclosed to create ambient light cubes/spheres/pentagonal cupolas/rhombo-hexagonal dodecahedrons/etc.  Each module is addressable and uses a PIC16F628 to control each of the RGB LEDs (which were purchased from the eBay seller jeledhk with the description “Superflux RGB 5mm R/H LEDLamp 8Kmcd COMMON CATHODE”).  The PCBs were created using BatchPCB.com for $5 each (+ ~$15 total for S&H and setup) and are beautifully etched, drilled, and silkscreened (although it took about 1.5 months to receive them).  Ok, less talk, more videos; one video on the front page and another after the jump:



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