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| GK:
Well then, here is a little more ;D The polar rose is a mathematical curve easily generated by my completed MK I polar coordinate oscilloscope adaptor. Here is a demo of a pair of 2 pi radian roses. The first is generated with a swept frequency sine function and the second with a triangle wave. |
| johnwa:
--- Quote from: GK on May 06, 2014, 09:02:40 am ---That looks neat. Another approach might be to use spherical polar coordinates and generate objects by just synthesizing the three signals for the radial distance, azimuth and polar angles. It's easy enough to transform the spherical polar coordinates to xyz Cartesian values, and then to 2-D X-Y projective views. --- End quote --- Yes, depending on the object, it might be possible to get better definition with fewer terms using polar coordinates. Although objects that deviate significantly from a spherical shape might still be better of in cartesian. Anyway, this was just a random idea I had, I don't think I will take it any further at this stage - too much other stuff to do :(. Your rose figures are pretty neat too. I think there is a vaguely similar process for manufacturing faceted shapes on a lathe. I think it uses planetary gearing of the spindle, to give the part a complex motion. See, e.g. http://en.wikipedia.org/wiki/Hypotrochoid Obviously, the lobes of the pentagram get chopped off, and only the centre section remains. I imagine it would be fairly easy to plot these figures on your scope GK, though it might take a bit of work to get the equations in to the correct form. |
| GK:
That Hypotrochoid looks interesting, but at a glance it looks like it needs 6 pi radians of rotation to be plotted in full. Unfortunately my MK I polar coordinate adapter is limited to 2 pi radians. While consumed in the technical side of the design I didn't realize how much of a limitation a fixed "sweep" of only 2 pi radians (360 degrees) for the angular coordinate would be; that came afterwards, reading up on geometric curves and finding applications for the completed unit. The Hypotrochoid will have to wait for the MK II version. However that will be a while off. ATM I'm currently struggling in my free hours here and there to complete the construction of my character generator and write it up on my webpage. I need to clear to bench to get onto others things that need attention. All that's left is installing the power supply, some fabrication of panels and screwing the case together. I also designed an additional, 5th PCB, giving LED status indication to the 12-bit parallel programming port (green for the 7 address lines, yellow for the 5 data lines and a single monostable-stretched red LED for the write strobe line) . This 2-relay-rack analog/hybrid computer is going to have plenty blinky LEDs to make it look really technical ;D |
| GK:
Here is a particular example of dither (these days known as triangular probability density function) that predates digital audio and video processing by a few years. I am currently applying the technique to my diode function generator design and it works well, turning the sharp diode discontinuities parabolic. This page is from my earliest analog computing text out of several that summarizes the technique: Analog computing techniques, Johnson, McGraw Hill, 1956. None of my old texts actually use the word "dither", however. Not sure when that term was first applied. Dithering techniques go back even further than this, applied to mechanical analog computers by means of vibrator motors to compensate for quantization errors incurred by gear sticking and backlash. The reference cited (8) is: Stone, J. J., Jr.: Smooth-curve Function Generation Using Diodes, IRE Airborne Electronics Digest, 1954. Does anyone out there know of any earlier examples of the application of electronic dithering? |
| GK:
--- Quote from: GK on May 14, 2014, 02:06:15 pm ---All that's left is installing the power supply, some fabrication of panels and screwing the case together. I also designed an additional, 5th PCB, giving LED status indication to the 12-bit parallel programming port (green for the 7 address lines, yellow for the 5 data lines and a single monostable-stretched red LED for the write strobe line) . This 2-relay-rack analog/hybrid computer is going to have plenty blinky LEDs to make it look really technical ;D --- End quote --- I finally got this thing finished and written up: http://www.glensstuff.com/fouriersynthchargen/fouriersynthchargen.htm |
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