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| robrenz:
Your anti screen burn orbit is very nice ;D |
| GK:
--- Quote from: robrenz on April 30, 2014, 03:35:43 pm ---Your anti screen burn orbit is very nice ;D --- End quote --- I think I might still slow it down to make it less obvious. I've got a half dozen NOS CRT's as used in the Tek 422 oscilloscope, still in their original packaging, just for this kind of thing. Think I'll make a dedicated CRT display unit for this instead of utilizing a 'scope. |
| johnwa:
Hi GK, That is some really nice work with the Fourier character display! Producing that display using analogue circuitry looks impossible at first glance, but we can all see that it is quite practical. The smooth curves give the characters a certain aesthetic appeal, too. Now, I was thinking about how this works, and also about the Rossler experiment last year, and I wondered: would it be possible to apply this technique to the synthesis of three dimensional objects? After a certain degree of head scratching, it appears that the maths works out, though I think building a physical implementation will be on the edge of practicality, due to the overall complexity required. For a 5th order approximation, the character generator requires ten frequencies plus a DC term. With these, it is possible to parameterise a curve as a function of one variable (s), in two dimensions, with a total of 22 coefficients. A 3D surface can be parameterised as a function of two variables (u and v). Therefore, instead of five frequencies, 25 will be required for the same order synthesis (5 x u x 5 x v). Allowing for the sin, cos, and DC components, a total of 121 terms would need to be synthesised. To cater for the three axes, up to 363 coefficients might be required (although many shapes would only need a relatively sparse coefficient matrix). The coefficients can be implemented fairly simply using resistors, so the main obstacle to using this technique would appear to be the generation of the signals at all of the different frequencies and phases. To generate them directly would require 100 analogue multipliers. It might be feasible to mix all the u harmonics and all of the v harmonics, multiply the sums, and then filter off the individual (m*u * n*v) components, but I suspect that this would involve a similar level of complexity. Ideally, the low frequency parameter would change in discrete steps, while the high frequency parameter swept continuously, to give a rectangular U-V grid. However, I think it would be simpler if each parameter changed continuously. This would result in a slightly skewed U-V grid, similar to a television raster scan. It would also be desirable to be able to switch the U and V signals, in order to give grid lines in both directions. I don't have any plans to actually try to build this - it would be huge! However, if anyone is crazy enough to give it a go, I might be able to offer some suggestions as to how to go about it. I have attached a couple of Matlab simulations of this method. Note that it is not limited to solids of revolution, though these are the only ones that I have managed to figure out the coefficients for so far :) |
| GK:
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. I am considering building a spherical polar coordinate to xyz Cartesian coordinate transformation unit to complement the function to my already-built 3-D projective unit. However the problem is finding an analog computing application for it. I'm not aware at the moment of any physical system analogs that provide three variables that are readily plotted and unambiguously readable in spherical polar coordinates. I have my polar coordinate oscilloscope adapter up and running and am planning to build another, more powerful MK II version. The current version can only generate plots over a polar angle of 2pi radians. The unit I am currently planning will be able to do 0.5 to 1024 pi radians in 0.5 pi radian steps. |
| Clocky:
That's really cool, I love this kind of stuff. |
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