Ahhhhh, Bach! (sorry, bad pun-ish MASH reference).
Yes some older recordings used the Z-axis to encode audio info but most use the radius (I believe "squiggles in the groove" is the technical term), so a simple polar coordinate system is usually sufficient. LP's/45's squiggle both sides of the groove independantly to encode stereo, so that does add a z-axis component.
All of this just shows how hard it really is to capture info from obsolete media, and how much harder it would be to "print" a record ("disc") with any usable fidelity.
BTW - Your description of Cylindrical co-ordinates was completely correct. I was referring to the description in the previous paragraph. It was your "polar" co-ordinates that I think you meant "Spherical" and put in an extra angle. It occurred to me after I posted that my reference was ambiguous.
Polar co-ordinates (without further specification) is a 2D system, locating a point in a plane by angle and distance from a reference point. The other common 2D system is Cartesian co-ordinates which locates a point by distance from a reference in two predefined directions. There is also higher dimensional Cartesian and Polar systems.
It sounded from your description like you were trying to define Spherical co-ordinates, a 3D system of TWO angles and a distance. The two angles correspond to lattitude and longitude on a globe. Spherical co-ordinates is one of two common 3D polar systems, the other is cylindrical co-ordinates, a system of two distances and an angle.
There is a 3D system that uses three angles. It involves two predefined reference points on a predefined reference plane. The three angles are the polar direction from each of the reference points and the angle from the plane. A 3D system that involved THREE angles and a distance would be overconstrained.
No, No, Rob. I was referring to planar discs, not recording cylinders, same as you.
Remember your coordinate systems from trigonometry class.
Polar coordinates are a system describing the location of a point from the origin by three angles and a radius.
Cylindrical coordinates are a system describing the location of a point from the origin by use of an angle, a radius, and a Z-axis displacement. This coordinate system (not the shape of the object) is much more appropriate for describing the groove geometry of a planar phonograph record. The angle and radius describe the location of the groove, and the Z-axis displacement describes the depth of the needle in the groove. It is the variation in depth (Z-axis) which stimulates the crystal or magnetic cartridge transducer, creating the sound.
In fact, a waveform of only the Z-axis sound would be a representation of the audio.
Interesting from the standpoint of analog/digital resolution performance. It's been estimated that the equivalent digital channel spec. needed to equal "obsolete" 30 i.p.s. analog tape, which was the standard for high-quality recording back in the day, is a 500Khz sampling rate at 24 bits of TRUE resolution. The smallest signal modulations encoded in the groove walls of a vinyl LP are on the scale of a wavelength of visible light. 3D printing will have to go a long way to match that.
Records (discs such as those shown in the article) use polar (radial?) coordinates (theta-radius). I would assume it would be extremely difficult to get adequate results printing a record in polar coord. using an x-y printer (and the article does imply this).
Interesting point about cylinders, though. Early commercial Edison recordings were cylinders. Of course, cylinders use both coordinate systems in three dimensions (fixed radius, with x axis and theta variables). You could print a cylinder by printing a flat sheet with x-y coordinates, soften the print and wrap it around a cylinder form. It would probably yield better results than a disk (except at the joint).
As someone who is just starting to rip their LP collection (I finished my first album just two days ago) I'm a bit perplexed. I understand the archival aspect of transferring old media (I wish I had something to scan records instead of playing them, an inherently damaging exercise). But I was expecting to read about someone printing a long gone DEVICE to play long obsolete media, not printing that obsolete media. Seems a bit of a waste, especially since printers are inherently rectilinear devices, not polar (as a record is), so getting a usable result would require a much higher resolution printer than currently exist.
Most of the new 3D printers and 3D printing technologies in this crop are breaking some boundaries, whether it's build volume-per-dollar ratios, multimaterials printing techniques, or new materials types.
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