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You might be interested in this YouTube video, which shows a vector graphics game (specifically Tempest) in slow motion, showing you how the graphics are built up over time. And then there's this one that shows how a 'normal' video game's graphics are displayed on a CRT.
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They are still there, just better hidden these days - you are using them right now, in the form of a scalable font to read this text. Font data is stored as vector info and "drawn" at the right size.
Many games still use vectors below the hood with a skin over it to make the visible surface - it makes clipping and collision a load simpler to calculate. Which is why Battlezone et al used them - the processors just weren't up the demands of modern games!
And GPU's can be thought of as vector processors at their most basic level.
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Honestly, from a certain perspective that is true. The data passed between the CPU, the video adapter, and even the monitor is rarely simple raster lines of pixels. Higher-level constructs are used throughout the pipeline to reduce the amount of information required per frame, which helps increase the overall frame rate possible with the device.
The other appeal of the original vector displays was the lack of pixelation in the image. Frankly, modern displays have such incredible pixel density that pixelation is only an issue in certain contrived scenarios.
If you are thinking of true, continuous and smooth lines on the screen with no hardware-induced limited resolution, like the old Tektronix storage tube displays: You couldn't make a color display with that technology. In theory, you could make stripes of R, B, G phosphor, with a shadow mask just like on plain color CRTs, but that would introduce a resolution limit; lines would not be continuous and smooth on the screen.
I will not rule out that there existed some sort of continuous line color screens, but I never ever saw any such thing out in the marketplace. If it existed, it seems to never have escaped from the development lab.
In the really old PC screens, the display driver was responsible for generating the signals to the coils do the horizontal and vertical deflection of the electron beam. While a proper driver would scan the screen line by line, in principle it could let the beam trace any path, drawing "true" vector lines, in the same pattern as you would on a Tektronix screen. Note that the Tektronix had a mechanism for keeping the phosphor "lit", once lit, until the (entire) screen was erased; no refresh was required. If you wanted to emulate X/Y plotting on a standard PC screen, you would have to refresh the figure at at frequency of at least 30 times a second. (Even 30 Hz gives significant visible flicker.) If you try this on a color screen, the mask would of course limit the resolution.
Lots of systems/standards specify representation of figures (both wireframe and surface), and processing of them, in a continuous, resolution independent vector format. Figures often remain in that format all the way into the GPU; lines are not digitized (pixelized) until immediately before the signals go out on the cable to the display. As long as the pixelized signal is created according to the true physical display resolution, you get the best possible image from that screen.
Side remark / old memory:
Deep down in my archives is a copy of one of the first issues of "Dr. Dobb's journal". At that time (second half of the 1970s) microcomputer owners didn't expect very much. This DIY article about "How to build a true 3D display" looked quite serious, in the opening paragraphs, describing how you could "draw" a line, like on Tektronix screens, with a LED that could be moved left and right, up and down, by small motors pulling the LED along a horizontal and a vertical rail. If you furthermore made a front-back rail, the LED could trace a wireframe figure in the cubic space delimited by the movements of the the three rails.
Of course the LED would have to retrace the wireframe figure at a high frequency. To simplify the mechanics, rather than a single LED, the horizontal rail could consist of a dense row of LEDs, to replace the horizontal movement. The next step would be to build a pile of such horizontal rails, forming a dense matrix of LEDs, to avoid the vertical movement as well.
Connecting the LED matrix to the computer would require thousands of wires, and a complex control logic. But we've got a matrix of lights that is far easier to handle, if we replace the LED mesh with a CRT. So all it takes to make a true 3D display is to build a mechanism for flipping a CRT back and forth 30 times a second ...
In those days, people built the craziest things for their micros, and the article was well written, so you could read half of it before realizing that it was all a big joke from the very beginning. Maybe I should dig up that old magazine and copy the article to CP. (It would probably be thrown out due to copyright infringement, even if I stated the source in all details.)
In the really old PC screens, the display driver was responsible for generating the signals to the coils do the horizontal and vertical deflection of the electron beam. While a proper driver would scan the screen line by line, in principle it could let the beam trace any path, drawing "true" vector lines, in the same pattern as you would on a Tektronix screen.
Not entirely accurate. You could do that only on CRTs with electrostatic deflection. The more common ones used as PC monitors had electromagnetic deflection with those big coils installed on the neck of the CRT. Trying to move the beam randomly on those was impossible due to the high induced voltage. For regular scans (CRTs and TVs) the horizontal fly-back was used to produce the high voltage for the secondary anode.
The electrostatic CRTs (like the ones used in scopes) had the drawback of a limited deflection angle, at least for any pretense of linearity and that made those very long necks.