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Images and videos have their own quality standards and protocols. There are either raster image file formats (.gif, .jpg) or vector graphics images (.svg, .pdf). No matter how much you zoom in on vector graphics, you will never see pixels, with diagonal lines still retaining their non-jagged smoothness.

In my opinion, video is always pixelated regardless of the resolution used (the 1080 format is going the way of the dinosaur already), while 4K and 8K (also just higher resolutions) still possess pixelation as well I think.

What then is the vector graphics equivalent of video file formats? or is there none

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The whole premise of vector graphics is that there is a drawing engine in the output device that can interpret graphical commands and output shapes and fonts at the maximum resolution of its rasterizer.

In simple terms, when someone produces a Postscript projector or media player, there will be a video equivalent of vector graphics.

But in another sense, this is already the case with video production software that lets you create titles and graphics using TrueType fonts and vector drawing tools. The renderer, such as the Media Export engine in Premiere Pro, rasterizes fonts and shapes at the maximum resolution of the output video format. You don't have to worry about pixelated graphics and fonts that would result from importing low- resolution artwork. This video rendering of vector sources is equivalent to the work of a RIP (raster image processor) or web browser, which render PostScript (vectors and fonts) at the maximum resolution of an imagesetter or printer for output on film or paper or a webpage.

Ultimately, shapes, images and text all have to be turned into dots/pixels at output time. All output devices -- with the exception of pen plotters -- can only print/display dots/pixels -- solid spots of a single color. That applies to laser and inkjet printers, computer monitors and TVs, digital platemakers, and even crowds of people holding up colored cards to make gigantic pictures in the stands of football stadiums.

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Video is a sampled, quantized series of pixels in an array - so I don't think they are directly comparable - it is inherently a series of bitmap images played sequentially.

The nearest equivalent to what you're asking about is SVG animation, where you are rendering a series of pixels in a web browser based on some instructions telling the computer how to render some vector graphics.

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There are video codecs that represent the video signal as a series of mathematical functions, similar to the way that a svg represents a picture as a series of mathematical curves. In fact if you've watched a video on the web in the last two decades, that's exactly what you've been seeing. h.264, the most ubiquitous video codec, and most other modern codecs use DCT compression, a kind of Fourier transformation, that can express any signal in terms of a number of overlayed cosine waves. In essence most codecs are actually vector codecs.

So why can't you infinitely zoom into a h.264 movie? Because the original source of that movie had only a finite number of pixels in its sensor or renderer. This acts as a lowpass filter, filtering out the higher frequencies of signal that you would need to be encoded in order to zoom into it. You can't get out what isn't put in.

Worth noting that no matter how you encode it, if you do encode more information, you have to increase the bandwidth. There is no free lunch. In a zoomable video codec, in order to have more detail visible when you zoom right in, you're going to need to encode more information, and you can only do that by making your data rate bigger. Clever encoding algorithms will help (usually throwing away stuff which you don't notice), but they can't do the impossible.

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