Why jaggies happen

Jagged, stair-stepped edges on a diagonal line, the “jaggies,” look like a rendering limitation, and they are, but the real cause is a single idea from signal processing that turns up everywhere once you’ve seen it.

The culprit is undersampling, and the governing rule is Nyquist–Shannon: to faithfully capture a signal you have to sample it at least twice as fast as its highest-frequency component. A pixel grid samples a continuous image at fixed points. When the image carries detail finer than the grid can resolve (and a sharp diagonal edge is, in frequency terms, very high-frequency), there aren’t enough samples, and the lost detail doesn’t simply vanish. It comes back disguised as lower-frequency structure: a false pattern, an “alias.” That disguise is exactly where the name comes from.

What makes it worth knowing is that the same mechanism wears different costumes:

• spatial aliasing: jaggies on geometry
• temporal aliasing: the wagon-wheel effect, where a spoked wheel filmed at a fixed frame rate appears to rotate slowly backwards, or worse, sits there spinning the wrong way while your brain quietly files a complaint
• texture aliasing: moiré shimmer on a detailed texture viewed at a distance

All three are the same undersampling failure, playing out in space, in time, and across a texture. And once you frame it that way, anti-aliasing stops being a grab-bag of tricks: it’s just sampling smarter (averaging several samples per pixel, or rendering at high resolution and scaling down) so the high frequencies can’t masquerade as low ones. The whole fight is just stopping detail from lying about its size.