Motion Blur

Pause a live-action film on a fast pan and the frame is a mess of streaks — a running figure smeared into a comet, wheel spokes dissolved into a haze. That "mess" is doing something vital: it is motion blur, and it is the single effect that makes a strip of still frames read as smooth continuous motion rather than a strobing flip-book. Turn it off in a CG render and fast motion suddenly judders — the eye catches each sharp, discrete position and the whole shot flickers like an old zoetrope, even at a high frame rate.

This page is the flip side of the sampling story from the foundations module: there we sampled a continuous motion at discrete frame times; here we ask what a physical camera records at each of those samples, and how faithfully reproducing that saves the animation from strobing.

Why a real camera blurs

A film or digital camera does not freeze an instant. Its shutter opens for a finite slice of each frame's duration, and during that slice light keeps piling onto the sensor. If the subject moves while the shutter is open, its image sweeps across a band of pixels and every one of them is exposed — the object is recorded not as a point but as a time-integral of every position it occupied during the exposure.

The shutter interval is the time the shutter stays open within one frame of duration \Delta t = 1/\text{fps}. The recorded image is the average of the scene over that interval.
The shutter angle \theta expresses that interval as a fraction of the frame: a mechanical rotary shutter is a spinning disc with a wedge cut out, and \theta is the wedge's angle. Open time is \Delta t \cdot \theta/360^\circ.
Motion blur is the streak an object leaves because it is sampled over a time interval, not a time instant. Its length is (object speed) × (shutter open time).

The classic film standard is the 180° shutter: the shutter is open for exactly half the frame, an interval of \Delta t / 2. (The other half of the disc's rotation was historically needed to advance the film without exposing it.) A century of cinema has trained our eyes on that particular amount of blur — it is the look we read as "natural motion".

The blurred footprint, interactively

Below, the tall faint bar is where a fast object would land without motion blur — all of its light packed into one sharp spot. The solid curve is its blurred footprint: raise the speed (how far it travels in one frame) or open the shutter angle wider and the same light spreads over more pixels, so the footprint grows wider and — because the light is conserved — fainter. At 0^\circ the shutter is shut and you get the sharp strobe; crank it toward 360^\circ and a fast object smears into a broad, low, unreadable band.

Watch the width readout track D \cdot \theta / 360^\circ: the blur is simply the frame's travel scaled by the shutter fraction. A widely-spaced (fast) move at a wide shutter is the most smeared; a slow move barely blurs at any shutter.

Worked example: 20 pixels in one frame

A ball crosses D = 20 px during a single frame of a 24 fps shot (frame duration \Delta t = 1/24 s). How long should its motion-blur streak be under the standard 180^\circ shutter?

The shutter is open for half the frame, so the ball travels for only half the frame while being exposed:

\text{blur length} \;=\; D \cdot \frac{\theta}{360^\circ} \;=\; 20\,\text{px} \cdot \frac{180^\circ}{360^\circ} \;=\; 10\,\text{px}.

The ball is recorded as a 10-px streak — half the frame's travel — smoothly connecting where it was to where it is. The next frame's streak begins right where this one ends, so across the shot the streaks tile the ball's path into an unbroken ribbon: the eye reads continuous motion.

Turn the blur off and instead you get a sharp ball at 0 px, then a sharp ball 20 px away, then 40, … — a sequence of crisp, discrete jumps with hard gaps between them. Twenty pixels is a big jump; the eye cannot fuse those separated snapshots and the ball appears to strobe or stutter, the exact judder you see in a video game with motion blur disabled.

Rendering it: sample many sub-times, or fake it fast

A renderer knows the object only at frame times, so it must reconstruct the exposure interval. Two families of technique dominate.

Temporal supersampling (the correct way). Split the shutter interval into many sub-times, render (or ray-trace) the scene at each, and average the results — a Monte Carlo estimate of the exposure integral. Physically accurate: it handles occlusion, rotation, deformation and reflections correctly. Cost is roughly linear in the number of sub-samples, so it is an offline / production tool.
Velocity-buffer post-process (the fast way). Render one sharp frame plus a per-pixel motion vector (screen-space velocity), then in a post pass smear each pixel along its own vector. Cheap and real-time — the games and compositing workhorse — but it is only an approximation of a 2-D image, so it produces artefacts at silhouette edges and occlusions (a blurred foreground can't reveal the correct background it never rendered), and it can't blur what a single frame didn't capture.

The choice is the usual one: supersampling buys correctness with render time; the velocity buffer buys speed with edge artefacts. Both are answering the same question — what did the sensor integrate while the shutter was open?

Blur is spacing, seen by the shutter

Notice that blur length is D \cdot \theta/360^\circ — directly proportional to D, the per-frame travel, which is exactly the spacing from the timing-and-spacing lesson. Widely-spaced (fast) frames get long streaks; tightly-spaced (slow) frames get almost none. So motion blur is not a separate phenomenon bolted on at render time — it is the shutter reading out the spacing as a smear. A move that the animator spaced to feel fast will automatically look fast, because the blur grows with the very spacing that carries the speed.

Early movie cameras used a spinning opaque disc with a pie-slice cut out of it. As the disc rotated, the open wedge swept past the film gate, exposing each frame; the solid part covered the gate while the film advanced. The size of that wedge — literally an angle — set how long each frame was exposed. A half-open disc (a 180^\circ wedge) exposes for half of each rotation, i.e. half the frame time. The number stuck as a unit even though modern digital sensors have no spinning disc at all: "shutter angle" is now just a familiar way to say "what fraction of the frame was the sensor collecting light", and 180^\circ still means "half".

On a very fast action — a punch, a whip-pan, a sword slash — even a correct 180^\circ streak may not be enough for the eye to connect one frame to the next, and the action reads as a hard pop. Traditional animators solved this with smear frames: a single drawing where the object is deliberately stretched into a long multi-armed streak spanning its whole travel, an exaggerated hand-drawn motion blur. Modern CG does the same thing by pushing the shutter past 180^\circ or stretching the mesh along its velocity. It is a stylistic cheat that trades physical accuracy for readability — the blur's job is to fuse the frames, and sometimes physics needs a little help.

It is tempting to think motion blur is a mere finishing polish. It is not — it is the thing that conceals the discrete-frame nature of the whole medium. Turn it off, or use too short a shutter (a small angle, sharp crisp frames), and fast motion strobes and judders because the eye now perceives each separate snapshot — and this happens even at a high frame rate; the notorious "60 fps soap-opera / video-game stutter" is largely missing or too-thin motion blur, not too few frames. But do not overcorrect: too much blur (too long a shutter, angle well past 180^\circ) smears everything into an unreadable mush and you lose all detail and crispness. Short shutter → judder; long shutter → mush. The 180^\circ rule is the century-tested sweet spot between them.