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I made a model of a projector, where the projection part is done with a spotlight with material like below.

node setup for projecting

Now when I move the spotlight away at a high speed, I'd expect some form of motion blur on the projector screen but the image is sharp as if the projector was stationary.

Just to convince myself that motion blur in the scene works at all I've added a light-emitting ball that moves in front of the screen at a rate similar to the spotlight.

Without motion blur

without motion blur

With motion blur (note blurry ball but sharp image)

swith motion blur

How can I make a projector that responds to motion blur?

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That's a real problem. Motion blur only records the difference in position, rotation, size of faces (all visible objects contain faces). From this it calculates speed vectors and blurs regions accordingly. That means objects will be blurry, even their reflections, while lamps (no faces, not directly visible) will show an unblurred spec. The same unfortunately goes for animated texture coordinates. There used to be a 'hack' where you would render subframes and combine them, but that multiplies the amount of rendered images by at least 4, usually 8 or more. Let me know if that's an option, then I'll research it again. Sorry that's not a solution, but it should contain some answers and it was too big to put it in a comment.

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