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How does this work? Much like sunlight glinting on curved chrome. Every viewpoint sees a glint in different place. The trick is to control the curvature of the reflecting surface so that all sightlines through glints meet at a point somewhere off the surface in 3D space:
Since your eyes always see a glint when looking at that point, your brain decides that the light is coming from the 3D point itself.
To make the 3D illusion work for many viewpoints without distortion, each mirror has to have a unique doubly-curved shape. Here are some typical mirrors shapes that I use. Each provides a single-point depth illusion to a 90° range of viewpoints. These animations show how the glint moves as your viewpoint swings left and right: