Hicks noted that, in reality, the mirror does not look like a disco ball up close. There are tens of thousands of such calculations to produce a mirror that has a smooth, nonuniform curve.
I imagine "tens of thousands of such calculations" is newspaper code for integration.
If someone assigned me the task of making such a mirror, I would start by treating the mirror like a monitor displaying a 3D scene, and calculate the vectors necessary to project a 45 degree view onto the surface of the mirror (i.e. start with a virtual camera behind the mirror such that it has a 45 degree field of view). I would then adjust those vectors so that the image will look like such a projection when seen by a viewer a few feet up and to the right, with the mirror occupying ~15 degrees of the viewer's FOV.
In other words, everything I need to know I learned from video games.
If I were asked to make such a device, I would build a flexible mirror whose curve could be adjusted by an array of attached screws. I'd fix said mirror to a car, and adjust the screws until the desired curve was reached. I'd then measure the curve and duplicate it in a rigid finished product.
It's actually amazing that it took a physicist/mathematician to think of this thing. I doubt I would have come up with the idea. It goes to show how domain knowledge shapes your perception of the world.
Hicks noted that, in reality, the mirror does not look like a disco ball up close. There are tens of thousands of such calculations to produce a mirror that has a smooth, nonuniform curve.
I imagine "tens of thousands of such calculations" is newspaper code for integration.
If someone assigned me the task of making such a mirror, I would start by treating the mirror like a monitor displaying a 3D scene, and calculate the vectors necessary to project a 45 degree view onto the surface of the mirror (i.e. start with a virtual camera behind the mirror such that it has a 45 degree field of view). I would then adjust those vectors so that the image will look like such a projection when seen by a viewer a few feet up and to the right, with the mirror occupying ~15 degrees of the viewer's FOV.
In other words, everything I need to know I learned from video games.