About: Body of constant brightness

In convex geometry, a body of constant brightness is a three-dimensional convex set all of whose two-dimensional projections have equal area. A sphere is a body of constant brightness, but others exist. Bodies of constant brightness are a generalization of curves of constant width, but are not the same as another generalization, the surfaces of constant width. The name comes from interpreting the body as a shining body with isotropic luminance, then a photo (with focus at infinity) of the body taken from any angle would have the same total light energy hitting the photo.