When viewing a curved mirror, it is apparent that some non-linear transformation is at work, which depends upon the mirror shape. In this talk I will address the problem of determining the mirror shape that will realize a prescribed transformation. The prescribed transformation determines a vector field which should be normal to the sought after mirror, but generally this vector field is not exact. Appealing to the Hodge theorem allows one to find "best fit" surfaces normal to the vector field. We will describe several applications, including several mirror based panoramic cameras, a car mirror with no blindspot, and a means of experimentally measuring the shape of the cornea. On closer inspection one finds that the underlying object of consideration should not be a vector field, but one of several other candidates. One, for example, is a planar distribution in R^3, and the best fit functional in this model then give rise to the mean curvature equation. Finally I will describe an alternative technological approach to the problem, namely to use silicon-based micromirror arrays that can "integrate" a non-integrable distribution.