The first photograph was created in 1827 by Joseph Nicephore Niepce. In 1828, William Rowan Hamilton's founding papers on geometric optics began to appear. This seems to be a remarkable coincidence and one would think that the two siblings, photography and geometric optics, would each contribute to the growth of the other. But this never happened. Optical design in the 19th century was largely empirical, and today design in the geometric realm is performed by optimizing a cost function which is defined via ray tracing. Recent advances in optical machining have made possible the manufacture of non-rotationally symmetric optical components. Using asymmetric surfaces, enough degrees of freedom are sometimes available to "directly" find solutions to design problems. This approach consists of numerically finding approximate integrals of non- integrable distributions. Hints of connections with Hamiltonian optics and exterior differential systems appear, but the full story remains unclear. Applications include the design of wide-angle and panoramic imaging systems, side view mirrors without blind spots, and low cost mirror lenses for thermal imaging. Several physical prototypes resulting from my work will be presented.