A number of approaches to patterning photosensitive materials on arbitrarily shaped surfaces have been attempted. For example, companies such as Panasonic and Aiscent Technologies have developed laser-based systems to pattern curved surfaces. These methods are limited by restrictions in material choice, patternable area, and throughput. Additionally, some of them are further restricted to patterning spherical surfaces. Alternative technologies for patterning 3D surfaces include direct printing using inkjet technology and adapting conventional stereolithographic techniques to print non-normally onto substrate surfaces. These approaches are unable to handle undercuts or concave areas, limiting their utility to surfaces viewable from a single axis. This invention proposes a novel method of patterning 3D surfaces that overcomes these limitations, enabling high-resolution patterning of arbitrarily shaped 3D surfaces over large areas.