CAD systems provide convenient tools for the creation of simple geometry by direct manipulation on the computer screen. They work well enough for two-dimensional construction, but are often inadequate for creating doubly-curved three-dimensional surfaces. The solution proposed here is to use the in-built programming language provided in most CAD systems for direct creation of geometry. Developed for didactic purposes, the stunning reconstructions of Gothic vaults suggest a method of working likely to be of great value to the geometrically adventurous architect.