In the paper, a new data structure, called the radial–annular tree (RAT) structure, is proposed and implemented to bridge the gaps between CAD, RP, and fractal geometry. A typical fractal curve, the Koch snowflake curve, will be examined in detail. Based on the RAT representation, higher-level fractal curves can be generated more efficiently, and repeated information can be represented concisely. Traversal algorithms are also devised to generate a maximally connected tool path directly. The tool path can then be used to generate a physical fractal curve without any additional conversion.