Two generalizations of the classic corner-stitched data structure for planar polygonal layouts to geometrics including circles or arbitrary curved shapes are introduced and analyzed. Such an extended data structure can be built with just the additional space required to store the more complicated curved boundaries. Alternatively, the definition of the curved shapes may also be based on geometrical area mapping similar to those used in finite-element methods. The tradeoffs between different encoding schemes that minimize either overall data storage needs or the complexity of individual tiles are discussed. The topology of the linkage of tiles by the corner-stitching pointers is equivalent to that of simpler patterns with trapezoidal tiles, but the various tests and operations running on this data structure may become considerably more complicated, and the achievable runtimes will be highly implementation dependent.>