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Corner stitching is a technique for representing rectangular two-dimensional objects. It is especially well suited for interactive VLSI layout editing systems. The data structure has two important features: first, empty space is represented explicitly; and second, rectangular areas are stitched together at their corners like a patchwork quilt. This organization results in fast algorithms (linear or constant expected time) for searching, creation, deletion, stretching, and compaction. The algorithms are presented under a simplified model of VLSI circuits, and the storage requirements of the structure are discussed. Corner stitching has been implemented in a working layout editor. Initial measurements indicate that it requires about three times as much memory space as the simplest possible representation.