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The common tile server with overlapping tiles is deep zoom. Tiles in the center of the image have overlap on all four sides, but tiles at the edges don't overlap past the conceptual image space. We properly handled the right and bottom, but the top and left edges were expecting tiles that were larger than deep zoom was providing. For instance, a 256x256 tile with an overlap of 1 produces a 258x258 tile in the center, but a 257x257 tile at the upper left and a 257x258 else on the left edge. This handles those properly.
The deepzoom example also maintains query parameters, making it easier to modify for testing.