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Placement migration is a critical step to address a variety of post-placement design closure issues, such as timing, routing congestion, signal integrity, and heat distribution. To fix a design problem, one would like to perturb the design as little as possible while preserving the integrity of the original placement. This work presents a novel computational geometry based placement migration method, and a new stability metric to more accurately measure the "similarity" between two placements. It has two stages, a bin-based spreading at coarse scale and a Delaunay triangulation based spreading at finer grain. It has clear advantage over conventional legalization algorithms such that the neighborhood characteristics of the original placement are preserved. Thus, the placement migration is much more stable, which is important to maintain. Applying this technique to placement legalization demonstrates significant improvements in wire length and stability compared to other popular legalization algorithms.