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Different coherence dimensions can be considered to improve the performances of an algorithm for computing collision translations of pairs of convex polyhedra. The algorithm's peculiar approach, based on convex minimization, is well suited to work without initialization and also endowed with an inherently embedded mechanism to exploit spatial coherence in a broader sense than other related approaches usually do. After a brief outline of the algorithm, we summarize the outcomes of several numerical experiments meant to explore extensively the incremental behavior of the algorithm while controlling the coherence parameters. In order to assess the efficacy and the potential of the approach, the performances are also discussed in the light of the results on H-Walk, an algorithm specifically designed to adapt to variable coherence.