McCann Displacement Interpolation Formula is a result from the foundations of optimal transport. For mathematical objects, and let mathematical objects. Let mathematical objects be an optimal coupling for the mathematical objects-Wasserstein distance, so that n n |x-y|p \, d(x,y) = Wp(0,1)p. For each mathe. It helps organize the relationship between Monge maps, Kantorovich plans, duality, and Wasserstein geometry.