A quadtree reduces this: rebuild the tree each frame, and for each object, query only the nearby region. Objects in distant quadrants are never compared.
Natural neighbour interpolation has a number of strengths over linear barycentric interpolation. Namely, it provides a smooth or continuous slope between samples3, and is always the same for a given point set, unlike the TIN where the quality of the triangulation can produce biases in the outcome, even in the best case.
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