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We study Min-Max affine approximants of a continuous convex or concavefunction $f:\Delta\subset \mathbb R^k\xrightarrow{} \mathbb R$ where $\Delta$is a convex compact subset of $\mathbb R^k$. In the case when $\Delta$ is asimplex we prove that there is a vertical translate of the supportinghyperplane in $\mathbb R^{k+1}$ of the graph of $f$ at the vertices which isthe unique best affine approximant to $f$ on $\Delta$. For $k=1$, this resultprovides an extension of the Chebyshev equioscillation theorem for linearapproximants. Our result has interesting connections to the computer graphicsproblem of rapid rendering of projective transformations.

On Min-Max affine approximants of convex or concave real valued functions from $\mathbb R^k$, Chebyshev equioscillation and graphics