This supplement consists of several parts that refer directly to specific topics in the paper: A Proof of Equation (2) B Proof of Lemma 3.1 (Symmetric biproportional fit) C Technical details on why ”local affinity” is sufficient in Section 4.1 D Proof of Theorem 4.2 (Convergence of PSIPF) E Proof of Lemma 4.4 (L1-monotony) F Proof of Lemma 4.5 (Volume bounds) G Proof of Lemma 4.6 (Limit points)...

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In the literature, methods for fitting superellipses to data tend to be computationally expensive due to the non-linear nature of the problem. This paper describes and tests several fitting techniques which provide different trade-offs between efficiency and accuracy. In addition, we describe various alternative error of fits (EOF) that can be applied by most superellipse fitting methods. keywo...