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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We discuss methods for fitting implicitly defined (e.g. piecewise algebraic) curves to scattered data, which may contain problematic regions, such as edges, cusps or vertices. As the main idea, we construct a bivariate function, whose zero contour approximates a given set of points, and whose gradient field simultaneously approximates an estimated normal field. The coefficients of the implicit ...

Although some of the lÝnear curve fitting techniques provide improvements over the classicalleast squares fit algorithm,most of them cannot globally stabilize majority of data sets, and are not robust enough to handIe moderate levels of noise or missing data. In this paper, we apply "ridge regression regularization" to strengthen the stability and robustness of a linear fitting method, 3L fitti...

We give a piecewise cubic curve fitting algorithm which preserves monotonicity of the data. The algorithm has a higher order of convergence than the Fritsch-Carlson algorithm and is simpler than the Eisenstat-Jackson-Lewis algorithm.

Fractal interpolation provides an efficient way to describe data that have an irregular or self-similar structure. Fractal interpolation literature focuses mainly on functions, i.e. on data points linearly ordered with respect to their abscissa. In practice, however, it is often useful to model curves as well as functions using fractal intepolation techniques. After reviewing existing methods f...