Wurm, E.Jüttler, B.Leif Kobbelt and Peter Schroeder and Hugues Hoppe2014-01-292014-01-2920033-905673-06-11727-8384https://doi.org/10.2312/SGP/SGP03/240-247We 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 representation are found by solving a system of linear equations. In order to allow for problematic input data, we introduce a criterion for detecting points close to possible singularities. Using this criterion we split the data into segments and develop methods for propagating the orientation of the normals globally. Furthermore we present a simple fallback strategy, that can be used when the process of orientation propagation fails. The method has been shown to work successfullyCategories and Subject Descriptors (according to ACM CCS): G.1.2 [Approximation]: Approximation of surfaces and contours, Spline and piecewise polynomial approximation; J.6 [Computer-Aided Engineering]: ; I.3.5 [Computational Geometry and Object Modelling]: Curve, surface, solid, and object representations