The Douglas-Peucker algorithm is a method for simplifying piecewise linear curves, efficiently reducing the number of points while keeping the geometric error bounded. In this thesis, we examine how the algorithm works and how it affects the quality of simplified curves when representing planar paths, in particular in the processing of GPS tracks. First, we present the mathematical background of the algorithm and analyze its time complexity. We then highlight key limitations of the classical procedure, such as the possibility of self-intersections when using larger tolerances and inadequate handling of closed curves. Based on related approaches, we implement extensions that improve the topological consistency of the simplification and enable a more stable treatment of closed curves. We evaluate the proposed solutions experimentally on real-world data and compare the results in terms of reduction rate, geometric error, and the occurrence of topological inconsistencies. In addition, we develop an interactive tool for visualizing the algorithm's execution, which allows real-time observation of how the tolerance influences point selection and the final shape of the curve.
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