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The dataset is composed of 520<jats:italic>k<\/jats:italic> curves, of which 280<jats:italic>k<\/jats:italic> are generated from specific families characterised by distinctive shapes, and 240<jats:italic>k<\/jats:italic> are obtained from B\u00e9zier or composite B\u00e9zier curves. The dataset was generated starting from the parametric equations of the selected curves making it easily extensible. It is split into training, validation, and test sets to make it usable by learning-based methods, and it contains curves perturbed with different kinds of point set artefacts. To evaluate the detection of curves in point sets, our benchmark includes various metrics with particular care on what concerns the classification and approximation accuracy. Finally, we provide a comprehensive set of accompanying demonstrations, showcasing curve classification, and parameter regression tasks using both ResNet-based and PointNet-based networks. 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