We consider practical aspects of reconstructing planar curves with prescribed Euclidean or affine curvatures.These curvatures are invariant under the special Euclidean group and the special affine groups, respectively, and play an important role in computer vision and shape analysis.We discuss and implement algorithms for such reconstruction, and give estimates on how close reconstructed curves are relative to the closeness of their curvatures in appropriate metrics.Several illustrative examples are provided.
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Agudelo et al. (2024) studied this question.