This analysis defines pedal surfaces and singularities in framed curves, highlighting their geometric properties.
We define pedal and negative pedal surfaces of framed curves in the Euclidean 3-space and find that the loci of singularities of them are pedal and negative pedal curves, respectively. Moreover, we give sufficient conditions that pedal and negative pedal surfaces to be framed base surfaces. We also give a sufficient condition that negative pedal curves to be framed base curves.
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Kaixin et al. (2025) studied this question.
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