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math.DG2025
A Complete Characterization of Pythagorean Hodograph Preserving Mappings
Amedeo Altavilla, Hans-Peter Schröcker, Zbyněk Šír +1
We fully characterize the mappings that send every Pythagorean-hodograph (PH) curve to a PH curve. We prove that in any dimension, such mappings are precisely the conformal fun…
math.DG2025
Lie Group Approach to Envelope Surfaces
Michal Molnár, Zbyněk Šír, Jana Vráblíková
In this paper, we develop a new and efficient approach to the computation of envelope surfaces. We interpret one-parameter systems of surfaces as curves in the homogeneous spaces o…