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Evolving evolutoids and pedaloids from viewpoints of envelope and singularity theory in Minkowski plane
(Elsevier, 2022) Yang, Zhichao; Li, Yanlin; Erdogdu, Melek; Zhu, Yushu
In this paper, we take advantage of envelope theory and singularity theory to study the evolutoids and pedaloids in Minkowski plane. We illustrate an internal correlation from algebraic and geometric viewpoints, and give the geometric explanation of evolutoids and pedaloids. Then, we generalize the notions of evolutoids and pedaloids to the category of frontals in Minkowski plane. Furthermore, we apply the technique of singularity theory, using the discriminants and versal unfolding tools, to consider evolving evolutoids and give the classifications of singularities of the evolutoids, and explain when cusps and inflexions occur and how evolutoids evolving. Besides, we found that there is a close relationship between the evolutoids and pedaloids and good correspondence between their singularities.(c) 2022 Elsevier B.V. All rights reserved.