Criteria for sharksfin and deltoid singularities from the plane into the plane and their applications

TL;DR

This paper establishes criteria for identifying sharksfin and deltoid singularities in plane-to-plane mappings, providing geometric insights and exploring their occurrences in projections and planar motions.

Contribution

It introduces new criteria for sharksfin and deltoid singularities and explores their geometric interpretations and applications in projections and planar motions.

Findings

Criteria for sharksfin and deltoid singularities are established.

Geometric meanings for sharksfin conditions are provided.

Applications include projections of Whitney umbrellas and planar motions with 2 degrees of freedom.

Abstract

We give criteria for sharksfin and deltoid singularities from the plane into the plane. We also give geometric meanings for the conditions in the criterion of a sharksfin. As applications, we investigate such singularities appearing on an orthogonal projection of a Whitney umbrella, and a sharksfin appearing on planar motions with 2-degrees of freedom.