Meaning of oscnode | Babel Free

Definitions

A node of a plane curve where two branches meet with contact order 3.

Examples

“Three nodes may coincide as consecutive points of a curve of finite curvature, giving rise⟳, not to a triple point⟳, but to the singularity called an oscnode; this is, in fact, an osculation or three-pointic contact⟳ of two branches of the curve.”

“Rhamphoid cuspidal lines possess⟳ two kinds of singular points which affect⟳ the class of the surface, and occur⟳ (i) when the rhamphoid cusp changes into an oscnode, (ii) when there are cubic nodes on the surface.”

“A tacnode is defined to be a singularity equivalent to the origin in the curve y²-x²#61;0, that is, the union of two smooth arcs meeting with contact⟳ of order⟳ two. Similarly, an oscnode is a singularity equivalent to y²-x⁶#61;0, i.e., consisting of two smooth branched with contact⟳ of order⟳ three, and so on.”

CEFR level