# Is there a name to refer to point $A$ / point $B$ when discussing vector $\overrightarrow{AB}$?

In a code, I am writing a concise documentation of a function that needs 2 vectors defining a triangle $$ABC$$. The function performs an operation which is invariant up to a translation, so two vectors only are necessary, named $$\vec{s}$$ and $$\vec{z}$$, and introducing points $$A$$, $$B$$ and $$C$$ is irrelevant and could even be misleading. However, the triangle $$ABC$$ has to be such that $$[AB]$$ is part of a polygonal chain (called polyline in computer science context) that is defined elsewhere in the code and $$C$$ of another. The function has little meaning independently of that setting.

I first document the properties of $$\vec{s}$$ as being one vector of the first polyline. Then I need to document $$\vec{z}$$, for that it would be convenient to say that $$\vec{z}$$ is such that $$A+\vec{z}$$ is a point of the other polyline.

    s: vector, base of triangle, along polyline Γ_1


However, not having given $$A$$ a name, I'm struggling, even when tolerating some abuse of notation:

    z: vector, pointing from [point of origin of] s along Γ_1 and to a point of Γ_2


Ιs there some elegant way to phrase this? Maybe

    z: vector, pointing from Γ_1 and to Γ_2, with (s,z) an angle.


...although again, it would properly be $$(A,\vec{s},\vec{z})$$ an angle.

• What is a polyline? Apr 18, 2022 at 17:16
• A name for polygonal chains. This is more of a computer science than a math term, you're right.
– Joce
Apr 18, 2022 at 17:20
• (I don’t know what a polygonal chain is either.) Apr 18, 2022 at 17:22
• Wikipedia: "a connected series of line segments. More formally, a polygonal chain P is a curve specified by a sequence of points ( A 1 , A 2 , … , A n ) called its vertices."
– Joce
Apr 18, 2022 at 17:29