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.

  • $\begingroup$ What is a polyline? $\endgroup$
    – littleO
    Apr 18, 2022 at 17:16
  • $\begingroup$ A name for polygonal chains. This is more of a computer science than a math term, you're right. $\endgroup$
    – Joce
    Apr 18, 2022 at 17:20
  • $\begingroup$ (I don’t know what a polygonal chain is either.) $\endgroup$
    – littleO
    Apr 18, 2022 at 17:22
  • $\begingroup$ 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." $\endgroup$
    – Joce
    Apr 18, 2022 at 17:29


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