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Consider the roads in a city or the strands in a spiders web. Consider the set of points coinciding with the roads, or strands. Is there any commonly used terminology for such a set? Perhaps its called a lattice?

Angelos
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    Depending on what exactly you're interested in (do you only care about the connections? Do you care about their shape?) this could be called a graph or a network: https://en.wikipedia.org/wiki/Graph_(discrete_mathematics) – Qiaochu Yuan Jun 30 '22 at 07:59
  • I am interested in both intersections and the curve segments inbetween. – Angelos Jun 30 '22 at 08:11
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    Probably there is a better term for it, but you could call it a planar embedding of a graph – Milten Jun 30 '22 at 10:29
  • Graphs and Networks concentrate only on the Nodes and the Connectedness, not on the set of Points on the line between 2 Nodes , @QiaochuYuan ; Eg When you make the Adjacency Matrix, there is no information about those Points. – Prem Jun 30 '22 at 11:10
  • In addition to the above comment, Planar Embedding of graphs will have no information about Distances/Areas/Angles ; @Milten ; I think the "Curves" must be on a Cartesian Plane. – Prem Jun 30 '22 at 11:21
  • @Prem Embedding a graph means placing all the edges as curves in a given space, and without intersections. A planar embedding is an embedding in the Cartesian plane. So yes, a planar embedding of a (planar) graph has well-defined distances and areas and all that. – Milten Jun 30 '22 at 11:37
  • I am not sure I am talking about the same thing you are talking about ; Given a Planar graph, there are many "Equivalent" Planar Embeddings, each of which might have arbitrary Distances/Areas/Angles ; There is no Single Unique Planar Embedding which can claim to Preserve the Original Values, because there are no Original Values in the Planar graph. Moreover, the roads are not only Connections between Nodes, but also lines with "Continuously Changing Directions" at each Point. @Milten – Prem Jun 30 '22 at 11:58
  • @Prem Yes, I agree. A graph has no concept of lengths and such, but a particular embedding is precisely a concrete choice of where everything is in the plane. It is a geometric realization of the graph. – Milten Jun 30 '22 at 13:08
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    Oh OK, got it. Now the Particular Planar Embedding of a graph which we want to use to Describe the roads, web, etc, can be represented by "multiple lines or curves" in the form $f(x,y)g(x,y)h(x,y)....=0$ which {I think} is Either (A) Level Set or (B) Algebraic Curve. @Milten – Prem Jun 30 '22 at 14:17

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