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Grid - "A pattern or structure made from horizontal and vertical lines crossing each other to form squares".

Tilemap - "A two-dimensional grid made up of rectangular tiles of equal size".

Hexagonal "grid/map". Hexagon image catlikecoding.com Source: catlikecoding.com

3D "grid/map". 3D grid Source: https://imgur.com/gallery/rPZIE

Regular "grid/map". Regular grid. Source: https://godotengine.org/qa/17425/grid-navigation-like-minecraft-dont-want-unity3d-again-please

But it could also be anything that doesn't have a definite pattern to it. Like Navigation Mesh. NavMesh Unity

It still consists of small parts/triangles that create whole "grid/map" area.

I guess that could be called just "map", but how do I define them afterwards? hex-map, 2D-grid-map, navigation-mesh-map? Does that sound ok to you (hex-map sounds good, but it's the usual case)?

Or the closest I could think - square-map, hex-map, mesh-map, but map-system - makes people think of a normal world map or something similar to it. So if there is a mathematical definition I would prefer that.

The reason I need this, is I am working on a program and 1 component will encompass behaviour/visual representation of all of those things depending on the settings. So I have to give that component a name that will describe all of these cases.

How do I call all of these types of grids/hexagons/other types with (1 word or sentence) that defines them all?

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  • The one word solution is decompositions. Tessellations is okay as a general term but tends to be thought of as 2D decompositions. Depending on your viewpoint, you may want to use "discretizations". But that is more about sampling the properties of the surface at different locations.
    – Phil Sweet
    Jun 11, 2021 at 19:10

3 Answers 3

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Whether 2-D, 3-D or more, this is called a

tiling or tessellation.

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  • Great answer! It will work for most people but won't work in my case because in 3D graphics Tessellation refers to a subdivision process or other techniques, frequently associated with shaders. Jun 9, 2021 at 18:27
  • In case someone is interested what I mean - en.wikipedia.org/wiki/Tessellation_(computer_graphics) . Jun 9, 2021 at 18:33
  • Re: "won't work in my case" - then I have misunderstood what you are looking for. Can you elaborate on how what you'e looking for is different from a tiling or tessellation? Also, you may have more luck at a graphics site since you're asking for vocabulary specifically used for that community.
    – Mitch
    Jun 9, 2021 at 18:54
  • I will accept any answer that has most upvotes, I just stated that it doesn't work for me, but it for sure may work for someone else, I didn't mean that you haven't answered my question if that looked like it. Before last sentence in the question I have described why I need this, and I assumed that previous examples would convey the meaning of what I am looking for. Basically it's cells that can be any shape in any dimension structured in a repetitive or non-repetitive way, and those cells have position, size and shape. Sorry if that was confusing. Jun 9, 2021 at 21:36
  • Also, graphics community would kick me out because of a question like this :) They would say that the website is for questions that touch technical subjects and not Use of English :( Jun 9, 2021 at 22:05
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I add the word lattice to other valid suggestions.

Cambridge has a restrictive definition of lattice that does not cover other wider uses:

lattice = a structure made from strips of wood or other material that cross over each other with spaces between

Cambridge

Wider use is given by:

Lattice =

2 An interlaced structure or pattern resembling a lattice.

"the lattice of branches above her"’

3 in Physics: A regular repeated three-dimensional arrangement of atoms, ions, or molecules in a metal or other crystalline solid

Oxford Lexico

The example of the branches shows that regularity is not a strict feature of a lattice. The mention of 3-dimensional leads naturally to the idea of a lattice in any number of dimensions. Hence it is easy to find mention of 2-D lattices such as you show.

For example, the title of an article:

Near-zero thermal expansivity 2-D lattice structures: Performance in terms of mass and mechanical properties

Science Direct

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  • I like lattice, because it is in use for a similar structure in musical tuning.
    – Theodore
    Jun 9, 2021 at 21:31
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This answer is about specific case of the question, I was looking for a word/combination of words which definition would include all of the different cases of tilemaps, be it 3D, 2D, have any shape, be some kind of structure which is divided into smaller chunks which can be represented visually using their shape.

Definition for poly- types describing shapes.

For 2D:

  • Polygon.

For 3D:

  • Polyhedron.

•• Polytope - it's definition is pretty vague, in mathematics it's used differently. But it's the closest thing I have found. Wiki Source.

The final touch would be to add something that defines structural behaviour/positioning of polytopes on a coordinate plane. Since we live in 3D(probably) and all applications usually use 3D to represent generic viewport of the world, we can use that information to think about polytopes in a 3-dimensional plane.

•• Cell - what can we use to describe a single entity in a 3D space? Probably a cell.

•• Structure - "The arrangement of and relations between the parts or elements of something complex".

We can come to conclusion that it could be: polytope-cell-structure or cellular-polytope-structure. Referring to cell might look like it's a biological structure, so not sure about that one, what do you think?

Could be: polytope-entity-structure, etc.

In the end I am not sure which one is the best to choose from cell, entity, etc. If you have any ideas, I would love to see them.

Node - doesn't really work because it's something connecting two lines/etc.

Section - more like it contains something.

Segment - works really well as a definition.

FINAL - polytopes-segmented-structure or polytope-segments-structure or polytopial-segments-structure

Personal choice: polytopial-segments-structure

Alternatives:

  • Coordinate plane (definition is not quite right, but it if you think about looking at definition - it makes sense that it could be any type of structure on that plane).
  • Cell divided plane.
  • Cell divided dimension.
  • Cell dimension.
  • Coordinate dimension.
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  • Why pluralize “segment(s)”??
    – Jim
    Jun 9, 2021 at 21:26
  • @Jim because if I say polytopial-segment-structure for me it looks like it means - "that structure consists of 1 polytopial segment". Jun 9, 2021 at 21:29
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    So you would also think a brick walkway only contains one brick. Or an apple pie only contains one apple?
    – Jim
    Jun 9, 2021 at 21:31
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    @Jim that is conversational English, I can derive the meaning from use. But when you are reading a technical document those little intricacies matter a lot and can change the meaning altogether. For example, imagine that you had no prior knowledge that "apple pie" means a whole pie that has apples in it. In that case when reading "apple pie" would you actually think that it's a pie that contains apples or would you think that someone just placed 2 random words near each other? A good example is this virus song when a guy says those 2 words separately. Unless segments is a grammatic error here. Jun 9, 2021 at 21:45
  • 1
    Well, I have no idea what a polytopial segments structure is either but I know using an s is wrong. I probably would have gone with a polytopic cell structure.
    – Jim
    Jun 9, 2021 at 21:56

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