# Orthotope grid type (generalization of AbstractRange)
**URL:** https://discourse.julialang.org/t/orthotope-grid-type-generalization-of-abstractrange/45072
**Category:** General Usage
**Tags:** question
**Created:** [August 17, 2020, 2:58am UTC](https://discourse.julialang.org/t/orthotope-grid-type-generalization-of-abstractrange/45072 "2020-08-17T02:58:33Z")
**Posts on this page:** 9
**Page:** 1
### Author:  [@chakravala](https://discourse.julialang.org/u/chakravala)
#### Post date: [August 17, 2020, 2:58am UTC](https://discourse.julialang.org/t/orthotope-grid-type-generalization-of-abstractrange/45072/1 "2020-08-17T02:58:33Z")
So, I’ve found that in several separate packages I need something like an `Orthotope` type
```nohighlight
struct Orthotope{N,T}
min::SVector{N,T}
max::SVector{N,T}
end
```
Or in other words, a hyper-rectangle, specified by minimum and maximum bounds.
```julia
struct Orthogrid{N,T}
x::Orthotope{N,T}
n::SVector{N,Int}
end
```
In addition to that, I need to specify a number of grid points in each dimension. That’s what the second wrapping type is for, thus `Orthogrid` contains the grid sizes and the `Orthotope` value.
However, I’m really not sure where to put this type. I’m planning to use it in various ways in multiple different packages. All the packages that I need this for are built on my [Grassmann.jl](https://github.com/chakravala/Grassmann.jl) package, so I am considering just adding it into that package. However, it doesn’t quite make sense to put it in there contextually I think, but I also don’t necessarily want to make a separate package for it.
I’m not really sure how to organize this type yet. It could go into `GeometryBasics` but I don’t want to load that as a dependency in my packages (only as an optional dependency).
It’s kind of like a generalization of an `AbstractRange` but for more than 1 dimension.
---
### Author:  [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)
#### Post date: [August 17, 2020, 3:29am UTC](https://discourse.julialang.org/t/orthotope-grid-type-generalization-of-abstractrange/45072/2 "2020-08-17T03:29:30Z")
Before adding this to `Grassmann.jl`, developing it separately may simplify focus and allow more of whatever is behind the reason for this facility to shine through. It is much easier to bring cleanly a small pkg into a larger home than vice versa.
fyi: [Vectorized … tessellations of d-orthotopes and their faces with high-order orthotopes or simplicial elements](https://hal-univ-paris13.archives-ouvertes.fr/hal-02425250/document)
---
### Author:  [@chakravala](https://discourse.julialang.org/u/chakravala)
#### Post date: [August 17, 2020, 3:13pm UTC](https://discourse.julialang.org/t/orthotope-grid-type-generalization-of-abstractrange/45072/3 "2020-08-17T15:13:26Z")
Figured it out, `Orthotpe` is essentially a multi-dimensional generalization of `AbstractRange` types.
```nohighlight
julia> dump(0:1)
UnitRange{Int64}
start: Int64 0
stop: Int64 1
```
The base range objects are constructed with `start` and `stop` of elements that are `Real`.
However, what’s really needed is a generalization of that for `SVector` inputs.
```nohighlight
(::Base.Colon)(min::SVector{N,T},max::SVector{N,T}) where {N,T} = Orthotope{N,T}(min,max)
```
In higher dimensions, what’s needed is simply an `SVector` specifying the min and max range.
```julia
julia> SVector(0,0,0):SVector(1,1,1)
Orthotope{3,Int64}([0, 0, 0], [1, 1, 1])
```
So why don’t we have that in Julia yet? Should it be in the base language maybe?
```nohighlight
SVector(0,0,0):SVector(0.1,0.1,0.1):SVector(1,1,1)
```
Also, having a 3 argument version would specify the number of grid points or interval lengths.
Either, this needs to be added to `StaticArrays` package to define the `:` constructor method without type piracy, or I need to add it to `Grassmann` and use my own vector input types for it.
Most likely, I’ll just add it to `Grassmann` since that has the least friction workflow for me, but if anyone else is interested, I can consider making a pull request to `StaticArrays` package.
---
### Author:  [@Zach\_Christensen](https://discourse.julialang.org/u/Zach_Christensen)
#### Post date: [August 17, 2020, 3:29pm UTC](https://discourse.julialang.org/t/orthotope-grid-type-generalization-of-abstractrange/45072/4 "2020-08-17T15:29:20Z")
Have you looked to GeometryBasics.jl for this? IRC, it has hyper rectangles and I make extensive use of StaticArrays
---
### Author:  [@chakravala](https://discourse.julialang.org/u/chakravala)
#### Post date: [August 17, 2020, 3:30pm UTC](https://discourse.julialang.org/t/orthotope-grid-type-generalization-of-abstractrange/45072/5 "2020-08-17T15:30:32Z")
Did you read my original post? I only use `GeometryBasics` as an optional dependency, because I have my own geometry defined in `Grassmann` and it would be superfluous to load `GeometryBasics` by default every time I use `Grassmann`.
I think it’s fairly clear that this would belong into `StaticArrays` due to type piracy of `:`, or I would define it on my own types in `Grassmann`.
---
### Author:  [@Zach\_Christensen](https://discourse.julialang.org/u/Zach_Christensen)
#### Post date: [August 17, 2020, 3:40pm UTC](https://discourse.julialang.org/t/orthotope-grid-type-generalization-of-abstractrange/45072/6 "2020-08-17T15:40:45Z")
> I only use `GeometryBasics` as an optional dependency, because I have my own geometry defined in `Grassmann` and it would be superfluous to load `GeometryBasics` by default every time I use `Grassmann` .
I’m just saying that GeometryBasics.jl may already have what you need and you don’t need to make it elsewhere or add it to GeometryBasics.
> I think it’s fairly clear that this would belong into `StaticArrays` due to type piracy of `:` , or I would define it on my own types in `Grassmann` .
`SVector:SVector:SVector` seems like a pretty specialized use of `:`. You could just `map(:, ::SVector...)` to accomplish basically the same thing and wrap it in whatever type you want to do stuff with.
---
### Author:  [@chakravala](https://discourse.julialang.org/u/chakravala)
#### Post date: [August 20, 2020, 10:55am UTC](https://discourse.julialang.org/t/orthotope-grid-type-generalization-of-abstractrange/45072/7 "2020-08-20T10:55:27Z")
[https://github.com/chakravala/Grassmann.jl/commit/02472f0f7c72a41d5ff0c1dba37b6fa4417ccfa2](https://github.com/chakravala/Grassmann.jl/commit/02472f0f7c72a41d5ff0c1dba37b6fa4417ccfa2)
```nohighlight
julia> using Grassmann; basis"3"
(⟨+++⟩, v, v₁, v₂, v₃, v₁₂, v₁₃, v₂₃, v₁₂₃)
julia> OG = Chain(1.0v1):(0.2v2+0.2v3):(1.0v1+v2+v3)
(1.0v₁ + 0.0v₂ + 0.0v₃):(0.0v₁ + 0.2v₂ + 0.2v₃):(1.0v₁ + 1.0v₂ + 1.0v₃)
```
---
### Author:  [@juthohaegeman](https://discourse.julialang.org/u/juthohaegeman)
#### Post date: [August 20, 2020, 11:19am UTC](https://discourse.julialang.org/t/orthotope-grid-type-generalization-of-abstractrange/45072/8 "2020-08-20T11:19:32Z")
`CartesianIndices` in Base represents multidimensional ranges, but of course only for `UnitRange{Int}`, and they can be created as range of two `CartesianIndex` instances e.g.
```julia
julia> CartesianIndices((1:5,3:8,1:7)) == CartesianIndex(1,3,1):CartesianIndex(5,8,7)
true
```
I think there was a time that this was called `CartesianRange`, but I don’t think it every supported anything beyond `UnitRange`. How about `Base.Iterators.product(range1, range2, range3)`?
---
### Author:  [@Zach\_Christensen](https://discourse.julialang.org/u/Zach_Christensen)
#### Post date: [August 20, 2020, 1:47pm UTC](https://discourse.julialang.org/t/orthotope-grid-type-generalization-of-abstractrange/45072/9 "2020-08-20T13:47:36Z")
> [@juthohaegeman](#):
>
> but of course only for `UnitRange{Int}` ,
Fun fact, you can actually use any `AbstractUnitRange{Int}` for `CartesianIndices`