# How to check if my gridded X and Y are inside a polygon?

I have gridded X and Y that are defined by

``````lon  = 20:0.25:379.75;
lat  = -90:0.25:89.75;
X, Y = ndgrid(lon, lat).
``````

My goal is to create a Boolean array (named `Index`) the same size as X (or Y) and their values should be 1 if they are inside a polygon. That way I can apply it to my Variable grid like: Variable[Index] .= NaN;

Below is what I found from the internet, but the generated Boolean array is a column data, instead of the size of X.

``````using PolygonOps
using StaticArrays

polygon = SVector.(lonW, latW);    # boundary of the polygon
lon  = 20:0.25:379.75;
lat  = -90:0.25:89.75;
points = vec(SVector.(lon',lat));

inW = [inpolygon(p, polygon; in=true, on=false, out=false) for p in points];
``````

How can I replace the `points` above with my gridded X and Y, so as to achieve my above goal? Thanks!

What is `ndgrid`?

Not knowing what `ndgrid` does (or more importantly, where it’s defined), I think

``````inW = [inpolygon((x, y), polygon; in=true, on=false, out=false) for x in lon, y in lat]
``````

should do what you want. In general, I haven’t seen very many strong use cases for “grids” in Julia, broadcasting and loops are just that much better.

1 Like

Let’s dig a square hole on Atlantic

``````using GMT

# Load the earth grid at 15 arc minutes

# A polygon
pol = [-58 13; -58 37; -20 37; -20 13; -58 13];

# Compute the mask. Here the ``inc`` and ``registration`` should be
# automatically assigned via the ``G`` argument in ``region`` but some bug ...
# Anyway, understanding *pixel vs grid* registration is fundamental
# https://docs.generic-mapping-tools.org/dev/cookbook/options.html#pixel-registration

# Now let's dig that hole

``````

3 Likes

Many thanks, All.

`ndgrid` is similar to `meshgrid`. It is a function within the DIVAnd.jl package.

Many thanks!

Is `G` a n1 x n2 gridded data? Can I apply the same thing to another grid that is produced with a different set of longitude and latitude? Or this is only applicable to internal GMT stored grids?

you want to use GMT.jl and for other reasons as well) you should `surface` (or other GMT gridders) instead of `ndgrid`

1 Like

GMT stored grids is just a Julia type. I already pointed you to them. It has a `G.z` member that is a plain 2D array.

1 Like

Ccing @Alexander-Barth here.

I think ndgrid is the preferred gridding method by DIVAnd, am I right? I hope it will not be too much different from the `surface` function within GMT.

I’m not comparing numeric merits (don’t even know that `ndgrid`, I thought it was the Matlab one) but you are having difficulties with the type conversions that would not exist if you computed the grid with a GMT method in first place.

Next question: What is `meshgrid`? That’s not a `Base` function either.

If `X, Y = ndgrid(x, y)` are matrices such that `X[i, j] == x[i]` and `Y[i, j] == y[j]` (or vice versa), this is a very wasteful way to store data. For languages like Matlab it might make sense to create large matrices to represent repeated data like this, because they perform all their calculations matrixwise anyway. But Julia is intentionally designed to quickly and intelligently broadcast across the elements of vectors (or tuples, generators …). For instance, your `lon` and `lat` essentially store three numbers each: `start`, `end` and `step`. Turning them into a vector (`lon_vec = collect(lon)`) increases that number to `length(lon) == 1438` and `length(lat) == 720` respectively. That’s pretty wasteful. Now doing `ndgrid` spreads that same six-number (`384 b`) information over `2*length(lon)*length(lat) == 2070720` numbers (`132 Mb`). Unless of course the return type of `ndgrid` is just a wrapper of the original range, in which case I don’t see what use it is to begin with.

2 Likes

I may be wrong, but from memory, some parametric 3D surface plots (using plotlyjs, pyplot, Makie, etc.) seem to require the creation of grids first?

And I bet your gorgeous golden stripes, too.

1 Like

@joa-quim, there may be job opportunities for a goldsmith and jewelry designer using Julia… I think your understanding is correct.

Basically `ndgrid` creates a matrix for both longitude and latitude. That way, the program knows the exact longitude and latitude values at each of the grid points.

That said, I agree the Julia way is more efficient.

`Plots.jl` (which I’ve spent most of my time using) has `plot(-2:0.1:2, 0:0.1:4, (x, y) -> exp(- x^2/4 - y^2/2))`. Internally it might be using grids (depending on backend), which I would guess is at least not a bottleneck in the plotting flow, but at least you’re not required to drag the grids around as a user.

Sure, but that is far from a parametric 3D surface like a torus or something fancy (and on top of which one may want to display some scalar field too).

No need to go for fancy surfaces. If one has a measured quantity (e.g., temperature) on a regular mesh we must deal with grids.

1 Like

And let’s not start talking about data on unstructured meshes!

1 Like

Not really.

``````T = 273u"K" + 15u"K"*randn(501,501)
x = range(-5,5; length=501)u"cm"
y = range(-5,5; length=501)u"cm"

plot(x, y, T; st=:surface)
``````

Of course you need all of your samples, but you really don’t need to gridify `x` and `y`.