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How to draw a heatmap with grids of different colors in a map?

Recently I have been reading a paper called Modeling Taxi Drivers’ Behaviour for the Next Destination Prediction. There is a figure(Fig.1) that I wonder how to draw. Based on what I know, it may be drawn by Python. Then what library of Python should I use to draw such a heatmap?
Thanks a lot in advance for your time and your expertise.
Best Regards

I have built something very similar for myself in the past. However, as you are just wondering how this would be drawn and not exactly asking how to do it with Python, I will share how I did it.
1. Building Grid:
The grids on the map are squares of X-size latitude and longitude. In short, those are latitude and longitude grids. I used an interactive map library named leaflet.js to build the world map with an overlay of latitude and longitude grids. This is the tutorial I followed from the leaflet: https://leafletjs.com/examples/choropleth/
Remember, you have to and can build your version of the grid to overlay on a world map using GeoJSON as discussed in the tutorial. At least, when I was building, there wasn't a publicly available version of the lat/long square grid.
2. Showing Colors (Heatmap):
Once you build the grid with GeoJSON, the leaflet can take the whole GeoJSON as it is and overlay it on any map of your choice. That means you can put the numbers(aka data) for each grid in the GeoJSON. This part is also shown in the same tutorial.
For my project, I used to create a complete GeoJSON formatted file with normalized data in Python and then visualize it in leaflet.js. Below is an example of what I have built using these tools.

Simple 3D Graphics in Python

I am working in a project where 3D visualizations are important to see what is happening during the setup stage and perhaps for visual validation by making a short videos of what is happening.
The problem that I have is that 3D visualizations in Python are too sophisticated, and complicated to learn for what I need. I find that Mathematica is the perfect kind of software...but it is not portable and is very expensive.
Question
Is there any Python package similar to Mathematica?
Clarification
I don't want a "plotting" program, since plotting is not what I am looking for. I want to generate simple geometric shapes like spheres and cubes that can move around, this is more than enough. Give some coordinates, perhaps a rotation, and the program just shows the desired image(s) to export as a .png or make a quick video; as in Mathematica.
Packages like Pygame, Panda3D, Pyglet, etc., look too complicated and an overkill for what I need, as well as software like Blender, etc. Jupyter notebooks are similar, but they don't have the 3D graphics capabilities. I found a Python module named Fresnel, but it looks too sophisticated for what I need.
I have read several answers to this question here in Stack Overflow, but they seem outdated and not really what I am looking for.
Further Clarification
To draw spheres in Mathematica you do:
coordinates = Flatten[Table[Table[Table[ {i,j,k}, {k,1,10}], {j,1,10}], {i,1,10}],1]
spheres= Flatten[Table[Graphics3D[{Sphere[coordinates[[i]],0.5]}],{i,1,Length[coordinates]}]]
Show[{spheres}]
This is a simple quick and easy way of displaying a group of spheres. To use any program in Python to do the same, it seems like you must be an expert in 3D graphics to do this simple thing.
Programs that have capabilities of using Python scripts, like Blender, make it difficult to use the interface in a straight forward way (try doing the same in Blender, it will take a while just to learn the basics!).

I know several other user-friendly plotting libraries than matplotlib, but not a lot provide an interactive view. There is of course the well known vtk but it's not for end-user
plotly
For usage in a notebook, like jupyter and mathematica, you probably would go for plotly It's using a browser-based interface with plots very similar to mathematica
pymadcad
If you need a more offline version and what you are looking for is some view you can rotate/zoom/pan to look on your geometry by different sides, you can take a look at pymadcad
It even works with touchscreens.
It is not centered on 3D visualization, so it's a bit overkill to use it only for it, but for 3D curves, 3D surfaces, spheres and cubes as you said, it can do the job
simple plots with pymadcad:
from madcad import *
from madcad.rendering import Displayable
from madcad.displays import GridDisplay
# create a wire from custom points
s = 100
mycurve = Wire([ vec3(sin(t/s), cos(t/s), 0.1*t/s)
for t in range(int(s*6*pi)) ])
# create a sphere
mysphere = uvsphere(vec3(0), 0.5)
# display in a separated window
show([
mycurve, # displaying the curve
mysphere, # displaying the sphere
Displayable(GridDisplay, vec3(0)), # this is to have a 2D grid centered on origin
])
result:
(The window is dark because so is my system theme, but likely it will adapt to yours)

Is it an orthogonal projection in the Nearside Perspective?

I'm currently working on world map visualizations. For now, I can use a home-made software for visualizations and point projections (Java), but I would like to upgrade the soft to be able to use a similar tool in Python.
Thus, I wanted to use cartopy with the module PROJ4, not to re-code everything, and use the wonderfull existing libraries.
It perfectly works for the PlateCarree projection, but when I want to use the Nearside Perspective, I observe a small difference between the two methods.
The two following pictures are extracted from the Java software (1) and the cartopy plot (2).
Cartopy (0.17) is used with matplotlib (3.0.2) and proj4 (4.9.1). In both pictures, we are observing at lon=lat=0° and at 400 km.
Here is the first image (Java):
Java visualization
Here is the second one (Cartopy):
Cartopy representation
As one can observe, lands are over-represented in the cartopy plot. Asuming that I want to get exactly the same projection as the one in my Java software (same representation as the "TrueView angles" in Telecom fields), I discovered in the cartopy crs module:
class NearsidePerspective(_Satellite):
"""
Perspective view looking directly down from above a point on the globe.
In this projection, the projected coordinates are x and y measured from
the origin of a plane tangent to the Earth directly below the perspective
point (e.g. a satellite).
"""
So I got this question: which projection is this about? Are the angles kept, which would means that I have an undetected problem? Or is it an orthogonal projection on the tangent plane? In this case, angles are not conserved, and I would need a solution to apply another projection (the correct one in my case). I might use the wrong one...
Thanks for your time,
Lou

I'm not sure if it's an orthogonal projection, but what CartoPy is using is directly from Proj4:
https://proj4.org/operations/projections/nsper.html
I think coordinates in this Nearside Perspective coordinates are Cartesian distances (distances from the origin on a plane), not angles. It sounds like angles are what's being used for your projection. Have you looked at using the Geostationary projection, but with a different satellite height?
https://scitools.org.uk/cartopy/docs/latest/crs/projections.html#geostationary
I can say that in this projection, the coordinates are angles (multiplied by the satellite height). Might be what you're looking for.

How to slice 2D grid from 3D irrigular data?

I have some data of soil's moisture content (Theta) in the form of 3D-domain points (CSV file of the columns x, y, z, Theta). I want to take cross sections from the 3D domain in some specific positions (section ABCD in the figure). I want to calculate the value of Theta in a 5*5 grid in the cross-section, but the points around each node of the grid are not coplanar with the unknown point. I did this before for 2D domains in python, but the 3D domains seem more complicated for me. I found that plotly can make something like that in its virtual environment but I want this to output a numpy array or pandas DataFrame to draw it as a contour in the jupyter notebook.
I know that finding the grid involves finding the value of each point like P0 in the figure by interpolation or gridding from its neighbors, then to draw the cross section using matplotlib, but I don' know how to do it.
Related question, Is slicing 2D grids from 3D grids available in matplotlib or similar libraries?
Thanks for all help.

The underlying problem is 3D interpolation. There are numerous packages which can do this type of thing, or you can write your own (using, e.g. KDE, which is basically just a type of smoothing/binning). There is a lot of material on the topic, like
This answer https://stackoverflow.com/a/15753011/230468
The scipy docs
This extensive set of option on scicomp.stack
And this blog post (with some good examples)

Have you tried playing with pyugrid? It's a library specifically for manipulating unstructured grids, so it sounds like it might be of some use to you. Check out these example notebooks.

Best way to create a 2D Contour Map with Python

I am trying to create a 2D Contour Map in Python that looks like this:
In this case, it is a map of chemical concentration for a number of points on the map. But for the sake of simplicity, we could just say it's elevation.
I am given the map, in this case 562 by 404px. I am given a number of X & Y coordinates with the given value at that point. I am not given enough points to smoothly connect the line, and sometimes very few data points to draw from. It's my understanding that Spline plots should be used to smoothly connect the points.
I see that there are a number of libraries out there for Python which assist in creation of the contour maps similar to this.
Matplotlib's Pyplot Contour looks promising.
Numpy also looks to have some potential
But to me, I don't see a clear winner. I'm not really sure where to start, being new to this programming graphical data such as this.
So my question really is, what's the best library to use? Simpler would be preferred. Any insight you could provide that would help get me started the proper way would be fantastic.
Thank you.

In the numpy example that you show, the author is actually using Matplotlib. While there are several plotting libraries, Matplotlib is the most popular for simple 2D plots like this. I'd probably use that unless there is a compelling reason not to.
A general strategy would be to try to find something that looks like what you want in the Matplotlib example gallery and then modify the source code. Another good source of high quality Matplotlib examples that I like is:
http://astroml.github.com/book_figures/

Numpy is actually a N-dimensional array object, not a plotting package.
You don't need every pixel with data. Simply mask your data array. Matplotlib will automatically plot the area that it can and leave other area blank.

I was having this same question. I found that matplotlib has interpolation which can be used to smoothly connect discrete X-Y points.
See the following docs for what helped me through:
Matplotlib's matplotlib.tri.LinearTriInterpolator docs.
Matplotlib's Contour Plot of Irregularly Spaced Data example
How I used the above resources loading x, y, z points in from a CSV to make a topomap end-to-end