(basic) Why using 3d grid cells? - graphics

I'm studying about collision detection in 3d world but it really confused actually why we using 3d grid cells in 3d world.
If we think the world looks like 'minecraft', it will be efficient but our real world doesn't fit well in 3d grid cells(different shape of objects..).
So my question is this:
1) Why we use 3d grid cells?
2) Is 3d grid cells really efficient while performing 3d simulation?
3) What does it mean 'different 3d grid cells'? Just different size of grid?
Thanks!

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How to convert x and y coordinates into a heat map in excel?

I currently have a data set of x and y coordinates (position of an animal in an arena) over a period of time. I just used the coordinates to plot a scatter plot of what that looks like. However, instead of having every single coordinate as a separate point, i was wondering if there was a way to create a heat map of the points? So, the higher the likelihood of the animal in a specific area/ similar coordinates, the warmer the color? Hoping for the final product to be a depiction of the arena with a gradient of colors based on the likelihood the animal explores those regions?
Well with that many points, I don't know if Excel is the right choice if wanting to color-coordinate. The site https://app.rawgraphs.io/ has some really cool graphing capabilities. I use this when needing sankey's or something unusual that Excel cannot easily handle.
Here I used 1500 x/y points between 0 and 20. Then I selected the graph type called "Contour Plot".
Would this work?
Or here's a Hexagonal Binning chart of the same data...

Gnuplot Plotting Multiple Interpolated Surfaces in One Image

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How to calculate what percentage of a pixel is within the bounds of a shape

I have a 2d grid where pixel centers are at the intersection of two half-grid lines, as shown below.
I also have a shape that is drawn on this grid. In my case the shape is a glyph, and is described by segments. Each segment has a start point, end point and a number of off-curve points. These segments can be quadratic curves or lines. What's important is that I can know the points and functions that make up the outline of the shape.
The rule for deciding which pixels should be turned on is simple: if the center of the pixel falls within the shape outline, turn that pixel on. The following image shows an example of applying this rule.
Now the problem I'm facing has to do with anti aliasing. What I'd like to do is to calculate what percentage of the area of a given pixel falls within the outline. As an example, in the image above, I've drawn a red square around a pixel that would be about 15% inside the shape.
The purpose of this would be so that I can then turn that pixel on only by 15% and thus get some cleaner edges for the final raster image.
While I was able to find algorithms for determining if a given point falls within a polygon (ray casting), I wasn't able to find anything about this type of problem.
Can someone can point me toward some algorithms to achieve this? Also let me know if I'm going about this problem in the wrong way!
This sounds like an X, Y problem.
You are asking for a way to calculate the perecentage of pixel coverage, but based on your question, it sounds that what you want to do is anti alias a polygon.
If you are working only with single color 2D shapes (i.e red, blue, magenta... squares, lines, curves...) A very simple solution is to create your image and blur the result afterwards.
This will automatically give you a smooth outline and is simple to implement in many languages.

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in my final paper I needed to create a 3d graph, on this occasion the graph was a cross of latitude, longitude and radioactive intensity. I used the plotly, check if it's help you plotly documentation.
My graph created with this biblioteca

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I have an image with some curve draw in it and I want to extrapolate positions of next few pixels based on already drawn ones. An example is shown in figure 1. For this situation it is easy to fit curve (some parabola) using the least square fit (figure 2) and then based on this fit rasterize the curve to find next pixels (I also need the vector curve for some further calculations).
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