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What I found so far: a commonly used method, e.g. in finite element simulations, is meshing or triangulation. The following is an attempt of a gnuplot implementation of the "Delaunay Triangulation" of a set of points. https://en.wikipedia.org/wiki/Delaunay_triangulation However, I'm aware that gnuplot is not really the tool for such a task.

So, probably, there are better solutions which I am not aware of. I am curious to learn about them.

Delaunay triangulation:

The following code is certainly not the most efficient way to get the triangulation, improvements are welcome

Procedure (short version):

1. sort your N data points by increasing x and if identical x then by increasing y
2. find the first m>=3 points which are not collinear
3. loop points from m to N

3.1) find all hull points whose connections to point m+1 do not intersect with any current hull segment

3.2) connect these hull points to point m+1 and modify the hull accordingly

1. loop all inner edges

4.1) find the 2 triangles containing the current edge. These form a quadrangle

4.2) if the quadrangle is convex, check if the diagonal needs to be flipped ("Lawson-flip")

4.3) start over with 4) until no flips are necessary anymore

In order to color the triangles

1. split each triangle into 3 quadrangles using the centroid as a 4th point

1. color the 3 sub-quadrangles according to the z-value of the respective data point

Comments:

• gnuplot has no native sort capability (especially sorting by >=2 columns), so you have to use sort (already included on Linux, on Windows you have to install, e.g. CoreUtils from GnuWin.
• Flipping the edges will take some time. I guess, it scales with O(n^2). So, above 100 datapoints it becomes unpractial, because it will simply take too long. But there seem to be algorithms which should run in O(n log n).
• Improvements are welcome, or maybe even an implementation in gnuplot would be great ;-)

Code:

In your button_click function, in the for loop it should be