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Ideas on filling each shape in triangle mesh with values

I'm trying to write python code that creates a 2D NumPy array (e.g. 128x128) containing a mesh of raster triangles in which each triangle has a random value.
Does anyone know of any python package that could do this?
I tried using this triangle package (https://rufat.be/triangle/examples.html) but i can't seem figure out how to link that to my problem.
The ideal results would be something like this https://people.sc.fsu.edu/~jburkardt/data/triangle_files/double_hex2.2.ele.png)
but each triangle will show different color because it has different values.

Generate k random points inside the rectangle (0,0,128,128) and generate the Delaunay Triangulation of the set of the points plus the four corners of the rectangle.
Construct the NumPy array from the list of triangles by either
Implementing the filled triangle rasterization algorithm of your choice -- e.g. Bresenham's -- using a NumPy array as the target.
or more realistically, painting the triangles into a 128x128 pixel bitmap using a Python raster painting library of your choice and then converting the bitmap to a NumPy array.
Another idea would be to start with a tesselation of equilateral triangles with half triangles along two edges that cover a rectangle, stretch that to cover a square, randomly perturb the vertices, and then do (1) or (2) above ... but this will look less random in that all the internal vertices will have six triangles around them.

How to select the minimal set of circles that covers another circle?

I'm looking for some solutions that, given a set S of circles with 2D-center points and radii, returns a minimal sub-set M in S that covers entirely a specific circle with 2d-center point and radius. This last circle is not in S.
I've chosen circles, but it doesn't matter if we change them to squares, hexagons, etc.

You have two distinct problems: you need to turn the geometric problem into a combinatoric problem, and then you need to solve the combinatoric problem. For the latter, you are looking at a minimum set cover problem, and there should be plenty of literature on that. Personally I like Knuth's Dancing Links approach to enumerate all solutions of a set cover, but I guess for a single minimal solution you can do better. A CPLEX formulation (to match your tag) would use a binary variable for each row, and a ≥1 constraint for each column.
So now about turning geometry into combinatorics. All the lines of all your circles divide the plane into a bunch of areas. The areas are delimited by lines. Of particular relevance are the points where two or more circles meet. The exact shape of the line between these points is less relevant, and you might imagine pulling those arcs straight to come up with a more classical planar graph representation. So compute all the pair-wise intersections between all your circles. Order all intersections of a single circle by angle and connect them with graph edges in that order. Do so for all circles. Then you can do a kind of bucket fill to determine for each circle which graph faces are within and which are outside.
Now you have your matrix for the set cover: every graph face which is inside the big circle is a column you need to cover. Every circle is a row and covers some of these faces, and you know which.

Unordered cloud point of polygon contour to polygon

Dear Stackoverflow community,
I have contours of irregular polygons as unordered datapoints (like on the figure here: https://s16.postimg.org/pum4m0pn9/figure_4.png), and I am trying to order them (ie. to create a polygon).
I cannot use the convex hull envelope because of the non convex shape of the polygon. I cannot ase a minimum distance criterion because some points of other parts of the contour lie closer (example: point A has to be joined with B, but is closer to C). I cannot use a clockwise ordering because of the irregular shape of the contour.
Do anyone knos a way to implement (preferentially in Python) an algorithm that would reorder the datapoints from a starting point?

look here finding holes in 2D point set for some ideas on how to solve this
I would create point density map (similar to above linked answer)
create list of all lines
so add to it all possible combination of lines (between close points)
not intersecting empty area in map
remove all intersecting lines
apply closed loop / connectivity analysis on the lines
then handle the rest of unused points
by splitting nearest line by them ...
depending on you map grid size and point density you may need to blend/smooth the map to cover gaps
if grid size is too big then you can miss details like on the image between points A,C
if it is too small then significant gaps may occur near low density areas
But as said this has more then one solution so you need to tweak this a bit to make the wanted output perhaps some User input for shaking the solution a bit until wanted solution found...
[notes]
you can handle this as more covex polygons ...
add line only if winding rule met
stop when no more lines found
start again with unused points
and in the end try to connect found non closed polygons ...

Draw a curve joining a set of points in opencv python

I have a set of points extracted from an image. I need to join these points to from a smooth curve. After drawing the curve on the image, I need to find the tangent to the curve and represent it on the image. I looked at cv2.approxPolyDP but it already requires a curve??

You can build polyline, if order of points is defined. Then it is possible to simplify this polyline with Douglas-Peucker algorithm (if number of points is too large). Then you can construct some kind of spline interpolation to create smooth curve.

If your question is related to the points being extracted in random order, the tool you need is probably the so called 2D alpha-shape. It is a generalization of the convex hull and will let you trace the "outline" of your set of points, and from there perform interpolation.

How do you calculate the area of a series of random points?

So I'm working on a piece of code to take positional data for a RC Plane Crop Duster and compute the total surface area transversed (without double counting any area). I cannot figure out how to calculate the area for a given period of operation.
Given the following Table Calculate the area the points cover.
x,y
1,2
1,5
4,3
6,6
3,4
3,1
Any Ideas? I've browsed Greens Theorem and I'm left without a practical concept in which to code.
Thanks for any advise

Build the convex hull from the given points
Algorithms are described here
See a very nice python demo + src
Calculate its area
Python code is here

Someone mathier than me may have to verify the information here. But it looks legit: http://www.wikihow.com/Calculate-the-Area-of-a-Polygon and fairly easy to apply in code.

I'm not entirely sure that you're looking for "Surface area" as much as you're looking for Distance. It seems like you want to calculate the distance between one point and the next for that list. If that's the case, simply use the Distance Formula.
If the plane drops a constant width of dust while flying between those points, then the area is simply the distance between those points times the width of the spray.

If your points are guaranteed to be on an integer grid - as they are in your example - (and you really are looking for enclosed area) would Pick's Theorem help?

You will have to divide the complex polygon approximately into standard polygons (triangles, rectangles etc) and then find area of all of them. This is just like regular integration (only difference is that you are yet to find a formula to approximate your data).
The above points are when you assume that you are forming a closed polygon with your data.

Use to QHull to triangulate the region, then sum the areas of the resulting triangles.

Python now conveniently has a library that implements the method Lior provided. https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.ConvexHull.html will calculate the convex hull for any N dimensional space and calculate the area/volume for you as well. See the example and return value attributes towards the bottom of the page for details.