I would like to produce a tricontour plot similar to these with matplotlib. The difference between these examples and my situation is that I don't have the values of my function in the grid points: they are defined in my triangles (e.g. in the centroid of each triangle).
I would like to plot the result of a finite volume simulation, where the values are defined for each control volume, not for each grid point.
I suppose one simple solution would be to average the values at each grid point. I would like to know if there are any more direct solutions.
Maybe not exactly what you are looking for, but tripcolor function is designed for this use case (value defined at triangle centroid)
See for instance:
http://matplotlib.org/examples/pylab_examples/tripcolor_demo.html
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On the web, the only solution I find to plot the values of a two-dimensional function is to have a file with the matrix A(nxm) of the function's values and use matplotlib imshow. This will produce a map, whose extent (dimension along axes) has to be known and explicitly indicated.
Now, my concern arises from the fact that I need to plot two maps on the same axis, but one is slanted with respect to the other. So to say, I have a large main rectangular map and a smaller one that is oblique and superimposed.
In the end, the question is: is it possible to plot 2d maps starting from a file that is written as x, y, f(x,y) rather than just using f(x,y) so the plotting tool knows exactly where to draw?
I luckily found what I was looking for in pcolormesh that can draw a map given the coordinates of each point and its "colour"-value.
I'm trying to get statistics on a distribution but all the libraries I've seen require the input to be in histogram style. That is, with a huge long array of numbers like what plt.hist wants as an input.
I have the bar chart equivalent, i.e. 2 arrays; one with the x-axis centre points, and one with y-axis values for the corresponding value of each point. The plot looks like this:
My question is how can I apply statistics such as mean, range, skewness and kurtosis on this dataset. The numbers are not always integers. It seems very inefficient to force python to make a histogram style array with, for example, 180x 0.125's, 570x 0.25's e.t.c. as in the figure above.
Doing mean on the current array I have will give me the average frequency of all sizes, i.e. plotting a horizontal line on the figure above. I'd like a vertical line to show the average, as if it were a distribution.
Feels like there should be an easy solution! Thanks in advance.
I'm currently working with uncertainty visualization, using Python / Matplotlib, and I would like to be able to display the uncertainty about an isocontour in 2D. I will try to be more specific:
As input, I have N realizations of a scalar field.
These realizations are simulations of the same experiment.
For each of these N realizations, I have an isocontour.
Given that, I know that I can display the contour using the plt.contour function.
However, what I would like to do is to map each possible contour (by level) to a color map showing its probability of happening, something like its positional uncertainty. I.e, each one of the contour levels would be mapped to a color to represent its probability of happening.
It is possible to do that somehow? I don't know how I could verify if, for each contour at level b through n realizations, they are the same or not.
I have data points in x,y,z format. They form a point cloud of a closed manifold. How can I interpolate them using R-Project or Python? (Like polynomial splines)
It depends on what the points originally represented. Just having an array of points is generally not enough to derive the original manifold from. You need to know which points go together.
The most common low-level boundary representation ("brep") is a bunch of triangles. This is e.g. what OpenGL and Directx get as input. I've written a Python software that can convert triangular meshes in STL format to e.g. a PDF image. Maybe you can adapt that to for your purpose. Interpolating a triangle is usually not necessary, but rather trivail to do. Create three new points each halfway between two original point. These three points form an inner triangle, and the rest of the surface forms three triangles. So with this you have transformed one triangle into four triangles.
If the points are control points for spline surface patches (like NURBS, or Bézier surfaces), you have to know which points together form a patch. Since these are parametric surfaces, once you know the control points, all the points on the surface can be determined. Below is the function for a Bézier surface. The parameters u and v are the the parametric coordinates of the surface. They run from 0 to 1 along two adjecent edges of the patch. The control points are k_ij.
The B functions are weight functions for each control point;
Suppose you want to approximate a Bézier surface by a grid of 10x10 points. To do that you have to evaluate the function p for u and v running from 0 to 1 in 10 steps (generating the steps is easily done with numpy.linspace).
For each (u,v) pair, p returns a 3D point.
If you want to visualise these points, you could use mplot3d from matplotlib.
By "compact manifold" do you mean a lower dimensional function like a trajectory or a surface that is embedded in 3d? You have several alternatives for the surface-problem in R depending on how "parametric" or "non-parametric" you want to be. Regression splines of various sorts could be applied within the framework of estimating mean f(x,y) and if these values were "tightly" spaced you may get a relatively accurate and simple summary estimate. There are several non-parametric methods such as found in packages 'locfit', 'akima' and 'mgcv'. (I'm not really sure how I would go about statistically estimating a 1-d manifold in 3-space.)
Edit: But if I did want to see a 3D distribution and get an idea of whether is was a parametric curve or trajectory, I would reach for package:rgl and just plot it in a rotatable 3D frame.
If you are instead trying to form the convex hull (for which the word interpolate is probably the wrong choice), then I know there are 2-d solutions and suspect that searching would find 3-d solutions as well. Constructing the right search strategy will depend on specifics whose absence the 2 comments so far reflects. I'm speculating that attempting to model lower and higher order statistics like the 1st and 99th percentile as a function of (x,y) could be attempted if you wanted to use a regression effort to create boundaries. There is a quantile regression package, 'rq' by Roger Koenker that is well supported.
For a math fair project I want to make a program that will generate a Julia set fractal. To do this i need to plot complex numbers on a graph. Does anyone know how to do this? Remember I am using complex numbers, not regular coordinates. Thank You!
You could plot the real portion of the number along the X axis and plot the imaginary portion of the number along the Y axis. Plot the corresponding pixel with whatever color makes sense for the output of the Julia function for that point.
Julia set renderings are generally 2D color plots, with [x y] representing a complex starting point and the color usually representing an iteration count.