A piece of paper partially wrapped by a globe

[radiofeda]

Hi all,
In the paper "Broadband Ground-Plane Cloak" (http://www.sciencemag.org/cgi/content/abstract/323/5912/366), the author gave us a novel scheme to design non-Euclidean cloak. And the electromagnetic space is shown as bellow.

In the figure, the non-Euclidean space (the surface of a sphere) touches the Euclidean space (the plane) like a piece of paper partially wrapped by a globe. The plane carries bipolar coordinate grid and the surface of the sphere carry a grid too. The line where the sphere and the plane touch is a quarter circle or meridian.

So, my question is that: how can I draw the graph using Wolfram Mathematica or Maple?

Best wishes,

Yours,
Radiofeda​

 

[jvicens]

Dear Radiofeda,

Thank you for bringing this interesting paper to our attention. The concept of non-Euclidean cloak is indeed a novel and exciting one.

To answer your question, both Wolfram Mathematica and Maple have the capabilities to draw this graph. The first step would be to define the coordinates and grid lines for both the Euclidean plane and the non-Euclidean sphere. This can be done using the appropriate commands in either software.

Next, you can use the "Graphics" or "Plot" functions in Mathematica or the "plot" command in Maple to plot the coordinates and grid lines on the same graph. You can also use the "ParametricPlot" function in Mathematica or the "implicitplot" command in Maple to plot the quarter circle or meridian where the sphere and plane touch.

I recommend consulting the documentation or online resources for each software to learn more about the specific commands and syntax for plotting in Mathematica or Maple.

Best of luck in your graphing endeavors!