Picture If You Will
Apr. 29th, 2011 09:36 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowA few days ago, W and I sat down together, and he gave me his comments on the prisms paper. He pointed out a few obscurities and infelicities, but his main problem was with the pictures: they need more detail, and there should be more of them. He's right.
There are three kinds of pictures in the paper. There are pictures of actual prisms, and there are diagrams consisting of several rectangles, indicating the sequence of faces a geodesic passes through. Both of these I can construct using Geometer's Sketchpad, and I can copy them directly from GSP into the text. The third kind.... I constructed a parameter space for prisms, by drawing an equilateral triangle and describing a way of associating each shape a prism can have with a particular point in the interior of the triangle. (Prisms near the vertices are long and skinny; prisms near the midpoints of the edges are flat and squarish, like tiles; the cube is in the exact center.) Given a particular kind of geodesic, the feasibility region is the part of the parameter space where the prisms allow that kind of geodesic. The third kind of picture displays the feasibility region of a particular kind of geodesic, and these are harder to make work. The boundaries of feasibility regions are usually conics, and GSP doesn't handle conics very well. I have to construct those using Mathematica. Graphics from Mathematica can't be directly copied; they have to be converted into a particular type of graphic file. (There are plenty of options: .bmp, .jpg, .eps....) Now, I'd like to use fills and such to indicate the regions (rather than just showing the boundaries), but the only graphics program I have on either computer is Microsoft Paint, and - at least with .jpgs - Paint doesn't fill sections with conic boundaries very well. I haven't tried the other options; I'm not even sure which of them Paint can work with.
This may take a while. I may not be able to send off the paper until late May or early June.
There are three kinds of pictures in the paper. There are pictures of actual prisms, and there are diagrams consisting of several rectangles, indicating the sequence of faces a geodesic passes through. Both of these I can construct using Geometer's Sketchpad, and I can copy them directly from GSP into the text. The third kind.... I constructed a parameter space for prisms, by drawing an equilateral triangle and describing a way of associating each shape a prism can have with a particular point in the interior of the triangle. (Prisms near the vertices are long and skinny; prisms near the midpoints of the edges are flat and squarish, like tiles; the cube is in the exact center.) Given a particular kind of geodesic, the feasibility region is the part of the parameter space where the prisms allow that kind of geodesic. The third kind of picture displays the feasibility region of a particular kind of geodesic, and these are harder to make work. The boundaries of feasibility regions are usually conics, and GSP doesn't handle conics very well. I have to construct those using Mathematica. Graphics from Mathematica can't be directly copied; they have to be converted into a particular type of graphic file. (There are plenty of options: .bmp, .jpg, .eps....) Now, I'd like to use fills and such to indicate the regions (rather than just showing the boundaries), but the only graphics program I have on either computer is Microsoft Paint, and - at least with .jpgs - Paint doesn't fill sections with conic boundaries very well. I haven't tried the other options; I'm not even sure which of them Paint can work with.
This may take a while. I may not be able to send off the paper until late May or early June.
