New Project Looking for Help: Plotting great circles
asked 2010-12-01 04:17:24 -0500
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I'm working on a project and found that sage may be the best program to help. Information can be found at vividdynamics.com. I'm not a math student but study it as a hobby(mainly geometry) and have some art backround.
I'm looking for a way to generate a sphere with great circles plotted at cumulatively smaller intervals as they get closer to axis, x and y. Like I said, I'm not a math student so, I'm not sure how to define it in mathematical terms. basically it would look like an orange but with smaller and smaller pieces at, 90º, 180º, 270º, and 0º.
Are you looking for formulas to parametrize these various great circles (so that you can plot them with sage)? If so, maybe rotation matrices are one easy way to produce them. You could start with a great circle whose parametrization you know (e.g. the one in the x-z plane) and then get others by rotating about the z-axis, say 45º, 67.5º, 78.75º, etc. Is that something like what you're looking for?
If so, the Wikipedia article for rotation matrices looks useful. I believe you can plot parametric curves with sage, and apply arbitrary transformation matrices to them. For starters, here's a circle:
sage: u = var('u') sage: parametric_plot3d( (cos(u), 0, sin(u)), (u, 0, 2*pi))
Thanks for the reply. That sounds exactly what I'm looking to do. I must say though, I'm somewhat confused about the ask/answer system here. Initially I was looking for some kind of forum where I could have a discussion or look up any needed information but ask.sagemath.org was the closest thing I could find. Is editing the message like this the best way to have a discussion?
I looked at the Wikipedia article on rotation matrices. I suspect that SAGE doesn't have a command for rotation matrices so I would have to make an array defining my own range. And call the values of each circle from the matrix. Does that sound like a good way to go about it?