File talk:HEALPix projection SW.svg

Why is the grid drawn as it is?

This is not the way a grid is constructed on a HEALPix projection to make it practically usable. Why was the grid drawn in this way? The grid that is drawn on it now is rotated by 45 degrees relative to the way the HEALPix grid should be constructed, which is misleading. —Kri (talk) 15:30, 12 October 2023 (UTC)

@Kri: There are different ways of rotating 45°, so I don’t know what you mean. Do you have an example? If I do a Web search on “HEALPix”, I don’t see any evidence that people are orienting the projection in some standard way, nor any reason why you would say that the orientation here is not practically usable. Strebe (talk) 17:30, 12 October 2023 (UTC)

@Strebe: I differentiate between the projection and the grid. The grid is a discretization of the domain and is what you see as the horizontal and mostly vertical lines running through the image, and is used for representing various fields numerically, for example in weather simulations. The reason I say it's not practically usable is because the way the grid is drawn here, the width of the grid cells approach zero at the poles, which forces the time step to be very small not to cause numerical instability in numerical simulations, due to the Courant–Friedrichs–Lewy condition. This makes such simulations require many times more time steps to finish, and thus take longer time and use more computational resources. —Kri (talk) 02:27, 15 October 2023 (UTC)

@Kri: The “grid” lines on the image are not the discretization of the domain. They’re just the graticule of geographic latitude and longitude. The image isn’t intended to be used in any particular way; it just illustrates the projection as described by the sources. Strebe (talk) 19:09, 15 October 2023 (UTC)