4 ms·

Mollweide map projection and Newton's method

• 01HNNWZ0MV43FF 1y ago
  > If you were looking at the earth from a distance, the face you’re looking at would correspond to a circle in the middle of the Mollweide map. That doesn't look like the image. If you're looking at Earth from a distance, there will be foreshortening that squishes the meridians together. But the meridians look almost evenly spaced except for the far left and right edges of the ellipse.
  • tobr 1y ago
    It sounded very weird to me too. Perspective projection isn’t equal area. But I think he’s probably not trying to say that the projection would be identical, just that a circle in the center corresponds to one half of the globe.
    • johndcook 1y ago
      Yes. Thanks.
• raverbashing 1y ago
  Unfortunately I don't know how to think about the Mollweide projection https://xkcd.com/977/ https://xkcd.com/977/
  • mcphage 1y ago
    That comic is never not funny. Classic XKCD.
• shiandow 1y ago
  If you want to avoid the double root you could also solve for sin(2t). The derivative of the arcsin is simpler if anything. You may need some special handeling for sin(2t)=1 still. You could pretend the funtion continues there (just join it together with asin(z - 1) + z - 1 + pi/2). Or maybe some other transformation.