I can make bands from the north to the south pole; build triangles out of them one after the other….

I set out to make a small clickable div, big enough to easily click but small enough to make my offset a reasonable value. I then changed the size of this div to use for my world map, but the page has other ideas… What I can do instead is set up the world div and add an offset div to the world div, to get my x and y offset. Then we can start making my world map from points entered by clicking inside of the world div…

Once I can pick a point within the world div, I will use that to create the first band of surface area down from the north pole or maybe up from the south pole if the point is closer to the south pole. Each point the page accepts needs to be inside of the world div, and we will have the page ignore any other inputs. The x and y coordinates need to be modified by the offset and the height and width of the world div rectangle inside of which we will be creating an oval-shaped polygon which, again, represents the 3D ‘world peach’ polyhedron.

We get the width of the band from the height of the point relative to the center of the world div; it’s just Pythagoras and this gives us by default the nearest pole, the original point and the left and right edges of the shape, in effect a triangle or actually a triangle pair. We do need at least three triangles in the polar triangle fan, so we would subdivide that triangle pair.