How to Make a Sun Clock?

For an upcoming project the client wants an animated “Sun Clock” that shows the areas of the world map that are currently day/night. The Sun Clock changes continuously throughout the day to match the movement of the sun. I’ve attached an image of a Sun Clock as reference.

I’m really not sure where to start with this. I’ve found an example of a functional Sun Clock using Yahoo Widgets, but that’s a bit different because I need to embed the Sun Clock on a web page.

I know this is a big ask, but any thoughts or pointers in the right direction would be great.