A Total Ellipse on the Map

Or, how to choose the best way to walk to the beach after work

It was a cool autumn evening when Hila Kloper and I were thinking of going to the beach after work. The beach is about 2.5Km away from the office.

We were even considering strolling down the streets of Tel Aviv, willing to stretch our path to 3Km, and thinking to ourselves “mmm we wonder how far this stretch can take us?”

Well, long story short, we didn’t go to the beach. Instead, we wrote a script that draws an ellipse around the office and the beach. The ellipse covers the city area we may go through if we ever decide to go to the beach after work.

Or - why should we care about ellipses?

So all we have to do is make sure we have these inputs:

Then follow this plan:

And that’s it.

Sounds simple enough, right?

What we did here is that we took evenly spaced points on the x axis and for each one found the two points on the ellipse that project to it:

Well this was a tricky one, and the answer lies in understanding that

You might notice our ellipse is not perfect. The points are evenly spaced on the axis between the centers, but they are not evenly spaced on the perimeter of the ellipse. The GPS->meters->GPS transformation might result in loss of meters here and there. But hey, done is better than perfect, and we have to leave something to do for the next time we want to go to the beach, right?

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