Correct way of storing the "reach profile" of an object

We've got to store information about a diversity of mechanical "arms" that have a certain reach profile. We need to store the information about what kind of reach profile the arm has. Since there are a multitude of joints in the arms, the reach is not a perfect parabola, it could look as follows. The porpuse of the data in our database is for a "webshop" to be able to filter on horizontal reach versus vertical reach. As you can imagine, when a certain vertical reach has been entered, there is only a certain horizontal reach on that height. What would be the best format for storing this data? We're allowed to have a "resolution"-aspect of this, so the outcome of filtering this data does not have to be perfect.