mathematics - Efficiently transforming a series of points into curves to be serialized

I’m working on a video game where I need to display a map (in 2D) of an actual big European city (Paris, London, Madrid… that kind of big) and the player, displayed as a simple dot on the map, can take different routes while following the street lines.

To do so I extract real data from OpenStreetMap.org. Thanks to it I have access to a ton of data and geographic information, and among them I have street visual settings given as series of coordinates (long/lat converted to X/Y points using the right projection). In OpenStreetMap a street is composed of a set of points so drawing a line between these points is enough to display streets.

However it represents a huge number of points to load which means a lot of time spent processing the data which means: not ideal. For example, a big city like Paris is composed of 65.000 street points. That is huge. In order to reduce this number and still being able to draw / follow street curves I’m thinking about using a graph only composed of points implied in street intersections alongside curve equations to describe the street display. This way a street composed of 2000 points would be not much bigger than one composed of 10 points in theory.

In this example my initial set is composed of 13 points (red crosses) to display a street. What I’m aiming to in this case is keeping only 4 points (intersections with other streets) and an actual “equation” (or something similar) between each couple of points in order to reduce the size on disk of the final map.

This is where I’m stuck. I suck at Math (and regret it every day). So I can’t figure what would be the best way to transform a series of points into a simple equation that would allow me to follow the actual street curve at runtime.

I don’t know how to do it… I’ve read things about Bezier curves, about Clothoids, Circular Arcs… but I don’t know where to start, what is the best solution here, how to convert my series of points using one of these techniques, or if it’s really the clever thing to do in order to reduce the size (in bytes) of the map…