Highway Map

Inside data/highway_map.csv there is a list of waypoints that go all the way around the track. The track contains a total of 181 waypoints, with the last waypoint mapping back around to the first. The waypoints are in the middle of the double-yellow dividing line in the center of the highway.

The track is 6945.554 meters around (about 4.32 miles). If the car averages near 50 MPH, then it should take a little more than 5 minutes for it to go all the way around the highway.

The highway has 6 lanes total - 3 heading in each direction. Each lane is 4 m wide and the car should only ever be in one of the 3 lanes on the right-hand side. The car should always be inside a lane unless doing a lane change.

Waypoint Data

Each waypoint has an (x,y) global map position, and a Frenet s value and Frenet d unit normal vector (split up into the x component, and the y component).

The s value is the distance along the direction of the road. The first waypoint has an s value of 0 because it is the starting point.

The d vector has a magnitude of 1 and points perpendicular to the road in the direction of the right-hand side of the road. The d vector can be used to calculate lane positions. For example, if you want to be in the left lane at some waypoint just add the waypoint's (x,y) coordinates with the d vector multiplied by 2. Since the lane is 4 m wide, the middle of the left lane (the lane closest to the double-yellow dividing line) is 2 m from the waypoint.

If you would like to be in the middle lane, add the waypoint's coordinates to the d vector multiplied by 6 = (2+4), since the center of the middle lane is 4 m from the center of the left lane, which is itself 2 m from the double-yellow dividing line and the waypoints.

Converting Frenet Coordinates

We have included a helper function, getXY , which takes in Frenet (s,d) coordinates and transforms them to (x,y) coordinates.

Interpolating Points

If you need to estimate the location of points between the known waypoints, you will need to "interpolate" the position of those points.

In previous lessons we looked at fitting polynomials to waypoints. Once you have a polynomial function, you can use it to interpolate the location of a new point.

There are also other methods you could use. For example, Bezier curve fitting with control points, or spline fitting, which guarantees that the generated function passes through every point.

Here is a great and easy to setup and use spline tool for C++, contained in just a single header file.

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