Topic: Corner Geometry

The two values in a track section that describe a corner in an F1GP track are the curvature and the length.

The curvature value defines how tight a corner is.

The allowed curvature value for a corner goes from -32,768 to 32,768, where a positive value indicates a right-hand corner, and a negative value indicates a left-hand turn. A value of 0 thus means that the section is a straight.

The curvature value is converted to indicate the length of the radius of an imagined circle on the inside of the corner, like this:

In these two examples, the first corner has a smaller curvature value for the individual corner sections, and is therefore not as tight as the following corner, which has a larger curvature value.

The radius for an imagined circle on the inside of the corner is calculated according to the following formula:

1 / (curvature * 2 * 𝜋 / 65536)

Examples of calculated radius values:

So as you can see, the larger the curvature value, the smaller the radius.

Example: 90° corners

To create a 90° corner, the curvature multiplied by the length must be approximately 16,384.

In the first example, we have a 90° corner with three sections.

In this case, the curvature value for each section is 910, and the length of each section is 6.

This gives us the following calculation: 910 x 6 x 3 = 16,380.

In the next example, we have another 90° corner with three sections, but the corner is noticably tighter.

The curvature value for these sections is larger than the previous one, 2,730, but the length is lower, at 2 each.

This gives us the following calculation: 2,730 x 2 x 3 = 16,380.

So, as you can see, the total value for each corner is the same but by adjusting the curvature and length values differently, the corners are tighter or wider.