vector<double> bezierCurvature(VectorArr controlPoints, double t = 0.02)

Returns an array of the curvature at each point of the bezier curve defined by the parameters

Parameters

• controlPoints - The list of control points to make the curve from
• t - The number to increment t by. The default is 0.02

Returns

An array containing the curvature at each point of the curve

Explanation

Curvature is a measure of how tight a curve is at a point. It is equivalent to the radius of the circle tangent to the curve at that point. My curvature formula uses a weird implementation from page 7 of the pure pursuit paper. I use curvature in my drive code to limit the robot speed around tight turns.

Example

VectorArr controlPoints = {PVector(0, 0), PVector(0, 1), PVector(1, 1)};
auto curvatures = bezierCurvature(controlPoints);