# How to obtain $x$ and $y$ coordinates from curvature data

I want to visualize points that are given as curvature data (arclength along the path,curvature or radius) e.g.

$$\begin{array} {ccc} \hline \text{arclength} & \text{curvature} & \text{radius}\\ \hline 0.000 & 0.0145 & 68.9655\\ 5.000 & 0.0142 & 68.7350\\ 10.000 & 0.0138 & 71.7875\\ 15.000 & 0.0126 & -81.9672\\ 20.000 & 0.0115 & -90.7441\\ \hline \end{array}$$

At the moment I am using the mean radius between two data points and then I am calculating the $x$ and $y$ coordinates from a circle then displaying the starting coordinates such that they start from the origin. For the following sections I calculate the $dx, dy$ components and then I rotate the results into the tangential direction and add them to the previous coordinates. This solution is quite hacky, that is why I am interested in a more direct way/or alternative way as I assume that I am not the first person to do such a thing. Code snippets (e.g. for Python, MATLAB, Java, C, C++, C#...) are also welcome.