Matlab and R codes and free software for computation of trajectory smoothness of trace fossils

The MATLAB codes and R codes, along with a free software are uploaded here to help compute trajectory smoothness of the linear trace fossils. This is part of the paper titled "Smoothness analyses of trace fossils: expanding quantitative toolkits to unravel bilaterian movement ecology during the Ediacaran-Cambrian transition" published in Proceedings of the Royal Society B (https://doi.org/10.1098/rspb.2025.0889). Some basic knowledge to vectorize trace fossils and compute deviation angles series can also be found in https://doi.org/10.1111/pala.12686. The input data should be two series of numbers (x and y coordinates in any units, e.g., pixels) in txt format, and the sampling frequency is designed to be 2 for the presented codes and software when performing smoothness analyses. When making comparisons between the signal powers of different trajectories, trajectories should be at the same order of length. 

PS: There is a typographical error in Equation 2.5 in the paper. The correct expression should just be: P_unsmooth=∫S(fd)df* from 0.5 to 1. The coefficient F/N in the paper is equivalent to df* and was intended to represent the discretization step in the summation form (e.g. as implemented in the code), rather than in the integral form. The implementation in the code and software is correct.