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 typo in the section "Sensory and perceptual capacities" in the paper: γ of the Helminthopsis tenuis from Member 3 of the Chapel Island Formation is not 0.112, but 1-0.112, which is 0.888.