Tortuosity as a metric for evaluating branch motion paths under dynamic loading

We describe objective comparison of tree branch motion paths using tortuosity. Tortuosity is a measure of the bendiness or curviness of a path. Tree branch motion paths are piecewise linear curves created by collecting position information over time for fixed locations on a tree branch. Objective methods for comparing branch motion paths may improve computer simulations of tree motion for image synthesis by giving researchers another tool for evaluating and improving simulation methods. Three tortuosity metrics are computed and compared for 22 motion paths collected from a maple sapling in a laboratory environment. Appropriate metrics for tortuosity of tree branch motion paths must account for short chord lengths of those paths, admit analysis of space curves and match intuitive notions of bendiness. Tortuosity itself is a subjective measure. We present several images of branch motion paths along with their tortuosity values. Based on these results, average curvature is the most appropriate metric for characterizing tortuosity of tree branch motion paths because average curvature is not sensitive to chord length, is defined in 3D and is well correlated with our intuitive notion of tortuosity.