  Limbless animals such as snakes, limbless lizards, worms, eels, and lampreys
move their slender, long bodies in three dimensions to traverse diverse
environments. Accurately quantifying their continuous body's 3-D shape and
motion is important for understanding body-environment interactions in complex
terrain, but this is difficult to achieve (especially for local orientation and
rotation). Here, we describe an interpolation method to quantify continuous
body 3-D position and orientation. We simplify the body as an elastic rod and
apply a backbone optimization method to interpolate continuous body shape
between end constraints imposed by tracked markers. Despite over-simplifying
the biomechanics, our method achieves a higher interpolation accuracy (~50%
error) in both 3-D position and orientation compared with the widely-used cubic
B-spline interpolation method. Beyond snakes traversing large obstacles as
demonstrated, our method applies to other long, slender, limbless animals and
continuum robots. We provide codes and demo files for easy application of our
method.
