Muscle paths play an important role in musculoskeletal simulations by determining a muscle's length and how its force is distributed to joints. Most previous approaches estimate the way in which muscles 'wrap' around bones and other structures with smooth analytical wrapping surfaces. In this paper, we employ Newton's method with discrete differential geometry to permit muscle wrapping over arbitrary polygonal mesh surfaces that represent underlying bones and structures. Precomputing distance fields allows us to speed up computations for the common situation where many paths cross the same wrapping surfaces. We found positive results for the accuracy, robustness, and efficiency of the method. However the method did not exhibit continuous changes in path length for dynamic simulations. Nonetheless this approach provides a valuable step toward fast muscle wrapping on arbitrary meshes.
Keywords: Musculoskeletal simulation; discrete differential geometry; geodesics; muscle modeling; muscle wrapping.