Improved Muscle Wrapping Algorithms Using Explicit Path-Error Jacobians

Musclewrappingcomputationsareanimportantfeatureinmusculoskele- tal simulations. In this paper we present a novel Jacobian-based method for line- based muscle-path computations over multiple general smooth surfaces allowing for second-order Newton-Raphson iterations. The method is based on the analytical determination of infinitesimal displacements along geodesics using Jacobi fields. It does not share the disadvantages of discretized methods in terms of non-smoothness when using surface discretizations, and high computational costs when using dis- cretized spring-mass approaches. The paper focusses on the technical details of the proposed method, while specific biomechanical applications are left for future con- tributions. An example with three surfaces involving a surface with a general distri- bution of curvature shows the general applicability of the method.