Muscle wrapping on arbitrary meshes with the heat method

Abstract

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
• muscle modeling
• muscle wrapping
• discrete differential geometry
• geodesics

Acknowledgements

We thank John Lloyd and Michael Sherman for their informative discussions.

Notes

No potential conflict of interest was reported by the authors.

1 An optimized library is provided at http://www.cs.columbia.edu/keenan/index.html#code.

Additional information

Funding

This work was funded by the Natural Sciences and Engineering Research Council of Canada.