GSoC 25 Draft Proposal : Implement Wrapping Geometry and Pathways for Musculoskeletal Modeling
Rushabh Mehta
Hello everyone,
I have been contributing to SymPy and engaging with the community for a few months now. I’ve fixed bugs, participated in discussions, and opened issues. Thus I have gained some familiarity with the codebase, also I have been programming in Python for 2+ years.
I'm interested in contributing to SymPy Mechanics for GSoC 2025, specifically under the project "Classical Mechanics: Implement Wrapping Geometry and Pathways for Musculoskeletal Modeling" as listed on the ideas page.
I've been exploring and studying the existing WrappingCylinder and WrappingSphere classes, as well as the LinearPathway and ObstaclePathway. I believe a valuable addition would be:
- WrappingEllipsoid and WrappingCone: These can model more complex muscle wrapping geometries around bones/joints, extending the current wrapping surfaces.
- GeodesicPathway: This pathway would compute the shortest path along a curved surface (any instance of a wrapping geometry) between two attachment points, capturing more realistic muscle routing in biomechanical models.
Implementation Plan:
- WrappingEllipsoid & WrappingCone:
- Extend the existing WrappingGeometryBase class, ensuring all the required methods are implemented.
- Define parametric equations for the surfaces and add methods to compute geodesic lengths and end vectors.
- GeodesicPathway:
- Implement a general GeodesicPathway class that computes the shortest path along a surface (geometry) given two attachment points.
- Use differential geometry principles to compute geodesic equations and solve them symbolically using SymPy’s dsolve.
- Integrate force calculation along the geodesic (similar to LinearPathway.to_loads method) so that it can be used to generate equations of motion with Kane/Langrange method.
- Ensure it can interact with any WrappingGeometry object.
As with any software development endeavor, these additions will be accompanied by exhaustive tests, documentation and example usage.
I think these additions could significantly enhance the biomechanics modeling capabilities of SymPy, especially for musculoskeletal simulations.
I'd love to hear any feedback, especially on:
- The feasibility of computing geodesics symbolically especially in more complicated scenarios using dsolve.
- Anything I may have overlooked.
- Any suggestions on aligning this work with SymPy's current design.
Would this contribution align well with SymPy's current roadmap? I'm open to any guidance or suggestions to refine my approach.
Thanks!
Rushabh Mehta
Jason Moore
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Rushabh Mehta
Rushabh Mehta
Hello Jason,
Thanks for pointing me towards OpenSim. It is an interesting tool, and I've spent some time researching it. I now have a much clearer understanding of the types of wrapping geometries and pathways commonly used in musculoskeletal models.
OpenSim supports several standard wrapping geometries such as:
- Cylinders (for modeling wrapping around bones like the humerus)
- Spheres (for smooth rounded surfaces)
- Double Cylinders (for modeling wrapping around parallel bones, like the radius and ulna)
- Tori (for curved wrapping surfaces like joint capsules)
- Ellipsoids (for complex bone geometries like the hip joint)
In OpenSim, the shortest muscle path is calculated using a combination of points and wrapping geometries. It doesn't solve for the geodesic (shortest path on a curved surface) explicitly but instead uses a combination of line segments and wrap points, and then numerically computes everything needed.
How This Informs My Proposal
Given this, I think SymPy Mechanics can be enhanced in the following ways:
1. Expand WrappingGeometry to Support More Surfaces
- I propose adding WrappingEllipsoid and WrappingTorus. These geometries will extend the existing WrappingGeometryBase class, allowing users to model more complex muscle-bone interactions.
- This will align closely with OpenSim's existing wrap objects, making SymPy more compatible with existing biomechanical tools like OpenSim.
- Additionally, once these geometries are supported, extending SymPy Mechanics to more complex biomechanical models would become more straightforward.
2. Introduce GeodesicPathway for Shortest Path Calculation
- Instead of relying on discrete wrap points (like OpenSim), I propose implementing a GeodesicPathway class that computes the exact shortest path along the surface of a geometry using differential geometry.
- For example:
- On a sphere, the geodesic would be a great circle.
- On an ellipsoid, the geodesic can be computed symbolically using SymPy's dsolve() to solve the geodesic differential equation.
- On a cone, the geodesic would follow a logarithmic spiral path.
- By computing the geodesic symbolically, we could potentially offer a higher level of accuracy and analytical insight for musculoskeletal simulations.
3. Symbolic Force Calculation Along the Geodesic
- Another key advantage of a symbolic GeodesicPathway is that it can directly integrate with SymPy’s force calculation methods (to_loads()), allowing users to generate symbolic equations of motion using Kane or Lagrange methods.
- This could make SymPy uniquely positioned to perform symbolic musculoskeletal simulations — something OpenSim does not currently offer.
Queries
My main concern at the moment is:
The feasibility of computing geodesics for non-trivial surfaces (like ellipsoids or tori) using SymPy's dsolve(). Is it powerful enough?If there are any particular limitations or design choices I should be aware of, I would love to hear your feedback.
Best regards,
Rushabh Mehta
Rushabh Mehta
Rushabh Mehta
Here is the proposal.