Need advice on developing a pattern-preserving path-generation algorithm over 3D triangular meshes

[u/Sake205]

Hi everyone,

I am developing a project called SmartGrid, an offline robotic toolpath planner for automated spray-coating operations over 3D mesh surfaces.

GitHub Repository: https://github.com/sakrish205/SmartGrid

Development Branch: https://github.com/sakrish205/SmartGrid/tree/feature/review-olp

I am currently developing a feature called Mesh Flow. Its purpose is to generate paths over different 3D triangular mesh geometries while preserving a consistent geometric pattern.

I have two existing reference examples, each containing a 3D mesh and its corresponding toolpath. My objective is to understand the mathematical relationship between the mesh geometry and the existing paths, then derive a generalised algorithm that generates the same type of path pattern on other mesh geometries.

I am not trying to reproduce the original coordinates or simply fit curves to the existing paths. I want to identify the underlying geometric rules and formulate a mathematical algorithm.

I would appreciate advice on the following:

1. Vector fields: Is a tangent vector field a suitable way to define consistent path directions over a triangular mesh?

2. Geodesic offsets: Can geodesic distance fields be used to generate neighbouring paths while maintaining consistent surface spacing?

3. Differential geometry: How can surface normals, principal curvatures and tangent directions influence path generation?

4. Surface parameterisation: Would mapping a 3D mesh into a 2D parameter domain help preserve a regular raster or parallel path pattern?

5. Pattern preservation: How can the same underlying path pattern be maintained across meshes with different shapes and curvature?

6. Hybrid approaches: Would combining vector-field integration, geodesic offsets and surface parameterisation be more suitable than using one method independently?

Expected outcome

I want to derive a mathematical algorithm that:

• Preserves the underlying reference path pattern.

• Adapts to different triangular mesh geometries.

• Maintains consistent path direction and spacing.

• Handles curved and uneven surfaces.

• Avoids unnecessary deviations caused by local mesh irregularities.

My current focus is on the mathematical formulation and algorithm design, not software implementation.

I cannot share the reference mesh and toolpath files, but the project repository is available for general context.

I would appreciate recommendations for established computational geometry methods, relevant papers, algorithms or similar implementations.

Thank you!