Geodesic Engine

C++ engine that computes shortest-path approximations on 3D meshes using Dijkstra, the Heat Method, and analytic geodesic solvers for parametric surfaces.

Build

cmake -S . -B build -DBUILD_TESTING=OFF
cmake --build build --target geodesic_engine -j

The binary is written to ./main.

Run

# Dijkstra (shortest path along mesh edges)
./main <start_id> <end_id> <model_path>

# Heat Method (mesh geodesic approximation)
./main <start_id> <end_id> <model_path> heat

# Analytics (surface-specific analytic solver)
./main <start_id> <end_id> <model_path> analytics

Example:

./main 0 100 ./assets/models/stanford-bunny.obj

Results are written as JSON to the current working directory (result.json, heat_result.json, analytics.json).

Test

cmake -S . -B build-tests
cmake --build build-tests -j$(nproc)
ctest --test-dir build-tests --output-on-failure

Models

Sample OBJ files live in assets/models/. You can generate higher-resolution variants with:

python -m tools.meshgen.generate --out ./assets/models

Algorithms

1) Dijkstra on the Mesh Graph

Treats mesh vertices as nodes and edges as graph edges. Edge weights are Euclidean distances between adjacent vertices.

2) Heat Method

For general triangle meshes, solves:

1. Heat equation for a short time $t$
2. Normalizes the temperature gradient to get vector field $X$
3. Solves Poisson equation $\Delta \phi = \nabla\cdot X$
4. $\phi$ approximates geodesic distance; follow its gradient to extract a path

3) Analytic Geodesics

Closed-form or ODE solutions for special parametric surfaces (plane, sphere, torus, saddle).

References

[1] Crane, K., Weischedel, C. and Wardetzky, M. (2013). Geodesics in heat: A new approach to computing distance based on heat flow. ACM Transactions on Graphics, 32(5), pp.1–11.