[mfagerlund]

Motivation

For a single vertex-to-vertex geodesic, FlipEdgeNetwork::constructFromDijkstraPath() + iterativeShorten() spends almost all of its time on setup that doesn't depend on the query. Profile of one query on a 48k-vertex mesh (horse):

step	ms
Dijkstra over the whole mesh	16
SignpostIntrinsicTriangulation construction	29
FlipEdgeNetwork construction	10.6
iterativeShorten()	1.1
destruction	5.7

The shortening itself is under 2% of the query.

What this adds

FlipOutContext (flip_geodesics_context.h/.cpp) is built once per mesh and answers vertex-to-vertex queries:

• a flat intrinsic triangulation (connectivity, edge lengths, signpost angles, angle sums) built directly from the input mesh, with the same angle values as the signpost triangulation;
• the initial edge path by A* with a Euclidean heuristic when vertex positions are available (Dijkstra otherwise), using the same heap ordering as shortestEdgePath, so it returns the same path;
• the same shortening loop as iterativeShorten(): same wedge-angle queue, flip test, epsilons and angle updates;
• an undo log, so each query's flips are reverted in O(1) each and the next query starts from the original triangulation.

The existing FlipEdgeNetwork code is unchanged; this is a separate class.

Same output

The tests (flip_geodesics_context_test.cpp) check, on spot, bob_small, fox and cat_head (two of them with boundary), 40 random pairs each:

• the same intrinsic halfedge sequence as the FlipEdgeNetwork route, and the same length within 1e-12 relative;
• repeated queries and fresh contexts agree, so undoing a query leaves no trace;
• the traced polyline matches getPathPolyline() point by point.

On 14 benchmark meshes (300 random pairs each, 4,200 queries) no length differs from the shipped route by more than 1e-9 relative, and the flip counts match.

Speed

Ryzen 9 3950X, MSVC Release, 300 random vertex pairs per mesh, geometric mean over 14 meshes (1.8k–112k vertices):

• context reused across queries: 45x faster than the shipped route (e.g. horse 118 ms → 2.5 ms per query, happy-buddha 111 → 3.1, bimba 278 → 4.5);
• context built per query: 5x faster, since building the flat triangulation is cheaper than the full signpost triangulation and network.

The docs page for flip geodesics gets a short section with usage.

Happy to adjust naming, scope or API to fit the library.