braidpath op• Data kinds: image2d × any × any → table
• Call: import fullseye as fs; fs.ledger.homotopy_shortest_paths(grid, start, goal, k=4, obstacles=None, angle=0.1, max_states=400000, max_cost=None) (to call the implementation directly, import braidpath; braidpath.homotopy_shortest_paths(grid, start, goal, k=4, obstacles=None, angle=0.1, max_states=400000, max_cost=None); from the registry, opsdrive.get("homotopy_shortest_paths"))
• GPU: none (CPU reference implementation only)
On a grid (True = traversable, 4-neighbourhood), the k shortest paths from start to goal in distinct homotopy classes, shortest first.
State = (cell, Dynnikov coordinates of the braid). Obstacle points are treated as stationary strands; each move appends the crossing letter and updates the coordinates (the coordinates are a complete invariant of the class, so each (cell, coordinates) is expanded only once). Dijkstra expands this “class-lifted” grid in order of cost, so the order in which goal is reached with new coordinates is the shortest-first order of the per-class shortest paths.
obstacles : representative points of holes (M, 2). If omitted, grid_hole_points (one point per blocked component not touching the border).
max_states / max_cost : upper bounds on the number of expanded states and on the cost (there are infinitely many classes —— a hole can be circled any number of times).
Returns: dict paths (each class's (L, 2) sequence of (row, col), shortest first), costs, words (braid words including the obstacles), keys, obstacles, states (number of expanded states), complete (whether all k paths were found).
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• poc_braid_homotopy_classes — py -3.11 examples/poc_braid_homotopy_classes.py
table as input)course_layout · course_occupancy · course_contains · world_build · world_camera · world_move · lidar_scan · rss_longitudinal_same
braidpath)braid_from_trajectories · braid_reduce · braid_artin_images · dynnikov_coordinates · dynnikov_act · braid_equivalent · homotopy_class_compare · pairwise_winding
*Provenance: braidpath.py — DRIVE operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.