# Code Flow: Drifting Model

This chapter walks the drifting model one function at a time, in the order that the calls fire when a user presses Run Model. Pair it with the theory chapter Drifting Risk Calculations, which derives the formulas that each function below implements.

## Entry point

`DriftingModelMixin.run_drifting_model()` is phase 1 of `CalculationTask` (see Code Flow: From “Run Model” to Results). It takes a single `data` dict and writes

- `self.drifting_allision_prob`

- `self.drifting_grounding_prob`

- `self.drifting_report`

- `self.allision_result_layer`, `self.grounding_result_layer`

- `LEPDriftAllision.setText(...)` / `LEPDriftingGrounding.setText(...)`

Entry: `compute/drifting_model.py:1608` – run_drifting_model()

## Top-level call tree

    run_drifting_model(data)
      |
      +-- _build_transformed(data)                                         # UTM projection + geom prep
      |     +-- prepare_traffic_lists(data)                                # compute/data_preparation.py
      |     +-- split_structures_and_depths(data)
      |     +-- transform_to_utm(lines, structure+depth wkts)
      |     +-- shapely.make_valid  (per obstacle)
      |
      +-- _compute_reach_distance(data, longest_length)                    # drift-speed * T99 of repair dist
      |
      +-- merge depths by unique level (optional optimisation)             # shapely.unary_union per level
      |
      +-- _precompute_spatial(...)                                         # = "spatial" progress phase
      |     +-- compute_min_distance_by_object(...)                        # geometries/get_drifting_overlap.py
      |     +-- compute_probability_holes_analytical(...)                  # geometries/analytical_probability.py
      |           +-- ThreadPoolExecutor (per leg x direction)
      |                 +-- _compute_single_direction_analytical(...)
      |                       +-- compute_probability_analytical(...)
      |                             +-- _vectorized_edge_y_intervals(...)
      |                             +-- _merge_intervals_across_slices(...)
      |                             +-- dist.cdf(array)                    # batched scipy CDF
      |
      +-- _precompute_shadow_layer(...)                                    # = "shadow" progress phase (0..50%)
      |     +-- ThreadPoolExecutor (per leg x direction)
      |           +-- _shadow_task(leg_idx, d_idx)
      |                 +-- _create_drift_corridor(...)
      |                 +-- _build_blocker_shadow(..., shadow_memo)
      |                 |     +-- extract_polygons(geom)
      |                 |     +-- create_obstacle_shadow(p, compass, bounds)  # cached per (id(geom),dir)
      |                 +-- _edge_geom_for(poly)
      |                       +-- _extract_obstacle_segments(poly)
      |                       +-- _edge_weighted_holes(...)                # batched drift filter + shapely
      |                       |     +-- segment_corridor_overlap_length(...)
      |                       +-- directional_distances_to_points(...)    # vectorised drift distance
      |                       +-- get_not_repaired(...)                   # analytical ndtr / Weibull
      |
      +-- _precompute_bucket_memo(...)                                     # = "shadow" progress phase (50..100%)
      |     +-- ThreadPoolExecutor (per (leg, dir, ship-bucket))
      |           +-- _compute_bucket(...)
      |                 +-- geom.difference(blocker_union)
      |                 +-- _analytical_hole_for_geom(reach, ...)
      |                       +-- extract_polygons + _extract_polygon_rings
      |                       +-- compute_probability_analytical(...)
      |                 +-- shapely.unary_union
      |
      +-- _iterate_traffic_and_sum(...)                                    # = "cascade" progress phase (60..90%)
      |     +-- clean_traffic(data)
      |     +-- for each leg, ship cell, direction:
      |           _process_cell_direction(...)
      |             +-- lookup bucket_memo entry
      |             +-- per-entry: accumulate allision/grounding/anchoring
      |             +-- _update_report(...)
      |             +-- _update_anchoring_report(...)
      |             +-- _add_direct_segment_contrib(...)
      |
      +-- create_result_layers(report, ...)                                # = "layers" phase
      +-- _auto_generate_drifting_report(data)                             # writes Markdown

The sections below open each box above, in the order the code executes.

## `_build_transformed()`: lat/lon -> UTM

`DriftingModelMixin._build_transformed()` is a one-time geometry prep step that runs entirely on the calculation thread. It returns eight parallel lists used by every downstream helper.

Source: `compute/drifting_model.py:859` – _build_transformed()

Calls performed:

1. `compute.data_preparation.prepare_traffic_lists(data)()` - returns `(lines, distributions, weights, line_names)`.

   - `lines` is a list of `shapely.geometry.LineString` in EPSG:4326 (one per leg).

   - `distributions` is `list[list[scipy.stats.rv_frozen]]` – one list per leg with up to three superposed distributions parsed from `mean1_1`/`std1_1`/`weight1_1` … etc.

   - `weights` is the matching list of floats summing to 1.

   - `line_names` are the human labels shown in reports.

2. `compute.data_preparation.split_structures_and_depths(data)()` - converts the `depths` / `objects` lists of `[id, value, wkt]` into two lists of dicts with parsed shapely geometries. MultiPolygons are split into their component polygons so every entry has a single `shapely.geometry.Polygon`.

3. `compute.data_preparation.transform_to_utm(lines, obstacle_geoms)()` - picks the UTM zone best covering the combined bbox, transforms every leg and obstacle once via QGIS `QgsCoordinateTransform` when running inside QGIS, or `pyproj` otherwise. All subsequent geometry math is in metres.

4. `shapely.make_valid()` on every obstacle. If the result is a MultiPolygon it is again split into components. Each final polygon is stored with its WGS84 version (`wkt_wgs84`) so that result layers generated later use the same vertex order as the UTM version.

Output: `(lines, distributions, weights, line_names, structures, depths, structs_gdfs, depths_gdfs, transformed_lines)`.

## `_compute_reach_distance()`

Computes the “99th percentile drift distance”: how far a ship can drift before the repair distribution says it almost certainly got its engine back.

Source: `compute/drifting_model.py:92` – _compute_reach_distance()

Logic:

- If `drift.repair.dist_type == 'weibull'`, uses `scipy.stats.weibull_min(...)`.ppf(0.99).

- Else if `drift.repair.use_lognormal`, uses `scipy.stats.lognorm(...).ppf(0.99)`.

- Multiplies by the drift speed (m/s) to get metres.

- Caps at `10 x longest_leg_length` so that a poorly-parameterised repair distribution can’t make the reach distance degenerate.

## Depth merging (optional)

Before the spatial precompute, `run_drifting_model()` examines the set of depth polygons. If there are more polygons than unique depth values, the method merges all polygons with depth <= boundary into one cumulative polygon per boundary via `shapely.unary_union()`. The result is:

- `merged_depths_gdfs` / `merged_depths_meta` - a much smaller set of obstacles used by the expensive spatial phase.

- `threshold_to_idx` - maps any draught or anchor threshold to the index of the correct merged polygon. The cascade uses this to look up grounding / anchoring obstacles per ship cell in O(1).

This is the single biggest source of speedup for projects with dense bathymetry (tens of depth contours map to just a handful of unique levels).

## Phase 1: `_precompute_spatial()` (`spatial`, 0–40 %)

Ship-independent pre-computation of everything that depends on leg geometry only.

Source: `compute/drifting_model.py:986` – _precompute_spatial()

Returns four lists, each indexed `[leg_idx][math_dir_idx][obstacle_idx]`:

- `struct_min_dists` - nearest along-drift distance from leg to each structure (or `None` if the obstacle is out of reach in that direction). Computed by `geometries.get_drifting_overlap.compute_min_distance_by_object()`.

- `depth_min_dists` - same for depth (grounding / anchoring) polygons.

- `struct_probability_holes` - \(h_X\) = probability of drifting far enough in the obstacle’s direction to hit it, from a random start on the leg. Computed by `geometries.analytical_probability.compute_probability_holes_analytical()` (default) or `geometries.calculate_probability_holes.compute_probability_holes()` (Monte Carlo, opt-in via `data['use_analytical'] = False`).

- `depth_probability_holes` - same for depth polygons.

### Inside the analytical path

`compute_probability_holes_analytical()` parallelises per `(leg, direction)` across a `ThreadPoolExecutor` with `cpu_count() - 1` workers. Each worker calls `_compute_single_direction_analytical()`, which for each object calls `compute_probability_analytical()`:

1. Slice the leg into 100 cross-sections (`s_values` = midpoints of 100 equal intervals along the leg).

2. For every edge of the obstacle and every slice, solve for the `y`-range of `perp_offset` values whose drift ray crosses that edge. This is done in one batched numpy call (`_vectorized_edge_y_intervals()`) over all slices x all edges.

3. Per slice, merge the valid intervals into disjoint ones (`_merge_intervals_across_slices()`, batched over all slices).

4. Flatten every merged interval into two 1-D arrays `los` and `his` across every slice.

5. Evaluate the weighted distribution CDF once per distribution on both arrays (scipy’s `dist.cdf` is vectorised over array input), subtract, and sum. Divide by `n_slices` to get the probability hole.

Performance note: this used to call `dist.cdf` and `_merge_intervals_vectorized` per slice, which dominated `compute_probability_analytical`. Batching both turned the work into a handful of scipy calls per obstacle (see Code Flow: From “Run Model” to Results’s performance timeline).

## Phase 2: `_precompute_shadow_layer()` (`shadow`, 0–50 %)

For every `(leg, direction)` pair, build:

- the drift corridor polygon,

- the quad-sweep shadow for every reachable obstacle,

- per-edge geometry (edge length fractions of the corridor overlap, along-drift distance of each edge, \(P_{NR}\) at that distance).

Source: `compute/drifting_model.py:334` – _precompute_shadow_layer()

Pre-computation outside the thread pool:

1. Build `leg_precomputed[leg_idx]` with `dists_dir`, `w_dir` (normalised weights), `lateral_spread` = 5 x weighted std of the leg’s lateral distribution, and a `drifting.engine.LegState` for the scalar fallback path.

2. Compute a global shadow bounds: the bbox of all legs + all obstacle geometries, padded by `max(1 km, reach_distance)`. This is passed to every call to `create_obstacle_shadow()`, which derives its extrude distance from the corridor bounds. Using a single global bound lets a per-polygon shadow cache hit across legs, because the extrude distance (and thus the shadow shape) is now the same for every call.

Per-task work (`_shadow_task(leg_idx, d_idx)`):

1. Build the drift corridor via `compute.drift_corridor_geometry._create_drift_corridor()`: two rectangles (leg rect + drifted rect) unioned, falling back to convex hull if union produces a MultiPolygon.

2. For every structure and every depth (filtered via `struct_min_dists` / `depth_min_dists` to those within `reach_distance`):

   1. Build the quad-sweep shadow -> `_build_blocker_shadow()`.

   2. Build per-edge geometry -> inner `_edge_geom_for(poly)`.

3. Return `(key, entry)` where `entry` has `corridor`, `bounds`, `dists_list`, `weights_arr`, `lateral_spread`, `shadow` (dict of `(type, idx) -> Polygon`), and `edge_geom` (dict of `(type, idx) -> list[edge-dict]`).

Futures are collected with `concurrent.futures.as_completed()`, progress is reported every ~5 % of completed tasks, and a cancellation check aborts the remaining work if the user clicks stop.

Shadow cache helper: `compute/drifting_model.py:161` – _build_blocker_shadow()

### `_build_blocker_shadow()`

Memoises the full obstacle shadow (union over all Polygon components) by `(id(geom), compass_angle)`. Because every leg passes the same Python object for a given obstacle, the cache hits `(legs - 1) x 8` times per obstacle.

Implementation:

1. If `id(geom), compass_angle` already has a cached shadow, return it.

2. Call `geometries.drift.shadow.extract_polygons(geom)()` to split MultiPolygons.

3. For each component `Polygon` call `geometries.drift.shadow.create_obstacle_shadow()`, which:

   1. Computes an extrude distance = `2 * corridor_diagonal`.

   2. Translates the polygon that far in the drift direction.

   3. Builds one quad per original edge connecting original -> translated vertices. Quads with zero shoelace area are skipped (the previous implementation called `quad.is_valid` / `quad.area` per quad, which was >1 M shapely dispatch calls per proj.omrat run).

   4. Unions original + translated + quads into the final shadow polygon.

4. If more than one component, `shapely.ops.unary_union()` the per-component shadows.

5. Cache and return.

### Inner `_edge_geom_for()`

Works per obstacle inside `_shadow_task`. The result (`[{'seg_idx', 'len_frac', 'edge_dist', 'edge_p_nr'}, ...]`) is used by the cascade to split the obstacle’s hole probability across individual polygon edges.

1. `segments = _extract_obstacle_segments(poly)` - polygon edges as a list of `((x0,y0), (x1,y1))` tuples.

2. `raw = self._edge_weighted_holes(poly, drift_corridor, math_angle, line, 1.0, None)` - for each segment that survives the drift-direction pre-filter, returns `(seg_idx, overlap_length)`. The pre-filter runs numpy-batched so most rejected segments never touch shapely; the survivors go through `segment_corridor_overlap_length()` for the actual corridor intersection.

3. Collect the two endpoints of every selected edge into a flat `(2N, 2)` array and call `geometries.get_drifting_overlap.directional_distances_to_points()` once. That function returns per-point along-drift distances via a single vectorised edge-crossing pass, falling back to a vectorised nearest-point projection for points that miss every leg segment.

4. For each edge, average its two endpoint distances -> `edge_dist`.

5. \(P_{NR}\) = `compute.basic_equations.get_not_repaired()`. That function compiles the repair `func` string or matches the common `norm.cdf` / `weibull_min.cdf` patterns and caches a pure-`scipy.special.ndtr()` closure, so repeated calls are O(1) in Python – no scipy frozen-distribution dispatch.

## Phase 3: `_precompute_bucket_memo()` (`shadow`, 50–100 %)

Eagerly evaluates the shadow-coverage cascade for every distinct “ship bucket” per `(leg, direction)`. A bucket is the set of `(obstacle_type, obstacle_idx)` tuples a ship sees given its draught (grounding index) and anchor threshold (anchoring index). Many ships share the same bucket, so doing the carving once per bucket turns the later traffic cascade into pure arithmetic.

Source: `compute/drifting_model.py:617` – _precompute_bucket_memo()

Per bucket:

1. Sort obstacles by along-drift distance.

2. Walk the sorted list maintaining a running `blocker_union` (for grounding/allision) and `anchor_union` (for anchoring). The shadows come from the memo built in Phase 2.

3. For each obstacle:

   - Carve `reach = geom.difference(blocker_union)` - the part of the obstacle still reachable past closer blockers.

   - `h_reach` = `_analytical_hole_for_geom(reach, ...)()` - the probability hole of the carved region, computed via the same `compute_probability_analytical()` used in Phase 1.

   - `h_in_anchor` = probability hole of the carved region that ALSO intersects the anchoring region - so anchoring ships are subtracted out correctly.

4. Result: `memo[(leg, dir, bucket_key)] = [{'obs_type', 'obs_idx', 'dist', 'hole_pct', 'h_reach', 'h_in_anchor'}, ...]`.

Parallelised the same way as the shadow layer.

## Phase 4: `_iterate_traffic_and_sum()` (`cascade`, 60–90 %)

Walks the `traffic_data` dict and accumulates contributions using the bucket memo. The outer structure is:

    for leg_idx, line in enumerate(transformed_lines):
        for cell in ship_cells[leg_idx]:
            for d_idx in range(8):
                a_delta, g_delta, an_delta = _process_cell_direction(...)

Source: `compute/drifting_model.py:1067` – _iterate_traffic_and_sum()

Each ship cell contributes:

\[\mathrm{base}_{i,k} = \frac{L_i}{v_k \cdot 1852/3600} \cdot f_{i,k} \cdot \frac{\lambda_{bo}(\mathrm{ship\_type})}{365.25 \cdot 24}\]

and the per-direction contribution is:

\[\Delta = \mathrm{base}_{i,k} \cdot r_{p,d} \cdot h_{\mathrm{eff}} \cdot P_{NR}(d_{\mathrm{edge}})\]

`_process_cell_direction()` does the inner work:

Source: `compute/drifting_model.py:1296` – _process_cell_direction()

1. Build the obstacle list for this cell (respecting draught + anchor threshold), compute `bucket_key` from the tuple of sorted `(type, idx)` pairs.

2. Look up `entries = bucket_memo[(leg_idx, d_idx, bucket_key)]`. On a memo miss (rare), fall back to the pre-computed `hole_pct` without any shadow carving.

3. For each entry:

   - Compute `h_eff = max(0, h_reach - anchor_p * h_in_anchor)`.

   - If the obstacle has precomputed per-edge geometry, sum `contrib = base * r_p * (h_eff * len_frac) * edge_p_nr` across edges. Otherwise fall back to the obstacle-level contrib.

   - Call `_update_report()` / `_update_anchoring_report()` to record the per-leg-direction breakdown.

   - Call `_add_direct_segment_contrib()` to record the per-edge contribution so the result layer can colour the exact polygon edges that dominated the risk.

4. Accumulate `(allision_delta, grounding_delta, anchoring_delta)`.

Progress is reported approximately every 1 % of cascade completion.

## Completion (`layers`, 90–100 %)

After the cascade finishes `run_drifting_model()` does three things on the calculation thread:

1. Applies the user’s risk-reduction factors (`pc.allision_drifting_rf`, `pc.grounding_drifting_rf`) to the totals and stores the final numbers on `self`.

2. Calls `geometries.result_layers.create_result_layers()` to build two `QgsVectorLayer` objects that colour each obstacle polygon by its contribution to the total risk. Layer creation is graduated by Jenks natural breaks (or single-class fallback).

3. Calls `_auto_generate_drifting_report()` which delegates to `DriftingReportBuilderMixin.write_drifting_report_markdown()` (mixin from `compute/drifting_report_builder.py`). The report writes a Markdown file with:

   - Totals per accident type,

   - Per leg-direction tables,

   - Per obstacle tables (with drill-down to per-segment contributions),

   - Debug obstacle blocks when `drift.debug_trace = True`.

Finally the two result line-edits are updated:

    self.p.main_widget.LEPDriftAllision.setText(f"{self.drifting_allision_prob:.3e}")
    self.p.main_widget.LEPDriftingGrounding.setText(f"{self.drifting_grounding_prob:.3e}")

## Function reference

A flat list of every function reached from `run_drifting_model()`, grouped by source file.

### `compute/drifting_model.py`

- `run_drifting_model` - orchestrator (this chapter).

- `_build_transformed` - UTM projection + make_valid.

- `_compute_reach_distance` - T99 repair distance in metres.

- `_merge_depths_by_threshold` - optional per-threshold merge of depth polygons that share unique depth values; many traffic draughts then index into the same merged geometry.

- `_precompute_spatial` - min-distances + probability holes.

- `_precompute_shadow_layer` - corridor/shadow/edge geom per `(leg, dir)`. Now slimmer: pre-computes are pulled out into `_compute_global_shadow_bounds()` (uniform extrude bounds for the shadow memo) and `_precompute_leg_lateral_params()` (per-leg lateral-distribution scalars + `LegState`).

- `_run_shadow_pool` - dispatch the per-(leg, dir) worker across threads (or sequentially for tiny inputs); reports progress and honours cancellation. Extracted from `_precompute_shadow_layer`.

- `_precompute_bucket_memo` - shadow cascade per ship bucket.

- `_iterate_traffic_and_sum` - traffic cascade.

- `_process_cell_direction` - per cell x direction contribution.

- `_build_blocker_shadow` - cached per-obstacle quad-sweep union.

- `_edge_weighted_holes` - distribute hole across polygon edges by corridor overlap length.

- `_analytical_hole_for_geom` - probability hole for a carved geometry; wraps `compute_probability_analytical()`.

- `_update_report` / `_update_anchoring_report` / `_add_direct_segment_contrib` - report bookkeeping (in `DriftingReportBuilderMixin`).

- `_auto_generate_drifting_report` - writes Markdown report.

### `compute/data_preparation.py`

- `prepare_traffic_lists` - builds `(lines, distributions, weights, line_names)` for every leg.

- `split_structures_and_depths` - parses WKT, splits MultiPolygons.

- `transform_to_utm` - picks UTM zone; uses QGIS or pyproj.

- `clean_traffic` - flattens `traffic_data` into per-leg cell lists.

- `get_distribution` - parses a segment’s lateral distributions.

### `compute/basic_equations.py`

- `get_not_repaired` - analytical \(P_{NR}\); dispatches to cached `scipy.special.ndtr()` (normal / lognormal) or direct Weibull formula, else compiles `func` once and re-uses.

- `powered_na` - shared helper used by the powered model.

- `get_drifting_prob` / `get_drift_time` - legacy scalar helpers.

- `SHIP_TYPE_NAMES` / `default_blackout_by_ship_type` - per-type blackout rate table.

### `compute/drift_corridor_geometry.py`

- `_create_drift_corridor` - leg-rect + drift-rect unioned.

- `_extract_obstacle_segments` - polygon edges as `[(p0, p1), ...]`.

- `_segment_intersects_corridor` - kept for tests / callers outside the hot path.

- `segment_corridor_overlap_length` - drift-direction pre-filter then corridor intersection in one shapely pass.

- `_compass_idx_to_math_idx` - 0..7 compass -> math direction.

### `geometries/analytical_probability.py`

- `compute_probability_holes_analytical` - top-level batch across all legs/directions/objects. ThreadPoolExecutor.

- `_compute_single_direction_analytical` - per `(leg, dir)` worker.

- `compute_probability_analytical` - per obstacle; batched CDF.

- `_vectorized_edge_y_intervals` - numpy batch of (slice x edge) y-intervals.

- `_merge_intervals_vectorized` - single-slice merge (tests / callers outside the hot path).

- `_merge_intervals_across_slices` - flat merged intervals across every slice (hot-path helper).

- `_extract_polygon_rings` - polygon rings as numpy arrays.

### `geometries/get_drifting_overlap.py` and helper modules

The original 1400-line module has been split into four files; the top-level facade (`get_drifting_overlap.py`) re-exports the public helpers so existing callers don’t need to update imports.

`geometries/drift_overlap_geometry.py` – pure-data helpers (no Qt / matplotlib):

- `create_polygon_from_line` - leg buffered by the weighted lateral distribution.

- `extend_polygon_in_directions` - sweep that polygon in 8 drift directions; returns one corridor polygon per direction.

- `compare_polygons_with_objs` – per `(polygon, gdf, obj)` overlap matrix.

- `estimate_weighted_overlap` - PDF-weighted coverage of an intersection polygon.

- `compute_coverages_and_distances` - flat per-(polygon, gdf, obj) coverage + distance arrays.

- `compute_min_distance_by_object` - per `(leg, dir, obstacle)` minimum along-drift distance.

- `directional_distances_to_points` - vectorised per-point along- drift distance (used by `_edge_geom_for`).

- `directional_min_distance_reverse_ray` - wraps the helper above to return the min across a polygon’s vertices.

`geometries/drift_overlap_plot.py` – the bottom-axis matplotlib plot:

- `visualize` - paints PDF + failure-remains \(P_{NR}\) curve + green “intersection extent” axvspan, with a picture-in-picture zoom inset.

`geometries/drift_overlap_sidebar.py` – Qt sidebar builder:

- `DIRECTION_LABELS` / `polygon_to_compass` - 8 directions in the order the geometry helpers iterate.

- `split_leg_name` / `lookup_contribution` - parse leg names, look up `contrib_grounding` / `contrib_allision` from the calc’s `drifting_report['by_leg_direction']`.

- `build_overlap_sidebar` - construct the sortable `QTableWidget` used as the overlap-dialog sidebar.

`geometries/get_drifting_overlap.py` – the `DriftingOverlapVisualizer` class itself drives the three matplotlib axes (`ax1` legs, `ax2` direction polygons, `ax3` PDF). `show_in_dialog` is the dialog factory used from the View buttons in `AccidentResultsMixin`.

### `geometries/drift/shadow.py`

- `create_obstacle_shadow` - quad-sweep shadow polygon.

- `_create_edge_quads` - N quad polygons per obstacle edge (shoelace-filtered, no shapely validity).

- `extract_polygons` - flatten Polygon / MultiPolygon / GeometryCollection to a list of Polygons.

### `geometries/result_layers.py`

- `create_result_layers` - builds allision + grounding `QgsVectorLayer` from the drifting report.

### `geometries/calculate_probability_holes.py`

Monte-Carlo alternative to the analytical path, used when `data['use_analytical'] = False`. Same pipeline shape with `ThreadPoolExecutor` parallelism, but every `p_hole` is estimated by sampling rather than integrated analytically.

## Debug trace

Setting `data['drift']['debug_trace'] = True` enables a per-obstacle debug path in `_iterate_traffic_and_sum()` that records `exposure_factor`, `base`, `rp`, `freq`, `dist`, `h_eff`, and the accumulated contribution into `report['debug_obstacles']`. The debug block is embedded in the auto-generated Markdown report, giving a line-by-line breakdown of every obstacle / leg / direction.