parametrized s-bend

DOCS.md

@@ -11,7 +11,7 @@ The `AStarRouter` is the core pathfinding engine. It can be configured directly
 | `node_limit`          | `int`         | 1,000,000          | Maximum number of states to explore per net. Increase for very complex paths.         |
 | `straight_lengths`    | `list[float]` | `[1.0, 5.0, 25.0]` | Discrete step sizes for straight waveguides (µm). Larger steps speed up search.       |
 | `bend_radii`          | `list[float]` | `[10.0]`           | Available radii for 90-degree turns (µm). Multiple values allow best-fit selection.   |
-| `sbend_offsets`       | `list[float]` | `[-5, -2, 2, 5]`   | Lateral offsets for parametric S-bends (µm).                                          |
+| `sbend_offsets`       | `list[float] \| None` | `None` (Auto)      | Lateral offsets for parametric S-bends. `None` uses automatic grid-aligned steps. |
 | `sbend_radii`         | `list[float]` | `[10.0]`           | Available radii for S-bends (µm).                                                     |
 | `snap_to_target_dist` | `float`       | 20.0               | Distance (µm) at which the router attempts an exact bridge to the target port.        |
 | `bend_penalty`        | `float`       | 50.0               | Flat cost added for every 90-degree bend. Higher values favor straight lines.         |
@@ -87,4 +87,7 @@ In multi-net designs, if nets are overlapping:
 3.  If a solution is still not found, check if the `clearance` is physically possible given the design's narrowest bottlenecks.
 
 ### S-Bend Usage
-Parametric S-bends are triggered by the `sbend_offsets` list. If you need a specific lateral shift (e.g., 5.86µm for a 45° switchover), add it to `sbend_offsets`. The router will only use an S-bend if it can reach a state that is exactly on the lattice or the target.
+Parametric S-bends bridge lateral gaps without changing the waveguide's orientation. 
+- **Automatic Selection**: If `sbend_offsets` is set to `None` (the default), the router automatically chooses from a set of "natural" offsets (Fibonacci-aligned grid steps) and the offset needed to hit the target.
+- **Specific Offsets**: To use specific offsets (e.g., 5.86µm for a 45° switchover), provide them in the `sbend_offsets` list. The router will prioritize these but will still try to align with the target if possible.
+- **Constraints**: S-bends are only used for offsets $O < 2R$. For larger shifts, the router naturally combines two 90° bends and a straight segment.