inire/docs/plans/geometric_representation.md

Geometric Representation and Data Structures

This document defines the core data structures for representing the routing problem.

1. Port Definitions (Connectivity)

Routing requests are defined as a mapping of source ports to destination ports.

• Port Structure: (x, y, orientation)
  • x, y: Coordinates snapped to 1nm grid.
  • orientation: Strictly \{0, 90, 180, 270\} degrees.
• Netlist: A dictionary or list of tuples: {(start_port): (end_port)}. Each entry represents a single-layer path that must be routed.
• Heterogeneous Widths: The router supports different widths W_i per net. Dilation for a specific net i is calculated as (W_i + C)/2 to maintain the global clearance C.

2. Component Library (Move Generator)

The router uses a discrete set of components to expand states in the A* search.

2.1. Straight Waveguides

• A Expansion:* Generates "Straight" moves of varying lengths (e.g., 1\mu m, 5\mu m, 25\mu m).
• Snap-to-Target: If the destination port T is directly ahead and the current state's orientation matches $T$'s entry orientation, a special move is generated to close the gap exactly.

2.2. Fixed 90° Bends (PDK Cells)

• Parameters: radius, width.
• A Expansion:* A discrete move that changes orientation by \pm 90^\circ and shifts the coordinate by the radius.
• Grid Alignment: If the bend radius R is not a multiple of the search grid (default 1\mu m), the resulting state is snapped to the nearest grid point, and a warning is issued to the user.

2.3. Parametric S-Bends (Compact)

• Parameters: radius, width.
• A Expansion:* Used ONLY for lateral offsets O < 2R.
• Large Offsets (O \ge 2R): The router does not use a single S-bend move for large offsets. Instead, the A* search naturally finds the optimal path by combining two 90° bends and a straight segment. This ensures maximum flexibility in obstacle avoidance for large shifts.

3. Obstacle Representation

Obstacles are provided as raw polygons on a single layer.

• Pre-processing: All input polygons are inserted into an R-Tree.
• Buffer/Dilation: Obstacles are pre-dilated by (W_{max} + Clearance)/2 for initial pruning, but final collision tests use the net-specific width W_i.
• No Multi-layer: The router assumes all obstacles and paths share the same plane.
• Safety Zone: Ignore collisions within 2nm of start and end ports for robustness.