Geometry

reticle-geometry is the exact-integer foundation. It has no GPU, async, or UI code, so it is fast to test and simple to reason about.

Coordinates are integers

Chip layout lives on an integer grid measured in database units (DBU). Reticle uses type Dbu = i32, which matches GDSII and keeps points dense in memory. All area and product arithmetic widens to i64 (or i128 for area sums) to avoid overflow, so for example Rect::area returns an i64 and Polygon::signed_double_area returns an i128. See ADR 0002 for the reasoning and the trade-offs.

Primitives

• Point { x, y } on the DBU grid, with saturating translation and squared distance in i64.
• Rect stored as [min, max) corners, with width, height, area, containment, intersection, union, and margin expansion.
• Polygon, an implicitly-closed ring of vertices, with the shoelace signed double-area (exact in i128), winding classification, and a bounding box.
• Path, a polyline with a width and an end-cap style (flat, square, round, or a custom extension), with a conservative bounding box.
• Transform, an orientation from the dihedral group of eight (rotate by a multiple of 90 degrees, optionally reflected), a rational Magnification, and a translation, applied in that order. This matches the GDSII and OASIS placement model.

Robust booleans

Union, intersection, difference, and exclusive-or run on the i_overlay integer engine over DBU coordinates (ADR 0003), wrapped behind polygon_boolean so the dependency stays swappable. Input contours are interpreted by winding under the non-zero fill rule, so a clockwise ring is treated as a hole. Results are flattened to polygons with outer boundaries wound counter-clockwise and holes clockwise, so a caller can tell them apart by Polygon::winding.

Offsetting (growing or shrinking by a delta) runs on i_overlay’s float outline engine with mitered corners and is rounded back to the grid.

Testing

The boolean engine is validated two ways. Exact unit cases check known areas, including a difference that produces a hole. A property test compares the engine against an independent winding-number oracle: for randomized sets of rectangles and every operation, it asserts that a grid of off-edge query points is classified identically by the engine and by the oracle. This catches sign, winding, and hole-handling mistakes that example-based tests miss.