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+# Geometry-Based Push
+
+## Problem
+
+`PlateView.PushSelected` uses bounding boxes to determine how far to slide parts. For irregular shapes, this leaves large gaps between actual cut geometry. Parts should nestle together based on their true shape.
+
+## Behavior
+
+When pushing a selected part in a cardinal direction:
+
+1. The moving part's geometry is offset outward by `Plate.PartSpacing` (the kerf buffer)
+2. That offset geometry slides until it touches the **actual cut geometry** of stationary parts (zero gap between offset and cut)
+3. The actual cut paths end up separated by exactly `PartSpacing`
+4. For plate edges: the **actual geometry** bounding box stops at the work area boundary (no offset applied to edges — same as current behavior)
+
+## Algorithm: Analytical Polygon Directional-Distance
+
+### Conversion Pipeline
+
+```
+Part.Program → ConvertProgram.ToGeometry() → Helper.GetShapes() → Shape.ToPolygon() → Polygon.ToLines()
+```
+
+For the moving part, insert an offset step after getting shapes:
+
+```
+shapes → Shape.OffsetEntity(PartSpacing, OffsetSide.Left) → ToPolygon() → ToLines()
+```
+
+### Directional Distance
+
+For a given push direction, compute the minimum translation distance before any edge of the offset moving polygon contacts any edge of a stationary polygon.
+
+Three cases per polygon pair:
+
+1. **Moving vertex → stationary edge**: For each vertex of the offset polygon, cast a ray in the push direction. Find where it crosses a stationary edge. Record the distance.
+2. **Stationary vertex → moving edge**: For each vertex of the stationary polygon, cast a ray in the opposite direction. Find where it crosses an offset-moving edge. Record the distance.
+3. **Edge-edge sliding contact**: For non-parallel edge pairs, compute the translation distance along the push axis where they first intersect.
+
+The minimum positive distance across all cases and all polygon pairs is the push distance.
+
+### Early-Out
+
+Before polygon math, check bounding box overlap on the perpendicular axis. If a stationary part's bounding box doesn't overlap the moving part's bounding box on the axis perpendicular to the push direction, skip that pair.
+
+## Changes
+
+| File | Change |
+|------|--------|
+| `OpenNest.Core\Helper.cs` | Add `DirectionalDistance(List<Line>, List<Line>, PushDirection)` |
+| `OpenNest.Core\Helper.cs` | Add `RayEdgeDistance(Vector, Line, PushDirection)` helper |
+| `OpenNest\Controls\PlateView.cs` | Rewrite `PushSelected` to use polygon directional-distance |
+
+### What stays the same
+
+- Plate edge distance check (actual bounding box vs work area)
+- Key bindings (X/Y/Shift combinations)
+- Existing `ClosestDistance*` methods remain (may be used elsewhere)
+
+### What changes
+
+- `PushSelected` converts parts to polygons instead of using bounding boxes
+- Distance calculation uses actual geometry edges instead of box edges