Minkowski Sum Ladder¶
Who This Is For¶
Use this lane when the geometry object is the sum of convex regions, not one hull, one feasible intersection, or one plain polygon query.
Warm-Up¶
- convex polygon order
- lowest-vertex normalization
- comparing edge directions with cross products
Core¶
- linear merge of two convex polygons
- repeated sums of several convex polygons
- point-in-convex follow-up after the sum is built
Repo Anchors¶
Stretch¶
- explain why
P + (-Q)turns distance / collision questions into one query on the sum polygon - compare convex polygon sum against half-plane intersection and say why they are different objects
Compare Points¶
- outer boundary of a point set -> Convex Hull
- feasible polygon from directed lines -> Half-Plane Intersection
- one final point query on a polygon you already have -> Polygon Area And Point Location
This ladder is intentionally sparse. The point is not to collect many unrelated continuous-geometry problems. The point is to trust the convex-polygon sum route and recognize when it is the real model.
Exit Criteria¶
You are ready to move on when you can:
- normalize two convex polygons into the same start-vertex convention
- explain why their edge directions can be merged like sorted lists
- use repeated Minkowski sums without losing the exact route
- recognize when one query point should be scaled / reflected before testing membership