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Half-Plane Intersection Ladder

Who This Is For

Use this lane when geometry tasks stop being about one predicate and start being about the whole feasible region cut out by many directed lines.

Warm-Up

  • orientation and sidedness
  • line intersection
  • polygon area
  • the difference between point-set hulls and line-constraint intersections

Core

  • keep the left side of every directed boundary line
  • sort half-planes by angle
  • deduplicate equal directions by keeping the most restrictive one
  • maintain the surviving feasible boundary with a deque
  • flagship polygon-kernel rep: Big Brother

Stretch

  • explain why bounded polygon output is a narrower contract than general half-plane feasibility
  • compare polygon kernels against convex hull anti-cues
  • say when sweep line is the wrong abstraction even though "many lines" appear in the statement

Retrieval Layer

Repo Anchors

Exit Criteria

You are ready to move on when you can:

  • state the left-side convention without hesitation
  • explain why equal-direction tie-breaking matters
  • describe why deque pops only happen at the ends
  • spot when a polygon-kernel problem is just half-plane intersection in disguise

External Practice