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MURAGE

An AI Chief of Staff and a team that does the work. Free and open source, from Ferrox Labs.

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© 2026 Ferrox Labs. Murage is open source under AGPL-3.0.
Emerging tech skills

Computational Geometry Solver

Competitive programming computational geometry expertise covering convex hull algorithms, line segment intersection, sweep line techniques, polygon operations, Voronoi diagrams, closest pair, half-plane intersection, and robust geometric predicates with practical contest implementations.

Download Murage

Free and open source. macOS, Windows and Ubuntu.

Try it

Add the skill to a bot, then ask your Chief of Staff:

“Use the Computational Geometry Solver skill on this: [describe the job, or paste your notes].”

What it covers

  • Geometric Primitives
  • Line Segment Intersection
  • Convex Hull
  • Sweep Line Algorithms
  • Polygon Operations
  • Half-Plane Intersection
  • Numerical Robustness
  • Contest Problem Pattern Recognition

Skill Guard: clean

Scanned and clear. A bot can use it as soon as you add it.

Subject
Emerging tech
Level
intermediate
License
Apache-2.0
advancedcompetitive-programmingbeginner-friendlytesting

How to use it.

  1. 1

    Download Murage

    Free for Mac, Windows and Ubuntu.

  2. 2

    Add the skill

    Open Settings → Skills and switch on Computational Geometry Solver for any bot. Or ask your Chief of Staff to pick skills for a job.

  3. 3

    Give it a job

    The bot reads the skill when the job calls for it, and works the way it lays out.

Put this skill to work.

  • ResearchAsk a real question. Get one page with sources.
  • Skill GuardEvery skill is scanned before a bot can use it.

Questions.

What is the Computational Geometry Solver skill?+

Competitive programming computational geometry expertise covering convex hull algorithms, line segment intersection, sweep line techniques, polygon operations, Voronoi diagrams, closest pair, half-plane intersection, and robust geometric predicates with practical contest implementations.

How much does it cost?+

Nothing. It ships with Murage, which is free and open source. Your bots run on the AI plan you already have.

Can I change it?+

Yes. Open it in Settings → Skills to read, edit or duplicate it. Skill Guard scans it again after every edit.

More emerging tech skills.

  • Algorithm Pattern MasterGuides mastery of core algorithmic patterns including sliding window, two pointers, binary search, greedy, and backtracking with complexity analysis.
  • Bit Manipulation ExpertCompetitive programming bit manipulation mastery covering fundamental bit tricks, bitmask dynamic programming, XOR properties and applications.
  • Competitive Debugging MasterCompetitive programming debugging mastery covering stress testing with random test generators and systematic edge case identification.
  • Contest StrategistGuides competitive programming contest strategy including time management, problem selection, debugging under pressure and rating improvement.
  • Data Structure ExpertGuides advanced data structure mastery including segment trees, Fenwick trees, tries, union-find and sparse tables.
  • Dynamic Programming SolverGuides dynamic programming mastery including memoization, tabulation, state design, space optimization, and common DP patterns with complexity analysis.

All emerging tech skills

Give your first job to Murage.

Download the free app, connect the AI you already pay for, and tell your Chief of Staff what needs doing. Plan on about ten minutes from install to a working team.

Free · Download Murage

No account needed · Runs on the AI plan you already pay for