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---
slug: /plat/geo
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title: "Geometry"
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author: Benjamin Qi
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order: 4
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---
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Geometry primitives and convex hull.
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## Primitives
You should know basic operations like cross product and dot product. For platinum specifically, you should be fine as long as you know how to code convex hull.
### Tutorial
- CPH 29, 30.1
- [TopCoder ](https://www.topcoder.com/community/competitive-programming/tutorials/geometry-concepts-basic-concepts/ )
- [CF - Point Class ](https://codeforces.com/blog/entry/48122 )
- [C++ - std::complex ](https://codeforces.com/blog/entry/22175 )
- [cp-algo - "Elementary Operations" ](https://cp-algorithms.com/ )
- [vlecomte - geo book ](https://codeforces.com/blog/entry/59129 )
- [My Templates ](https://github.com/bqi343/USACO/tree/master/Implementations/content/geometry%20(13 )/Primitives)
## Sweep Line
- [TopCoder Line Sweep ](https://www.topcoder.com/community/competitive-programming/tutorials/line-sweep-algorithms/ )
- [Cow Steepchase II (Silver) ](http://www.usaco.org/index.php?page=viewproblem2&cpid=943 )
- :|
## Convex Hull
- [Kattis Convex Hull ](https://open.kattis.com/problems/convexhull )
### Tutorial
- Graham Scan
- [cp-algo ](https://cp-algorithms.com/geometry/grahams-scan-convex-hull.html )
- [My Implementation ](https://github.com/bqi343/USACO/blob/master/Implementations/content/geometry%20(13 )/Polygons/ConvexHull2.h)
- Monotone Chain
- CPH 30.3 (brief)
- [Wikipedia ](https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain )
- [My Implementation ](https://github.com/bqi343/USACO/blob/master/Implementations/content/geometry%20(13 )/Polygons/ConvexHull%20(13.2).h)
### Problems
- [USACO Plat Balance ](http://www.usaco.org/index.php?page=viewproblem2&cpid=864 )
- [USACO Plat Falling ](http://www.usaco.org/index.php?page=viewproblem2&cpid=998 )
- [USACO Old Gold - Fencing ](http://www.usaco.org/index.php?page=viewproblem2&cpid=534 )
- [USACO Old Gold - Cow Curling ](http://www.usaco.org/index.php?page=viewproblem2&cpid=382 )
- [AGC 44 Random Pawn ](https://atcoder.jp/contests/agc044/tasks/agc044_e )
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- Generalization of "Balance"
(old)
[CPC.12 ](https://github.com/SuprDewd/T-414-AFLV/tree/master/12_geometry )
## 4
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* Misc Stuff to Know
* Topics
* std::complex, pair operators
* Closest Pair
* MaxCollinear
* Point in Polygon
* Polygon Area
* Line Segment Intersection
* Tutorial
* [TopCoder ](https://www.topcoder.com/community/data-science/data-science-tutorials/geometry-concepts-basic-concepts/ )
* [Point Class ](http://codeforces.com/blog/entry/48122 )
* [Easy Geo w/ std::complex ](http://codeforces.com/blog/entry/22175 )
* [Geo Book ](http://codeforces.com/blog/entry/59129 )
* CPH (29, Geometry)
* Problems
* [Arpa & Geo ](http://codeforces.com/problemset/problem/851/B )
* [Tell Your World ](http://codeforces.com/problemset/problem/849/B )
* [Gleb & Pizza ](http://codeforces.com/problemset/problem/842/B )
* [Birthday Cake ](https://open.kattis.com/problems/birthdaycake )
* [Racing Off Track ](https://open.kattis.com/contests/acpc17open/problems/racingofftrack )
* [TopCoder Watchtower ](https://community.topcoder.com/stat?c=problem_statement&pm=2014&rd=4685 )
* Convex Hull
* Tutorial
* CPH (30, Sweep Line Algorithms)
* [TopCoder Line Sweep ](https://www.topcoder.com/community/data-science/data-science-tutorials/line-sweep-algorithms/ )
* Topics
* Convex Hull
* [Wikipedia ](https://en.wikipedia.org/wiki/Convex_hull_algorithms )
* Andrew's Monotone Chain (I prefer)
* Graham Scan
* Additional
* [Lichao Segment Tree ](http://codeforces.com/blog/entry/51275?#comment-351510 )
* Half-Plane Intersection
* [Blogewoosh (Ternary Search) ](https://codeforces.com/blog/entry/61710 )
* [retrograd ](https://codeforces.com/blog/entry/61710?#comment-457662 )
* [Petr (Linear ](https://petr-mitrichev.blogspot.com/2016/07/a-half-plane-week.html )
* LineContainer
* maintaining separate ones for bottom and top hulls should suffice?
* Problem(s)
* [Bridges ](https://csacademy.com/contest/archive/task/building-bridges/ )
* [Fence Orthogonality ](https://open.kattis.com/problems/fenceortho )
* [A2OJ ](https://a2oj.com/category?ID=22 )
