usaco-guide/content/6_Plat/Geometry.md

---
id: geo
title: "Geometry"
author: Benjamin Qi
---

<module-excerpt>

Geometry primitives and convex hull.

</module-excerpt>

## 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

 - [CPC.12](https://github.com/SuprDewd/T-414-AFLV/tree/master/12_geometry)
   - basic geometry
   - convex hulls
   - polygon area
   - point in polygon
   - closest pair of points
 - CPH 29
 - [TopCoder - Basic Geometry Concepts](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 - Geometry: "Elementary Operations"](https://cp-algorithms.com/)
 - [vlecomte - Geometry Handbook](https://codeforces.com/blog/entry/59129)
 - [My Templates](https://github.com/bqi343/USACO/tree/master/Implementations/content/geometry%20(13)/Primitives)

### Problems

 - Template Testing
   - [Kattis Segment Distance](https://open.kattis.com/problems/segmentdistance)
   - [Kattis Segment Intersection](https://open.kattis.com/problems/segmentintersection)
   - [Kattis Point in Polygon](https://open.kattis.com/problems/pointinpolygon)
   - [Kattis Polygon Area](https://open.kattis.com/problems/polygonarea)
   - [Kattis Max Collinear](https://open.kattis.com/problems/maxcolinear)
 - Misc
   - [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)

## Sweep Line

### Tutorial

 - CPH 30
 - [TopCoder Line Sweep](https://www.topcoder.com/community/competitive-programming/tutorials/line-sweep-algorithms/)

### Problems

 - [Cow Steepchase II (Silver)](http://www.usaco.org/index.php?page=viewproblem2&cpid=943)
   - :|
 - [Kattis Closest Pair](https://open.kattis.com/problems/closestpair2)

## [Convex Hull](https://en.wikipedia.org/wiki/Convex_hull_algorithms)

 - [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)
 - [Kattis Fence Orthogonality](https://open.kattis.com/problems/fenceortho)
 - [AGC 44 Random Pawn](https://atcoder.jp/contests/agc044/tasks/agc044_e)
   - Generalization of "Balance"

## Half-Plane Intersection / Convex Stuff

 - [Blogewoosh (Half-Plane Intersection w/ Ternary Search)](https://codeforces.com/blog/entry/61710)
 - [retrograd Half-Plane Intersection](https://codeforces.com/blog/entry/61710?#comment-457662)
 - [Petr (Linear Half-Plane Intersection)](https://petr-mitrichev.blogspot.com/2016/07/a-half-plane-week.html)
 - [KACTL LineContainer](https://github.com/kth-competitive-programming/kactl/blob/master/content/data-structures/LineContainer.h)
 - [Lichao Segment Tree](http://codeforces.com/blog/entry/51275?#comment-351510)

### Problems

 - [Bridges](https://csacademy.com/contest/archive/task/building-bridges/)
   - direct application of LineContainer
+ slugs 2020-06-04 02:09:42 +00:00			`---`
refactor order into ordering.js 2020-06-15 23:19:07 +00:00			`id: geo`
update frontmatter for all modules 2020-06-04 05:39:49 +00:00			`title: "Geometry"`
+ Plat 2020-06-04 03:26:53 +00:00			`author: Benjamin Qi`
+ slugs 2020-06-04 02:09:42 +00:00			`---`
make_docs 2020-06-03 14:17:07 +00:00
migrate to gatsby mdx 2020-06-17 22:18:07 +00:00			`<module-excerpt>`

add numbering 2020-06-04 14:20:28 +00:00			`Geometry primitives and convex hull.`
update frontmatter for all modules 2020-06-04 05:39:49 +00:00
migrate to gatsby mdx 2020-06-17 22:18:07 +00:00			`</module-excerpt>`
+ Plat 2020-06-04 03:26:53 +00:00
			`## 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`

+ General 2020-06-08 19:51:58 +00:00			`- [CPC.12](https://github.com/SuprDewd/T-414-AFLV/tree/master/12_geometry)`
			`- basic geometry`
			`- convex hulls`
			`- polygon area`
			`- point in polygon`
			`- closest pair of points`
			`- CPH 29`
			`- [TopCoder - Basic Geometry Concepts](https://www.topcoder.com/community/competitive-programming/tutorials/geometry-concepts-basic-concepts/)`
+ Plat 2020-06-04 03:26:53 +00:00			`- [CF - Point Class](https://codeforces.com/blog/entry/48122)`
			`- [C++ - std::complex](https://codeforces.com/blog/entry/22175)`
+ General 2020-06-08 19:51:58 +00:00			`- [cp-algo - Geometry: "Elementary Operations"](https://cp-algorithms.com/)`
			`- [vlecomte - Geometry Handbook](https://codeforces.com/blog/entry/59129)`
+ Plat 2020-06-04 03:26:53 +00:00			`- [My Templates](https://github.com/bqi343/USACO/tree/master/Implementations/content/geometry%20(13)/Primitives)`

+ General 2020-06-08 19:51:58 +00:00			`### Problems`

			`- Template Testing`
			`- [Kattis Segment Distance](https://open.kattis.com/problems/segmentdistance)`
			`- [Kattis Segment Intersection](https://open.kattis.com/problems/segmentintersection)`
			`- [Kattis Point in Polygon](https://open.kattis.com/problems/pointinpolygon)`
			`- [Kattis Polygon Area](https://open.kattis.com/problems/polygonarea)`
			`- [Kattis Max Collinear](https://open.kattis.com/problems/maxcolinear)`
			`- Misc`
			`- [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)`

+ Plat 2020-06-04 03:26:53 +00:00			`## Sweep Line`

+ General 2020-06-08 19:51:58 +00:00			`### Tutorial`

			`- CPH 30`
+ Plat 2020-06-04 03:26:53 +00:00			`- [TopCoder Line Sweep](https://www.topcoder.com/community/competitive-programming/tutorials/line-sweep-algorithms/)`
+ General 2020-06-08 19:51:58 +00:00
			`### Problems`

+ Plat 2020-06-04 03:26:53 +00:00			`- [Cow Steepchase II (Silver)](http://www.usaco.org/index.php?page=viewproblem2&cpid=943)`
			`- :\|`
+ General 2020-06-08 19:51:58 +00:00			`- [Kattis Closest Pair](https://open.kattis.com/problems/closestpair2)`
+ Plat 2020-06-04 03:26:53 +00:00
+ General 2020-06-08 19:51:58 +00:00			`## [Convex Hull](https://en.wikipedia.org/wiki/Convex_hull_algorithms)`
+ Plat 2020-06-04 03:26:53 +00:00
			`- [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)`
+ General 2020-06-08 19:51:58 +00:00			`- [Kattis Fence Orthogonality](https://open.kattis.com/problems/fenceortho)`
+ Plat 2020-06-04 03:26:53 +00:00			`- [AGC 44 Random Pawn](https://atcoder.jp/contests/agc044/tasks/agc044_e)`
+ plat stuff 2020-06-04 13:54:18 +00:00			`- Generalization of "Balance"`

+ General 2020-06-08 19:51:58 +00:00			`## Half-Plane Intersection / Convex Stuff`

			`- [Blogewoosh (Half-Plane Intersection w/ Ternary Search)](https://codeforces.com/blog/entry/61710)`
			`- [retrograd Half-Plane Intersection](https://codeforces.com/blog/entry/61710?#comment-457662)`
			`- [Petr (Linear Half-Plane Intersection)](https://petr-mitrichev.blogspot.com/2016/07/a-half-plane-week.html)`
			`- [KACTL LineContainer](https://github.com/kth-competitive-programming/kactl/blob/master/content/data-structures/LineContainer.h)`
			`- [Lichao Segment Tree](http://codeforces.com/blog/entry/51275?#comment-351510)`

			`### Problems`

			`- [Bridges](https://csacademy.com/contest/archive/task/building-bridges/)`
			`- direct application of LineContainer`