Add Geometry docs

docs/Geometry.md

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+# Geometry
+
+## Basic Geometry
+
+### Description
+- `sgn` `cross` `dot` `ori`
+- `quad` `argCmp` all-integer angle compare.
+- `area` be careful of type.
+- `rot90` multiply by $i$ (or left turn 90 degree)
+- `project` projection onto a vector
+### Test Status
+No test. Used extensively in other template.
+
+## 2D Convex Hull
+
+### Description
+Returns strict convex hull of given points.
+The result is counter-clockwise and the first point is the lex-min point.
+Be carefule about edge case (0/1/2 points on CV)
+### Test Status
+Used in some contest.
+
+## 2D Farthest Pair
+### Description
+Rotating caliper algorithm.
+Requires the input hull be strictly convex.
+### Test Status
+Passed AOJ CGL.
+
+## MinMax Enclosing Rect
+### Description
+Rotating caliper, but with more pointers.
+### Test Status
+Passed UVA 819
+
+## Minkowski Sum
+### Description
+Minkowski sum of two convex hulls.
+### Test Status
+Used in some contest. TODO.
+
+## Segment Intersection
+### Description
+Check whether the segment intersects. Touching at the ends counts.
+Be careful about edge case like parallel, does touching at ends count, ...
+Can be modified to `Ray` class or `Line` class.
+
+To get the intersection point, check next part (HPI)
+
+### Test Status
+Used in many contest. Passed AOJ CGL.
+
+## Half Plane Intersection
+### Description
+Calculate the area of half-plane-intersection.
+The result lines will be in `q` (this is why we need the reference).
+Result lines maybe wrong if the intersection area doesn't have positive area.
+### Test Status
+Passed 2020 Nordic NCPC Big brother.
+Used in many contest.
+
+## SegmentDist
+### Description
+Distance from point to segment and segment to segment.
+Can be used in checking sausage intersection.
+### Test Status
+Passed QOJ 2444 and PTZ 19 summer D3.
+
+## Rotating Sweep Line
+### Description
+A skeleton of rotating sweep line.
+### Test Status
+TODO. Needs template problem.
+
+## Point in Simple Polygon
+### Description
+Testing PIP.
+### Test Status
+Used in some contest. TODO.
+
+## Point in Hull (Fast)
+### Description
+Testing PIH in $O(\log N)$.
+### Test Status
+[Enclosure](codeforces.com/gym/101201/problem/E)
+Used in some contest.
+
+## Tangent of Points To Hull
+### Description
+Tangent of point to hull in $O(\log N)$.
+Requires the hull to be strictly convex.
+Can be modified to find extreme point on hull.
+
+### Test Status
+[Enclosure](codeforces.com/gym/101201/problem/E)
+
+## Circle Class & Intersection
+### Description
+Definition of `Cir` and some intersection function.
+### Test Status
+Passed AOJ CGL.
+
+## Circle Common Tangent
+### Description
+Common tangent point of circle.
+### Test Status
+Passed AOJ CGL and [CF 128E](https://codeforces.com/problemset/problem/128/E).
+
+## Line-Circle Intersection
+### Description
+The point of intersection of line and circle.
+### Test Status
+TODO.
+
+## Poly-Circle Intersection
+### Description
+The intersection area of a circle and a simple polygon.
+### Test Status
+Passed AOJ CGL_7_H.
+Copied from 8BQube and they say it passed HDU2892.
+
+## Minimum Covering Circle
+### Description
+Get minimum covering circle in $O(N)$ expected time.
+Also gives the circumcenter formula.
+### Test Status
+Passed TIOJ 1093, luogu P1742
+
+## Circle Union
+### Description
+Calculate the area that covered by at least $k$ circle for each $k$.
+Time complexity $O(N^2\log N)$.
+### Test Status
+Passed SPOJ.
+
+## Polygon Union
+### Description
+Union area of simple polygon.
+### Test Status
+TODO.
+
+## 3D Convex Hull
+### Description
+Return the face of 3d convex hull of $N$ points.
+There will be $O(N)$ faces and time complexity is $O(N^2)$.
+Be careful of degenerate cases.
+### Test Status
+TODO.
+
+## Delaunay
+### Description
+Delaunay triangulation.
+
+Usage TODO.
+
+### Test Status
+Passed [Brazil subregional](https://codeforces.com/gym/104555/submission/223452683).
+
+## kd Tree (Nearest Point)
+### Description
+KD Tree nearest point query.
+### Test Status
+TODO
+
+## kd Closest Pair (3D ver.)
+### Description
+3d closest pair
+### Test Status
+TODO. Cannot pass TIOJ.
+
+## Simulated Annealing
+### Description
+A skeleton of simulated annealing
+### Test Status
+TODO.
+
+## Triangle Centers 
+### Description
+Triangle centers formula.
+### Test Status
+No test.