From 3a404237ed05331e9d741fd2787706bd7e41c3f2 Mon Sep 17 00:00:00 2001
From: Piyush Sethia <piyushsethia1999@gmail.com>
Date: Tue, 2 Oct 2018 09:58:05 +0530
Subject: [PATCH] Adds point and convex hull classes

---
 mathx/geometry.h | 167 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 167 insertions(+)
 create mode 100644 mathx/geometry.h

diff --git a/mathx/geometry.h b/mathx/geometry.h
new file mode 100644
index 0000000..0f090a2
--- /dev/null
+++ b/mathx/geometry.h
@@ -0,0 +1,167 @@
+#ifndef MATHX_NUMBER_THEORY_H_
+#define MATHX_NUMBER_THEORY_H_
+
+namespace mathx {
+	template<typename T>
+	class point
+	{
+		T x, y;
+	public:
+		//Constructor
+		point(T x = static_cast<T>(0), T y = static_cast<T>(0)): x(x), y(y) {
+
+		};
+
+		point operator+=(const point &t) {
+			this->x += t.x;
+			this->y += t.y;
+			return *this;
+		}
+		point operator-=(const point &t) {
+			this->x -= t.x;
+			this->y -= t.y;
+			return *this;
+		}
+		point operator*=(const point &t) {
+			this->x *= t;
+			this->y *= t;
+			return *this;
+		}
+		point operator/=(const point &t) {
+			this->x /= t;
+			this->y /= t;
+			return *this;
+		}
+		point operator+(const point &t) const {
+			return point(this->x + t.x, this->y + t.y);
+		}
+		point operator-(const point &t) const {
+			return point(this->x - t.x, this->y - t.y);
+		}
+		point operator*(const T &t) const {
+			return point(this->x * t, this->y * t);
+		}
+		point operator/(const T &t) const {
+			return point(this->x / t, this->y / t);
+		}
+		friend istream& operator>>(istream& is, point& p) { 
+			is >> p.x >> p.y; 
+			return is;
+		}
+		friend ostream& operator<<(ostream& os, const point& p) { 
+			os << p.x << ' ' << p.y; 
+			return os;
+		}
+		T operator*(const point &p) const { 
+			return (this->x * p.x + this->y * p.y); 
+		}
+		T operator^(const point &p) const { 
+			return (this->x * p.y - this->y * p.x); 
+		}
+		friend point operator* (T const &t, point const &p) { 
+			return p * t;
+		}
+		
+		long double polarAngle() {
+			if (this->x == static_cast<T>(0))
+				return ((this->y > static_cast<T>(0)) ? PI * (0.5) : PI * static_cast<long double>(1.5));
+			if (this->y == static_cast<T>(0) && this->x > static_cast<T>(0))
+				return (0.0);
+			if (this->y == static_cast<T>(0))
+				return (PI);
+			long double res = atan(abs(y / x));
+			if (y > static_cast<T>(0) && x > static_cast<T>(0))
+				return res;
+			if (y > static_cast<T>(0) && x < static_cast<T>(0))
+				return (PI - res);
+			if (y < static_cast<T>(0) && x > static_cast<T>(0))
+				return (static_cast<long double>(2) * PI - res);
+			return (PI + res);
+		}
+		point rotate(long double sintheta, long double costheta) const { 
+			return (costheta * this->x - sintheta * this->y, sintheta * this->x + costheta * this->y); 
+		}
+		point rotate(long double theta) const { 
+			return this->rotate(sin(theta), cos(theta)); 
+		}
+		long double dist(const point &a = point()) { 
+			return sqrt((a - *this) * (a - *this)); 
+		}
+		static long double area(const point &a, const point &b, const point &c) { 
+			long double a1 = sqrt((a - b) * (a - b)); 
+			long double a2 = sqrt((b - c) * (b - c)); 
+			long double a3 = sqrt((a - c) * (a - c)); 
+			long double s = (a1 + a2 + a3) / ((long double) (2.0)); 
+			return sqrt((s) * (s - a1) * (s - a2) * (s - a3)); 
+		}
+		static T dist(const point &a, const point &b) {
+			return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
+		}
+		T distFromLine(point a, const long double& c) { 
+			return sqrt((((*this) * a + c) * ((*this) * a + c)) / (a * a)); 
+		}
+		T distFromLine(point x, point y) { 
+			point p = (x + ((((*this - x) * y) / (y * y)) * y)); 
+			return sqrt((p - *this) * (p - *this)); 
+		}
+		static bool clockwise(point a, point b, point c) { 
+			return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) < 0; 
+		}
+		static bool counterClockwise(point a, point b, point c) {
+			return a.x * (b.y - c.y) + b.x * (c.y - a.y) + c.x * (a.y - b.y) > 0;
+		}
+	};
+
+	template<typename T>
+	class ConvexHull //Graham's Scan
+	{
+		vector<point<T> > Hull;
+		int n;
+		
+		int nextin(int i) { 
+			return (i == n - 1 ? 0 : i + 1);
+		}
+
+	public:
+		ConvexHull(vector<point<T> >& a)
+		{
+			if (a.size() <= 1) 
+				return;
+
+			sort(a.begin(), a.end(), [](point<T> a, point<T> b) { 
+				return ((a.x < b.x) || (a.x == b.x && a.y < b.y)); 
+			});
+
+			point<T> pa = a[0], pb = a.back(); std::vector<point<T> > upper, lower; 
+			upper.pb(pa), lower.pb(pa);
+
+			for (int i = 1; i < (int)a.size(); ++i)
+			{
+				if (i == a.size() - 1 || clockwise(pa, a[i], pb))
+				{
+					while (upper.size() >= 2 && !clockwise(upper[upper.size() - 2], upper[upper.size() - 1], a[i]))
+						upper.pop_back();
+					upper.pb(a[i]);
+				}
+				if (i == a.size() - 1 || counterClockwise(pa, a[i], pb))
+				{
+					while (lower.size() >= 2 && !counterClockwise(lower[lower.size() - 2], lower[lower.size() - 1], a[i]))
+						lower.pop_back();
+					lower.pb(a[i]);
+				}
+			}
+			for (int i = 0; i < (int)upper.size(); ++i)
+				Hull.pb(upper[i]);
+
+			for (int i = lower.size() - 2; i > 0 ; i--)
+				Hull.pb(lower[i]);
+
+			n = Hull.size();
+		}
+		std::vector<point<T>> Hullify() { 
+			return Hull; 
+		}
+	};
+}
+
+#endif
\ No newline at end of file