Merge pull request #732 from NurlashKO/add_geometry_2d

Add Geometry in 2D section and source code for line intersection.

Author: matthewsamuel95

Geometry 2D/Lines Intersection/lines_intersection.cpp

@@ -0,0 +1,79 @@
+// Solution of UVA 378 problem.
+// https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=5&problem=314
+// Short statement: Find intersection of two lines or output if there is no such or it is infinite.
+
+#include <iostream>
+#include <cmath>
+#include <cstring>
+
+using namespace std;
+
+struct pt {
+	double x, y;
+};
+
+struct line {
+	double a, b, c;
+	line(pt p1, pt p2) {
+		a = p2.y - p1.y;
+		b = p1.x - p2.x;
+		c = -a * p1.x - b * p1.y;
+	}
+};
+
+const double EPS = 1e-9;
+
+double det (double a, double b, double c, double d) {
+	return a * d - b * c;
+}
+
+bool intersect (line m, line n, pt & res) {
+	double zn = det (m.a, m.b, n.a, n.b);
+	if (abs (zn) < EPS)
+		return false;
+	res.x = - det (m.c, m.b, n.c, n.b) / zn;
+	res.y = - det (m.a, m.c, n.a, n.c) / zn;
+	return true;
+}
+
+bool parallel (line m, line n) {
+	return abs (det (m.a, m.b, n.a, n.b)) < EPS;
+}
+
+bool equivalent (line m, line n) {
+	return abs (det (m.a, m.b, n.a, n.b)) < EPS
+		&& abs (det (m.a, m.c, n.a, n.c)) < EPS
+		&& abs (det (m.b, m.c, n.b, n.c)) < EPS;
+}
+
+void solve(line a, line b) {
+	if (equivalent(a, b)) {
+		cout << "LINE\n";
+		return ;
+	}
+	if (parallel(a, b)) {
+		cout << "NONE\n";
+		return ;
+	}
+	pt res;
+	intersect(a, b, res);
+	cout.precision(2);
+	cout << "POINT " << fixed << res.x << " " << res.y << "\n";
+}
+
+int main() {
+	int t;
+	cin >> t;
+	cout << "INTERSECTING LINES OUTPUT\n";
+	while (t--) {
+	    pt p1, p2;
+		cin >> p1.x >> p1.y >> p2.x >> p2.y;
+		line a = line(p1, p2);
+		cin >> p1.x >> p1.y >> p2.x >> p2.y;
+		line b = line(p1, p2);
+
+		solve(a, b);
+	}
+	cout << "END OF OUTPUT\n";
+    return 0;
+}

README.md

@@ -202,3 +202,5 @@ ACM-ICPC Algorithms is a collection of important algorithms and data structures
    * [Top K Frequent Words In Java](/String/top_k_frequent_words_in_java)
    * [Uncompressing Strings](/String/Uncompressing_Strings)
    * [Parsing Arithmetic](/String/ParsingArithmetic)
+* [Geometry 2D](/Geometry%202D)
+   * [Lines Intersection](/Geometry%202D/Lines%20Intersection)