Implement IFS in C++ (#701)

* Implement IFS in C++

* Add my name to contributors

* Simpler version, no template

* Separate rand function for int

* Add comments

* fix comment

Author: VincentZalzal

CONTRIBUTORS.md

@@ -48,3 +48,4 @@ This file lists everyone, who contributed to this repo and wanted to show up her
 - dovisutu
 - Antetokounpo
 - Akash Dhiman
+- Vincent Zalzal

contents/IFS/IFS.md

@@ -128,6 +128,8 @@ Here, instead of tracking children of children, we track a single individual tha
 {% method %}
 {% sample lang="jl" %}
 [import:4-17, lang:"julia"](code/julia/IFS.jl)
+{% sample lang="cpp" %}
+[import:39-52, lang:"cpp"](code/c++/IFS.cpp)
 {% endmethod %}
 
 If we set the initial points to the on the equilateral triangle we saw before, we can see the Sierpinski triangle again after a few thousand iterations, as shown below:
@@ -180,6 +182,8 @@ In addition, we have written the chaos game code to take in a set of points so t
 {% method %}
 {% sample lang="jl" %}
 [import, lang:"julia"](code/julia/IFS.jl)
+{% sample lang="cpp" %}
+[import, lang:"cpp"](code/c++/IFS.cpp)
 {% endmethod %}
 
 ### Bibliography

contents/IFS/code/c++/IFS.cpp

@@ -0,0 +1,65 @@
+#include <cmath>
+#include <fstream>
+#include <random>
+#include <vector>
+
+// Simple X-Y point structure, along with some operators
+struct Point {
+  double x, y;
+};
+
+Point operator+(Point lhs, Point rhs) { return {lhs.x + rhs.x, lhs.y + rhs.y}; }
+Point operator*(double k, Point pt) { return {k * pt.x, k * pt.y}; }
+Point operator*(Point pt, double k) { return k * pt; }
+
+using PointVector = std::vector<Point>;
+
+// Returns a pseudo-random number generator
+std::default_random_engine& rng() {
+  // Initialize static pseudo-random engine with non-deterministic random seed
+  static std::default_random_engine randEngine(std::random_device{}());
+  return randEngine;
+}
+
+// Returns a random double in [0, 1)
+double drand() {
+  return std::uniform_real_distribution<double>(0.0, 1.0)(rng());
+}
+
+// Returns a random integer in [0, numElems-1]
+std::size_t randrange(std::size_t numElems) {
+  return std::uniform_int_distribution<std::size_t>(0, numElems - 1)(rng());
+}
+
+// Return a random point from the non-empty PointVector
+Point choose(const PointVector& points) {
+  return points[randrange(points.size())];
+}
+
+// This is a function to simulate a "chaos game"
+PointVector chaosGame(int numOutputPoints, const PointVector& inputPoints) {
+  // Choose first point randomly
+  Point curPoint = {drand(), drand()};
+
+  // For each output point, compute midpoint to random input point
+  PointVector outputPoints(numOutputPoints);
+  for (auto& outPoint : outputPoints) {
+    outPoint = curPoint;
+    curPoint = 0.5 * (curPoint + choose(inputPoints));
+  }
+
+  return outputPoints;
+}
+
+int main() {
+  // This will generate a Sierpinski triangle with a chaos game of n points for
+  // an initial triangle with three points on the vertices of an equilateral
+  // triangle.
+  PointVector inputPoints = {{0.0, 0.0}, {0.5, std::sqrt(0.75)}, {1.0, 0.0}};
+  auto outputPoints = chaosGame(10000, inputPoints);
+
+  // It will output the file sierpinski.dat, which can be plotted after
+  std::ofstream ofs("sierpinski.dat");
+  for (auto pt : outputPoints)
+    ofs << pt.x << '\t' << pt.y << '\n';
+}