Add Boolean for strictly_convex construction

Author: AbdeltwabMF

geometry/CMakeLists.txt

@@ -2,4 +2,4 @@ cmake_minimum_required(VERSION 3.16)
 
 project(Geometry)
 
-add_executable(main main.cpp)
+add_executable(geometry geometry.cpp)

geometry/convex_hull.h

@@ -4,12 +4,11 @@
 
 #include <vector>
 #include <algorithm>
-#include <cmath>
 
 namespace geometry
 {
 	[[nodiscard]] static inline std::vector<ivec2>
-	convex_hull_construct(std::vector<ivec2> points)
+	convex_hull_construct(std::vector<ivec2> points, bool strictly_convex = true)
 	{
 		// lowest y-coordinate and leftmost point
 		ivec2 pivot = *std::min_element(points.begin(), points.end());
@@ -20,11 +19,27 @@ namespace geometry
 			[&pivot](const ivec2& a, const ivec2& b)
 			{
 				auto area = (a - pivot) * (b - pivot);
-				auto a_smaller = ::abs(pivot.x - a.x) + ::abs(pivot.y - a.y) < ::abs(pivot.x - b.x) + ::abs(pivot.y - b.y);
-				return (area != 0) * (area > 0) + (area == 0) * a_smaller;
+				if (area == 0)
+				{
+					auto pivot_a = a - pivot;
+					auto pivot_b = b - pivot;
+					return pivot_a.dot(pivot_a) < pivot_b.dot(pivot_b);
+				}
+				else
+				{
+					return area > 0;
+				}
 			}
 		);
 
+		if (!strictly_convex)
+		{
+			int reverse_index = (int)points.size() - 2;
+			while (reverse_index > 0 && (points.back() - pivot) * (points[reverse_index] - pivot) == 0)
+				reverse_index--;
+			std::reverse(points.begin() + reverse_index + 1, points.end());
+		}
+
 		std::vector<ivec2> polygon;
 		polygon.reserve(points.size());
 
@@ -34,9 +49,8 @@ namespace geometry
 			{
 				auto a = polygon.end()[-2];
 				auto b = polygon.end()[-1];
-				auto& c = points[i];
-
-				if ((b - a) * (c - a) > 0)
+				auto area = (b - a) * (points[i] - a);
+				if (area > 0 || (area == 0 && !strictly_convex))
 					break;
 
 				// remove last point if it results in a clockwise orientation or if the points are collinear
@@ -45,6 +59,9 @@ namespace geometry
 			polygon.push_back(points[i]);
 		}
 
+		if (strictly_convex && polygon.size() == 2 && polygon[0] == polygon[1])
+			polygon.pop_back();
+
 		polygon.shrink_to_fit();
 		return polygon;
 	}

geometry/main.cpp renamed to geometry/geometry.cpp

@@ -17,8 +17,6 @@ int main()
 			std::cin >> points[i];
 
 		auto polygon = geometry::convex_hull_construct(points);
-		if (polygon.size() == 2 && polygon[0] == polygon[1])
-			polygon.pop_back();
 
 		std::cout << polygon.size() << '\n';
 		for (size_t i = 0; i < polygon.size(); ++i)

geometry/types.h

@@ -32,6 +32,11 @@ struct ivec2
 	{
 		return x * other.y - y * other.x;
 	}
+
+	inline int64_t dot(const ivec2& other) const
+	{
+		return x * other.x + y * other.y;
+	}
 };
 
 std::ostream& operator<<(std::ostream& out, const ivec2& vec)