Add methods to calculate polygon geometric center & center of mass

libs/cg/include/psemek/cg/area.hpp

@@ -40,4 +40,47 @@ namespace psemek::cg
 		return result / scalar_type{12};
 	}
 
+	template <typename Iterator>
+	auto polygon_center(Iterator begin, Iterator end)
+	{
+		auto const first = *begin;
+
+		auto offset = decltype(*begin - *begin)::zero();
+
+		std::size_t count = 0;
+
+		for (; begin != end; ++begin)
+		{
+			offset += *begin - first;
+			++count;
+		}
+
+		using scalar_type = std::remove_cvref_t<decltype((*begin)[0])>;
+		return first + offset / static_cast<scalar_type>(count);
+	}
+
+	template <typename Iterator>
+	auto polygon_mass_center(Iterator begin, Iterator end)
+	{
+		using scalar_type = std::remove_cvref_t<decltype((*begin)[0])>;
+		using result_type = std::remove_cvref_t<decltype(*begin)>;
+
+		auto result = result_type::zero();
+
+		for (auto it = begin, prev = std::prev(end); it != end; prev = it++)
+		{
+			auto const v0 = *prev;
+			auto const v1 = *it;
+			result[0] += (v1[1] - v0[1]) * (v0[0] * v0[0] + v0[0] * v1[0] + v1[0] * v1[0]);
+			result[1] -= (v1[0] - v0[0]) * (v0[1] * v0[1] + v0[1] * v1[1] + v1[1] * v1[1]);
+		}
+
+		scalar_type a = polygon_area(begin, end) * 6;
+
+		result[0] /= a;
+		result[1] /= a;
+
+		return result;
+	}
+
 }