ENH: improve bridge direction detection

Thanks to Prusa.
Jira: STUDIO-2453

Change-Id: Iadcc59df44d5abc552f5d558a500fd9bcd66d43f
(cherry picked from commit c19156fd037df4231f3e0cb1e9a899c9b7525372)

src/libslic3r/PrincipalComponents2D.hpp

@@ -0,0 +1,24 @@
+#ifndef slic3r_PrincipalComponents2D_hpp_
+#define slic3r_PrincipalComponents2D_hpp_
+
+#include "AABBTreeLines.hpp"
+#include "BoundingBox.hpp"
+#include "libslic3r.h"
+#include <vector>
+#include "Polygon.hpp"
+
+namespace Slic3r {
+
+// returns triangle area, first_moment_of_area_xy, second_moment_of_area_xy, second_moment_of_area_covariance
+// none of the values is divided/normalized by area.
+// The function computes intgeral over the area of the triangle, with function f(x,y) = x for first moments of area (y is analogous)
+// f(x,y) = x^2 for second moment of area
+// and f(x,y) = x*y for second moment of area covariance
+std::tuple<float, Vec2f, Vec2f, float> compute_moments_of_area_of_triangle(const Vec2f &a, const Vec2f &b, const Vec2f &c);
+
+// returns two eigenvectors of the area covered by given polygons. The vectors are sorted by their corresponding eigenvalue, largest first
+std::tuple<Vec2f, Vec2f> compute_principal_components(const Polygons &polys);
+
+}
+
+#endif