Add a method for calculating the centroid of a polygon

[Xrayez]

Required for #29867 to work for calculating the exact center of mass of polygon shapes.

C++:

Vector2 centroid = Geometry::get_polygon_centroid(polygon)

GDScript:

var centroid = Geometry.get_polygon_centroid(polygon)

@raphael10241024 please take a look at this. 🙂

[Raphael2048]

That's great, how about adding another function for calculating polygon area?

[Xrayez]

@raphael10241024 there are a few places where area can be computed for polygons within engine:

This one can already be used within the engine now, but not from script (currently used by CSG module):

godot/core/math/triangulate.cpp

Lines 33 to 44 in b16c309

	real_t Triangulate::get_area(const Vector<Vector2> &contour) {
	int n = contour.size();
	const Vector2 *c = &contour[0];
	real_t A = 0.0;
	for (int p = n - 1, q = 0; q < n; p = q++) {
	A += c[p].cross(c[q]);
	}
	return A * 0.5;
	}

Usage:

#include "core/math/triangulate.h"
/* ... */
real_t area = Triangulate::get_area(polygon)

This one needs to compute polygon's area and decide whether it's clockwise or not based on computed signed area.

godot/core/math/geometry.h

Lines 891 to 904 in 24e9a88

	static bool is_polygon_clockwise(const Vector<Vector2> &p_polygon) {
	int c = p_polygon.size();
	if (c < 3)
	return false;
	const Vector2 *p = p_polygon.ptr();
	real_t sum = 0;
	for (int i = 0; i < c; i++) {
	const Vector2 &v1 = p[i];
	const Vector2 &v2 = p[(i + 1) % c];
	sum += (v2.x - v1.x) * (v2.y + v1.y);
	}
	return sum > 0.0f;
	}

So now I wonder that it might be a good idea to make a dedicated function for it in Geometry as the functionality is already present but just used indirectly.

[Xrayez]

This is still needed by #29867, but given that #29867 already uses the implementation from this PR, and given there's no particular reason why this should be part of the core, I'll close this for now unless people explicitly express their interest/provide a real-life use case for this.

The method is in fact already implemented in GeometryTools module. 🙂