local M = {}

-- Source with pseudocode: https://de.wikipedia.org/wiki/Punkt-in-Polygon-Test_nach_Jordan
-- see also https://en.wikipedia.org/wiki/Point_in_polygon
-- parameters: points A = (x_a, y_a), B = (x_b, y_b), C = (x_c, y_c)
-- return value: −1 if the ray from A to the right bisects the edge [BC] (the lower vortex of [BC]
-- is not seen as part of [BC]);
--                0 if A is on [BC];
--                +1 else
function M.cross_prod_test(x_a, y_a, x_b, y_b, x_c, y_c)
	if y_a == y_b and y_b == y_c then
		if (x_b <= x_a and x_a <= x_c) or (x_c <= x_a and x_a <= x_b) then
			return 0
		end
		return 1
	end
	if not (y_a == y_b and x_a == x_b) then
		if y_b > y_c then
			-- swap b and c
			local h = x_b
			x_b = x_c
			x_c = h
			h = y_b
			y_b = y_c
			y_c = h
		end
		if y_a <= y_b or y_a > y_c then
			return 1
		end
		local delta = (x_b-x_a) * (y_c-y_a) - (y_b-y_a) * (x_c-x_a)
		if delta > 0 then
			return 1
		end
		if delta < 0 then
			return -1
		end
	end
	return 0
end

-- Source with pseudocode: https://de.wikipedia.org/wiki/Punkt-in-Polygon-Test_nach_Jordan
-- see also: https://en.wikipedia.org/wiki/Point_in_polygon
-- let P be a 2D Polygon and Q a 2D Point
-- return value:  +1 if Q within P;
--                −1 if Q outside of P;
--                0 if Q on an edge of P
function M.point_in_polygon(poly, point)
	local t = -1
	for i=1, #poly-1 do
		t = t * M.cross_prod_test(point.lon, point.lat, poly[i].lon, poly[i].lat, poly[i+1].lon, poly[i+1].lat)
		if t == 0 then break end
	end
	return t
end

-- Convert rectangle defined by two point into polygon
function M.two_point_rec_to_poly(rec)
	return {
		rec[1],
		{ lon = rec[2].lon, lat = rec[1].lat },
		rec[2],
		{ lon = rec[1].lon, lat = rec[2].lat },
	}
end

return M