-- tkz_elements_functions_points.lua
-- date 2025/03/04
-- version 3.34c
-- Copyright 2025  Alain Matthes
-- This work may be distributed and/or modified under the
-- conditions of the LaTeX Project Public License, either version 1.3
-- of this license or (at your option) any later version.
-- The latest version of this license is in
-- http://www.latex-project.org/lppl.txt
-- and version 1.3 or later is part of all distributions of LaTeX
-- version 2005/12/01 or later.
-- This work has the LPPL maintenance status “maintained”.
-- The Current Maintainer of this work is Alain Matthes.

function id()
	for i, k in pairs(z) do
		if _G[i] == k then
		else
			_G[i] = k
		end
	end
end

function polar_(radius, phi)
	return point(radius * math.cos(phi), radius * math.sin(phi))
end

function polar(radius, phi)
  return polar_(radius, phi)
end

function polar_deg(radius, phi)
  return polar_(radius, phi * math.pi / 180)
end

function barycenter_(...)
	local cp = table.pack(...)
	local sum = 0
	local weight = 0
	for i = 1, cp.n do
		sum = sum + cp[i][1] * cp[i][2]
		weight = weight + cp[i][2]
	end
	return sum / weight
end

function rotation_(c, a, pt)
	local z = point(math.cos(a), math.sin(a))
	return z * (pt - c) + c
end

-- Define the set_rotation_ function
function set_rotation_(c, angle, ...)
	local tp = table.pack(...)
	local t = {}
	for i = 1, tp.n do
		table.insert(t, rotation_(c, angle, tp[i]))
	end
	return table.unpack(t)
end

function symmetry_(c, pt)
	return 2 * c - pt
end

function set_symmetry_(c, ...)
	local tp = table.pack(...)
	local t = {}
	for i = 1, tp.n do
		table.insert(t, symmetry_(c, tp[i]))
	end
	return table.unpack(t)
end

function homothety_(c, t, p)
	return c + t * (p - c)
end

function set_homothety_(c, coeff, ...)
	local tp = table.pack(...)
	local t = {}
	for i = 1, tp.n do
		table.insert(t, homothety_(c, coeff, tp[i]))
	end
	return table.unpack(t)
end

function translation_(a, p)
	return a + p
end

function set_translation_(u, ...)
	local tp = table.pack(...)
	local t = {}
	for i = 1, tp.n do
		table.insert(t, (u + tp[i]))
	end
	return table.unpack(t)
end

function random_point_(lower, upper)
	math.randomseed(tonumber(tostring(os.time()):reverse():sub(1, 6)))
	x = math.random(lower, upper)
	y = math.random(lower, upper)
	return point(x, y)
end

function midpoints_(...)
	local arg = table.pack(...)
	local n = arg.n
	local t = {}
	for i = 1, n - 1 do
		table.insert(t, (arg[i] + arg[i + 1]) / 2)
	end
	table.insert(t, (arg[n] + arg[1]) / 2)
	return table.unpack(t)
end