-- File: tkz_elements_point.lua
-- Copyright (c) 2026 Alain Matthes
-- SPDX-License-Identifier: LPPL-1.3c
-- Maintainer: Alain Matthes

-- point.lua
-- Définition locale de class

local function class(init, base)
	local cls = {}
	cls.__index = cls

	if base then
		setmetatable(cls, { __index = base })
		cls._base = base
	end

	setmetatable(cls, {
		__call = function(class_tbl, ...)
			local self = setmetatable({}, class_tbl)
			if init then
				init(self, ...)
			elseif base and base.init then
				base.init(self, ...)
			end
			return self
		end,
	})

	cls.init = init

	function cls:is_a(klass)
		local m = getmetatable(self)
		while m do
			if m == klass then
				return true
			end
			m = m._base
		end
		return false
	end

	return cls
end

point = class(function(p, re, im)
	-- Cas 1 : appel standard point(x, y)
	if type(re) == "number" and type(im) == "number" then
		p.re = re
		p.im = im

	-- Cas 2 : appel interne point({re=..., im=...})
	elseif type(re) == "table" and im == nil and type(re.re) == "number" and type(re.im) == "number" then
		p.re = re.re
		p.im = re.im

	-- Cas invalide
	else
		tex.error(
			"Invalid point: expected two numbers or a complex {re,im}, got re = "
				.. tostring(re)
				.. ", im = "
				.. tostring(im)
		)
	end

	p.type = "point"
	p.argument = math.atan(p.im, p.re)
	p.modulus = math.sqrt(p.re * p.re + p.im * p.im)
	p.mtx = matrix:new({ { p.re }, { p.im } })
end)

local sqrt = math.sqrt
local cos = math.cos
local sin = math.sin
local exp = math.exp
local atan = math.atan
local min = math.min
local max = math.max
local abs = math.abs


local function is_point(obj)
	if type(obj) ~= "table" then
		return false
	end
	local mt = getmetatable(obj)
	while mt do
		if mt == point then
			return true
		end
		mt = mt._base
	end
	return false
end

local function topoint(z)
	if is_point(z) then
		return z
	elseif type(z) == "number" then
		return point(z, 0)
	elseif type(z) == "table" and type(z.re) == "number" and type(z.im) == "number" then
		return point(z) -- It is managed in the constructor.
	else
		tex.error("topoint: cannot convert value to point")
	end
end


local function check(z1, z2)
	local p1, p2 = topoint(z1), topoint(z2)
	if not p1 or not p2 then
		tex.error("check: expected point or number")
	end
	return p1, p2
end
-- -------------------------------------------------------------------
-- metamethods
-- -------------------------------------------------------------------
-- redefine arithmetic operators!
function point.__add(z1, z2)
	local c1, c2 = check(z1, z2)
	return point(c1.re + c2.re, c1.im + c2.im)
end

function point.__sub(z1, z2)
	local c1, c2 = check(z1, z2)
	return point(c1.re - c2.re, c1.im - c2.im)
end

function point.__unm(z)
	local z = topoint(z)
	return point(-z.re, -z.im)
end

function point.__mul(z1, z2)
	local c1, c2 = check(z1, z2)
	return point(c1.re * c2.re - c1.im * c2.im, c1.im * c2.re + c1.re * c2.im)
end

-- dot product is '..'  (a+ib) (c-id) = ac+bd + i(bc-ad)
function point.__concat(z1, z2)
	local c1, c2 = check(z1, z2)
	local z = c1 * point.conj(c2)
	return z.re
end

-- determinant  is '^'   (a-ib) (c+id) = ac+bd + i(ad - bc)
function point.__pow(z1, z2)
	local c1, c2 = check(z1, z2)
	local z = point.conj(c1) * c2
	return z.im
end

function point.__div(z1, z2)
	local c1, c2 = check(z1, z2)
	local den = c2.re * c2.re + c2.im * c2.im
	if den == 0 then
		tex.error("Division by zero in point.__div")
	end
	return point((c1.re * c2.re + c1.im * c2.im) / den, (c1.im * c2.re - c1.re * c2.im) / den)
end

function point.__tostring(z)
	local real = z.re
	local imag = z.im
	local tolerance = 1e-10 -- Définir une tolérance

	local function format_real(r)
		if math.abs(r - math.round(r)) < tolerance then
			return tostring(math.round(r)) -- Utiliser un entier
		else
			return string.format("%." .. tkz.dc .. "f", r) -- Utiliser un flottant
		end
	end

	if real == 0 then
		if imag == 0 then
			return "0"
		else
			if imag == 1 then
				return "i"
			elseif imag == -1 then
				return "-i"
			else
				return string.format("%." .. tkz.dc .. "f", imag) .. "i"
			end
		end
	else
		if imag > 0 then
			if imag == 1 then
				return format_real(real) .. "+i"
			else
				return format_real(real) .. "+" .. string.format("%." .. tkz.dc .. "f", imag) .. "i"
			end
		elseif imag < 0 then
			if imag == -1 then
				return format_real(real) .. "-i"
			else
				return format_real(real) .. string.format("%." .. tkz.dc .. "f", imag) .. "i"
			end
		else
			return format_real(real)
		end
	end
end

function point.__tonumber(z)
	if z.im == 0 then
		return z.re
	else
		return nil
	end
end

function point.__eq(z1, z2)
	local epsilon = 1e-10
	return math.abs(z1.re - z2.re) < epsilon and math.abs(z1.im - z2.im) < epsilon
end

function point:identity(pt)
	return point.abs(self - pt) < tkz.epsilon
end

-- -------------------------------------------------------------------
local function pyth(a, b)
	if a == 0 and b == 0 then
		return 0
	end
	a, b = abs(a), abs(b)
	a, b = max(a, b), min(a, b)
	return a * sqrt(1 + (b / a) ^ 2)
end

function point.conj(z)
	local cx = topoint(z)
	return point(cx.re, -cx.im)
end

function point.mod(z)
	local cx = topoint(z)
	local function sqr(x)
		return x * x
	end
	return pyth(cx.re, cx.im)
end

function point.abs(z)
	local cx = topoint(z)
	local function sqr(x)
		return x * x
	end
	return sqrt(sqr(cx.re) + sqr(cx.im))
end

function point.norm(z)
	local cx = topoint(z)
	local function sqr(x)
		return x * x
	end
	return (sqr(cx.re) + sqr(cx.im))
end

function point.power(z, n)
	if type(z) == "number" then
		return z ^ n
	else
		local m = z.modulus ^ n
		local a = angle_normalize_(z.argument * n)
		return polar_(m, a)
	end
end

function point.arg(z)
	local cx = topoint(z)
	return math.atan(cx.im, cx.re)
end

function point.get(z)
	return z.re, z.im
end

function point.sqrt(z)
	local cx = topoint(z)
	local len = math.sqrt(cx.re ^ 2 + cx.im ^ 2)
	local sign = (cx.im < 0 and -1) or 1
	return point(math.sqrt((cx.re + len) / 2), sign * math.sqrt((len - cx.re) / 2))
end

-- ============= methods =========--
-- the result is a point
function point:new(a, b)
	return point(a, b)
end

function point:polar(radius, phi)
	return point:new(radius * math.cos(phi), radius * math.sin(phi))
end

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

function point:north(d)
	local d = d or 1
	return self + polar_(d, math.pi / 2)
end

function point:south(d)
	local d = d or 1
	return self + polar_(d, 3 * math.pi / 2)
end

function point:east(d)
	local d = d or 1
	return self + polar_(d, 0)
end

function point:west(d)
	local d = d or 1
	return self + polar_(d, math.pi)
end

function point:length(p)
	return length_(self, p)
end

function point:normalize()
	local d = point.abs(self)
	if d < tkz.epsilon then
	 tex.error("division by zero" )
  else
		return point(self.re / d, self.im / d)
		end
end

function point:normalize_from(p)
	local u = (self - p)
	local d = point.abs(u)
	if d < tkz.epsilon then
	 tex.error("division by zero" )
	else
	return point(u.re / d, u.im / d) + p
end
end

-- function point:identity(pt)
-- 	return point.abs(self - pt) < tkz.epsilon
-- end

function point:orthogonal(d)
	local m
	if d == nil then
		-- If no scaling factor d is provided, return the point rotated 90 degrees counterclockwise
		return point(-self.im, self.re)
	else
		m = point.mod(self) -- Get the modulus (magnitude) of the current point
		return point(-self.im * d / m, self.re * d / m) -- Return the scaled orthogonal point
	end
end

function point:at(z)
	return point(self.re + z.re, self.im + z.im)
end

function point:print()
	tex.print(tostring(self))
end

-- Shift the current point A orthogonally to the direction (AB)
-- by a distance "dist"
function point:shift_orthogonal_to(B, dist)
	local v = B - self             -- vecteur AB
	local n = v:orthogonal(dist)   -- vecteur normal de norme "dist"
	return n:at(self)              -- applique le décalage à A
end

-- Shift the current point A along the direction (AB)
-- by a distance "dist"
function point:shift_collinear_to(B, dist)
	local v = (B - self):normalize()
	return self + v*dist
end

function point:scale(kx, ky)
	ky = ky or kx
	return point(kx * self.re, ky * self.im)
end
-- =====================
-- the result is a circle
-- =====================
-- Circle through three points: self, a, b
-- point:PPP — cercle passant par trois points (circonscrit)
-- Retourne :
--   PA_center : path des centres
--   PA_through: path des points "through"
--   n         : nombre de cercles trouvés (0 si dégénéré, 1 sinon)
function point:PPP(a, b)
	-- paths de sortie (toujours créés, même si n = 0)
	local PA_center = path()
	local PA_through = path()

	-- cas dégénéré : points alignés ou deux points confondus
	if tkz.aligned(self, a, b)
		 or self:identity(a) or self:identity(b) or a:identity(b) then
		return PA_center, PA_through, 0
	end

	-- centre du cercle circonscrit
	local o = circum_center_(self, a, b)

	-- on choisit "self" comme point-through (n'importe lequel des 3 convient)
	PA_center:add_point(o)
	PA_through:add_point(self)

	return PA_center, PA_through, 1
end

-- ----------------------------------------------------------------
-- transformations
-- ----------------------------------------------------------------
-- function point: symmetry(pt)
--     return symmetry_ (self ,pt)
-- end

function point:symmetry(...)
	local tp = table.pack(...) -- Pack arguments into a table
	local nb = tp.n -- Number of arguments
	local obj = tp[1] -- The first object in the arguments

	if nb == 1 then -- If there's only one argument
		if obj.type == "point" then
			return symmetry_(self, obj) -- Apply symmetry on the point
		elseif obj.type == "line" then
			return line:new(set_symmetry_(self, obj.pa, obj.pb)) -- Create a new line
		elseif obj.type == "circle" then
			return circle:new(set_symmetry_(self, obj.center, obj.through)) -- Create a new circle
		else
			return triangle:new(set_symmetry_(self, obj.pa, obj.pb, obj.pc)) -- Create a new triangle
		end
	else -- If there are multiple arguments
		local results = {} -- Initialize a table to store results
		for i = 1, nb do
			table.insert(results, symmetry_(self, tp[i])) -- Apply symmetry on each object
		end
		return table.unpack(results) -- Return the results as separate values
	end
end

function point:set_symmetry(...)
	return set_symmetry_(self, ...)
end

function point:rotation_pt(angle, pt)
	return rotation_(self, angle, pt)
end

function point:set_rotation(angle, ...)
	return set_rotation_(self, angle, ...)
end

function point:rotation(angle, ...)
	local tp = table.pack(...) -- Pack arguments into a table
	local nb = tp.n -- Number of arguments
	local obj = tp[1] -- The first object in the arguments

	if nb == 1 then -- If there's only one argument
		if obj.type == "point" then
			return rotation_(self, angle, obj) -- Rotate the point
		elseif obj.type == "line" then
			return line:new(set_rotation_(self, angle, obj.pa, obj.pb)) -- Rotate the line
		elseif obj.type == "triangle" then
			return triangle:new(set_rotation_(self, angle, obj.pa, obj.pb, obj.pc)) -- Rotate the triangle
		elseif obj.type == "circle" then
			return circle:new(set_rotation_(self, angle, obj.center, obj.through)) -- Rotate the circle
		else -- For other shapes like square
			return square:new(set_rotation_(self, angle, obj.pa, obj.pb, obj.pc, obj.pd)) -- Rotate the square
		end
	else -- If there are multiple arguments
		local results = {} -- Initialize a table to store results
		for i = 1, nb do
			table.insert(results, rotation_(self, angle, tp[i])) -- Rotate each object
		end
		return table.unpack(results) -- Return the results as separate values
	end
end

function point:homothety(coeff, ...)
	local tp = table.pack(...) -- Pack arguments into a table
	local nb = tp.n -- Number of arguments
	local obj = tp[1] -- The first object in the arguments
	local t = {} -- Initialize a table to store results

	if nb == 1 then -- If there's only one argument
		if obj.type == "point" then
			return homothety_(self, coeff, obj) -- Apply homothety to the point
		elseif obj.type == "line" then
			return line:new(set_homothety_(self, coeff, obj.pa, obj.pb)) -- Apply homothety to the line
		elseif obj.type == "triangle" then
			return triangle:new(set_homothety_(self, coeff, obj.pa, obj.pb, obj.pc)) -- Apply homothety to the triangle
		elseif obj.type == "circle" then
			return circle:new(set_homothety_(self, coeff, obj.center, obj.through)) -- Apply homothety to the circle
		else -- For other shapes like square
			return square:new(set_homothety_(self, coeff, obj.pa, obj.pb, obj.pc, obj.pd)) -- Apply homothety to the square
		end
	else -- If there are multiple arguments
		for i = 1, nb do
			table.insert(t, homothety_(self, coeff, tp[i])) -- Apply homothety to each object
		end
		return table.unpack(t) -- Return the results as separate values
	end
end