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-- tkz_elements_point.lua
-- date 23/12/08
-- version 1.50c
-- Copyright 2023 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.
-- point.lua
require 'tkz_elements_class'
point = class(function(p,re,im)
if type(re) == 'number' then
p.re = re
p.im = im
else
p.re = re.re
p.im = re.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)
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 topoint (z1)
if (type(z1) == "number") then return point(z1,0) else return z1 end
end
local function check(z1,z2)
if type(z1) == 'number' then return point(z1,0),z2
elseif type(z2) == 'number' then return z1,point(z2,0)
else return z1,z2
end
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 z
z = z1 * point.conj(z2)
return z.re
end
-- determinant is '^' (a-ib) (c+id) = ac+bd + i(ad - bc)
function point.__pow(z1,z2)
local z
z = point.conj(z1) * z2
return z.im
end
function point.__div(x,y)
local xx = topoint(x); local yy = topoint(y)
return point(
(xx.re * yy.re + xx.im * yy.im) / (yy.re * yy.re + yy.im * yy.im),
(xx.im * yy.re - xx.re * yy.im) / (yy.re * yy.re + yy.im * yy.im)
)
end
function point.__tostring(z)
if (z.re == 0) then
if (z.im == 0) then
return "0"
else
if (z.im ==1) then
return "" .. "i"
else
if (z.im ==-1) then
return "" .. "-i"
else
return "" .. z.im .. "i"
end
end
end
else
if (z.im > 0) then
if (z.im ==1) then
return "" .. z.re .. "+" .. "i"
else
return "" .. z.re .. "+" .. z.im .. "i"
end
elseif (z.im < 0) then
if (z.im ==-1) then
return "" .. z.re .. "-" .. "i"
else
return "" .. z.re .. z.im .. "i"
end
else
return "" .. z.re
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)
return z1.re==z2.re and z1.im==z2.im
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)
return point(z.re,-z.im)
end
function point.mod(z)
local function sqr(x) return x*x end
return pyth (z.re,z.im)
end
function point.abs (z)
local function sqr(x) return x*x end
return sqrt(sqr(z.re) + sqr(z.im))
end
function point.norm (z)
local function sqr(x) return x*x end
return (sqr(z.re) + sqr(z.im))
end
function point.arg (z)
return math.atan(z.im, z.re)
end
function point.get(z)
return z.re, z.im
end
function point: sqrt()
local y = sqrt((point.mod(self)-self.re)/2)
local x = self.im/(2*y)
return point(x,y)
end
-- methods ---
function point: new ( a,b )
return scale * point (a,b )
end
function point: polar ( radius, phi )
return scale * polar_ ( radius, phi )
end
function point: polar_deg ( radius, phi )
return scale * polar_ ( radius, phi * math.pi/180 )
end
function point: north(d)
local d = d or 1
return self+ polar_ ( d * scale, math.pi/2 )
end
function point: south(d)
local d = d or 1
return self + polar_ ( d * scale, 3 * math.pi/2 )
end
function point: east(d)
local d = d or 1
return self+ polar_( d * scale, 0 )
end
function point: west(d)
local d = d or 1
return self + polar_ ( d * scale, math.pi )
end
-- ----------------------------------------------------------------
-- transformations
-- ----------------------------------------------------------------
-- function point: symmetry(pt)
-- return symmetry_ (self ,pt)
-- end
function point: symmetry (...)
local obj,nb,t
local tp = table.pack(...)
obj = tp[1]
nb = tp.n
if nb == 1 then
if obj.type == "point" then
return symmetry_ (self,obj)
elseif obj.type == "line" then
return line: new (set_symmetry_ (self,obj.pa,obj.pb))
elseif obj.type == "circle" then
return circle: new (set_symmetry_ (self,obj.center,obj.through))
else
return triangle: new (set_symmetry (self,obj.pa,obj.pb,obj.pc))
end
else
local t = {}
for i=1,tp.n do
table.insert( t , symmetry_ (self , tp[i]) )
end
return table.unpack ( t )
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 obj,nb,t
local tp = table.pack(...)
obj = tp[1]
nb = tp.n
if nb == 1 then
if obj.type == "point" then
return rotation_ (self,angle,obj )
elseif obj.type == "line" then
return line : new (set_rotation_ (self, angle,obj.pa,obj.pb ))
elseif obj.type == "triangle" then
return triangle: new (set_rotation_ (self, angle,obj.pa,obj.pb,obj.pc))
elseif obj.type == "circle" then
return circle : new (set_rotation_ (self,angle,obj.center,obj.through))
else
return square: new (set_rotation_(self,angle,obj.pa,obj.pb,obj.pc,obj.pd))
end
else
t = {}
for i=1,tp.n do
table.insert( t , rotation_ ( self,angle,tp[i]))
end
return table.unpack ( t )
end
end
function point : homothety (coeff,...)
local obj,nb,t
local tp = table.pack(...)
obj = tp[1]
nb = tp.n
if nb == 1 then
if obj.type == "point" then
return homothety_ (self,coeff,obj )
elseif obj.type == "line" then
return line : new (set_homothety_ (self, coeff,obj.pa,obj.pb ))
elseif obj.type == "triangle" then
return triangle: new (set_homothety_(self,coeff,obj.pa,obj.pb,obj.pc))
elseif obj.type == "circle" then
return circle: new (set_homothety_(self,coeff,obj.center,obj.through))
else
return square: new (set_homothety_(self,coeff,obj.pa,obj.pb))
end
else
t = {}
for i=1,tp.n do
table.insert( t , homothety_ ( self,coeff,tp[i]))
end
return table.unpack ( t )
end
end
function point: normalize()
local d = point.abs(self)
return point(self.re/d,self.im/d)
end
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