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-- tkz_elements_functions_maths.lua
-- date 23/12/14
-- version 1.60c
-- 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.
-- ----------------------------------------------------------------
--
-- ----------------------------------------------------------------
function get_points (obj)
if obj.type == 'line' then return obj.pa,obj.pb
elseif
obj.type == 'triangle' then return obj.pa,obj.pb,obj.pc
elseif
obj.type == 'circle' then return obj.center,obj.through
elseif
obj.type == 'ellipse' then return obj.pc,obj.pa,obj.pb
elseif
obj.type == 'square' or obj.type == 'rectangle' or obj.type == 'quadrilateral' or obj.type == 'parallelogram'
then return obj.pa,obj.pb,obj.pc,obj.pd
end
end
function set_lua_to_tex (t)
for k,v in pairs(t) do
token.set_macro(v,_ENV[v],'global')
end
end
-- version 1.60 center pour deux cercles ?
function radical_center (C1,C2,C3)
local t1,t2,t3,t4
t1,t2 = radical_axis_ (C1.center,C1.through,C2.center,C2.through)
if C3 == nil then
return intersection_ll_ (t1,t2,C1.center,C2.center)
else
t3,t4 = radical_axis_ (C3.center,C3.through,C2.center,C2.through)
return intersection_ll_ (t1,t2,t3,t4)
end
end
-- version 1.60 modif case 2 circles
function radical_circle (C1,C2,C3)
local rc
if C3 == nil then
rc = radical_center (C1,C2)
return C1 : orthogonal_from (rc)
else
rc = radical_center (C1,C2,C3)
return C1 : orthogonal_from (rc)
end
end
-- version 1.60 new
function circles_position(C1,C2)
local d,max,min
d = point.mod(C1.center-C2.center)
max = C1.radius + C2.radius
min = math.abs ( C1.radius - C2.radius)
if d > max then return "outside"
elseif d == max then return "outside tangent" -- epsilon
elseif d == min then return "inside tangent" -- epsilon
elseif d < min then return "inside"
else return "intersect"
end
end
-- version 1.60 new
function midcircle_(C1,C2)
local state,r,s,t1,t2,T1,T2,p,a,b,c,d,Cx,Cy,i,j
state = circles_position(C1,C2)
i = barycenter_ ({C2.center,C1.radius},{C1.center,-C2.radius})
j = barycenter_ ({C2.center,C1.radius},{C1.center,C2.radius})
t1,t2 = tangent_from_ (C1.center,C1.through,i)
T1,T2 = tangent_from_ (C2.center,C2.through,i)
if (state == 'outside') or (state == 'outside tangent')then
p = math.sqrt(point.mod(i-t1)*point.mod(i-T1))
return circle : radius (i,p)
elseif state == 'intersect' then
r,s = intersection (C1,C2)
return circle : radius (i,point.mod(r-i)) , circle : radius (j,point.mod(r-j))
elseif (state == 'inside') or (state == 'inside tangent') then
a,b = intersection_lc_ (C1.center,C2.center,C1.center,C1.through)
c,d = intersection_lc_ (C1.center,C2.center,C2.center,C2.through)
if C1.radius < C2.radius then
z.u, z.v, z.r, z.s = a, b, c, d
else
z.u, z.v, z.r, z.s = c, d, a, b
end
if (in_segment_ (z.s,z.v,z.u) == true)
then
Cx = circle : diameter (z.r,z.v)
Cy = circle : diameter (z.u,z.s)
else
Cx = circle : diameter (z.s,z.v)
Cy = circle : diameter (z.u,z.r)
end
if (Cx.radius) < (Cy.radius) then
return Cy : orthogonal_from (j)
else
return Cx : orthogonal_from (j)
end
end
end
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