-- tkz_elements_functions_lines.lua
-- date 2023/11/10
-- version 1.20b
-- 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.

---------------------------------------------------------------------------
--                 Lines
---------------------------------------------------------------------------
function normalize_ (a,b)
   return a+(b-a)/point.mod(b-a)
end

function ortho_from_ ( p , a , b )
	return  p+(b-a)*point(0,1) 
end

function ll_from_ ( p , a , b )
	return  p+b-a
end

function slope_ (a,b)
  local z = b - a
  angle = point.arg(z)
  return angle
end

function gold_segment_ (a,b)
  return a + (b-a)*tkzinvphi
end

function online_ (a,b,t)
   return barycenter_({a,(1-t)},{b,t})
 end
 
 function mediator_ (a,b) 
   local m = midpoint_ (a,b)
   return m , rotation_ (m,math.pi/2,b)
 end
 
 function midpoint_ (z1 , z2)	
   return (z1+z2)/2
 end
-- triangle specific
function equilateral_tr (a,b)
   return rotation_ (a,math.pi/3,b)
end

function isosceles_right_tr (a,b)
     local pt
     pt = rotation_ (a,math.pi/4,b)
   return a + (pt-a) * math.sin(math.pi/4)
end

function gold_tr (a,b)
   local pt
   pt = rotation_ (a,math.pi/2,b)
   return a + (pt-a) * tkzinvphi
end

function euclide_tr (a,b)
     return rotation_ (a,math.pi/5,b)
end

function golden_tr (a,b)
    local pt
    pt = rotation_ (a,2*math.pi/5,b)
     return a + (pt-a) * tkzphi
end

function div_harmonic_int_(a,b,n)
  local k = point.abs(a-n)/point.abs(b-n)
  return barycenter_ ( {a,1} , {b,k} )
end

function div_harmonic_ext_(a,b,n)
  local k = point.abs(a-n)/point.abs(b-n)
  return barycenter_ ( {a,1} , {b,-k} )
end

function div_harmonic_both_(a,b,k)
  return barycenter_ ( {a,1} , {b,k} ) , barycenter_ ( {a,1} , {b,-k} )
end

function golden_ratio_(a,b)
   local invphi = ( math.sqrt(5) - 1 )/2
   return   a  + (b-a) * invphi
end
-- projection
function projection ( Dt,pt )
  return projection_ ( Dt.pa,Dt.pb,pt )
end

function projection_ ( pa,pb,pt )
   local v
   local z
   if aligned ( pa,pb,pt ) then
   return pt
   else
    v = pb - pa
         z = ((pt - pa)..v)/(point.norm(v)) -- .. dot product
   return pa + z * v  
   end
end

function symmetry_axial_(pa,pb,pt)
    local p 
    p = projection_ (pa,pb,pt)
    return symmetry_(p,pt)
end


function square_ (a,b)
    return rotation_ (b,-math.pi/2,a), rotation_ (a,math.pi/2,b)
end