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|
-- tkz_elements_lines.lua
-- date 2024/07/16
-- version 2.30c
-- Copyright 2024 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
-- -------------------------------------------------------------------------
line = {}
function line: new(za, zb)
local type = 'line'
local mid = (za+zb)/2
local north_pa = rotation_ (za,math.pi/2,zb)
local south_pa = rotation_ (za,-math.pi/2,zb)
local north_pb = rotation_ (zb,-math.pi/2,za)
local south_pb = rotation_ (zb,math.pi/2,za)
local west = rotation_ (za,math.pi/2,north_pa)
local east = rotation_ (zb,math.pi/2,south_pb)
local slope = angle_normalize_(point.arg(zb-za))
local length = point.mod(zb-za)
local vec = vector : new (za,zb)
local o = {pa = za,
pb = zb,
north_pa = north_pa,
south_pa = south_pa,
west = west,
east = east,
north_pb = north_pb,
south_pb = south_pb,
slope = slope,
mid = mid,
type = type,
vec = vec,
length = length}
setmetatable(o, self)
self.__index = self
return o
end
-------------------
-- Result -> real
-------------------
function line: distance (pt)
return point.mod(projection(self,pt)-pt)
end
function length(a,b)
return point.abs (a-b)
end
function line: slope ()
return slope_(self.pa,self.pb)
end
-------------------
-- Result -> boolean
-------------------
function line: in_out (pt)
local sc
sc = math.abs ((pt-self.pa)^(pt-self.pb))
if sc <= tkz_epsilon
then
return true
else
return false
end
end
function line: in_out_segment (pt)
local sc
sc = point.mod (pt-self.pa) + point.mod (pt-self.pb) - point.mod(self.pb-self.pa)
if sc <= tkz_epsilon
then
return true
else
return false
end
end
-------------------
-- Result -> point
-------------------
function line: barycenter (ka,kb)
return barycenter_({self.pa,ka},{self.pb,kb})
end
function line: point (t) -- t=o A t=1 B t = AM / AB
return barycenter_({self.pa,1-t},{self.pb,(t)})
end
function line: midpoint ()
return (self.pa+self.pb)/2
end
function line: harmonic_int (pt)
return div_harmonic_int_(self.pa,self.pb,pt)
end
function line: harmonic_ext (pt)
return div_harmonic_ext_(self.pa,self.pb,pt)
end
function line: harmonic_both (k)
return div_harmonic_both_(self.pa,self.pb,k)
end
function line: gold_ratio()
return self.pa + (self.pb-self.pa)*tkzinvphi
end
function line: normalize ()
return self.pa+(self.pb-self.pa)/point.mod(self.pb-self.pa)
end
function line: normalize_inv ()
return normalize_ (self.pb,self.pa)
end
function line: _east (d)
local d = d or 1
return self.pb+ d/self.length * (self.pb-self.pa)
end
function line: _west (d)
local d = d or 1
return self.pa+ d/self.length * (self.pa-self.pb)
end
function line: _north_pa (d)
local d = d or 1
return d/self.length * ( self.north_pa - self.pa ) + self.pa
end
function line: _south_pa (d)
local d = d or 1
return d/self.length *( self.south_pa - self.pa ) + self.pa
end
function line: _south_pb (d)
local d = d or 1
return d/self.length *( self.south_pb - self.pb ) + self.pb
end
function line: _north_pb (d)
local d = d or 1
return d/self.length *( self.north_pb - self.pb ) + self.pb
end
function line : report (d,pt)
local t
t = d/self.length
if pt == nil
then
return barycenter_({self.pa,1-t},{self.pb,(t)})
else
return barycenter_({self.pa,1-t},{self.pb,(t)}) +pt-self.pa
end
end
function line : colinear_at (pt,k)
if k == nil
then
return colinear_at_ (self.pa,self.pb,pt,1)
else
return colinear_at_ (self.pa,self.pb,pt,k)
end
end
-------------- transformations -------------
function line: translation_pt ( pt )
return translation_ ( self.pb-self.pa,pt )
end
function line: translation_C ( obj )
local pa,pb,x,y
pa = obj.center
pb = obj.through
x,y = set_translation_ ( self.pb-self.pa,pa,pb )
return circle : new (x,y)
end
function line: translation_T ( obj )
local pa,pb,pc,x,y,z
pa = obj.pa
pb = obj.pb
pc = obj.pc
x,y,z = set_translation_ ( self.pb-self.pa,pa,pb,pc )
return triangle : new (x,y,z)
end
function line: translation_L ( obj )
local pa,pb,x,y
pa = obj.pa
pb = obj.pb
x,y = set_translation_ ( self.pb-self.pa,pa,pb )
return line : new (x,y)
end
function line: translation (...)
local obj,nb,t
local tp = table.pack(...)
obj = tp[1]
nb = tp.n
if nb == 1 then
if obj.type == "point" then
return translation_ ( self.pb-self.pa,obj )
elseif obj.type == "line" then
return self: translation_L (obj)
elseif obj.type == "triangle" then
return self: translation_T (obj)
else
return self: translation_C (obj)
end
else
t = {}
for i=1,tp.n do
table.insert(t , translation_ ( self.pb-self.pa , tp[i]))
end
return table.unpack ( t )
end
end
function line: set_translation ( ...)
return set_translation_ ( self.pb-self.pa,... )
end
function line: projection (...)
local obj,nb,t
local tp = table.pack(...)
obj = tp[1]
nb = tp.n
if nb == 1 then
return projection_ ( self.pa, self.pb, obj )
else
t = {}
for i=1,tp.n do
table.insert( t , projection_ (self.pa, self.pb, tp[i]) )
end
return table.unpack ( t )
end
end
function line: set_projection (...)
local tp = table.pack(...)
local i
local t = {}
for i=1,tp.n do
table.insert( t , projection_ (self.pa,self.pb , tp[i]) )
end
return table.unpack ( t )
end
function line: symmetry_axial_L ( obj )
local pa,pb,x,y
pa = obj.pa
pb = obj.pb
x,y = self:set_reflection ( pa,pb )
return line : new (x,y)
end
function line: symmetry_axial_T ( obj )
local pa,pb,pc,x,y,z
pa = obj.pa
pb = obj.pb
pc = obj.pc
x,y,z = self:set_reflection ( pa,pb,pc )
return triangle : new (x,y,z)
end
function line: symmetry_axial_C ( obj )
local pa,pb,x,y
pa = obj.center
pb = obj.through
x,y = self:set_reflection ( pa,pb )
return circle : new (x,y)
end
function line: reflection (...)
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_axial_ ( self.pa,self.pb,obj )
elseif obj.type == "line" then
return self: symmetry_axial_L (obj)
elseif obj.type == "triangle" then
return self: symmetry_axial_T (obj)
else
return self: symmetry_axial_C (obj)
end
else
t = {}
for i=1,tp.n do
table.insert( t , symmetry_axial_ ( self.pa,self.pb , tp[i]) )
end
return table.unpack ( t )
end
end
function line: set_reflection (...)
return set_symmetry_axial_ ( self.pb,self.pa,... )
end
-------------------
-- Result -> line
-------------------
function line: ll_from ( pt )
return line : new (pt,pt+self.pb-self.pa)
end
function line: ortho_from ( pt )
return line : new (pt+(self.pb-self.pa)*point(0,-1),pt+(self.pb-self.pa)*point(0,1))
end
function line: mediator ()
local m
m = midpoint_ (self.pa,self.pb)
return line : new (rotation_ (m,-math.pi/2,self.pb),rotation_ (m,math.pi/2,self.pb))
end
function line : perpendicular_bisector ()
local m
m = midpoint_ (self.pa,self.pb)
return line : new (rotation_ (m,-math.pi/2,self.pb),rotation_ (m,math.pi/2,self.pb))
end
-------------------
-- Result -> circle
-------------------
function line: circle (swap)
if swap == nil then
swap = false
end
if swap then
return circle : new (self.pb,self.pa)
else
return circle : new (self.pa,self.pb)
end
end
function line: circle_swap ()
return circle : new (self.pb,self.pa)
end
function line : diameter ()
local c = midpoint_ (self.pa,self.pb)
return circle : new (c,self.pb)
end
function line : apollonius (k)
local z1,z2,c
z1 = barycenter_ ({self.pa,1},{self.pb,k})
z2 = barycenter_ ({self.pa,1},{self.pb,-k})
c = midpoint_ (z1,z2)
return circle : new (c,z2)
end
----------------------
-- Result -> triangle
----------------------
function line: equilateral (swap)
if swap == nil then
swap = false
end
if swap then
return triangle : new (self.pa,self.pb,rotation_ (self.pa,-math.pi/3,self.pb))
else
return triangle : new (self.pa,self.pb,rotation_ (self.pa,math.pi/3,self.pb))
end
end
function line: isosceles (phi,swap)
local pta,ptb
if swap == nil then
swap = false
end
if swap then
pta = rotation_ (self.pa,-phi,self.pb)
ptb = rotation_ (self.pb,phi,self.pa)
return triangle : new (self.pa,self.pb, intersection_ll_ (self.pa,pta,self.pb,ptb ))
else
pta = rotation_ (self.pa,phi,self.pb)
ptb = rotation_ (self.pb,-phi,self.pa)
return triangle : new (self.pa,self.pb, intersection_ll_ (self.pa,pta,self.pb,ptb ))
end
end
function line: two_angles (alpha,beta)
local pta,ptb,pt
pta = rotation_ (self.pa,alpha,self.pb)
ptb = rotation_ (self.pb,-beta,self.pa)
pt = intersection_ll_ (self.pa,pta,self.pb,ptb)
return triangle : new (self.pa,self.pb,pt)
end
function line: school ()
local pta,ptb,pt
pta = rotation_ (self.pa,math.pi/6,self.pb)
ptb = rotation_ (self.pb,-math.pi/3,self.pa)
pt = intersection_ll_ (self.pa,pta,self.pb,ptb)
return triangle : new (self.pa,self.pb,pt)
end
function line: half ()
local x,pt
x = midpoint_(self.pa,self.pb)
pt = rotation_ (self.pb,-math.pi/2,x)
return triangle : new (self.pa,self.pb,pt)
end
function line: sss (a,b)
local pta,ptb,i,j
pta = self.pa + point ( a, 0 )
ptb = self.pb + point ( -b , 0)
i,j = intersection_cc_ (self.pa,pta,self.pb,ptb)
return triangle : new (self.pa,self.pb,i),triangle : new (self.pa,self.pb,j)
end
function line: ssa (a,phi)
local x,y,pt
x = rotation_ (self.pb,-phi,self.pa)
y = self.pa + polar_ ( a , self.slope)
i,j = intersection_lc_ (self.pb,x,self.pa,y)
return triangle : new (self.pa,self.pb,i),triangle : new (self.pa,self.pb,j)
end
function line: sas (a,phi)
local x,pt
x = self.pa + polar_ ( a , self.slope)
pt = rotation_ (self.pa,phi,x)
return triangle : new (self.pa,self.pb,pt)
end
---- sacred triangles ----
function line: gold (swap)
local pt
if swap == nil then
swap = false
end
if swap then
pt = rotation_ (self.pa,-math.pi/2,self.pb)
return triangle : new (self.pa,self.pb, self.pa + (pt-self.pa) * tkzinvphi)
else
pt = rotation_ (self.pa,math.pi/2,self.pb)
return triangle : new (self.pa,self.pb, self.pa + (pt-self.pa) * tkzinvphi)
end
end
function line: sublime ()
local pta,ptb,pt
pta = rotation_ (self.pa,2*math.pi/5,self.pb)
ptb = rotation_ (self.pb,-2*math.pi/5,self.pa)
pt = intersection_ll_ (self.pa,pta,self.pb,ptb)
return triangle : new (self.pa,self.pb,pt)
end
line.euclid = line.sublime
function line: euclide (swap)
if swap == nil then
return triangle : new (self.pa,self.pb, rotation_ (self.pa,math.pi/5,self.pb))
else
return triangle : new (self.pa,self.pb, rotation_ (self.pa,-math.pi/5,self.pb))
end
end
function line: divine ()
local pta,ptb,pt,h
pta = rotation_ (self.pa,math.pi/5,self.pb)
ptb = rotation_ (self.pb,-math.pi/5,self.pa)
pt = intersection_ll_ (self.pa,pta,self.pb,ptb)
return triangle : new (self.pa,self.pb,pt)
end
function line: cheops ()
local m,n,pt
m = midpoint_ (self.pa,self.pb)
n = rotation_ (m,- math.pi/2,self.pa)
pt = m + (n-m)* tkzsqrtphi
return triangle : new (self.pa,self.pb,pt)
end
function line: egyptian ()
local n,pt
n = rotation_ (self.pb,- math.pi/2,self.pa)
pt = self.pb + (n-self.pb)/point.mod(n-self.pb)*self.length* 0.75
return triangle : new (self.pa,self.pb,pt)
end
line.pythagoras = line.egyptian
line.isis = line.egyptian
line.golden = line.sublime
line.golden_gnomon = line.divine
------------------------------
-- Result -> square
------------------------------
function line: square (swap)
if swap == nil
then
return square : side (self.pa,self.pb)
else
return square : side (self.pa,self.pb,indirect)
end
end
return line
|