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local G = love.graphics
local function atanh(x)
return (1/2) * math.log((1+x)/(1-x))
end
local function solve_for_A(r)
local A
if r < 3 then
A = math.sqrt(6 * (r-1))
else
A = math.log(2*r) + math.log(math.log(2*r))
end
for i=1,5 do
A = A - (math.sinh(A) - r*A)/(math.cosh(A)-r)
end
return A
end
local function plot(f,x0,xn)
local n = 30
x0 = x0 or G.inverseTransformPoint(0,0)
xn = xn or G.inverseTransformPoint(G.getDimensions(),0)
if xn < x0 then
xn,x0 = x0,xn
end
local h = (xn-x0)/n
local ps = {}
for i=0,n do
local x = x0 + i*h
local y = f(x)
table.insert(ps,x)
table.insert(ps,y)
end
return ps
end
local function catenary0(x1,y1,x2,y2, L)
-- https://math.stackexchange.com/a/3557768
y1 = -y1
y2 = -y2
local dx = x2-x1
local dy = y2-y1
local mx = (x1+x2)/2
local my = (y1+y2)/2
local D = math.sqrt(dx^2+dy^2)
L = L or D+(1/(D+0.3))
local r = math.sqrt(L^2 - dy^2)/dx
local A = solve_for_A(r)
local a = dx/(2*A)
local b = mx - a*atanh(dy/L)
local c = my - L/(2*math.tanh(A))
return function(x) return -(a * math.cosh((x-b)/a) + c) end
end
local function catenary(x1,y1, x2,y2, L)
local D = math.sqrt((x2-x1)^2 + (y2-y1)^2)
-- L = L or D+(1/(D+0.3))
L = L or D+(0.1/(D+0.1))
-- L = D + 0.1
if x2 < x1 then
x1,x2 = x2,x1
y1,y2 = y2,y1
end
if math.abs(x1-x2) < 0.0001 then
x1 = x1 - 0.01
x2 = x2 + 0.01
end
local f = catenary0(x1,y1,x2,y2,L)
return plot(f, x1,x2)
end
return {
catenary = catenary
}
--[[
local Ps = {{-1,1}, {1,1}}
function love.update(dt)
for b = 1,2 do
if love.mouse.isDown(b) then
Ps[b] = {G.inverseTransformPoint(love.mouse.getPosition())}
end
end
end
function love.draw()
local W,H = G.getDimensions()
G.clear(1,1,1)
G.setColor(0,0,0)
G.origin()
local dx = Ps[1][1] - Ps[2][1]
local dy = Ps[1][2] - Ps[2][2]
local D = math.sqrt(dx^2+dy^2)
local L = D+(1/(D+0.3))
-- local L = D+1
G.print(("%.2f\n%.2f\n%.2f"):format(L,D,L-D),10,10)
G.setLineWidth(0.01)
G.translate(W/2,H/2)
G.scale(50)
G.setColor(0.8,0.8,0.8)
for i=-10,10 do
G.line(-10,i,10,i)
G.line(i,-10,i,10)
end
G.circle('line',0,0,1)
-- G.setColor(0,0,0)
-- -- plot(function(x) return x^2 end)
-- plot(math.tanh)
-- G.setColor(0,1,0)
-- plot(atanh)
G.setColor(0,0,0)
G.line(catenary(Ps[1][1],Ps[1][2], Ps[2][1], Ps[2][2]))
G.setColor(1,0,0)
G.circle('fill',Ps[1][1],Ps[1][2],0.05)
G.setColor(0,0,1)
G.circle('fill',Ps[2][1],Ps[2][2],0.05)
end
--]]
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