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local G = love.graphics
local function plot(f,x0,xn)
local n = 30
x0 = x0 or G.inverseTransformPoint(0,0)
xn = xn or G.inverseTransformPoint(G.getDimensions(),0)
local h = (xn-x0)/n
local ps = {}
for x=x0,xn+h,h do
local y = f(x)
table.insert(ps,x)
table.insert(ps,y)
print(x,xn)
end
G.line(ps)
end
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 L = 20
function love.wheelmoved(x,y)
L = L + (y/5)
end
local function catenary(x1,y1,x2,y2)
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)
-- local L = D*1.2
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 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()
G.print(L,10,10)
G.setLineWidth(0.01)
G.translate(W/2,H/2)
G.scale(150)
-- G.setColor(0.8,0.8,0.8)
-- G.line(-10,0,10,0)
-- G.line(0,-10,0,10)
-- 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)
plot(catenary(Ps[1][1],Ps[1][2], Ps[2][1], Ps[2][2]),
Ps[1][1], Ps[2][1])
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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