From 0814d3731bce2270f3471570f1f3bdb4f54c5495 Mon Sep 17 00:00:00 2001
From: ubq323 <ubq323@ubq323.website>
Date: Thu, 4 Jan 2024 19:28:02 +0000
Subject: catenary

---
 main.lua | 102 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 102 insertions(+)
 create mode 100644 main.lua

diff --git a/main.lua b/main.lua
new file mode 100644
index 0000000..ae9595c
--- /dev/null
+++ b/main.lua
@@ -0,0 +1,102 @@
+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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