1 files changed, 133 insertions, 0 deletions
diff --git a/catenary.lua b/catenary.lua
new file mode 100644
index 0000000..abe18e1
--- /dev/null
+++ b/catenary.lua
@@ -0,0 +1,133 @@
+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
+
+	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
+--]]
+