Clamps a given 2D screen coordinate to a radial space. Created for the game Garry's Mod.

Screen Radial Clamp.lua

local math = math

function ScreenRadialClamp(x,y,padding)

	local w, h = ScrW(), ScrH()
	local ratio = w / h

	-- Default padding is 10% of the screen height
	padding = padding or h * 0.1

	-- Radius of width and height of screen
	-- Equivalent to the center of the screen
	local rx, ry = w / 2, h / 2

	-- Vector to given point w/ equalize ratio
	local targetx, targety = x - rx, ratio * (y - ry)

	-- Angle to target coordinate (in radians)
	local ang = math.atan2( targety, targetx )

	-- Find maximum point on screen given the angle
	local clampx, clampy = 
		(rx - padding) * math.cos(ang),
		(ry - padding) * math.sin(ang) * ratio

	-- If our clamped vector is smaller than the target vector
	-- we will return the clamped vector
	local targetmag = math.sqrt( targetx^2 + targety^2 )
	local clampmag = math.sqrt( clampx^2 + clampy^2 )

	if targetmag > clampmag then
		return clampx + rx, clampy * 1/ratio + ry, true
	else
		return x, y, false
	end

end

hook.Add( "HUDPaint", "ScreenRadialClampTest", function()

	local pos = LocalPlayer():GetPos():ToScreen()
	local x, y, clamped = ScreenRadialClamp( pos.x, pos.y )
	local size = 16
	local color = Color(255,0,0)

	surface.SetDrawColor( color )
	surface.DrawRect( x - size/2, y - size/2, size, size )

	if clamped then
		draw.SimpleText( "clamped", "DermaDefault", x, y + size*2, 
			color, TEXT_ALIGN_CENTER, TEXT_ALIGN_CENTER )
	end

end )