axis + face button -> letters. the guts of a controller keyboard.

chord.lua

function gate(axis, num)
	local function wrap(x)
		return math.fmod(x, math.pi * 2)
	end

	if math.abs(axis.x) < 0.1 and math.abs(axis.y) < 0.1 then
		return num + 1
	end

	local angle = math.atan2(axis.y, axis.x) -- in radians
	angle = wrap(math.pi * 3 - angle) -- CCW -> CW + half rotation
	--print(axis.x, axis.y, angle)

	-- offset to the left by half the width of a segment
	local angle_offset = angle + ((math.pi * 2) / (num * 2))
	--print(angle_offset)

	-- map to number of segments
	local final_angle = angle_offset * (num / (math.pi * 2))
	--print(final_angle)

	-- un-quantized output is useful for display.
	return math.floor(final_angle) + 1, final_angle + 1
end

-- This function is REALLY defensive because of how easy it is to screw up
-- key mappings when playing with different setups.
function chord(mapping, axis, face)
	-- standard setup: 8x4. section #num_gates+1 is neutral.
	local num_gates = 8
	local num_faces = 4

	assert(#mapping == num_gates + 1, "Invalid key map! Wrong number of sections.")
	assert(axis ~= nil, "No axis!")
	assert(axis.x ~= nil and axis.y ~= nil, "Axis needs x/y!")
	assert(face ~= nil, "No face!")
	assert(face >= 0, "Face in the wrong base! This data has become waste in your haste!")

	-- gate the axis to one of 8 directions
	local section = mapping[gate(axis, num_gates)]

	assert(#section == num_faces, "Invalid key map! Wrong number of faces.")

	return section[face]
end

-- mappings: in LURD order (CW from left)
local standard_map = {
	{"e","t","a","o"}, -- left
	{"i","n","s","r"},
	{"h","d","l","u"}, -- up
	{"c","m","f","y"},
	{"w","g","p","b"}, -- right
	{"v","k","x","q"},
	{"j","z","\'","\""}, -- down
	{",","!","?","."},
	{":","(",")","/"} -- neutral
}

local tests = {
	{
		map = standard_map,
		axis = { x = -1, y = 0 },
		face = 1,
		output = standard_map[1][1]
	}
	--
	, {
		map = standard_map,
		axis = { x = 1, y = 0 },
		face = 4,
		output = standard_map[5][4]
	}, {
		map = standard_map,
		axis = { x = 0, y = 1 },
		face = 3,
		output = standard_map[3][3]
	}
	--]]
}

for i, test in ipairs(tests) do
	local output = chord(standard_map, test.axis, test.face)
	local str = "Test #" .. i .. ": "
	if output ~= test.output then
		print(str .. "FAILED. Expected " .. test.output .. ", but got " .. output .. "!")
	else
		print(str .. "PASSED. (" .. output .. ")")
	end
end