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-- Combines two colors in CIELUV space.
-- function<function<Color3 result>(float t)>(Color3 fromColor, Color3 toColor)

-- https://www.w3.org/Graphics/Color/srgb

local clamp = math.clamp
local C3 = Color3.new
local black = C3(0, 0, 0)

-- Convert from linear RGB to scaled CIELUV
local function RgbToLuv13(c)
	local r, g, b = c.r, c.g, c.b
	-- Apply inverse gamma correction
	r = r < 0.0404482362771076 and r/12.92 or 0.87941546140213*(r + 0.055)^2.4
	g = g < 0.0404482362771076 and g/12.92 or 0.87941546140213*(g + 0.055)^2.4
	b = b < 0.0404482362771076 and b/12.92 or 0.87941546140213*(b + 0.055)^2.4
	-- sRGB->XYZ->CIELUV
	local y = 0.2125862307855956*r + 0.71517030370341085*g + 0.0722004986433362*b
	local z = 3.6590806972265883*r + 11.4426895800574232*g + 4.1149915024264843*b
	local l = y > 0.008856451679035631 and 116*y^(1/3) - 16 or 903.296296296296*y
	if z > 1e-15 then
		local x = 0.9257063972951867*r - 0.8333736323779866*g - 0.09209820666085898*b
		return l, l*x/z, l*(9*y/z - 0.46832)
	else
		return l, -0.19783*l, -0.46832*l
	end
end
function LerpCIELUV(c0, c1)
	local l0, u0, v0 = RgbToLuv13(c0)
	local l1, u1, v1 = RgbToLuv13(c1)

	return function(t)
		-- Interpolate
		local l = (1 - t)*l0 + t*l1
		if l < 0.0197955 then
			return black
		end
		local u = ((1 - t)*u0 + t*u1)/l + 0.19783
		local v = ((1 - t)*v0 + t*v1)/l + 0.46832

		-- CIELUV->XYZ
		local y = (l + 16)/116
		y = y > 0.206896551724137931 and y*y*y or 0.12841854934601665*y - 0.01771290335807126
		local x = y*u/v
		local z = y*((3 - 0.75*u)/v - 5)

		-- XYZ->linear sRGB
		local r =  7.2914074*x - 1.5372080*y - 0.4986286*z
		local g = -2.1800940*x + 1.8757561*y + 0.0415175*z
		local b =  0.1253477*x - 0.2040211*y + 1.0569959*z

		-- Adjust for the lowest out-of-bounds component
		if r < 0 and r < g and r < b then
			r, g, b = 0, g - r, b - r
		elseif g < 0 and g < b then
			r, g, b = r - g, 0, b - g
		elseif b < 0 then
			r, g, b = r - b, g - b, 0
		end

		return C3(
			-- Apply gamma correction and clamp the result
			clamp(r < 3.1306684425e-3 and 12.92*r or 1.055*r^(1/2.4) - 0.055, 0, 1),
			clamp(g < 3.1306684425e-3 and 12.92*g or 1.055*g^(1/2.4) - 0.055, 0, 1),
			clamp(b < 3.1306684425e-3 and 12.92*b or 1.055*b^(1/2.4) - 0.055, 0, 1)
		)
	end
end

function BezierCIELUV(c1, c2, c3)
	return function(t)
		local lerpFunc1 = LerpCIELUV(c1, c2)
		local lerpFunc2 = LerpCIELUV(c2, c3)
		local midColor1 = lerpFunc1(t)
		local midColor2 = lerpFunc2(t)
		local lerpFunc3 = LerpCIELUV(midColor1, midColor2)
		return lerpFunc3(t)
	end
end

function AverageCIELUVBezier(c1, c2, c3)
	local bezierFunc = BezierCIELUV(c1, c2, c3)
	local avgColor = bezierFunc(0.5)
	return avgColor
end
local function AverageRGB(...)
	local r, g, b = 0, 0, 0
	local count = select("#", ...)

	for i = 1, count do
		local color = select(i, ...)
		r += color.R^2
		g += color.G^2
		b += color.B^2
	end

	return Color3.new((r / count)^0.5, (g / count)^0.5, (b / count)^0.5)
end
function AverageCIELUV(c1, c2, c3)
	local function v3FromColor(c)
		local l, u, v = RgbToLuv13(c)
		return Vector3.new(l, u, v)
	end
	local v1 = v3FromColor(c1)
	local v2 = v3FromColor(c2)
	local v3 = v3FromColor(c3)

	local avgVector = (v1 + v2 + v3)/3

	-- Convert the resulting Vector3 back to a Color3
	-- CIELUV->XYZ
	local y = (avgVector.x + 16)/116
	y = y > 0.206896551724137931 and y*y*y or 0.12841854934601665*y - 0.01771290335807126
	local x = y*avgVector.y/avgVector.z
	local z = y*((3 - 0.75*avgVector.y)/avgVector.z - 5)

	-- XYZ->linear sRGB
	local r =  7.2914074*x - 1.5372080*y - 0.4986286*z
	local g = -2.1800940*x + 1.8757561*y + 0.0415175*z
	local b =  0.1253477*x - 0.2040211*y + 1.0569959*z

	-- Apply gamma correction and clamp the result
	return C3(
		clamp(r < 3.1306684425e-3 and 12.92*r or 1.055*r^(1/2.4) - 0.055, 0, 1),
		clamp(g < 3.1306684425e-3 and 12.92*g or 1.055*g^(1/2.4) - 0.055, 0, 1),
		clamp(b < 3.1306684425e-3 and 12.92*b or 1.055*b^(1/2.4) - 0.055, 0, 1)
	)
end


local avg = AverageRGB(game.Selection:Get()[1].Color,game.Selection:Get()[1].Color,game.Selection:Get()[3].Color)
workspace.TestColor.Color = avg

task.wait(2)

local avg = AverageCIELUVBezier(game.Selection:Get()[1].Color,game.Selection:Get()[1].Color,game.Selection:Get()[3].Color)
workspace.TestColor.Color = avg

task.wait(2)

local avg = AverageCIELUV(game.Selection:Get()[1].Color,game.Selection:Get()[1].Color,game.Selection:Get()[3].Color)
workspace.TestColor.Color = avg

return LerpCIELUV