How do I slow the camera down as it reaches its target using Bezier curves? Like easing styles in animations

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#1 

local function cubicBezier(t, p0, p1, p2, p3)
	return (1 - t)^3*p0 + 3*(1 - t)^2*t*p1 + 3*(1 - t)*t^2*p2 + t^3*p3
end

local function createLUT(numSegments, ...)
	local distSum = 0
	local sums = {}
	local step = 1/numSegments
	for i = 0, 1, step do
		local firstPoint = cubicBezier(i, ...)
		local secondPoint = cubicBezier(i + step, ...)
		local dist = (secondPoint - firstPoint).Magnitude
		table.insert(sums, distSum)
		distSum += dist
	end
	return sums 
end

local function remap(n, oldMin, oldMax, min, max)
	return (min + ((max-min) * ((n - oldMin) / (oldMax - oldMin))))
end

local Bezier = {}
Bezier.__index = Bezier

function Bezier.new(numSegments, p0, p1, p2, p3)
	local self = setmetatable({}, Bezier)
	self._points = {p0,p1,p2,p3}
	self._distLUT = createLUT(numSegments, p0, p1, p2, p3)

	return self 
end

function Bezier:Calc(t)
	local LUT = self._distLUT
	local arcLength = LUT[#LUT]
	local targetDist = arcLength * t

	for i, dist in ipairs(LUT) do
		local nextDist = LUT[i+1]
		if targetDist >= dist and targetDist < nextDist then
			local adjustedT = remap(targetDist, dist, nextDist, i/#LUT, (i+1)/#LUT)
			return cubicBezier(adjustedT, unpack(self._points))
		end
	end

end

return Bezier
#2

One way to achieve this is to calculate the distance between the current point and the target point using the Vector3.Magnitude function, and then use this distance to modify the t parameter passed to the cubicBezier function. One possible approach is to define a variable that represents the maximum distance at which the camera should start slowing down, and then adjust the t parameter based on the distance between the current point and the target point as follows:

function Bezier:Calc(t)
	local LUT = self._distLUT
	local arcLength = LUT[#LUT]
	local targetDist = arcLength * t

	local maxDist = 5 -- Adjust this value to control when the camera should start slowing down

	for i, dist in ipairs(LUT) do
		local nextDist = LUT[i+1]
		if targetDist >= dist and targetDist < nextDist then
			local adjustedT = remap(targetDist, dist, nextDist, i/#LUT, (i+1)/#LUT)
			local currentPoint = cubicBezier(adjustedT, unpack(self._points))
			local targetPoint = cubicBezier(math.min(adjustedT + 0.01, 1), unpack(self._points)) -- Adjust the second parameter (0.01) to control the speed of the slowdown
			local distToTarget = (targetPoint - currentPoint).Magnitude
			if distToTarget < maxDist then
				local slowdownFactor = distToTarget / maxDist
				adjustedT = adjustedT - slowdownFactor * (adjustedT - i/#LUT)
			end
			return cubicBezier(adjustedT, unpack(self._points))
		end
	end
end