points = nil

function getPoints()
	return points
end

function init(points_)
	points = points_
	pointDistances = {}
	local distAd2Sum = 0
	local lastP = nil
	for pointIdx, p in ipairs(points) do
		if lastP ~= nil then
			local distAd2 = lastP:distAd2(p)
			pointDistances[pointIdx-1] = distAd2
			distAd2Sum = distAd2Sum + distAd2
		end
		lastP = p
	end
	for pointIdx, distAd2 in ipairs(pointDistances) do
		pointDistances[pointIdx] = distAd2 / distAd2Sum
	end
end

function eval(t)
	if points == nil or #points == 0 then
		return nil
	end

	-- find the closest points for the given t parameter
	local pointIdx = 1
	while pointIdx <= #pointDistances and t - pointDistances[pointIdx] >= 0 do
		t = t - pointDistances[pointIdx]
		pointIdx = pointIdx + 1
	end
	if pointIdx == #pointDistances + 1 then
		return points[pointIdx]
	end
	
	-- normalize the t parameter to only mean the distance between the two closest points
	t = t / pointDistances[pointIdx]
	return circleInterpolate(points[pointIdx], points[pointIdx+1], t)
end

function circleInterpolate(p1, p2, t)
	local dxa, dya = p2:getX()-p1:getX(), p2:getY()-p1:getY()
	local x, y = (p1:getX()+p2:getX())/2, (p1:getY()+p2:getY())/2
	local r = p1:dist(p2) / 2
	local alpha = math.atan(dya/dxa) + ((p1:getX() < p2:getX()) and (1-t) or t)*math.pi

	return point.new(x + r*math.cos(alpha), y + r*math.sin(alpha))
end