Fix overlapping points erroring

src/Chain.lua

@@ -1,42 +1,14 @@
+local FuzzyEq = require(script.Parent.FuzzyEq)
 local Spline = require(script.Parent.Spline)
 local Types = require(script.Parent.Types)
 
 local Chain = {}
 Chain.__index = Chain
 
-local EPSILON = 1e-4
-
 -- Type checking
 local tUnitInterval = Types.tUnitInterval
 local tOptionalUnitInterval = Types.tOptionalUnitInterval
 
-local function FuzzyEq(a, b)
-	local aType = typeof(a)
-
-	if aType == "number" then
-		return a == b or math.abs(a - b) <= (math.abs(a) + 1) * EPSILON
-	elseif aType == "Vector3" then
-		return a:FuzzyEq(b, EPSILON)
-	elseif aType == "Vector2" then
-		local aX, bX = a.X, b.X
-		if aX == bX or math.abs(aX - bX) <= (math.abs(aX) + 1) * EPSILON then
-			local aY, bY = a.Y, b.Y
-			if aY == bY or math.abs(aY - bY) <= (math.abs(aY) + 1) * EPSILON then
-				return true
-			end
-		end
-	elseif aType == "CFrame" then
-		if a.Position:FuzzyEq(b.Position, EPSILON)
-			and a.RightVector:FuzzyEq(b.RightVector, EPSILON)
-			and a.UpVector:FuzzyEq(b.UpVector, EPSILON)
-			and a.LookVector:FuzzyEq(b.LookVector, EPSILON) then
-			return true
-		end
-	end
-
-	return false
-end
-
 -- Constructor
 function Chain.new(points: {Types.Knot}, alpha: number?, tension: number?)
 	assert(#points >= 2, "2 or more points are required to create a chain.")
@@ -99,10 +71,14 @@ local function AlphaToSpline(self, alpha: number)
 	end
 
 	-- Special cases for when alpha is outside of the unti interval.
-	if alpha <= 0 then
+	if alpha < 0 then
 		-- (alpha - 0) / (intervals[2] - 0)
 		return splines[1], alpha / intervals[2]
-	elseif alpha >= 1 then
+	elseif alpha == 0 then
+		return splines[1], 0
+	elseif alpha == 1 then
+		return splines[#splines], 1
+	elseif alpha > 1 then
 		local n = #splines
 		return splines[n], (alpha - intervals[n]) / (1 - intervals[n])
 	end

src/FuzzyEq.lua

@@ -0,0 +1,30 @@
+local EPSILON = 1e-4
+
+local function FuzzyEq(a, b)
+	local aType = typeof(a)
+
+	if aType == "number" then
+		return a == b or math.abs(a - b) <= (math.abs(a) + 1) * EPSILON
+	elseif aType == "Vector3" then
+		return a:FuzzyEq(b, EPSILON)
+	elseif aType == "Vector2" then
+		local aX, bX = a.X, b.X
+		if aX == bX or math.abs(aX - bX) <= (math.abs(aX) + 1) * EPSILON then
+			local aY, bY = a.Y, b.Y
+			if aY == bY or math.abs(aY - bY) <= (math.abs(aY) + 1) * EPSILON then
+				return true
+			end
+		end
+	elseif aType == "CFrame" then
+		if a.Position:FuzzyEq(b.Position, EPSILON)
+			and a.RightVector:FuzzyEq(b.RightVector, EPSILON)
+			and a.UpVector:FuzzyEq(b.UpVector, EPSILON)
+			and a.LookVector:FuzzyEq(b.LookVector, EPSILON) then
+			return true
+		end
+	end
+
+	return false
+end
+
+return FuzzyEq

src/Spline.lua

@@ -1,3 +1,4 @@
+local FuzzyEq = require(script.Parent.FuzzyEq)
 local Squad = require(script.Parent.Squad)
 local Types = require(script.Parent.Types)
 
@@ -31,17 +32,28 @@ function Spline.new(k0: Types.Knot, k1: Types.Knot, k2: Types.Knot, k3: Types.Kn
 		className = "CFrameSpline"
 	end
 
-	-- https://qroph.github.io/2018/07/30/smooth-paths-using-catmull-rom-splines.html
-	local t0 = 0
-	local t1 = (p1 - p0).Magnitude ^ alpha + t0
-	local t2 = (p2 - p1).Magnitude ^ alpha + t1
-	local t3 = (p3 - p2).Magnitude ^ alpha + t2
-	local m1 = (1 - tension) * (t2 - t1) * ((p1 - p0)/(t1 - t0) - (p2 - p0)/(t2 - t0) + (p2 - p1)/(t2 - t1))
-	local m2 = (1 - tension) * (t2 - t1) * ((p2 - p1)/(t2 - t1) - (p3 - p1)/(t3 - t1) + (p3 - p2)/(t3 - t2))
-	local a: Vector3 = 2 * (p1 - p2) + m1 + m2
-	local b: Vector3 = 3 * (p2 - p1) - 2 * m1 - m2
-	local c: Vector3 = m1
-	local d: Vector3 = p1
+	local a, b, c
+	if FuzzyEq(p1, p2) then
+		a = p1 * 0
+		b = a
+		c = a
+	elseif FuzzyEq(p0, p1) or FuzzyEq(p2, p3) then
+		a = p1 * 0
+		b = a
+		c = p2 - p1
+	else
+		-- https://qroph.github.io/2018/07/30/smooth-paths-using-catmull-rom-splines.html
+		local t0 = 0
+		local t1 = (p1 - p0).Magnitude ^ alpha + t0
+		local t2 = (p2 - p1).Magnitude ^ alpha + t1
+		local t3 = (p3 - p2).Magnitude ^ alpha + t2
+		local m1 = (1 - tension) * (t2 - t1) * ((p1 - p0)/(t1 - t0) - (p2 - p0)/(t2 - t0) + (p2 - p1)/(t2 - t1))
+		local m2 = (1 - tension) * (t2 - t1) * ((p2 - p1)/(t2 - t1) - (p3 - p1)/(t3 - t1) + (p3 - p2)/(t3 - t2))
+		a = 2 * (p1 - p2) + m1 + m2
+		b = 3 * (p2 - p1) - 2 * m1 - m2
+		c = m1
+	end
+
 
 	local self = setmetatable({
 		ClassName = className,
@@ -58,7 +70,7 @@ function Spline.new(k0: Types.Knot, k1: Types.Knot, k2: Types.Knot, k3: Types.Kn
 		a = a,
 		b = b,
 		c = c,
-		d = d
+		d = p1
 	}, Spline)
 	self.Length = self:SolveLength()