diff --git a/polygon.lua b/polygon.lua
index d628580..ad1a92e 100644
--- a/polygon.lua
+++ b/polygon.lua
@@ -419,56 +419,11 @@ function Polygon:contains(x,y)
 	return in_polygon
 end
 
-function Polygon:intersectsRay(x,y, dx,dy)
-	--local p = vector(x,y)
-	--local v = vector(dx,dy)
+function Polygon:intersectionsWithRay(x,y, dx,dy)
 	local nx,ny = vector.perpendicular(dx,dy)
 	local wx,xy,det
 
-	local tmin = math.huge
-	local q1,q2 = nil, self.vertices[#self.vertices]
-	for i = 1, #self.vertices do
-		q1,q2 = q2,self.vertices[i]
-		wx,wy = q2.x - q1.x, q2.y - q1.y
-		det = vector.det(dx,dy, wx,wy)
-
-		if det ~= 0 then
-			-- there is an intersection point. check if it lies on both
-			-- the ray and the segment.
-			local rx,ry = q2.x - x, q2.y - y
-			local l = vector.det(rx,ry, wx,wy) / det
-			local m = vector.det(dx,dy, rx,ry) / det
-			if l >= 0 and m >= 0 and m <= 1 then
-				-- we cannot jump out early here (i.e. when l > tmin) because
-				-- the polygon might be concave
-				tmin = math.min(tmin, l)
-			end
-		else
-			-- lines parralel or incident. get distance of line to
-			-- anchor point. if they are incident, check if an endpoint
-			-- lies on the ray
-			local dist = vector.dot(q1.x-x,q1.y-y, nx,ny)
-			if dist == 0 then
-				local l = vector.dot(dx,dy, q1.x-x,q1.y-y)
-				local m = vector.dot(dx,dy, q2.x-x,q2.y-y)
-				if l >= 0 and l >= m then
-					tmin = math.min(tmin, l)
-				elseif m >= 0 then
-					tmin = math.min(tmin, m)
-				end
-			end
-		end
-	end
-	return tmin ~= math.huge, tmin
-end
-
-function Polygon:intersectionsRay(x,y, dx,dy)
-	--local p = vector(x,y)
-	--local v = vector(dx,dy)
-	local nx,ny = vector.perpendicular(dx,dy)
-	local wx,xy,det
-
-	local ts = {}
+	local ts = {} -- ray parameters of each intersection
 	local q1,q2 = nil, self.vertices[#self.vertices]
 	for i = 1, #self.vertices do
 		q1,q2 = q2,self.vertices[i]
@@ -484,7 +439,7 @@ function Polygon:intersectionsRay(x,y, dx,dy)
 			if m >= 0 and m <= 1 then
 				-- we cannot jump out early here (i.e. when l > tmin) because
 				-- the polygon might be concave
-				table.insert(ts, l)
+				ts[#ts+1] = l
 			end
 		else
 			-- lines parralel or incident. get distance of line to
@@ -495,9 +450,9 @@ function Polygon:intersectionsRay(x,y, dx,dy)
 				local l = vector.dot(dx,dy, q1.x-x,q1.y-y)
 				local m = vector.dot(dx,dy, q2.x-x,q2.y-y)
 				if l >= m then
-					table.insert(ts, l)
+					ts[#ts+1] = l
 				else
-					table.insert(ts, m)
+					ts[#ts+1] = m
 				end
 			end
 		end
@@ -506,6 +461,14 @@ function Polygon:intersectionsRay(x,y, dx,dy)
 	return ts
 end
 
+function Polygon:intersectsRay(x,y, dx,dy)
+	local tmin = math.huge
+	for _, t in ipairs(self:intersectionsWithRay(x,y,dx,dy)) do
+		tmin = math.min(tmin, t)
+	end
+	return tmin ~= math.huge, tmin
+end
+
 Polygon = common_local.class('Polygon', Polygon)
 newPolygon = function(...) return common_local.instance(Polygon, ...) end
 return Polygon
diff --git a/shapes.lua b/shapes.lua
index 23bdea7..9b4a48d 100644
--- a/shapes.lua
+++ b/shapes.lua
@@ -213,12 +213,12 @@ function ConvexPolygonShape:intersectsRay(x,y, dx,dy)
 	return self._polygon:intersectsRay(x,y, dx,dy)
 end
 
-function ConcavePolygonShape:intersectionsRay(x,y, dx,dy)
-	return self._polygon:intersectionsRay(x,y, dx,dy)
+function ConcavePolygonShape:intersectionsWithRay(x,y, dx,dy)
+	return self._polygon:intersectionsWithRay(x,y, dx,dy)
 end
 
-function ConvexPolygonShape:intersectionsRay(x,y, dx,dy)
-	return self._polygon:intersectionsRay(x,y, dx,dy)
+function ConvexPolygonShape:intersectionsWithRay(x,y, dx,dy)
+	return self._polygon:intersectionsWithRay(x,y, dx,dy)
 end
 
 -- circle intersection if distance of ray/center is smaller
@@ -228,27 +228,7 @@ end
 -- solving [with c = (cx,cy)]:
 --
 --     d*d s^2 + 2 d*(p-c) s + (p-c)*(p-c)-r^2 = 0
-function CircleShape:intersectsRay(x,y, dx,dy)
-	local pcx,pcy = x-self._center.x, y-self._center.y
-
-	local a = vector.len2(dx,dy)
-	local b = 2 * vector.dot(dx,dy, pcx,pcy)
-	local c = vector.len2(pcx,pcy) - self._radius * self._radius
-	local discr = b*b - 4*a*c
-	if discr < 0 then return false end
-
-	discr = math_sqrt(discr)
-	local s1,s2 = discr-b, -discr-b
-	if s1 < 0 then -- first solution is off the ray
-		return s2 >= 0, s2/(2*a)
-	elseif s2 < 0 then -- second solution is off the ray
-		return s1 >= 0, s1/(2*a)
-	end
-	-- both solutions on the ray
-	return true, math_min(s1,s2)/(2*a)
-end
-
-function CircleShape:intersectionsRay(x,y, dx,dy)
+function CircleShape:intersectionsWithRay(x,y, dx,dy)
 	local pcx,pcy = x-self._center.x, y-self._center.y
 
 	local a = vector.len2(dx,dy)
@@ -259,9 +239,18 @@ function CircleShape:intersectionsRay(x,y, dx,dy)
 	if discr < 0 then return {} end
 
 	discr = math_sqrt(discr)
-	local s1, s2 = (discr-b)/(2*a), (-discr-b)/(2*a)
+	local ts, t1, t2 = {}, discr-b, -discr-b
+	if t1 >= 0 then ts[#ts+1] = t1/(2*a) end
+	if t2 >= 0 then ts[#ts+1] = t2/(2*a) end
+	return ts
+end
 
-	return {math.min(s1, s2), math.max(s1, s2)}
+function CircleShape:intersectsRay(x,y, dx,dy)
+	local tmin = math_huge
+	for _, t in ipaits(self:intersectionsWithRay(x,y,dx,dy)) do
+		tmin = math_min(t, tmin)
+	end
+	return tmin ~= math_huge, tmin
 end
 
 -- point shape intersects ray if it lies on the ray
@@ -271,10 +260,9 @@ function PointShape:intersectsRay(x,y, dx,dy)
 	return t >= 0, t
 end
 
-function PointShape:intersectionsRay(x,y, dx,dy)
-	local px,py = self._pos.x-x, self._pos.y-y
-	local t = vector.dot(px,py, dx,dy) / vector.len2(dx,dy)
-	return {t}
+function PointShape:intersectionsWithRay(x,y, dx,dy)
+	local intersects, t = self:intersectsRay(x,y, dx,dy)
+	return intersects and {t} or {}
 end
 
 --