diff --git a/functional.lua b/functional.lua
index 6f077ca..801868c 100644
--- a/functional.lua
+++ b/functional.lua
@@ -13,6 +13,7 @@
 
 local path = (...):gsub("functional", "")
 local tablex = require(path .. "tablex")
+local mathx = require(path .. "mathx")
 
 local functional = setmetatable({}, {
 	__index = tablex,
@@ -172,6 +173,54 @@ function functional.zip(t1, t2, f)
 	return ret
 end
 
+-----------------------------------------------------------
+--specialised maps
+--	(experimental: let me know if you have better names for these!)
+-----------------------------------------------------------
+
+--maps a sequence {a, b, c} -> collapse { f(a), f(b), f(c) }
+-- (ie results from functions should generally be sequences,
+--  which are appended onto each other, resulting in one big sequence)
+-- (automatically drops any nils, same as map)
+function functional.stitch(t, f)
+	local result = {}
+	for i, v in ipairs(t) do
+		local v = f(v, i)
+		if v ~= nil then
+			if type(v) == "table" then
+				for _, e in ipairs(v) do
+					table.insert(result, e)
+				end
+			else
+				table.insert(result, v)
+			end
+		end
+	end
+	return result
+end
+
+--alias
+functional.map_stitch = functional.stitch
+
+--maps a sequence {a, b, c} -> { f(a, b), f(b, c), f(c, a) }
+-- useful for inter-dependent data
+-- (automatically drops any nils, same as map)
+
+function functional.cycle(t, f)
+	local result = {}
+	for i, a in ipairs(t) do
+		local b = t[mathx.wrap(i + 1, 1, #t + 1)]
+		local v = f(a, b, i)
+		if v ~= nil then
+			table.insert(result, v)
+		end
+	end
+	return result
+end
+
+functional.map_cycle = functional.cycle
+
+
 -----------------------------------------------------------
 --generating data
 -----------------------------------------------------------
diff --git a/intersect.lua b/intersect.lua
index b661e70..5740734 100644
--- a/intersect.lua
+++ b/intersect.lua
@@ -55,7 +55,7 @@ function intersect.circle_circle_collide(a_pos, a_rad, b_pos, b_rad, into)
 			into = vec2:zero()
 		end
 		--normalise, scale to separating distance
-		into:vset(_ccc_delta):sdiv(dist):smuli(rad - dist)
+		into:vset(_ccc_delta):sdivi(dist):smuli(rad - dist)
 		return into
 	end
 	return false
@@ -97,7 +97,7 @@ function intersect._line_displacement_to_sep(a_start, a_end, separation, total_r
 	if sep <= 0 then
 		if distance <= COLLIDE_EPS then
 			--point intersecting the line; push out along normal
-			separation:vset(a_end):vsub(a_start):normalisei():rot90li()
+			separation:vset(a_end):vsubi(a_start):normalisei():rot90li()
 		else
 			separation:smuli(-sep)
 		end
@@ -418,4 +418,60 @@ function intersect.point_in_poly(point, poly)
 	return wn ~= 0
 end
 
+--resolution helpers
+
+--resolve a collision between two bodies, given a (minimum) separating vector
+--	from a's frame of reference, like the result of any of the _collide functions
+--requires the two positions of the bodies, the msv, and a balance factor
+--balance should be between 1 and 0;
+--	1 is only a_pos moving to resolve
+--	0 is only b_pos moving to resolve
+--	0.5 is balanced between both (default)
+--note: this wont work as-is for line segments, which have two separate position coordinates
+--		you will need to understand what is going on and move the second coordinate yourself
+function intersect.resolve_msv(a_pos, b_pos, msv, balance)
+	balance = balance or 0.5
+	a_pos:fmai(msv, balance)
+	b_pos:fmai(msv, -(1 - balance))
+end
+
+--bounce a velocity off of a normal (modifying velocity)
+--essentially flips the part of the velocity in the direction of the normal
+function intersect.bounce_off(velocity, normal, conservation)
+	--(default)
+	conservation = conservation or 1
+	--take a copy, we need it
+	local old_vel = vec2.pooled_copy(velocity)
+	--reject on the normal (keep velocity tangential to the normal)
+	velocity:vreji(normal)
+	--add back the complement of the difference;
+	--basically "flip" the velocity in line with the normal.
+	velocity:fmai(old_vel:vsubi(velocity), -conservation)
+	--clean up
+	old_vel:release()
+	return velocity
+end
+
+--mutual bounce; two similar bodies bounce off each other, transferring energy
+function intersect.mutual_bounce(velocity_a, velocity_b, normal, conservation)
+	--(default)
+	conservation = conservation or 1
+	--take copies, we need them
+	local old_a_vel = vec2.pooled_copy(velocity_a)
+	local old_b_vel = vec2.pooled_copy(velocity_b)
+	--reject on the normal
+	velocity_a:vreji(normal)
+	velocity_b:vreji(normal)
+	--calculate the amount remaining from the old velocity
+	--(transfer ownership)
+	local a_remaining = old_a_vel:vsubi(velocity_a)
+	local b_remaining = old_b_vel:vsubi(velocity_b)
+	--transfer it to the other body
+	velocity_a:fmai(b_remaining, conservation)
+	velocity_b:fmai(a_remaining, conservation)
+	--clean up
+	a_remaining:release()
+	b_remaining:release()
+end
+
 return intersect
diff --git a/sequence.lua b/sequence.lua
index 4dcb722..6964e83 100644
--- a/sequence.lua
+++ b/sequence.lua
@@ -24,73 +24,85 @@ sequence.sort = stable_sort
 --patch various interfaces in a type-preserving way, for method chaining
 
 --import copying tablex
-function sequence:keys()
-	return sequence(table.keys(self))
+--(common case where something returns another sequence for chaining)
+for _, v in ipairs({
+	"keys",
+	"values",
+	"dedupe",
+	"collapse",
+	"append",
+	"overlay",
+	"copy",
+}) do
+	local table_f = table[v]
+	sequence[v] = function(self, ...)
+		return sequence(table_f(self, ...))
+	end
 end
 
-function sequence:values()
-	return sequence(table.values(self))
+--aliases
+for _, v in ipairs({
+	{"flatten", "collapse"},
+}) do
+	sequence[v[1]] = sequence[v[2]]
 end
 
-function sequence:dedupe()
-	return sequence(table.dedupe(self))
+--import functional interface in method form
+
+--(common case where something returns another sequence for chaining)
+for _, v in ipairs({
+	"map",
+	"map_inplace",
+	"filter",
+	"filter_inplace",
+	"remove_if",
+	"zip",
+	"stitch",
+	"cycle",
+}) do
+	local functional_f = functional[v]
+	sequence[v] = function(self, ...)
+		return sequence(functional_f(self, ...))
+	end
 end
 
-function sequence:collapse()
-	return sequence(table.collapse(self))
-end
-sequence.flatten = sequence.collapse
-
-function sequence:append(...)
-	return sequence(table.append(self, ...))
+--(cases where we don't want to construct a new sequence)
+for _, v in ipairs({
+	"foreach",
+	"reduce",
+	"any",
+	"none",
+	"all",
+	"count",
+	"contains",
+	"sum",
+	"mean",
+	"minmax",
+	"max",
+	"min",
+	"find_min",
+	"find_max",
+	"find_nearest",
+	"find_match",
+}) do
+	sequence[v] = functional[v]
 end
 
-function sequence:overlay(...)
-	return sequence(table.overlay(self, ...))
-end
-
-function sequence:copy(...)
-	return sequence(table.copy(self, ...))
-end
-
---import functional interface
-function sequence:foreach(f)
-	return functional.foreach(self, f)
-end
-
-function sequence:reduce(seed, f)
-	return functional.reduce(self, seed, f)
-end
-
-function sequence:map(f)
-	return sequence(functional.map(self, f))
-end
-
-function sequence:map_inplace(f)
-	return sequence(functional.map_inplace(self, f))
-end
-
-sequence.remap = sequence.map_inplace
-
-function sequence:filter(f)
-	return sequence(functional.filter(self, f))
-end
-
-function sequence:filter_inplace(f)
-	return sequence(functional.filter_inplace(self, f))
-end
-
-function sequence:remove_if(f)
-	return sequence(functional.remove_if(self, f))
+
+--aliases
+for _, v in ipairs({
+	{"remap", "map_inplace"},
+	{"map_stitch", "stitch"},
+	{"map_cycle", "cycle"},
+	{"find_best", "find_max"},
+}) do
+	sequence[v[1]] = sequence[v[2]]
 end
 
+--(anything that needs bespoke wrapping)
 function sequence:partition(f)
 	local a, b = functional.partition(self, f)
 	return sequence(a), sequence(b)
 end
 
-function sequence:zip(other, f)
-	return sequence(functional.zip(self, other, f))
-end
-
 return sequence
diff --git a/stringx.lua b/stringx.lua
index b0568ab..10e189f 100644
--- a/stringx.lua
+++ b/stringx.lua
@@ -215,11 +215,8 @@ function stringx.trim(s)
 	return s:sub(head, tail)
 end
 
+--trim the start of a string
 function stringx.ltrim(s)
-	if s == "" or s == string.rep(" ", s:len()) then
-		return ""
-	end
-
 	local head = 1
 	for i = 1, #s do
 		if not _whitespace_bytes[s:byte(i)] then
@@ -227,13 +224,14 @@ function stringx.ltrim(s)
 			break
 		end
 	end
+	if head == 1 then
+		return s
+	end
 	return s:sub(head)
 end
 
+--trim the end of a string
 function stringx.rtrim(s)
-	if s == "" or s == string.rep(" ", s:len()) then
-		return ""
-	end
 	local tail = #s
 
 	for i = #s, 1, -1 do
@@ -243,6 +241,10 @@ function stringx.rtrim(s)
 		end
 	end
 
+	if tail == #s then
+		return s
+	end
+
 	return s:sub(1, tail)
 end
 
@@ -322,13 +324,13 @@ function stringx.starts_with(s, prefix)
 	return true
 end
 
-function stringx.ends_with(s, posfix)
-	if posfix == "" then return true end
-
-	if #posfix > #s then return false end
-
-	for i = 0, #posfix-1 do
-		if s:byte(#s-i) ~= posfix:byte(#posfix-i) then
+--check if a given string ends with another
+--(without garbage)
+function stringx.ends_with(s, suffix)
+	local len = #s
+	local suffix_len = #suffix
+	for i = 0, suffix_len - 1 do
+		if s:byte(len - i) ~= suffix:byte(suffix_len - i) then
 			return false
 		end
 	end
diff --git a/vec2.lua b/vec2.lua
index 31657ac..7769742 100644
--- a/vec2.lua
+++ b/vec2.lua
@@ -16,7 +16,7 @@ end
 
 --probably-too-flexible ctor
 function vec2:new(x, y)
-	if x and y then
+	if type(x) == "number" and type(y) == "number" then
 		return vec2:xy(x,y)
 	elseif x then
 		if type(x) == "number" then