diff --git a/basis/math/geometry/rect/rect.factor b/basis/math/geometry/rect/rect.factor
index a7cefceae8..08cfbbcc46 100644
--- a/basis/math/geometry/rect/rect.factor
+++ b/basis/math/geometry/rect/rect.factor
@@ -60,9 +60,14 @@ M: rect set-height! ( rect height -- rect ) over dim>> set-second ;
 M: rect set-x! ( rect x -- rect ) over loc>> set-first  ;
 M: rect set-y! ( rect y -- rect ) over loc>> set-second ;
 
+: rect-containing ( points -- rect )
+    [ vleast ] [ vgreatest ] bi
+    [ drop ] [ swap v- ] 2bi <rect> ;
+
 ! Accessing corners
 
 : top-left     ( rect -- point ) loc>> ;
 : top-right    ( rect -- point ) [ loc>> ] [ width  1 - ] bi v+x ;
 : bottom-left  ( rect -- point ) [ loc>> ] [ height 1 - ] bi v+y ;
 : bottom-right ( rect -- point ) [ loc>> ] [ dim>> ] bi v+ { 1 1 } v- ;
+
diff --git a/basis/math/vectors/vectors.factor b/basis/math/vectors/vectors.factor
index a6967a7218..4d9a0916b5 100644
--- a/basis/math/vectors/vectors.factor
+++ b/basis/math/vectors/vectors.factor
@@ -19,6 +19,9 @@ IN: math.vectors
 : vmax ( u v -- w ) [ max ] 2map ;
 : vmin ( u v -- w ) [ min ] 2map ;
 
+: vgreatest ( array -- vmax ) { -1.0/0.0 -1.0/0.0 } [ vmax ] reduce ; 
+: vleast    ( array -- vmax ) {  1.0/0.0  1.0/0.0 } [ vmin ] reduce ; 
+
 : v. ( u v -- x ) [ * ] [ + ] 2map-reduce ;
 : norm-sq ( v -- x ) [ absq ] [ + ] map-reduce ;
 : norm ( v -- x ) norm-sq sqrt ;
diff --git a/extra/quadtrees/quadtrees-docs.factor b/extra/quadtrees/quadtrees-docs.factor
index f2de89ce3d..7b0d3772a0 100644
--- a/extra/quadtrees/quadtrees-docs.factor
+++ b/extra/quadtrees/quadtrees-docs.factor
@@ -2,17 +2,25 @@ USING: arrays assocs help.markup help.syntax math.geometry.rect quadtrees quotat
 IN: quadtrees
 
 ARTICLE: "quadtrees" "Quadtrees"
-"The " { $snippet "quadtrees" } " vocabulary implements the quadtree structure in Factor. Quadtrees follow the " { $link "assocs-protocol" } " for insertion, deletion, and querying of exact points, using two-dimensional vectors as keys. Additional words are provided for spatial queries and pruning the tree structure:"
-{ $subsection prune }
+"The " { $snippet "quadtrees" } " vocabulary implements the quadtree data structure in Factor."
+{ $subsection <quadtree> }
+"Quadtrees follow the " { $link "assocs-protocol" } " for insertion, deletion, and querying of exact points, using two-dimensional vectors as keys. Additional words are provided for spatial queries and pruning the tree structure:"
 { $subsection in-rect }
+{ $subsection prune-quadtree }
 "The following words are provided to help write quadtree algorithms:"
 { $subsection descend }
 { $subsection each-quadrant }
-{ $subsection map-quadrant } ;
+{ $subsection map-quadrant }
+"Quadtrees can be used to \"swizzle\" a sequence to improve the locality of spatial data in memory:"
+{ $subsection swizzle } ;
 
 ABOUT: "quadtrees"
 
-HELP: prune
+HELP: <quadtree>
+{ $values { "bounds" rect } { "quadtree" quadtree } }
+{ $description "Constructs an empty quadtree covering the axis-aligned rectangle indicated by " { $snippet "bounds" } ". All the keys of " { $snippet "quadtree" } " must be two-dimensional vectors lying inside " { $snippet "bounds" } "." } ;
+
+HELP: prune-quadtree
 { $values { "tree" quadtree } }
 { $description "Removes empty nodes from " { $snippet "tree" } "." } ;
 
@@ -32,3 +40,6 @@ HELP: map-quadrant
 { $values { "node" quadtree } { "quot" quotation } { "array" array } }
 { $description "Calls " { $snippet "quot" } " with each subnode of " { $snippet "node" } " on the top of the stack in turn, collecting the four results into " { $snippet "array" } "." } ;
 
+HELP: swizzle
+{ $values { "sequence" sequence } { "quot" quotation } { "sequence'" sequence } }
+{ $description "Swizzles " { $snippet "sequence" } " based on the two-dimensional vector values returned by calling " { $snippet "quot" } " on each element of " { $snippet "sequence" } "." } ;
diff --git a/extra/quadtrees/quadtrees-tests.factor b/extra/quadtrees/quadtrees-tests.factor
index b96cdd82bf..7a17c1fb44 100644
--- a/extra/quadtrees/quadtrees-tests.factor
+++ b/extra/quadtrees/quadtrees-tests.factor
@@ -1,5 +1,5 @@
 ! (c) 2009 Joe Groff, see BSD license
-USING: assocs kernel tools.test quadtrees math.geometry.rect sorting ;
+USING: accessors assocs kernel tools.test quadtrees math.geometry.rect sorting ;
 IN: quadtrees.tests
 
 : unit-bounds ( -- rect ) { -1.0 -1.0 } { 2.0 2.0 } <rect> ;
@@ -98,7 +98,7 @@ IN: quadtrees.tests
         "d" {  0.75  0.25 } value>>key
 
         {  0.25  0.25 } delete>>key
-        prune
+        prune-quadtree
 ] unit-test
 
 [ T{ quadtree f T{ rect f { -1.0 -1.0 } { 2.0 2.0 } } f f
@@ -116,7 +116,7 @@ IN: quadtrees.tests
 
         {  0.25  0.25 } delete>>key
         {  0.75  0.25 } delete>>key
-        prune
+        prune-quadtree
 ] unit-test
 
 [ T{ quadtree f T{ rect f { -1.0 -1.0 } { 2.0 2.0 } } f f
@@ -160,7 +160,7 @@ IN: quadtrees.tests
         "g" {  0.25  0.25 } value>>key
         "h" {  0.75  0.75 } value>>key
 
-        prune
+        prune-quadtree
 ] unit-test
 
 [ 8 ] [
@@ -200,3 +200,42 @@ IN: quadtrees.tests
         >alist natural-sort
 ] unit-test
 
+TUPLE: pointy-thing center ;
+
+[ {
+    T{ pointy-thing f { 0 0 } }
+    T{ pointy-thing f { 1 0 } }
+    T{ pointy-thing f { 0 1 } }
+    T{ pointy-thing f { 1 1 } }
+    T{ pointy-thing f { 2 0 } }
+    T{ pointy-thing f { 3 0 } }
+    T{ pointy-thing f { 2 1 } }
+    T{ pointy-thing f { 3 1 } }
+    T{ pointy-thing f { 0 2 } }
+    T{ pointy-thing f { 1 2 } }
+    T{ pointy-thing f { 0 3 } }
+    T{ pointy-thing f { 1 3 } }
+    T{ pointy-thing f { 2 2 } }
+    T{ pointy-thing f { 3 2 } }
+    T{ pointy-thing f { 2 3 } }
+    T{ pointy-thing f { 3 3 } }
+} ] [
+    {
+        T{ pointy-thing f { 3 1 } }
+        T{ pointy-thing f { 2 3 } }
+        T{ pointy-thing f { 3 2 } }
+        T{ pointy-thing f { 0 1 } }
+        T{ pointy-thing f { 2 2 } }
+        T{ pointy-thing f { 1 1 } }
+        T{ pointy-thing f { 3 0 } }
+        T{ pointy-thing f { 3 3 } }
+        T{ pointy-thing f { 1 3 } }
+        T{ pointy-thing f { 2 1 } }
+        T{ pointy-thing f { 0 0 } }
+        T{ pointy-thing f { 2 0 } }
+        T{ pointy-thing f { 1 0 } }
+        T{ pointy-thing f { 0 2 } }
+        T{ pointy-thing f { 1 2 } }
+        T{ pointy-thing f { 0 3 } }
+    } [ center>> ] swizzle
+] unit-test
diff --git a/extra/quadtrees/quadtrees.factor b/extra/quadtrees/quadtrees.factor
index 60446f4bf8..d9bdbe4aeb 100644
--- a/extra/quadtrees/quadtrees.factor
+++ b/extra/quadtrees/quadtrees.factor
@@ -1,12 +1,15 @@
 ! (c) 2009 Joe Groff, see BSD license
 USING: assocs kernel math.geometry.rect combinators accessors
 math.vectors vectors sequences math math.points math.geometry
-combinators.short-circuit arrays fry locals ;
+combinators.short-circuit arrays fry ;
 IN: quadtrees
 
 TUPLE: quadtree { bounds rect } point value ll lr ul ur leaf? ;
 
-: <quadtree> ( bounds -- quadtree ) f f f f f f t quadtree boa ;
+: <quadtree> ( bounds -- quadtree )
+    quadtree new
+        swap >>bounds
+        t >>leaf? ;
 
 : rect-ll ( rect -- point ) loc>> ;
 : rect-lr ( rect -- point ) [ loc>> ] [ width  ] bi v+x ;
@@ -26,11 +29,13 @@ TUPLE: quadtree { bounds rect } point value ll lr ul ur leaf? ;
 : descend ( pt node -- pt subnode )
     [ drop ] [ quadrant ] 2bi ; inline
 
-:: each-quadrant ( node quot -- )
-    node ll>> quot call
-    node lr>> quot call
-    node ul>> quot call
-    node ur>> quot call ; inline
+: each-quadrant ( node quot -- )
+    {
+        [ [ ll>> ] [ call ] bi* ] 
+        [ [ lr>> ] [ call ] bi* ] 
+        [ [ ul>> ] [ call ] bi* ] 
+        [ [ ur>> ] [ call ] bi* ] 
+    } 2cleave ; inline
 : map-quadrant ( node quot: ( child-node -- x ) -- array )
     each-quadrant 4array ; inline
 
@@ -73,6 +78,7 @@ DEFER: in-rect*
     [ node-insert ] [ node-insert ] bi ;
 
 : leaf-replaceable? ( pt leaf -- ? ) point>> { [ nip not ] [ = ] } 2|| ;
+
 : leaf-insert ( value point leaf -- )
     2dup leaf-replaceable?
     [ [ (>>point) ] [ (>>value) ] bi ]
@@ -165,7 +171,7 @@ DEFER: in-rect*
 
 PRIVATE>
 
-: prune ( tree -- tree ) [ (prune) ] keep ;
+: prune-quadtree ( tree -- tree ) [ (prune) ] keep ;
 
 : in-rect ( tree rect -- values )
     [ 16 <vector> ] 2dip in-rect* ;
@@ -186,3 +192,8 @@ M: quadtree clear-assoc ( assoc -- )
     f >>value
     drop ;
 
+: swizzle ( sequence quot -- sequence' )
+    [ dup ] dip map
+    [ zip ] [ rect-containing <quadtree> ] bi
+    [ '[ first2 _ set-at ] each ] [ values ] bi ;
+