diff --git a/collects/plot/common/math.rkt b/collects/plot/common/math.rkt
index 311daea418..c9eaf7083e 100644
--- a/collects/plot/common/math.rkt
+++ b/collects/plot/common/math.rkt
@@ -558,6 +558,10 @@
                     [x2  (in-list (rest xs))])
            (ivl x1 x2))]))
 
+(defproc (clamp-real [x real?] [i ivl?]) real?
+  (match-define (ivl a b) i)
+  (max (min x b) a))
+
 ;; ===================================================================================================
 ;; Rectangles
 
diff --git a/collects/plot/common/plot-element.rkt b/collects/plot/common/plot-element.rkt
index 2b7035bedb..c5d491a3ab 100644
--- a/collects/plot/common/plot-element.rkt
+++ b/collects/plot/common/plot-element.rkt
@@ -36,8 +36,7 @@
   (λ (r)
     (match-define (vector xi yi) r)
     (cond [(ivl-known? xi)
-           (match-define (ivl x-min x-max) xi)
-           (match-define (sample xs ys y-min y-max) (f x-min x-max samples))
+           (match-define (sample xs ys y-min y-max) (f xi samples))
            (vector xi (ivl y-min y-max))]
           [else  r])))
 
@@ -45,8 +44,7 @@
   (λ (r)
     (match-define (vector xi yi) r)
     (cond [(ivl-known? yi)
-           (match-define (ivl y-min y-max) yi)
-           (match-define (sample ys xs x-min x-max) (f y-min y-max samples))
+           (match-define (sample ys xs x-min x-max) (f yi samples))
            (vector (ivl x-min x-max) yi)]
           [else  r])))
 
@@ -66,10 +64,8 @@
   (λ (r)
     (match-define (vector xi yi zi) r)
     (cond [(and (ivl-known? xi) (ivl-known? yi))
-           (match-define (ivl x-min x-max) xi)
-           (match-define (ivl y-min y-max) yi)
            (match-define (2d-sample xs ys zss z-min z-max)
-             (f x-min x-max samples y-min y-max samples))
+             (f (vector xi yi) (vector samples samples)))
            (vector xi yi (ivl z-min z-max))]
           [else  r])))
 
@@ -87,12 +83,21 @@
   (let/ec break
     ;; Shortcut eval: if the plot bounds are all given, the code below just returns them anyway
     (when (rect-known? given-bounds-rect) (break given-bounds-rect))
-    ;; Objective: find the fixpoint of F starting at given-bounds-rect
+    ;; A list of elements' known bounds rects
+    (define elem-bounds-rects (filter values (map plot-element-bounds-rect elems)))
+    ;; The minimum bounding rectangle
+    (define min-bounds-rect
+      (cond [(empty? elem-bounds-rects)  given-bounds-rect]
+            [else  (rect-join given-bounds-rect
+                              (rect-meet given-bounds-rect
+                                         (apply rect-join elem-bounds-rects)))]))
+    ;; Objective: find the fixpoint of F starting at min-bounds-rect
     (define (F bounds-rect) (rect-meet given-bounds-rect (apply-bounds* elems bounds-rect)))
     ;; Iterate joint bounds to (hopefully) a fixpoint
     (define-values (bounds-rect area delta-area)
-      (for/fold ([bounds-rect  given-bounds-rect]
-                 [area  (rect-area given-bounds-rect)] [delta-area  #f]
+      (for/fold ([bounds-rect  min-bounds-rect]
+                 [area  (rect-area min-bounds-rect)]
+                 [delta-area  #f]
                  ) ([n  (in-range max-iters)])
         ;(printf "bounds-rect = ~v~n" bounds-rect)
         ;; Get new bounds from the elements' bounds functions
@@ -120,13 +125,6 @@
 (define (apply-bounds elem bounds-rect)
   (match-define (plot-element elem-bounds-rect elem-bounds-fun _) elem)
   ;(printf "elem-bounds-rect = ~v~n" elem-bounds-rect)
-  (let* ([new-bounds-rect  (if elem-bounds-rect
-                               (rect-meet bounds-rect elem-bounds-rect)
-                               bounds-rect)]
-         [new-bounds-rect  (if elem-bounds-fun
-                               (elem-bounds-fun (rect-inexact->exact new-bounds-rect))
-                               new-bounds-rect)]
-         [new-bounds-rect  (if elem-bounds-rect
-                               (rect-join new-bounds-rect elem-bounds-rect)
-                               new-bounds-rect)])
-    new-bounds-rect))
+  (let* ([bounds-rect  (if elem-bounds-fun (elem-bounds-fun bounds-rect) bounds-rect)]
+         [bounds-rect  (if elem-bounds-rect (rect-join elem-bounds-rect bounds-rect) bounds-rect)])
+    bounds-rect))
diff --git a/collects/plot/common/sample.rkt b/collects/plot/common/sample.rkt
index 32c2449464..9f311bd37e 100644
--- a/collects/plot/common/sample.rkt
+++ b/collects/plot/common/sample.rkt
@@ -10,9 +10,16 @@
 (provide (all-defined-out))
 
 (defproc (build-linear-seq [start real?] [step real?]
-                           [num exact-nonnegative-integer?]) (listof real?)
-  (for/list ([n  (in-range num)])
-    (+ start (* n step))))
+                           [num exact-nonnegative-integer?]
+                           [min-val real? start]
+                           [max-val real? (+ start (* (- num 1) step))]
+                           ) (listof real?)
+  (define n-start (max 0 (inexact->exact (floor (/ (- min-val start) step)))))
+  (define n-end (min num (+ (inexact->exact (ceiling (/ (- max-val start) step))) 1)))
+  (for*/list ([n  (in-range n-start n-end)]
+              [x  (in-value (+ start (* n step)))]
+              #:when (<= min-val x max-val))
+    x))
 
 (defproc (linear-seq [start real?] [end real?] [num exact-nonnegative-integer?]
                      [#:start? start? boolean? #t]
@@ -57,6 +64,41 @@
   (match-define (invertible-function _ finv) (apply-axis-transform transform start end))
   (map finv (linear-seq start end num #:start? start? #:end? end?)))
 
+;; ===================================================================================================
+
+(define (ensure-endpoints xs i-min i-max)
+  (cond [(empty? xs)  (cond [(i-min . = . i-max)  (list i-min)]
+                            [else  (list i-min i-max)])]
+        [else
+         (define xs-min (first xs))
+         (define xs-max (last xs))
+         (let* ([xs  (if (xs-min . <= . i-min) xs (cons i-min xs))]
+                [xs  (if (xs-max . >= . i-max) xs (append xs (list i-max)))])
+           xs)]))
+
+(defproc (sample-points [outer-ivl rational-ivl?] [inner-ivl ivl?]
+                        [num exact-nonnegative-integer?]
+                        [transform axis-transform/c id-transform]) (listof real?)
+  (let* ([inner-ivl  (ivl-meet inner-ivl outer-ivl)]
+         [inner-ivl  (ivl-inexact->exact inner-ivl)]
+         [outer-ivl  (ivl-inexact->exact outer-ivl)])
+    (match-define (ivl o-min o-max) outer-ivl)
+    (match-define (ivl i-min i-max) inner-ivl)
+    (match-define (invertible-function f finv) (apply-axis-transform transform o-min o-max))
+    (cond
+      [(ivl-empty? inner-ivl)  empty]
+      [(= num 0)  empty]
+      [(or (= o-min o-max) (= num 1))
+       (cond [(<= i-min o-min i-max)  (build-list num (λ _ o-min))]
+             [else  empty])]
+      [else
+       (define step (/ (- o-max o-min) (- num 1)))
+       (let* ([xs  (map finv (build-linear-seq o-min step num (f i-min) (f i-max)))]
+              [xs  (remove-duplicates (map (λ (x) (clamp-real x inner-ivl)) xs))])
+         (ensure-endpoints xs i-min i-max))])))
+
+;; ===================================================================================================
+
 (struct mapped-function (f fmap) #:transparent
   #:property prop:procedure
   (λ (g x) ((mapped-function-f g) x)))
@@ -75,26 +117,28 @@
 (struct 2d-sample (xs ys zss z-min z-max) #:transparent)
 (struct 3d-sample (xs ys zs dsss d-min d-max) #:transparent)
 
-(defcontract sampler/c (real? real? exact-nonnegative-integer? . -> . sample?))
+(defcontract sampler/c
+  (-> rational-ivl? exact-nonnegative-integer? sample?))
 
-(defcontract 2d-sampler/c (real? real? exact-nonnegative-integer?
-                                 real? real? exact-nonnegative-integer?
-                                 . -> . 2d-sample?))
+(defcontract 2d-sampler/c
+  (-> (vector/c rational-ivl? rational-ivl?)
+      (vector/c exact-nonnegative-integer? exact-nonnegative-integer?)
+      2d-sample?))
 
-(defcontract 3d-sampler/c (real? real? exact-nonnegative-integer?
-                                 real? real? exact-nonnegative-integer?
-                                 real? real? exact-nonnegative-integer?
-                                 . -> . 3d-sample?))
+(defcontract 3d-sampler/c
+  (-> (vector/c rational-ivl? rational-ivl? rational-ivl?)
+      (vector/c exact-nonnegative-integer? exact-nonnegative-integer? exact-nonnegative-integer?)
+      3d-sample?))
 
 (defproc (make-function->sampler [transform-thnk (-> axis-transform/c)]
-                                 ) ((real? . -> . real?) . -> . sampler/c)
-  (λ (f)
+                                 ) (-> (real? . -> . real?) ivl? sampler/c)
+  (λ (f inner-ivl)
     (define memo (make-hash))
-    (λ (x-min x-max x-samples)
+    (λ (outer-ivl num)
       (define tx (transform-thnk))
-      (hash-ref! memo (vector x-min x-max x-samples tx)
+      (hash-ref! memo (vector outer-ivl num tx)
                  (λ ()
-                   (define xs (nonlinear-seq x-min x-max x-samples tx))
+                   (define xs (sample-points outer-ivl inner-ivl num tx))
                    (define ys (map* f xs))
                    (define rys (filter rational? ys))
                    (define-values (y-min y-max)
@@ -106,20 +150,25 @@
 
 (defproc (make-2d-function->sampler [transform-x-thnk (-> axis-transform/c)]
                                     [transform-y-thnk (-> axis-transform/c)]
-                                    ) ((real? real? . -> . real?) . -> . 2d-sampler/c)
-  (λ (f)
+                                    ) (-> (real? real? . -> . real?)
+                                          (vector/c ivl? ivl?)
+                                           2d-sampler/c)
+  (λ (f inner-rect)
     (define memo (make-hash))
-    (λ (x-min x-max x-samples y-min y-max y-samples)
+    (λ (outer-rect nums)
       (define tx (transform-x-thnk))
       (define ty (transform-y-thnk))
-      (hash-ref! memo (vector x-min x-max x-samples tx y-min y-max y-samples ty)
+      (hash-ref! memo (vector outer-rect nums tx ty)
                  (λ ()
-                   (define xs (nonlinear-seq x-min x-max x-samples tx))
-                   (define ys (nonlinear-seq y-min y-max y-samples ty))
+                   (match-define (vector outer-x-ivl outer-y-ivl) outer-rect)
+                   (match-define (vector inner-x-ivl inner-y-ivl) inner-rect)
+                   (match-define (vector x-num y-num) nums)
+                   (define xs (sample-points outer-x-ivl inner-x-ivl x-num tx))
+                   (define ys (sample-points outer-y-ivl inner-y-ivl y-num ty))
                    (define z-min #f)
                    (define z-max #f)
-                   (define zss (for/vector #:length y-samples ([y  (in-list ys)])
-                                 (for/vector #:length x-samples ([x  (in-list xs)])
+                   (define zss (for/vector #:length (length ys) ([y  (in-list ys)])
+                                 (for/vector #:length (length xs) ([x  (in-list xs)])
                                    (let ([z  (f x y)])
                                      (when (rational? z)
                                        (unless (and z-min (z . >= . z-min)) (set! z-min z))
@@ -132,25 +181,28 @@
 (defproc (make-3d-function->sampler [transform-x-thnk (-> axis-transform/c)]
                                     [transform-y-thnk (-> axis-transform/c)]
                                     [transform-z-thnk (-> axis-transform/c)]
-                                    ) ((real? real? real? . -> . real?) . -> . 3d-sampler/c)
-  (λ (f)
+                                    ) (-> (real? real? real? . -> . real?)
+                                          (vector/c ivl? ivl? ivl?)
+                                          3d-sampler/c)
+  (λ (f inner-rect)
     (define memo (make-hash))
-    (λ (x-min x-max x-samples y-min y-max y-samples z-min z-max z-samples)
+    (λ (outer-rect nums)
       (define tx (transform-x-thnk))
       (define ty (transform-y-thnk))
       (define tz (transform-z-thnk))
-      (hash-ref! memo (vector x-min x-max x-samples tx
-                              y-min y-max y-samples ty
-                              z-min z-max z-samples tz)
+      (hash-ref! memo (vector outer-rect nums tx ty tz)
                  (λ ()
-                   (define xs (nonlinear-seq x-min x-max x-samples tx))
-                   (define ys (nonlinear-seq y-min y-max y-samples ty))
-                   (define zs (nonlinear-seq z-min z-max z-samples tz))
+                   (match-define (vector outer-x-ivl outer-y-ivl outer-z-ivl) outer-rect)
+                   (match-define (vector inner-x-ivl inner-y-ivl inner-z-ivl) inner-rect)
+                   (match-define (vector x-num y-num z-num) nums)
+                   (define xs (sample-points outer-x-ivl inner-x-ivl x-num tx))
+                   (define ys (sample-points outer-y-ivl inner-y-ivl y-num ty))
+                   (define zs (sample-points outer-z-ivl inner-z-ivl z-num tz))
                    (define d-min #f)
                    (define d-max #f)
-                   (define dsss (for/vector #:length z-samples ([z  (in-list zs)])
-                                  (for/vector #:length y-samples ([y  (in-list ys)])
-                                    (for/vector #:length x-samples ([x  (in-list xs)])
+                   (define dsss (for/vector #:length (length zs) ([z  (in-list zs)])
+                                  (for/vector #:length (length ys) ([y  (in-list ys)])
+                                    (for/vector #:length (length xs) ([x  (in-list xs)])
                                       (let ([d  (f x y z)])
                                         (when (rational? d)
                                           (unless (and d-min (d . >= . d-min)) (set! d-min d))
diff --git a/collects/plot/common/samplers.rkt b/collects/plot/common/samplers.rkt
index e27a66105a..91e58d59e4 100644
--- a/collects/plot/common/samplers.rkt
+++ b/collects/plot/common/samplers.rkt
@@ -5,18 +5,23 @@
 (require racket/match racket/flonum racket/math racket/contract racket/list
          unstable/latent-contract/defthing
          "parameters.rkt"
-         "sample.rkt")
+         "sample.rkt"
+         "math.rkt")
 
 (provide (all-defined-out))
 
-(defthing function->sampler ((real? . -> . real?) . -> . sampler/c)
+(defthing function->sampler ((real? . -> . real?) ivl? . -> . sampler/c)
   (make-function->sampler plot-x-transform))
 
-(defthing inverse->sampler ((real? . -> . real?) . -> . sampler/c)
+(defthing inverse->sampler ((real? . -> . real?) ivl? . -> . sampler/c)
   (make-function->sampler plot-y-transform))
 
-(defthing 2d-function->sampler ((real? real? . -> . real?) . -> . 2d-sampler/c)
+(defthing 2d-function->sampler (-> (real? real? . -> . real?)
+                                   (vector/c ivl? ivl?)
+                                   2d-sampler/c)
   (make-2d-function->sampler plot-x-transform plot-y-transform))
 
-(defthing 3d-function->sampler ((real? real? real? . -> . real?) . -> . 3d-sampler/c)
+(defthing 3d-function->sampler (-> (real? real? real? . -> . real?)
+                                   (vector/c ivl? ivl? ivl?)
+                                   3d-sampler/c)
   (make-3d-function->sampler plot-x-transform plot-y-transform plot-z-transform))
diff --git a/collects/plot/contracted/math.rkt b/collects/plot/contracted/math.rkt
index 61ff02d7fb..5a234e2173 100644
--- a/collects/plot/contracted/math.rkt
+++ b/collects/plot/contracted/math.rkt
@@ -21,7 +21,7 @@
          empty-ivl unknown-ivl rational-ivl?
          (activate-contract-out
           ivl-empty? ivl-known? ivl-rational? ivl-singular? ivl-length ivl-center ivl-zero-length?
-          ivl-inexact->exact ivl-contains? bounds->intervals))
+          ivl-inexact->exact ivl-contains? bounds->intervals clamp-real))
 
 ;; Rectangles
 (provide (contract-out [rect-meet (->* () () #:rest (listof (vectorof ivl?)) (vectorof ivl?))]
diff --git a/collects/plot/plot2d/contour.rkt b/collects/plot/plot2d/contour.rkt
index a64ebdf2ca..09c072a1f6 100644
--- a/collects/plot/plot2d/contour.rkt
+++ b/collects/plot/plot2d/contour.rkt
@@ -13,9 +13,11 @@
 ;; One contour line
 
 (define ((isoline-render-proc g z samples color width style alpha label) area)
-  (match-define (vector (ivl x-min x-max) (ivl y-min y-max)) (send area get-bounds-rect))
-  (define sample (g x-min x-max (animated-samples samples)
-                    y-min y-max (animated-samples samples)))
+  (match-define (vector x-ivl y-ivl) (send area get-bounds-rect))
+  (match-define (ivl x-min x-max) x-ivl)
+  (match-define (ivl y-min y-max) y-ivl)
+  (define num (animated-samples samples))
+  (define sample (g (vector x-ivl y-ivl) (vector num num)))
   (match-define (2d-sample xs ys zss z-min z-max) sample)
   
   (when (<= z-min z z-max)
@@ -43,8 +45,10 @@
           [#:alpha alpha (real-in 0 1) (line-alpha)]
           [#:label label (or/c string? #f) #f]
           ) renderer2d?
-  (define g (2d-function->sampler f))
-  (renderer2d (vector (ivl x-min x-max) (ivl y-min y-max)) #f default-ticks-fun
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (define g (2d-function->sampler f (vector x-ivl y-ivl)))
+  (renderer2d (vector x-ivl y-ivl) #f default-ticks-fun
               (isoline-render-proc g z samples color width style alpha label)))
 
 ;; ===================================================================================================
@@ -52,9 +56,11 @@
 
 (define ((contours-render-proc g levels samples colors widths styles alphas label) area)
   (let/ec return
-    (match-define (vector (ivl x-min x-max) (ivl y-min y-max)) (send area get-bounds-rect))
-    (define sample (g x-min x-max (animated-samples samples)
-                      y-min y-max (animated-samples samples)))
+    (match-define (vector x-ivl y-ivl) (send area get-bounds-rect))
+    (match-define (ivl x-min x-max) x-ivl)
+    (match-define (ivl y-min y-max) y-ivl)
+    (define num (animated-samples samples))
+    (define sample (g (vector x-ivl y-ivl) (vector num num)))
     (match-define (2d-sample xs ys zss z-min z-max) sample)
     (match-define (list (tick zs _ labels) ...) (contour-ticks (plot-z-ticks) z-min z-max levels #f))
     
@@ -95,8 +101,10 @@
           [#:alphas alphas (alphas/c (listof real?)) (contour-alphas)]
           [#:label label (or/c string? #f) #f]
           ) renderer2d?
-  (define g (2d-function->sampler f))
-  (renderer2d (vector (ivl x-min x-max) (ivl y-min y-max)) #f default-ticks-fun
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (define g (2d-function->sampler f (vector x-ivl y-ivl)))
+  (renderer2d (vector x-ivl y-ivl) #f default-ticks-fun
               (contours-render-proc g levels samples colors widths styles alphas label)))
 
 ;; ===================================================================================================
@@ -106,9 +114,11 @@
           g levels samples colors styles contour-colors contour-widths contour-styles alphas label)
          area)
   (let/ec return
-    (match-define (vector (ivl x-min x-max) (ivl y-min y-max)) (send area get-bounds-rect))
-    (define sample (g x-min x-max (animated-samples samples)
-                      y-min y-max (animated-samples samples)))
+    (match-define (vector x-ivl y-ivl) (send area get-bounds-rect))
+    (match-define (ivl x-min x-max) x-ivl)
+    (match-define (ivl y-min y-max) y-ivl)
+    (define num (animated-samples samples))
+    (define sample (g (vector x-ivl y-ivl) (vector num num)))
     (match-define (2d-sample xs ys zss z-min z-max) sample)
     (match-define (list (tick zs _ labels) ...) (contour-ticks (plot-z-ticks) z-min z-max levels #t))
     
@@ -171,8 +181,10 @@
           [#:alphas alphas (alphas/c (listof ivl?)) (contour-interval-alphas)]
           [#:label label (or/c string? #f) #f]
           ) renderer2d?
-  (define g (2d-function->sampler f))
-  (renderer2d (vector (ivl x-min x-max) (ivl y-min y-max)) #f default-ticks-fun
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (define g (2d-function->sampler f (vector x-ivl y-ivl)))
+  (renderer2d (vector x-ivl y-ivl) #f default-ticks-fun
               (contour-intervals-render-proc g levels samples colors styles
                                              contour-colors contour-widths contour-styles
                                              alphas label)))
diff --git a/collects/plot/plot2d/interval.rkt b/collects/plot/plot2d/interval.rkt
index b031871b7a..edc89e8fe9 100644
--- a/collects/plot/plot2d/interval.rkt
+++ b/collects/plot/plot2d/interval.rkt
@@ -125,9 +125,9 @@
                                         line2-color line2-width line2-style
                                         alpha label)
          area)
-  (match-define (vector (ivl x-min x-max) y-ivl) (send area get-bounds-rect))
-  (match-define (sample x1s y1s y1-min y1-max) (f1 x-min x-max samples))
-  (match-define (sample x2s y2s y2-min y2-max) (f2 x-min x-max samples))
+  (match-define (vector x-ivl y-ivl) (send area get-bounds-rect))
+  (match-define (sample x1s y1s _ _) (f1 x-ivl samples))
+  (match-define (sample x2s y2s _ _) (f2 x-ivl samples))
   (define v1s (map vector x1s y1s))
   (define v2s (map vector x2s y2s))
   
@@ -153,9 +153,11 @@
           [#:alpha alpha (real-in 0 1) (interval-alpha)]
           [#:label label (or/c string? #f) #f]
           ) renderer2d?
-  (define g1 (function->sampler f1))
-  (define g2 (function->sampler f2))
-  (renderer2d (vector (ivl x-min x-max) (ivl y-min y-max))
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (define g1 (function->sampler f1 x-ivl))
+  (define g2 (function->sampler f2 x-ivl))
+  (renderer2d (vector x-ivl y-ivl)
               (function-interval-bounds-fun g1 g2 samples)
               default-ticks-fun
               (function-interval-render-proc g1 g2 samples color style
@@ -171,9 +173,9 @@
                                        line2-color line2-width line2-style
                                        alpha label)
          area)
-  (match-define (vector x-ivl (ivl y-min y-max)) (send area get-bounds-rect))
-  (match-define (sample y1s x1s x1-min x1-max) (f1 y-min y-max samples))
-  (match-define (sample y2s x2s x2-min x2-max) (f2 y-min y-max samples))
+  (match-define (vector x-ivl y-ivl) (send area get-bounds-rect))
+  (match-define (sample y1s x1s _ _) (f1 y-ivl samples))
+  (match-define (sample y2s x2s _ _) (f2 y-ivl samples))
   (define v1s (map vector x1s y1s))
   (define v2s (map vector x2s y2s))
   
@@ -199,9 +201,11 @@
           [#:alpha alpha (real-in 0 1) (interval-alpha)]
           [#:label label (or/c string? #f) #f]
           ) renderer2d?
-  (define g1 (inverse->sampler f1))
-  (define g2 (inverse->sampler f2))
-  (renderer2d (vector (ivl x-min x-max) (ivl y-min y-max))
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (define g1 (inverse->sampler f1 y-ivl))
+  (define g2 (inverse->sampler f2 y-ivl))
+  (renderer2d (vector x-ivl y-ivl)
               (inverse-interval-bounds-fun g1 g2 samples)
               default-ticks-fun
               (inverse-interval-render-proc g1 g2 samples color style
diff --git a/collects/plot/plot2d/line.rkt b/collects/plot/plot2d/line.rkt
index 980ebde674..22732d5e4e 100644
--- a/collects/plot/plot2d/line.rkt
+++ b/collects/plot/plot2d/line.rkt
@@ -76,8 +76,8 @@
 ;; Function
 
 (define ((function-render-proc f samples color width style alpha label) area)
-  (match-define (vector (ivl x-min x-max) y-ivl) (send area get-bounds-rect))
-  (match-define (sample xs ys y-min y-max) (f x-min x-max samples))
+  (match-define (vector x-ivl y-ivl) (send area get-bounds-rect))
+  (match-define (sample xs ys y-min y-max) (f x-ivl samples))
   
   (send area put-alpha alpha)
   (send area put-pen color width style)
@@ -96,18 +96,20 @@
                    [#:alpha alpha (real-in 0 1) (line-alpha)]
                    [#:label label (or/c string? #f) #f]
                    ) renderer2d?
-  (define g (function->sampler f))
-  (renderer2d (vector (ivl x-min x-max) (ivl y-min y-max))
-              (function-bounds-fun g samples)
-              default-ticks-fun
-              (function-render-proc g samples color width style alpha label)))
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (let ([f  (function->sampler f x-ivl)])
+    (renderer2d (vector x-ivl y-ivl)
+                (function-bounds-fun f samples)
+                default-ticks-fun
+                (function-render-proc f samples color width style alpha label))))
 
 ;; ===================================================================================================
 ;; Inverse function
 
 (define ((inverse-render-proc f samples color width style alpha label) area)
-  (match-define (vector x-ivl (ivl y-min y-max)) (send area get-bounds-rect))
-  (match-define (sample ys xs x-min x-max) (f y-min y-max samples))
+  (match-define (vector x-ivl y-ivl) (send area get-bounds-rect))
+  (match-define (sample ys xs x-min x-max) (f y-ivl samples))
   
   (send area put-alpha alpha)
   (send area put-pen color width style)
@@ -126,8 +128,10 @@
                   [#:alpha alpha (real-in 0 1) (line-alpha)]
                   [#:label label (or/c string? #f) #f]
                   ) renderer2d?
-  (define g (inverse->sampler f))
-  (renderer2d (vector (ivl x-min x-max) (ivl y-min y-max))
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (define g (inverse->sampler f y-ivl))
+  (renderer2d (vector x-ivl y-ivl)
               (inverse-bounds-fun g samples)
               default-ticks-fun
               (inverse-render-proc g samples color width style alpha label)))
diff --git a/collects/plot/plot3d/contour.rkt b/collects/plot/plot3d/contour.rkt
index aed91db4a9..2bc72588ad 100644
--- a/collects/plot/plot3d/contour.rkt
+++ b/collects/plot/plot3d/contour.rkt
@@ -11,10 +11,12 @@
 ;; One contour line in 3D (using marching squares)
 
 (define ((isoline3d-render-proc f z samples color width style alpha label) area)
-  (match-define (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max))
-    (send area get-bounds-rect))
-  (define sample (f x-min x-max (animated-samples samples)
-                    y-min y-max (animated-samples samples)))
+  (match-define (vector x-ivl y-ivl z-ivl) (send area get-bounds-rect))
+  (match-define (ivl x-min x-max) x-ivl)
+  (match-define (ivl y-min y-max) y-ivl)
+  (match-define (ivl z-min z-max) z-ivl)
+  (define num (animated-samples samples))
+  (define sample (f (vector x-ivl y-ivl) (vector num num)))
   
   (when (<= z-min z z-max)
     (send area put-alpha alpha)
@@ -45,10 +47,13 @@
           [#:alpha alpha (real-in 0 1) (line-alpha)]
           [#:label label (or/c string? #f) #f]
           ) renderer3d?
-  (define g (2d-function->sampler f))
   (let ([z-min  (if z-min z-min z)]
         [z-max  (if z-max z-max z)])
-    (renderer3d (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max))
+    (define x-ivl (ivl x-min x-max))
+    (define y-ivl (ivl y-min y-max))
+    (define z-ivl (ivl z-min z-max))
+    (define g (2d-function->sampler f (vector x-ivl y-ivl)))
+    (renderer3d (vector x-ivl y-ivl z-ivl)
                 #f default-ticks-fun
                 (isoline3d-render-proc g z samples color width style alpha label))))
 
@@ -56,10 +61,12 @@
 ;; Contour lines in 3D (using marching squares)
 
 (define ((contours3d-render-proc f levels samples colors widths styles alphas label) area)
-  (match-define (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max))
-    (send area get-bounds-rect))
-  (define sample (f x-min x-max (animated-samples samples)
-                    y-min y-max (animated-samples samples)))
+  (match-define (vector x-ivl y-ivl z-ivl) (send area get-bounds-rect))
+  (match-define (ivl x-min x-max) x-ivl)
+  (match-define (ivl y-min y-max) y-ivl)
+  (match-define (ivl z-min z-max) z-ivl)
+  (define num (animated-samples samples))
+  (define sample (f (vector x-ivl y-ivl) (vector num num)))
   ;; can't use the actual z ticks because some or all could be collapsed
   (match-define (list (tick zs _ labels) ...) (contour-ticks (plot-z-ticks) z-min z-max levels #f))
   
@@ -101,8 +108,11 @@
           [#:alphas alphas (alphas/c (listof real?)) (contour-alphas)]
           [#:label label (or/c string? #f) #f]
           ) renderer3d?
-  (define g (2d-function->sampler f))
-  (renderer3d (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max))
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (define z-ivl (ivl z-min z-max))
+  (define g (2d-function->sampler f (vector x-ivl y-ivl)))
+  (renderer3d (vector x-ivl y-ivl z-ivl)
               (surface3d-bounds-fun g samples)
               default-ticks-fun
               (contours3d-render-proc g levels samples colors widths styles alphas label)))
@@ -114,10 +124,12 @@
           f levels samples colors styles line-colors line-widths line-styles
           contour-colors contour-widths contour-styles alphas label)
          area)
-  (match-define (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max))
-    (send area get-bounds-rect))
-  (define sample (f x-min x-max (animated-samples samples)
-                    y-min y-max (animated-samples samples)))
+  (match-define (vector x-ivl y-ivl z-ivl) (send area get-bounds-rect))
+  (match-define (ivl x-min x-max) x-ivl)
+  (match-define (ivl y-min y-max) y-ivl)
+  (match-define (ivl z-min z-max) z-ivl)
+  (define num (animated-samples samples))
+  (define sample (f (vector x-ivl y-ivl) (vector num num)))
   ;; can't use the actual z ticks because some or all could be collapsed
   (match-define (list (tick zs _ labels) ...) (contour-ticks (plot-z-ticks) z-min z-max levels #t))
   
@@ -193,8 +205,11 @@
           [#:alphas alphas (alphas/c (listof ivl?)) (contour-interval-alphas)]
           [#:label label (or/c string? #f) #f]
           ) renderer3d?
-  (define g (2d-function->sampler f))
-  (renderer3d (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max))
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (define z-ivl (ivl z-min z-max))
+  (define g (2d-function->sampler f (vector x-ivl y-ivl)))
+  (renderer3d (vector x-ivl y-ivl z-ivl)
               (surface3d-bounds-fun g samples)
               default-ticks-fun
               (contour-intervals3d-render-proc g levels samples colors styles
diff --git a/collects/plot/plot3d/isosurface.rkt b/collects/plot/plot3d/isosurface.rkt
index c0a016a79c..3c2e153aa3 100644
--- a/collects/plot/plot3d/isosurface.rkt
+++ b/collects/plot/plot3d/isosurface.rkt
@@ -13,11 +13,12 @@
 (define ((isosurface3d-render-proc
           f d samples color style line-color line-width line-style alpha label)
          area)
-  (match-define (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max))
-    (send area get-bounds-rect))
-  (define sample (f x-min x-max (animated-samples samples)
-                    y-min y-max (animated-samples samples)
-                    z-min z-max (animated-samples samples)))
+  (match-define (vector x-ivl y-ivl z-ivl) (send area get-bounds-rect))
+  (match-define (ivl x-min x-max) x-ivl)
+  (match-define (ivl y-min y-max) y-ivl)
+  (match-define (ivl z-min z-max) z-ivl)
+  (define num (animated-samples samples))
+  (define sample (f (vector x-ivl y-ivl z-ivl) (vector num num num)))
   (match-define (3d-sample xs ys zs dsss d-min d-max) sample)
   
   (send area put-alpha alpha)
@@ -50,8 +51,11 @@
                        [#:alpha alpha (real-in 0 1) (surface-alpha)]
                        [#:label label (or/c string? #f) #f]
                        ) renderer3d?
-  (define g (3d-function->sampler f))
-  (renderer3d (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max)) #f default-ticks-fun
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (define z-ivl (ivl z-min z-max))
+  (define g (3d-function->sampler f (vector x-ivl y-ivl z-ivl)))
+  (renderer3d (vector x-ivl y-ivl z-ivl) #f default-ticks-fun
               (isosurface3d-render-proc
                g d samples color style line-color line-width line-style alpha label)))
 
@@ -61,11 +65,12 @@
 (define ((isosurfaces3d-render-proc f rd-min rd-max levels samples colors styles
                                     line-colors line-widths line-styles alphas label)
          area)
-  (match-define (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max))
-    (send area get-bounds-rect))
-  (define sample (f x-min x-max (animated-samples samples)
-                    y-min y-max (animated-samples samples)
-                    z-min z-max (animated-samples samples)))
+  (match-define (vector x-ivl y-ivl z-ivl) (send area get-bounds-rect))
+  (match-define (ivl x-min x-max) x-ivl)
+  (match-define (ivl y-min y-max) y-ivl)
+  (match-define (ivl z-min z-max) z-ivl)
+  (define num (animated-samples samples))
+  (define sample (f (vector x-ivl y-ivl z-ivl) (vector num num num)))
   (match-define (3d-sample xs ys zs dsss fd-min fd-max) sample)
   
   (define d-min (if rd-min rd-min fd-min))
@@ -103,7 +108,6 @@
            (send area put-polygons polys
                  (vector (* 1/2 (+ xa xb)) (* 1/2 (+ ya yb)) (* 1/2 (+ za zb)))))))))
   
-  
   (cond
     [(and label (not (empty? ds)))  (rectangle-legend-entries
                                      label ds colors styles line-colors line-widths line-styles)]
@@ -125,8 +129,11 @@
           [#:alphas alphas (alphas/c (listof real?)) (isosurface-alphas)]
           [#:label label (or/c string? #f) #f]
           ) renderer3d?
-  (define g (3d-function->sampler f))
-  (renderer3d (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max)) #f default-ticks-fun
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (define z-ivl (ivl z-min z-max))
+  (define g (3d-function->sampler f (vector x-ivl y-ivl z-ivl)))
+  (renderer3d (vector x-ivl y-ivl z-ivl) #f default-ticks-fun
               (isosurfaces3d-render-proc g d-min d-max levels samples colors styles
                                          line-colors line-widths line-styles alphas
                                          label)))
@@ -135,11 +142,12 @@
 
 (define ((polar3d-render-proc f g samples color style line-color line-width line-style alpha label)
          area)
-  (match-define (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max))
-    (send area get-bounds-rect))
-  (define sample (g x-min x-max (animated-samples samples)
-                    y-min y-max (animated-samples samples)
-                    z-min z-max (animated-samples samples)))
+  (match-define (vector x-ivl y-ivl z-ivl) (send area get-bounds-rect))
+  (match-define (ivl x-min x-max) x-ivl)
+  (match-define (ivl y-min y-max) y-ivl)
+  (match-define (ivl z-min z-max) z-ivl)
+  (define num (animated-samples samples))
+  (define sample (g (vector x-ivl y-ivl z-ivl) (vector num num num)))
   (match-define (3d-sample xs ys zs dsss d-min d-max) sample)
   
   (define (draw-cube xa xb ya yb za zb d d1 d2 d3 d4 d5 d6 d7 d8)
@@ -218,9 +226,12 @@
                [y-max  (if y-max y-max (apply max* rys))]
                [z-min  (if z-min z-min (apply min* rzs))]
                [z-max  (if z-max z-max (apply max* rzs))])
+           (define x-ivl (ivl x-min x-max))
+           (define y-ivl (ivl y-min y-max))
+           (define z-ivl (ivl z-min z-max))
            (define new-f (2d-polar->3d-function f))
-           (define g (3d-function->sampler new-f))
-           (renderer3d (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max)) #f
+           (define g (3d-function->sampler new-f (vector x-ivl y-ivl z-ivl)))
+           (renderer3d (vector x-ivl y-ivl z-ivl) #f
                        default-ticks-fun
                        (polar3d-render-proc new-f g samples color style
                                             line-color line-width line-style alpha label)))]))
diff --git a/collects/plot/plot3d/surface.rkt b/collects/plot/plot3d/surface.rkt
index 1566e7f29d..355bb4fb1c 100644
--- a/collects/plot/plot3d/surface.rkt
+++ b/collects/plot/plot3d/surface.rkt
@@ -11,11 +11,14 @@
 
 (define ((surface3d-render-proc f samples color style line-color line-width line-style alpha label)
          area)
-  (match-define (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max))
-    (send area get-bounds-rect))
-  (define sample (f x-min x-max (animated-samples samples)
-                    y-min y-max (animated-samples samples)))
+  (match-define (vector x-ivl y-ivl z-ivl) (send area get-bounds-rect))
+  (define num (animated-samples samples))
+  (define sample (f (vector x-ivl y-ivl) (vector num num)))
   
+  (match-define (ivl x-min x-max) x-ivl)
+  (match-define (ivl y-min y-max) y-ivl)
+  (match-define (ivl z-min z-max) z-ivl)
+
   (send area put-alpha alpha)
   (send area put-brush color style)
   (send area put-pen line-color line-width line-style)
@@ -43,8 +46,11 @@
           [#:alpha alpha (real-in 0 1) (surface-alpha)]
           [#:label label (or/c string? #f) #f]
           ) renderer3d?
-  (define g (2d-function->sampler f))
-  (renderer3d (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max))
+  (define x-ivl (ivl x-min x-max))
+  (define y-ivl (ivl y-min y-max))
+  (define z-ivl (ivl z-min z-max))
+  (define g (2d-function->sampler f (vector x-ivl y-ivl)))
+  (renderer3d (vector x-ivl y-ivl z-ivl)
               (surface3d-bounds-fun g samples)
               default-ticks-fun
               (surface3d-render-proc g samples color style
diff --git a/collects/plot/scribblings/utils.scrbl b/collects/plot/scribblings/utils.scrbl
index c9bd25e349..866c6d7db6 100644
--- a/collects/plot/scribblings/utils.scrbl
+++ b/collects/plot/scribblings/utils.scrbl
@@ -461,6 +461,9 @@ Use this to construct inputs for @(racket rectangles) and @(racket rectangles3d)
 @examples[#:eval plot-eval (bounds->intervals (linear-seq 0 1 5))]
 }
 
+@doc-apply[clamp-real]{
+}
+
 @;----------------------------------------------------------------------------------------------------
 @;{
 @subsection[#:tag "math.rectangles"]{Rectangles and Rectangle Functions}
diff --git a/collects/plot/tests/low-level-tests.rkt b/collects/plot/tests/low-level-tests.rkt
old mode 100755
new mode 100644