diff --git a/collects/plot/common/contract.rkt b/collects/plot/common/contract.rkt
index e88210ad09..be93e9a1e7 100644
--- a/collects/plot/common/contract.rkt
+++ b/collects/plot/common/contract.rkt
@@ -75,13 +75,3 @@
 
 (defcontract alphas/c (or/c (listof (real-in 0 1))
                             ((listof real?) . -> . (listof (real-in 0 1)))))
-
-(defcontract bounding-box-corner/c
-  (or/c (vector/c (or/c real? #f) (or/c real? #f))
-        (vector/c (or/c real? #f) (or/c real? #f) (or/c real? #f))))
-
-(defcontract bounds-function/c
-  (bounding-box-corner/c
-   bounding-box-corner/c
-   . -> . (values bounding-box-corner/c
-                  bounding-box-corner/c)))
diff --git a/collects/plot/common/math.rkt b/collects/plot/common/math.rkt
index 41887f2a51..c30bb174b4 100644
--- a/collects/plot/common/math.rkt
+++ b/collects/plot/common/math.rkt
@@ -14,7 +14,7 @@
 (defproc (infinite? [x any/c]) boolean?
   (and (flonum? x) (or (unsafe-fl= x +inf.0) (unsafe-fl= x -inf.0))))
 
-(defproc (special? [x any/c]) boolean?
+(defproc (special-real? [x any/c]) boolean?
   (and (flonum? x) (or (unsafe-fl= x +inf.0) (unsafe-fl= x -inf.0) (eqv? x +nan.0))))
 
 (defproc (flblend [x flonum?] [y flonum?] [α flonum?]) flonum?
@@ -57,8 +57,8 @@
 ;; ===================================================================================================
 ;; Reals
 
-(defproc (regular? [x any/c]) boolean?
-  (and (real? x) (not (special? x))))
+(defproc (regular-real? [x any/c]) boolean?
+  (and (real? x) (not (special-real? x))))
 
 (define equal?*
   (case-lambda
@@ -197,6 +197,38 @@
 ;; ===================================================================================================
 ;; Vectors
 
+(define vector-andmap
+  (case-lambda
+    [(f v)  (let/ec break
+              (for ([e  (in-vector v)])
+                (unless (f e) (break #f)))
+              #t)]
+    [(f v . vs)  (define ns (cons (vector-length v) (map vector-length vs)))
+                 (unless (apply equal?* ns)
+                   (error 'vector-andmap "all vectors must have same size; arguments were ~e ~e ~e"
+                          f v (string-join (map (λ (v) (format "~e" v)) vs) " ")))
+                 (let/ec break
+                   (define ess (apply map list (map vector->list vs)))
+                   (for ([e  (in-vector v)] [es  (in-list ess)])
+                     (when (not (apply f e es)) (break #f)))
+                   #t)]))
+
+(define vector-ormap
+  (case-lambda
+    [(f v)  (let/ec break
+              (for ([e  (in-vector v)])
+                (when (f e) (break #t)))
+              #f)]
+    [(f v . vs)  (define ns (cons (vector-length v) (map vector-length vs)))
+                 (unless (apply equal?* ns)
+                   (error 'vector-andmap "all vectors must have same size; arguments were ~e ~e ~e"
+                          f v (string-join (map (λ (v) (format "~e" v)) vs) " ")))
+                 (let/ec break
+                   (define ess (apply map list (map vector->list vs)))
+                   (for ([e  (in-vector v)] [es  (in-list ess)])
+                     (when (apply f e es) (break #t)))
+                   #f)]))
+
 (defproc (vcross [v1 (vector/c real? real? real?)] [v2 (vector/c real? real? real?)]
                  ) (vector/c real? real? real?)
   (match v1
@@ -206,25 +238,25 @@
         (vector (- (* y1 z2) (* z1 y2))
                 (- (* z1 x2) (* x1 z2))
                 (- (* x1 y2) (* y1 x2)))]
-       [_  (raise-type-error 'vcross "vector of 3 reals" 1 v1 v2)])]
-    [_  (raise-type-error 'vcross "vector of 3 reals" 0 v1 v2)]))
+       [_  (raise-type-error 'vcross "vector of 3 real numbers" 1 v1 v2)])]
+    [_  (raise-type-error 'vcross "vector of 3 real numbers" 0 v1 v2)]))
 
 (defproc (vcross2 [v1 (vector/c real? real?)] [v2 (vector/c real? real?)]) real?
   (match v1
     [(vector (? real? x1) (? real? y1))
      (match v2
        [(vector (? real? x2) (? real? y2))  (- (* x1 y2) (* y1 x2))]
-       [_  (raise-type-error 'vcross "vector of 2 reals" 1 v1 v2)])]
-    [_  (raise-type-error 'vcross "vector of 2 reals" 0 v1 v2)]))
+       [_  (raise-type-error 'vcross "vector of 2 real numbers" 1 v1 v2)])]
+    [_  (raise-type-error 'vcross "vector of 2 real numbers" 0 v1 v2)]))
 
 (define-syntax-rule (vmap name f v)
   (let ()
     (unless (vector? v)
-      (raise-type-error name "vector of reals" v))
+      (raise-type-error name "vector of real numbers" v))
     (define n (vector-length v))
     (for/vector #:length n ([x  (in-vector v)])
       (cond [(real? x)    (f x)]
-            [else  (raise-type-error name "vector of real" v)]))))
+            [else  (raise-type-error name "vector of real numbers" v)]))))
 
 (define-syntax-rule (unrolled-vmap name f v)
   (let ()
@@ -236,29 +268,29 @@
 (define-syntax-rule (vmap2 name f v1 v2)
   (let ()
     (unless (vector? v1)
-      (raise-type-error name "vector of reals" 0 v1 v2))
+      (raise-type-error name "vector of real numbers" 0 v1 v2))
     (unless (vector? v2)
-      (raise-type-error name "vector of reals" 1 v1 v2))
+      (raise-type-error name "vector of real numbers" 1 v1 v2))
     (define n (vector-length v1))
     (unless (= n (vector-length v2))
-      (raise-type-error name (format "vector of ~a reals" n) 1 v1 v2))
+      (raise-type-error name (format "vector of ~a real numbers" n) 1 v1 v2))
     (for/vector #:length n ([x  (in-vector v1)] [y  (in-vector v2)])
       (if (real? x)
           (if (real? y)
               (f x y)
-              (raise-type-error name "vector of real" 1 v1 v2))
-          (raise-type-error name "vector of real" 0 v1 v2)))))
+              (raise-type-error name "vector of real numbers" 1 v1 v2))
+          (raise-type-error name "vector of real numbers" 0 v1 v2)))))
 
 (define-syntax-rule (unrolled-vmap2 name f v1 v2)
   (match v1
     [(vector (? real? x1) (? real? y1))
      (match v2
        [(vector (? real? x2) (? real? y2))  (vector (f x1 x2) (f y1 y2))]
-       [_  (raise-type-error name "vector of 2 reals" 1 v1 v2)])]
+       [_  (raise-type-error name "vector of 2 real numbers" 1 v1 v2)])]
     [(vector (? real? x1) (? real? y1) (? real? z1))
      (match v2
        [(vector (? real? x2) (? real? y2) (? real? z2))  (vector (f x1 x2) (f y1 y2) (f z1 z2))]
-       [_  (raise-type-error name "vector of 3 reals" 1 v1 v2)])]
+       [_  (raise-type-error name "vector of 3 real numbers" 1 v1 v2)])]
     [_  (vmap2 name f v1 v2)]))
 
 (defproc (v+ [v1 (vectorof real?)] [v2 (vectorof real?)]) (vectorof real?)
@@ -285,10 +317,10 @@
     [(vector (? real? x) (? real? y))              (+ (* x x) (* y y))]
     [(vector (? real? x) (? real? y) (? real? z))  (+ (* x x) (* y y) (* z z))]
     [_  (unless (vector? v)
-          (raise-type-error 'vmag^2 "vector of reals" v))
+          (raise-type-error 'vmag^2 "vector of real numbers" v))
         (for/fold ([mag  0]) ([x  (in-vector v)])
           (+ mag (cond [(real? x)    (* x x)]
-                       [else  (raise-type-error 'vmag^2 "vector of reals" v)])))]))
+                       [else  (raise-type-error 'vmag^2 "vector of real numbers" v)])))]))
 
 (defproc (vmag [v (vectorof real?)]) real?
   (sqrt (vmag^2 v)))
@@ -307,19 +339,19 @@
     [(vector (? real? x1) (? real? y1))
      (match v2
        [(vector (? real? x2) (? real? y2))  (+ (* x1 x2) (* y1 y2))]
-       [_  (raise-type-error 'vdot "vector of 2 reals" 1 v1 v2)])]
+       [_  (raise-type-error 'vdot "vector of 2 real numbers" 1 v1 v2)])]
     [(vector (? real? x1) (? real? y1) (? real? z1))
      (match v2
        [(vector (? real? x2) (? real? y2) (? real? z2))  (+ (* x1 x2) (* y1 y2) (* z1 z2))]
-       [_  (raise-type-error 'vdot "vector of 3 reals" 1 v1 v2)])]
+       [_  (raise-type-error 'vdot "vector of 3 real numbers" 1 v1 v2)])]
     [_  (unless (= (vector-length v1) (vector-length v2))
-          (raise-type-error 'vdot (format "vector of ~a reals" (vector-length v1)) 1 v1 v2))
+          (raise-type-error 'vdot (format "vector of ~a real numbers" (vector-length v1)) 1 v1 v2))
         (for/fold ([dot  0]) ([x1  (in-vector v1)] [x2  (in-vector v2)])
           (if (real? x1)
               (if (real? x2)
                   (+ dot (* x1 x2))
-                  (raise-type-error 'vdot "vector of real" 1 v1 v2))
-              (raise-type-error 'vdot "vector of real" 0 v1 v2)))]))
+                  (raise-type-error 'vdot "vector of real numbers" 1 v1 v2))
+              (raise-type-error 'vdot "vector of real numbers" 0 v1 v2)))]))
 
 (defproc (vcos-angle [v1 (vectorof real?)] [v2 (vectorof real?)]) real?
   (define d (vdot v1 v2))
@@ -343,31 +375,32 @@
            [(flonum? y)  (unsafe-flregular? y)]
            [(flonum? z)  (unsafe-flregular? z)]
            [else  #t])]
-    [_  (let/ec break
-          (for ([x  (in-vector v)])
-            (when (and (flonum? x) (unsafe-flspecial? x))
-              (break #f)))
-          #t)]))
+    [_  (cond [(vector-andmap real? v)  (let/ec break
+                                          (for ([x  (in-vector v)])
+                                            (when (and (flonum? x) (unsafe-flspecial? x))
+                                              (break #f)))
+                                          #t)]
+              [else  (raise-type-error 'vregular? "vector of real numbers" v)])]))
 
 (defproc (v= [v1 (vectorof real?)] [v2 (vectorof real?)]) boolean?
   (match v1
     [(vector (? real? x1) (? real? y1))
      (match v2
        [(vector (? real? x2) (? real? y2))  (and (= x1 x2) (= y1 y2))]
-       [_  (raise-type-error 'v= "vector of 2 reals" 1 v1 v2)])]
+       [_  (raise-type-error 'v= "vector of 2 real numbers" 1 v1 v2)])]
     [(vector (? real? x1) (? real? y1) (? real? z1))
      (match v2
        [(vector (? real? x2) (? real? y2) (? real? z2))  (and (= x1 x2) (= y1 y2) (= z1 z2))]
-       [_  (raise-type-error 'v= "vector of 3 reals" 1 v1 v2)])]
+       [_  (raise-type-error 'v= "vector of 3 real numbers" 1 v1 v2)])]
     [_  (unless (= (vector-length v1) (vector-length v2))
-          (raise-type-error 'v= (format "vector of ~a reals" (vector-length v1)) 1 v1 v2))
+          (raise-type-error 'v= (format "vector of ~a real numbers" (vector-length v1)) 1 v1 v2))
         (let/ec break
           (for ([x1  (in-vector v1)] [x2  (in-vector v2)])
             (if (real? x1)
                 (if (real? x2)
                     (unless (= x1 x2) (break #f))
-                    (raise-type-error 'v= "vector of real" 1 v1 v2))
-                (raise-type-error 'v= "vector of real" 0 v1 v2)))
+                    (raise-type-error 'v= "vector of real numbers" 1 v1 v2))
+                (raise-type-error 'v= "vector of real numbers" 0 v1 v2)))
           #t)]))
 
 (defproc (vcenter [vs (listof (vectorof real?))]) (vectorof real?)
@@ -455,7 +488,10 @@
 
 (defproc (ivl-regular? [i ivl?]) boolean?
   (match-define (ivl a b) i)
-  (and (regular? a) (regular? b)))
+  (and (regular-real? a) (regular-real? b)))
+
+(defproc (regular-ivl? [i any/c]) boolean?
+  (and (ivl? i) (ivl-regular? i)))
 
 (defproc (ivl-singular? [i ivl?]) boolean?
   (match-define (ivl a b) i)
@@ -515,38 +551,6 @@
 ;; ===================================================================================================
 ;; Rectangles
 
-(define vector-andmap
-  (case-lambda
-    [(f v)  (let/ec break
-              (for ([e  (in-vector v)])
-                (unless (f e) (break #f)))
-              #t)]
-    [(f v . vs)  (define ns (cons (vector-length v) (map vector-length vs)))
-                 (unless (apply equal?* ns)
-                   (error 'vector-andmap "all vectors must have same size; arguments were ~e ~e ~e"
-                          f v (string-join (map (λ (v) (format "~e" v)) vs) " ")))
-                 (let/ec break
-                   (define ess (apply map list (map vector->list vs)))
-                   (for ([e  (in-vector v)] [es  (in-list ess)])
-                     (when (not (apply f e es)) (break #f)))
-                   #t)]))
-
-(define vector-ormap
-  (case-lambda
-    [(f v)  (let/ec break
-              (for ([e  (in-vector v)])
-                (when (f e) (break #t)))
-              #f)]
-    [(f v . vs)  (define ns (cons (vector-length v) (map vector-length vs)))
-                 (unless (apply equal?* ns)
-                   (error 'vector-andmap "all vectors must have same size; arguments were ~e ~e ~e"
-                          f v (string-join (map (λ (v) (format "~e" v)) vs) " ")))
-                 (let/ec break
-                   (define ess (apply map list (map vector->list vs)))
-                   (for ([e  (in-vector v)] [es  (in-list ess)])
-                     (when (apply f e es) (break #t)))
-                   #f)]))
-
 (defproc (empty-rect [n exact-nonnegative-integer?]) (vectorof ivl?)
   (make-vector n empty-ivl))
 
diff --git a/collects/plot/common/non-renderer.rkt b/collects/plot/common/non-renderer.rkt
index 32396a032a..0d4d2e2376 100644
--- a/collects/plot/common/non-renderer.rkt
+++ b/collects/plot/common/non-renderer.rkt
@@ -35,11 +35,13 @@
 (defproc (z-ticks [ts (listof tick?)] [#:far? far? boolean? #f]) non-renderer?
   (non-renderer #f #f (z-ticks-fun ts far?)))
 
-(defproc (invisible-box [x-min (or/c real? #f)] [x-max (or/c real? #f)]
-                        [y-min (or/c real? #f)] [y-max (or/c real? #f)]) non-renderer?
+(defproc (invisible-box [x-min (or/c regular-real? #f)] [x-max (or/c regular-real? #f)]
+                        [y-min (or/c regular-real? #f)] [y-max (or/c regular-real? #f)]
+                        ) non-renderer?
   (non-renderer (vector (ivl x-min x-max) (ivl y-min y-max)) #f #f))
 
-(defproc (invisible-box3d [x-min (or/c real? #f)] [x-max (or/c real? #f)]
-                          [y-min (or/c real? #f)] [y-max (or/c real? #f)]
-                          [z-min (or/c real? #f)] [z-max (or/c real? #f)]) non-renderer?
+(defproc (invisible-box3d [x-min (or/c regular-real? #f)] [x-max (or/c regular-real? #f)]
+                          [y-min (or/c regular-real? #f)] [y-max (or/c regular-real? #f)]
+                          [z-min (or/c regular-real? #f)] [z-max (or/c regular-real? #f)]
+                          ) non-renderer?
   (non-renderer (vector (ivl x-min x-max) (ivl y-min y-max) (ivl z-min z-max)) #f #f))
diff --git a/collects/plot/common/sample.rkt b/collects/plot/common/sample.rkt
index 74dc285c29..6f9dda8892 100644
--- a/collects/plot/common/sample.rkt
+++ b/collects/plot/common/sample.rkt
@@ -9,7 +9,8 @@
 
 (provide (all-defined-out))
 
-(defproc (build-linear-seq [start real?] [step real?] [num exact-nonnegative-integer?]) (listof real?)
+(defproc (build-linear-seq [start real?] [step real?]
+                           [num exact-nonnegative-integer?]) (listof real?)
   (for/list ([n  (in-range num)])
     (+ start (* n step))))
 
@@ -96,7 +97,7 @@
                  (λ ()
                    (define xs (nonlinear-seq x-min x-max x-samples tx))
                    (define ys (map* f xs))
-                   (define rys (filter regular? ys))
+                   (define rys (filter regular-real? ys))
                    (define-values (y-min y-max)
                      (cond [(empty? rys)  (values #f #f)]
                            [else  (values (apply min* rys) (apply max* rys))]))
@@ -119,7 +120,7 @@
                    (define zss (for/vector #:length y-samples ([y  (in-list ys)])
                                  (for/vector #:length x-samples ([x  (in-list xs)])
                                    (let ([z  (f x y)])
-                                     (when (regular? z)
+                                     (when (regular-real? z)
                                        (unless (and z-min (z . >= . z-min)) (set! z-min z))
                                        (unless (and z-max (z . <= . z-max)) (set! z-max z)))
                                      z))))
@@ -148,7 +149,7 @@
                                   (for/vector #:length y-samples ([y  (in-list ys)])
                                     (for/vector #:length x-samples ([x  (in-list xs)])
                                       (let ([d  (f x y z)])
-                                        (when (regular? d)
+                                        (when (regular-real? d)
                                           (unless (and d-min (d . >= . d-min)) (set! d-min d))
                                           (unless (and d-max (d . <= . d-max)) (set! d-max d)))
                                         d)))))
diff --git a/collects/plot/contracted/math.rkt b/collects/plot/contracted/math.rkt
index 1715977c2d..40e104d18f 100644
--- a/collects/plot/contracted/math.rkt
+++ b/collects/plot/contracted/math.rkt
@@ -5,10 +5,10 @@
 (require "../common/math.rkt")
 (provide equal?*
          ;; Flonums
-         nan? infinite? special?
+         nan? infinite? special-real?
          flblend flatan2 flsum flmodulo fldistance
          ;; Reals
-         regular?
+         regular-real?
          min* max* degrees->radians radians->degrees blend atan2 sum real-modulo distance
          floor-log/base ceiling-log/base
          polar->cartesian 3d-polar->3d-cartesian
@@ -19,7 +19,7 @@
 (provide (contract-out (struct ivl ([min (or/c real? #f)] [max (or/c real? #f)]))
                        [ivl-meet  (->* () () #:rest (listof ivl?) ivl?)]
                        [ivl-join  (->* () () #:rest (listof ivl?) ivl?)])
-         empty-ivl unknown-ivl
+         empty-ivl unknown-ivl regular-ivl?
          (activate-contract-out
           ivl-empty? ivl-known? ivl-regular? ivl-singular? ivl-length ivl-center ivl-zero-length?
           ivl-inexact->exact ivl-contains? bounds->intervals))
diff --git a/collects/plot/contracted/sample.rkt b/collects/plot/contracted/sample.rkt
index 02da226644..c48b9cd9cb 100644
--- a/collects/plot/contracted/sample.rkt
+++ b/collects/plot/contracted/sample.rkt
@@ -2,22 +2,23 @@
 
 (require racket/contract unstable/latent-contract)
 
-(require "../common/sample.rkt")
+(require "../common/sample.rkt"
+         "../common/math.rkt")
 (provide (contract-out (struct sample ([xs (listof real?)]
                                        [ys (listof real?)]
-                                       [y-min (or/c real? #f)]
-                                       [y-max (or/c real? #f)]))
+                                       [y-min (or/c regular-real? #f)]
+                                       [y-max (or/c regular-real? #f)]))
                        (struct 2d-sample ([xs (listof real?)]
                                           [ys (listof real?)]
                                           [zss (vectorof (vectorof real?))]
-                                          [z-min (or/c real? #f)]
-                                          [z-max (or/c real? #f)]))
+                                          [z-min (or/c regular-real? #f)]
+                                          [z-max (or/c regular-real? #f)]))
                        (struct 3d-sample ([xs (listof real?)]
                                           [ys (listof real?)]
                                           [zs (listof real?)]
                                           [dsss (vectorof (vectorof (vectorof real?)))]
-                                          [d-min (or/c real? #f)]
-                                          [d-max (or/c real? #f)])))
+                                          [d-min (or/c regular-real? #f)]
+                                          [d-max (or/c regular-real? #f)])))
          (activate-contract-out build-linear-seq linear-seq linear-seq* nonlinear-seq
                                 sampler/c 2d-sampler/c 3d-sampler/c
                                 make-function->sampler
diff --git a/collects/plot/plot2d/contour.rkt b/collects/plot/plot2d/contour.rkt
index 50a4479447..7ff7c8db6c 100644
--- a/collects/plot/plot2d/contour.rkt
+++ b/collects/plot/plot2d/contour.rkt
@@ -40,8 +40,10 @@
 
 (defproc (isoline
           [f (real? real? . -> . real?)] [z real?]
-          [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-          [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
+          [x-min (or/c regular-real? #f) #f]
+          [x-max (or/c regular-real? #f) #f]
+          [y-min (or/c regular-real? #f) #f]
+          [y-max (or/c regular-real? #f) #f]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (contour-samples)]
           [#:color color plot-color/c (line-color)]
           [#:width width (>=/c 0) (line-width)]
@@ -96,8 +98,10 @@
 
 (defproc (contours
           [f (real? real? . -> . real?)]
-          [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-          [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
+          [x-min (or/c regular-real? #f) #f]
+          [x-max (or/c regular-real? #f) #f]
+          [y-min (or/c regular-real? #f) #f]
+          [y-max (or/c regular-real? #f) #f]
           [#:levels levels (or/c 'auto exact-positive-integer? (listof real?)) (contour-levels)]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (contour-samples)]
           [#:colors colors plot-colors/c (contour-colors)]
@@ -180,8 +184,10 @@
 
 (defproc (contour-intervals
           [f (real? real? . -> . real?)]
-          [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-          [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
+          [x-min (or/c regular-real? #f) #f]
+          [x-max (or/c regular-real? #f) #f]
+          [y-min (or/c regular-real? #f) #f]
+          [y-max (or/c regular-real? #f) #f]
           [#:levels levels (or/c 'auto exact-positive-integer? (listof real?)) (contour-levels)]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (contour-samples)]
           [#:colors colors plot-colors/c (contour-interval-colors)]
diff --git a/collects/plot/plot2d/interval.rkt b/collects/plot/plot2d/interval.rkt
index ddf249ba1e..81ca37ce0f 100644
--- a/collects/plot/plot2d/interval.rkt
+++ b/collects/plot/plot2d/interval.rkt
@@ -35,8 +35,10 @@
 (defproc (lines-interval
           [v1s (listof (vector/c real? real?))]
           [v2s (listof (vector/c real? real?))]
-          [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) #f]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) #f]
+          [#:y-max y-max (or/c regular-real? #f) #f]
           [#:color color plot-color/c (interval-color)]
           [#:style style plot-brush-style/c (interval-style)]
           [#:line1-color line1-color plot-color/c (interval-line1-color)]
@@ -67,8 +69,10 @@
           [f1 (real? . -> . (vector/c real? real?))]
           [f2 (real? . -> . (vector/c real? real?))]
           [t-min real?] [t-max real?]
-          [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) #f]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) #f]
+          [#:y-max y-max (or/c regular-real? #f) #f]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
           [#:color color plot-color/c (interval-color)]
           [#:style style plot-brush-style/c (interval-style)]
@@ -93,8 +97,10 @@
 (defproc (polar-interval
           [f1 (real? . -> . real?)] [f2 (real? . -> . real?)]
           [θ-min real? 0] [θ-max real? (* 2 pi)]
-          [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) #f]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) #f]
+          [#:y-max y-max (or/c regular-real? #f) #f]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
           [#:color color plot-color/c (interval-color)]
           [#:style style plot-brush-style/c (interval-style)]
@@ -139,8 +145,10 @@
 
 (defproc (function-interval
           [f1 (real? . -> . real?)] [f2 (real? . -> . real?)]
-          [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+          [x-min (or/c regular-real? #f) #f]
+          [x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) #f]
+          [#:y-max y-max (or/c regular-real? #f) #f]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
           [#:color color plot-color/c (interval-color)]
           [#:style style plot-brush-style/c (interval-style)]
@@ -185,8 +193,10 @@
 
 (defproc (inverse-interval
           [f1 (real? . -> . real?)] [f2 (real? . -> . real?)]
-          [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
-          [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
+          [y-min (or/c regular-real? #f) #f]
+          [y-max (or/c regular-real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) #f]
+          [#:x-max x-max (or/c regular-real? #f) #f]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
           [#:color color plot-color/c (interval-color)]
           [#:style style plot-brush-style/c (interval-style)]
diff --git a/collects/plot/plot2d/kde.rkt b/collects/plot/plot2d/kde.rkt
index 3495221d38..2e9c828e94 100644
--- a/collects/plot/plot2d/kde.rkt
+++ b/collects/plot/plot2d/kde.rkt
@@ -82,8 +82,8 @@
 (define series-terms 9)
 
 (defproc (kde [xs (listof real?)] [h real?]) (values mapped-function?
-                                                     (or/c real? #f)
-                                                     (or/c real? #f))
+                                                     (or/c regular-real? #f)
+                                                     (or/c regular-real? #f))
   (if (empty? xs)
       (values (mapped-function (λ (y) 0) (λ (ys) (map (λ _ 0.0) ys))) #f #f)
       (let* ([xs  (list->vector (sort (map exact->inexact xs) fl<))]
@@ -132,8 +132,10 @@
         (values (mapped-function (λ (x) (first (fmap (list x)))) fmap) x-min x-max))))
 
 (defproc (density [xs (listof real?)] [bw-adjust real? 1]
-                  [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                  [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+                  [#:x-min x-min (or/c regular-real? #f) #f]
+                  [#:x-max x-max (or/c regular-real? #f) #f]
+                  [#:y-min y-min (or/c regular-real? #f) #f]
+                  [#:y-max y-max (or/c regular-real? #f) #f]
                   [#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
                   [#:color color plot-color/c (line-color)]
                   [#:width width (>=/c 0) (line-width)]
diff --git a/collects/plot/plot2d/line.rkt b/collects/plot/plot2d/line.rkt
index ff4560ce58..37bd3138b9 100644
--- a/collects/plot/plot2d/line.rkt
+++ b/collects/plot/plot2d/line.rkt
@@ -20,8 +20,10 @@
         [else   empty]))
 
 (defproc (lines [vs  (listof (vector/c real? real?))]
-                [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+                [#:x-min x-min (or/c regular-real? #f) #f]
+                [#:x-max x-max (or/c regular-real? #f) #f]
+                [#:y-min y-min (or/c regular-real? #f) #f]
+                [#:y-max y-max (or/c regular-real? #f) #f]
                 [#:color color plot-color/c (line-color)]
                 [#:width width (>=/c 0) (line-width)]
                 [#:style style plot-pen-style/c (line-style)]
@@ -40,9 +42,11 @@
                        (lines-render-proc vs color width style alpha label)))]))
 
 (defproc (parametric [f (real? . -> . (vector/c real? real?))]
-                     [t-min real?] [t-max real?]
-                     [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                     [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+                     [t-min regular-real?] [t-max regular-real?]
+                     [#:x-min x-min (or/c regular-real? #f) #f]
+                     [#:x-max x-max (or/c regular-real? #f) #f]
+                     [#:y-min y-min (or/c regular-real? #f) #f]
+                     [#:y-max y-max (or/c regular-real? #f) #f]
                      [#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
                      [#:color color plot-color/c (line-color)]
                      [#:width width (>=/c 0) (line-width)]
@@ -57,8 +61,10 @@
 
 (defproc (polar [f (real? . -> . real?)]
                 [θ-min real? 0] [θ-max real? (* 2 pi)]
-                [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+                [#:x-min x-min (or/c regular-real? #f) #f]
+                [#:x-max x-max (or/c regular-real? #f) #f]
+                [#:y-min y-min (or/c regular-real? #f) #f]
+                [#:y-max y-max (or/c regular-real? #f) #f]
                 [#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
                 [#:color color plot-color/c (line-color)]
                 [#:width width (>=/c 0) (line-width)]
@@ -87,8 +93,10 @@
         [else   empty]))
 
 (defproc (function [f (real? . -> . real?)]
-                   [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-                   [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+                   [x-min (or/c regular-real? #f) #f]
+                   [x-max (or/c regular-real? #f) #f]
+                   [#:y-min y-min (or/c regular-real? #f) #f]
+                   [#:y-max y-max (or/c regular-real? #f) #f]
                    [#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
                    [#:color color plot-color/c (line-color)]
                    [#:width width (>=/c 0) (line-width)]
@@ -117,8 +125,10 @@
         [else   empty]))
 
 (defproc (inverse [f (real? . -> . real?)]
-                  [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
-                  [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
+                  [y-min (or/c regular-real? #f) #f]
+                  [y-max (or/c regular-real? #f) #f]
+                  [#:x-min x-min (or/c regular-real? #f) #f]
+                  [#:x-max x-max (or/c regular-real? #f) #f]
                   [#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
                   [#:color color plot-color/c (line-color)]
                   [#:width width (>=/c 0) (line-width)]
diff --git a/collects/plot/plot2d/plot.rkt b/collects/plot/plot2d/plot.rkt
index 8eab65d4a2..fc9f1aa400 100644
--- a/collects/plot/plot2d/plot.rkt
+++ b/collects/plot/plot2d/plot.rkt
@@ -27,10 +27,10 @@
 (defproc (plot/dc [renderer-tree (treeof (or/c renderer2d? non-renderer?))]
                   [dc (is-a?/c dc<%>)]
                   [x real?] [y real?] [width (>=/c 0)] [height (>=/c 0)]
-                  [#:x-min x-min (or/c real? #f) #f]
-                  [#:x-max x-max (or/c real? #f) #f]
-                  [#:y-min y-min (or/c real? #f) #f]
-                  [#:y-max y-max (or/c real? #f) #f]
+                  [#:x-min x-min (or/c regular-real? #f) #f]
+                  [#:x-max x-max (or/c regular-real? #f) #f]
+                  [#:y-min y-min (or/c regular-real? #f) #f]
+                  [#:y-max y-max (or/c regular-real? #f) #f]
                   [#:title title (or/c string? #f) (plot-title)]
                   [#:x-label x-label (or/c string? #f) (plot-x-label)]
                   [#:y-label y-label (or/c string? #f) (plot-y-label)]
@@ -89,8 +89,10 @@
 
 ;; Plot to a bitmap
 (defproc (plot-bitmap [renderer-tree (treeof (or/c renderer2d? non-renderer?))]
-                      [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                      [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+                      [#:x-min x-min (or/c regular-real? #f) #f]
+                      [#:x-max x-max (or/c regular-real? #f) #f]
+                      [#:y-min y-min (or/c regular-real? #f) #f]
+                      [#:y-max y-max (or/c regular-real? #f) #f]
                       [#:width width exact-positive-integer? (plot-width)]
                       [#:height height exact-positive-integer? (plot-height)]
                       [#:title title (or/c string? #f) (plot-title)]
@@ -106,8 +108,10 @@
   bm)
 
 (defproc (plot-pict [renderer-tree (treeof (or/c renderer2d? non-renderer?))]
-                    [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                    [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+                    [#:x-min x-min (or/c regular-real? #f) #f]
+                    [#:x-max x-max (or/c regular-real? #f) #f]
+                    [#:y-min y-min (or/c regular-real? #f) #f]
+                    [#:y-max y-max (or/c regular-real? #f) #f]
                     [#:width width exact-positive-integer? (plot-width)]
                     [#:height height exact-positive-integer? (plot-height)]
                     [#:title title (or/c string? #f) (plot-title)]
@@ -126,8 +130,10 @@
 
 ;; Plot to a snip
 (defproc (plot-snip [renderer-tree (treeof (or/c renderer2d? non-renderer?))]
-                    [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                    [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+                    [#:x-min x-min (or/c regular-real? #f) #f]
+                    [#:x-max x-max (or/c regular-real? #f) #f]
+                    [#:y-min y-min (or/c regular-real? #f) #f]
+                    [#:y-max y-max (or/c regular-real? #f) #f]
                     [#:width width exact-positive-integer? (plot-width)]
                     [#:height height exact-positive-integer? (plot-height)]
                     [#:title title (or/c string? #f) (plot-title)]
@@ -144,8 +150,10 @@
 
 ;; Plot to a frame
 (defproc (plot-frame [renderer-tree (treeof (or/c renderer2d? non-renderer?))]
-                     [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                     [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+                     [#:x-min x-min (or/c regular-real? #f) #f]
+                     [#:x-max x-max (or/c regular-real? #f) #f]
+                     [#:y-min y-min (or/c regular-real? #f) #f]
+                     [#:y-max y-max (or/c regular-real? #f) #f]
                      [#:width width exact-positive-integer? (plot-width)]
                      [#:height height exact-positive-integer? (plot-height)]
                      [#:title title (or/c string? #f) (plot-title)]
@@ -164,8 +172,10 @@
 (defproc (plot-file [renderer-tree (treeof (or/c renderer2d? non-renderer?))]
                     [output (or/c path-string? output-port?)]
                     [kind (one-of/c 'auto 'png 'jpeg 'xmb 'xpm 'bmp 'ps 'pdf 'svg) 'auto]
-                    [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                    [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+                    [#:x-min x-min (or/c regular-real? #f) #f]
+                    [#:x-max x-max (or/c regular-real? #f) #f]
+                    [#:y-min y-min (or/c regular-real? #f) #f]
+                    [#:y-max y-max (or/c regular-real? #f) #f]
                     [#:width width exact-positive-integer? (plot-width)]
                     [#:height height exact-positive-integer? (plot-height)]
                     [#:title title (or/c string? #f) (plot-title)]
@@ -205,8 +215,10 @@
 
 ;; Plot to a frame or a snip, depending on (plot-new-window?)
 (defproc (plot [renderer-tree (treeof (or/c renderer2d? non-renderer?))]
-               [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-               [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+               [#:x-min x-min (or/c regular-real? #f) #f]
+               [#:x-max x-max (or/c regular-real? #f) #f]
+               [#:y-min y-min (or/c regular-real? #f) #f]
+               [#:y-max y-max (or/c regular-real? #f) #f]
                [#:width width exact-positive-integer? (plot-width)]
                [#:height height exact-positive-integer? (plot-height)]
                [#:title title (or/c string? #f) (plot-title)]
diff --git a/collects/plot/plot2d/point.rkt b/collects/plot/plot2d/point.rkt
index 6623dfa81c..dac7624ed0 100644
--- a/collects/plot/plot2d/point.rkt
+++ b/collects/plot/plot2d/point.rkt
@@ -19,8 +19,10 @@
   (if label (point-legend-entry label sym color size line-width) empty))
 
 (defproc (points [vs  (listof (vector/c real? real?))]
-                 [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                 [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+                 [#:x-min x-min (or/c regular-real? #f) #f]
+                 [#:x-max x-max (or/c regular-real? #f) #f]
+                 [#:y-min y-min (or/c regular-real? #f) #f]
+                 [#:y-max y-max (or/c regular-real? #f) #f]
                  [#:sym sym point-sym/c (point-sym)]
                  [#:color color plot-color/c (point-color)]
                  [#:size size (>=/c 0) (point-size)]
@@ -86,8 +88,10 @@
 (defproc (vector-field
           [f (or/c (real? real? . -> . (vector/c real? real?))
                    ((vector/c real? real?) . -> . (vector/c real? real?)))]
-          [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-          [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
+          [x-min (or/c regular-real? #f) #f]
+          [x-max (or/c regular-real? #f) #f]
+          [y-min (or/c regular-real? #f) #f]
+          [y-max (or/c regular-real? #f) #f]
           [#:samples samples exact-positive-integer? (vector-field-samples)]
           [#:scale scale (or/c real? (one-of/c 'auto 'normalized)) (vector-field-scale)]
           [#:color color plot-color/c (vector-field-color)]
@@ -122,8 +126,10 @@
 
 (defproc (error-bars
           [bars (listof (vector/c real? real? real?))]
-          [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) #f]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) #f]
+          [#:y-max y-max (or/c regular-real? #f) #f]
           [#:color color plot-color/c (error-bar-color)]
           [#:line-width line-width (>=/c 0) (error-bar-line-width)]
           [#:line-style line-style plot-pen-style/c (error-bar-line-style)]
diff --git a/collects/plot/plot2d/rectangle.rkt b/collects/plot/plot2d/rectangle.rkt
index f8e3db03a3..4f8566b84f 100644
--- a/collects/plot/plot2d/rectangle.rkt
+++ b/collects/plot/plot2d/rectangle.rkt
@@ -25,8 +25,10 @@
 
 (defproc (rectangles
           [rects  (listof (vector/c ivl? ivl?))]
-          [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) #f]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) #f]
+          [#:y-max y-max (or/c regular-real? #f) #f]
           [#:color color plot-color/c (rectangle-color)]
           [#:style style plot-brush-style/c (rectangle-style)]
           [#:line-color line-color plot-color/c (rectangle-line-color)]
@@ -36,8 +38,8 @@
           [#:label label (or/c string? #f) #f]
           ) renderer2d?
   (match-define (list (vector (ivl x1s x2s) (ivl y1s y2s)) ...) rects)
-  (define rxs (filter regular? (append x1s x2s)))
-  (define rys (filter regular? (append y1s y2s)))
+  (define rxs (filter regular-real? (append x1s x2s)))
+  (define rys (filter regular-real? (append y1s y2s)))
   (cond
     [(or (empty? rxs) (empty? rys))  (renderer2d #f #f #f #f)]
     [else
@@ -55,8 +57,10 @@
 (defproc (area-histogram
           [f (real? . -> . real?)]
           [bin-bounds (listof real?)]
-          [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) 0] [#:y-max y-max (or/c real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) #f]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) 0]
+          [#:y-max y-max (or/c regular-real? #f) #f]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
           [#:color color plot-color/c (rectangle-color)]
           [#:style style plot-brush-style/c (rectangle-style)]
@@ -66,7 +70,7 @@
           [#:alpha alpha (real-in 0 1) (rectangle-alpha)]
           [#:label label (or/c string? #f) #f]
           ) renderer2d?
-  (let* ([bin-bounds  (filter regular? bin-bounds)]
+  (let* ([bin-bounds  (filter regular-real? bin-bounds)]
          [bin-bounds  (sort bin-bounds <)])
     (cond
       [((length bin-bounds) . < . 2)  (renderer2d #f #f #f #f)]
@@ -100,8 +104,10 @@
 
 (defproc (discrete-histogram
           [cat-vals (listof (vector/c any/c real?))]
-          [#:x-min x-min (or/c real? #f) 0] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) 0] [#:y-max y-max (or/c real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) 0]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) 0]
+          [#:y-max y-max (or/c regular-real? #f) #f]
           [#:gap gap (real-in 0 1) (discrete-histogram-gap)]
           [#:color color plot-color/c (rectangle-color)]
           [#:style style plot-brush-style/c (rectangle-style)]
@@ -113,7 +119,7 @@
           [#:far-ticks? far-ticks? boolean? #f]
           ) renderer2d?
   (match-define (list (vector cats ys) ...) cat-vals)
-  (define rys (filter regular? ys))
+  (define rys (filter regular-real? ys))
   (cond
     [(empty? rys)  (renderer2d #f #f #f #f)]
     [else
diff --git a/collects/plot/plot3d/contour.rkt b/collects/plot/plot3d/contour.rkt
index 2adb0f8e3a..fd59b2227b 100644
--- a/collects/plot/plot3d/contour.rkt
+++ b/collects/plot/plot3d/contour.rkt
@@ -43,9 +43,12 @@
 
 (defproc (contour3d
           [f (real? real? . -> . real?)] [z real?]
-          [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-          [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
-          [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+          [x-min (or/c regular-real? #f) #f]
+          [x-max (or/c regular-real? #f) #f]
+          [y-min (or/c regular-real? #f) #f]
+          [y-max (or/c regular-real? #f) #f]
+          [#:z-min z-min (or/c regular-real? #f) #f]
+          [#:z-max z-max (or/c regular-real? #f) #f]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (plot3d-samples)]
           [#:color color plot-color/c (line-color)]
           [#:width width (>=/c 0) (line-width)]
@@ -105,9 +108,12 @@
 
 (defproc (contours3d
           [f (real? real? . -> . real?)]
-          [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-          [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
-          [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+          [x-min (or/c regular-real? #f) #f]
+          [x-max (or/c regular-real? #f) #f]
+          [y-min (or/c regular-real? #f) #f]
+          [y-max (or/c regular-real? #f) #f]
+          [#:z-min z-min (or/c regular-real? #f) #f]
+          [#:z-max z-max (or/c regular-real? #f) #f]
           [#:levels levels (or/c 'auto exact-positive-integer? (listof real?)) (contour-levels)]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (plot3d-samples)]
           [#:colors colors plot-colors/c (contour-colors)]
@@ -179,9 +185,12 @@
 
 (defproc (contour-intervals3d
           [f (real? real? . -> . real?)]
-          [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-          [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
-          [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+          [x-min (or/c regular-real? #f) #f]
+          [x-max (or/c regular-real? #f) #f]
+          [y-min (or/c regular-real? #f) #f]
+          [y-max (or/c regular-real? #f) #f]
+          [#:z-min z-min (or/c regular-real? #f) #f]
+          [#:z-max z-max (or/c regular-real? #f) #f]
           [#:levels levels (or/c 'auto exact-positive-integer? (listof real?)) (contour-levels)]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (plot3d-samples)]
           [#:colors colors plot-colors/c (contour-interval-colors)]
diff --git a/collects/plot/plot3d/isosurface.rkt b/collects/plot/plot3d/isosurface.rkt
index be65ac5059..640602d8cd 100644
--- a/collects/plot/plot3d/isosurface.rkt
+++ b/collects/plot/plot3d/isosurface.rkt
@@ -64,9 +64,12 @@
         [else  empty]))
 
 (defproc (isosurface3d [f (real? real? real? . -> . real?)] [d real?]
-                       [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-                       [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
-                       [z-min (or/c real? #f) #f] [z-max (or/c real? #f) #f]
+                       [x-min (or/c regular-real? #f) #f]
+                       [x-max (or/c regular-real? #f) #f]
+                       [y-min (or/c regular-real? #f) #f]
+                       [y-max (or/c regular-real? #f) #f]
+                       [z-min (or/c regular-real? #f) #f]
+                       [z-max (or/c regular-real? #f) #f]
                        [#:samples samples (and/c exact-integer? (>=/c 2)) (plot3d-samples)]
                        [#:color color plot-color/c (surface-color)]
                        [#:line-color line-color plot-color/c (surface-line-color)]
@@ -150,10 +153,14 @@
        [else  empty])]))
 
 (defproc (isosurfaces3d [f (real? real? real? . -> . real?)]
-                        [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-                        [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
-                        [z-min (or/c real? #f) #f] [z-max (or/c real? #f) #f]
-                        [#:d-min d-min (or/c real? #f) #f] [#:d-max d-max (or/c real? #f) #f]
+                        [x-min (or/c regular-real? #f) #f]
+                        [x-max (or/c regular-real? #f) #f]
+                        [y-min (or/c regular-real? #f) #f]
+                        [y-max (or/c regular-real? #f) #f]
+                        [z-min (or/c regular-real? #f) #f]
+                        [z-max (or/c regular-real? #f) #f]
+                        [#:d-min d-min (or/c regular-real? #f) #f]
+                        [#:d-max d-max (or/c regular-real? #f) #f]
                         [#:levels levels (or/c 'auto exact-positive-integer? (listof real?))
                                   (isosurface-levels)]
                         [#:samples samples (and/c exact-integer? (>=/c 2)) (plot3d-samples)]
@@ -248,9 +255,12 @@
     (fl- (exact->inexact (f θ ρ)) (distance x y z))))
 
 (defproc (polar3d [f (real? real? . -> . real?)]
-                  [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                  [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-                  [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+                  [#:x-min x-min (or/c regular-real? #f) #f]
+                  [#:x-max x-max (or/c regular-real? #f) #f]
+                  [#:y-min y-min (or/c regular-real? #f) #f]
+                  [#:y-max y-max (or/c regular-real? #f) #f]
+                  [#:z-min z-min (or/c regular-real? #f) #f]
+                  [#:z-max z-max (or/c regular-real? #f) #f]
                   [#:samples samples (and/c exact-integer? (>=/c 2)) (plot3d-samples)]
                   [#:color color plot-color/c (surface-color)]
                   [#:line-color line-color plot-color/c (surface-line-color)]
diff --git a/collects/plot/plot3d/line.rkt b/collects/plot/plot3d/line.rkt
index 2df546d1fa..657b561cb8 100644
--- a/collects/plot/plot3d/line.rkt
+++ b/collects/plot/plot3d/line.rkt
@@ -34,9 +34,12 @@
 
 (defproc (lines3d
           [vs  (listof (vector/c real? real? real?))]
-          [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-          [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) #f]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) #f]
+          [#:y-max y-max (or/c regular-real? #f) #f]
+          [#:z-min z-min (or/c regular-real? #f) #f]
+          [#:z-max z-max (or/c regular-real? #f) #f]
           [#:color color plot-color/c (line-color)]
           [#:width width (>=/c 0) (line-width)]
           [#:style style plot-pen-style/c (line-style)]
@@ -47,10 +50,13 @@
 
 (defproc (parametric3d
           [f (real? . -> . (vector/c real? real? real?))]
-          [t-min real?] [t-max real?]
-          [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-          [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+          [t-min regular-real?] [t-max regular-real?]
+          [#:x-min x-min (or/c regular-real? #f) #f]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) #f]
+          [#:y-max y-max (or/c regular-real? #f) #f]
+          [#:z-min z-min (or/c regular-real? #f) #f]
+          [#:z-max z-max (or/c regular-real? #f) #f]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (line-samples)]
           [#:color color plot-color/c (line-color)]
           [#:width width (>=/c 0) (line-width)]
diff --git a/collects/plot/plot3d/plot.rkt b/collects/plot/plot3d/plot.rkt
index 870ca26315..9960c0ccb6 100644
--- a/collects/plot/plot3d/plot.rkt
+++ b/collects/plot/plot3d/plot.rkt
@@ -28,9 +28,12 @@
 (defproc (plot3d/dc [renderer-tree  (treeof (or/c renderer3d? non-renderer?))]
                     [dc  (is-a?/c dc<%>)]
                     [x real?] [y real?] [width (>=/c 0)] [height (>=/c 0)]
-                    [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                    [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-                    [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+                    [#:x-min x-min (or/c regular-real? #f) #f]
+                    [#:x-max x-max (or/c regular-real? #f) #f]
+                    [#:y-min y-min (or/c regular-real? #f) #f]
+                    [#:y-max y-max (or/c regular-real? #f) #f]
+                    [#:z-min z-min (or/c regular-real? #f) #f]
+                    [#:z-max z-max (or/c regular-real? #f) #f]
                     [#:angle angle real? (plot3d-angle)] [#:altitude altitude real? (plot3d-altitude)]
                     [#:title title (or/c string? #f) (plot-title)]
                     [#:x-label x-label (or/c string? #f) (plot-x-label)]
@@ -108,9 +111,12 @@
 
 ;; Plot to a bitmap
 (defproc (plot3d-bitmap [renderer-tree (treeof (or/c renderer3d? non-renderer?))]
-                        [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                        [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-                        [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+                        [#:x-min x-min (or/c regular-real? #f) #f]
+                        [#:x-max x-max (or/c regular-real? #f) #f]
+                        [#:y-min y-min (or/c regular-real? #f) #f]
+                        [#:y-max y-max (or/c regular-real? #f) #f]
+                        [#:z-min z-min (or/c regular-real? #f) #f]
+                        [#:z-max z-max (or/c regular-real? #f) #f]
                         [#:width width exact-positive-integer? (plot-width)]
                         [#:height height exact-positive-integer? (plot-height)]
                         [#:angle angle real? (plot3d-angle)]
@@ -130,9 +136,12 @@
   bm)
 
 (defproc (plot3d-pict [renderer-tree (treeof (or/c renderer3d? non-renderer?))]
-                      [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                      [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-                      [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+                      [#:x-min x-min (or/c regular-real? #f) #f]
+                      [#:x-max x-max (or/c regular-real? #f) #f]
+                      [#:y-min y-min (or/c regular-real? #f) #f]
+                      [#:y-max y-max (or/c regular-real? #f) #f]
+                      [#:z-min z-min (or/c regular-real? #f) #f]
+                      [#:z-max z-max (or/c regular-real? #f) #f]
                       [#:width width exact-positive-integer? (plot-width)]
                       [#:height height exact-positive-integer? (plot-height)]
                       [#:angle angle real? (plot3d-angle)]
@@ -155,9 +164,12 @@
 
 ;; Plot to a snip
 (defproc (plot3d-snip [renderer-tree (treeof (or/c renderer3d? non-renderer?))]
-                      [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                      [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-                      [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+                      [#:x-min x-min (or/c regular-real? #f) #f]
+                      [#:x-max x-max (or/c regular-real? #f) #f]
+                      [#:y-min y-min (or/c regular-real? #f) #f]
+                      [#:y-max y-max (or/c regular-real? #f) #f]
+                      [#:z-min z-min (or/c regular-real? #f) #f]
+                      [#:z-max z-max (or/c regular-real? #f) #f]
                       [#:width width exact-positive-integer? (plot-width)]
                       [#:height height exact-positive-integer? (plot-height)]
                       [#:angle angle real? (plot3d-angle)]
@@ -180,9 +192,12 @@
 
 ;; Plot to a frame
 (defproc (plot3d-frame [renderer-tree (treeof (or/c renderer3d? non-renderer?))]
-                       [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                       [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-                       [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+                       [#:x-min x-min (or/c regular-real? #f) #f]
+                       [#:x-max x-max (or/c regular-real? #f) #f]
+                       [#:y-min y-min (or/c regular-real? #f) #f]
+                       [#:y-max y-max (or/c regular-real? #f) #f]
+                       [#:z-min z-min (or/c regular-real? #f) #f]
+                       [#:z-max z-max (or/c regular-real? #f) #f]
                        [#:width width exact-positive-integer? (plot-width)]
                        [#:height height exact-positive-integer? (plot-height)]
                        [#:angle angle real? (plot3d-angle)]
@@ -205,9 +220,12 @@
 (defproc (plot3d-file [renderer-tree (treeof (or/c renderer3d? non-renderer?))]
                       [output (or/c path-string? output-port?)]
                       [kind (one-of/c 'auto 'png 'jpeg 'xmb 'xpm 'bmp 'ps 'pdf 'svg) 'auto]
-                      [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                      [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-                      [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+                      [#:x-min x-min (or/c regular-real? #f) #f]
+                      [#:x-max x-max (or/c regular-real? #f) #f]
+                      [#:y-min y-min (or/c regular-real? #f) #f]
+                      [#:y-max y-max (or/c regular-real? #f) #f]
+                      [#:z-min z-min (or/c regular-real? #f) #f]
+                      [#:z-max z-max (or/c regular-real? #f) #f]
                       [#:width width exact-positive-integer? (plot-width)]
                       [#:height height exact-positive-integer? (plot-height)]
                       [#:angle angle real? (plot3d-angle)]
@@ -252,9 +270,12 @@
 
 ;; Plot to a frame or a snip, depending on the value of plot-new-window?
 (defproc (plot3d [renderer-tree (treeof (or/c renderer3d? non-renderer?))]
-                 [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                 [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-                 [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+                 [#:x-min x-min (or/c regular-real? #f) #f]
+                 [#:x-max x-max (or/c regular-real? #f) #f]
+                 [#:y-min y-min (or/c regular-real? #f) #f]
+                 [#:y-max y-max (or/c regular-real? #f) #f]
+                 [#:z-min z-min (or/c regular-real? #f) #f]
+                 [#:z-max z-max (or/c regular-real? #f) #f]
                  [#:width width exact-positive-integer? (plot-width)]
                  [#:height height exact-positive-integer? (plot-height)]
                  [#:angle angle real? #f] [#:altitude altitude real? #f]
diff --git a/collects/plot/plot3d/point.rkt b/collects/plot/plot3d/point.rkt
index a2c9912872..6976c168c2 100644
--- a/collects/plot/plot3d/point.rkt
+++ b/collects/plot/plot3d/point.rkt
@@ -18,9 +18,12 @@
 
 (defproc (points3d
           [vs  (listof (vector/c real? real? real?))]
-          [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-          [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) #f]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) #f]
+          [#:y-max y-max (or/c regular-real? #f) #f]
+          [#:z-min z-min (or/c regular-real? #f) #f]
+          [#:z-max z-max (or/c regular-real? #f) #f]
           [#:sym sym point-sym/c (point-sym)]
           [#:color color plot-color/c (point-color)]
           [#:size size (>=/c 0) (point-size)]
diff --git a/collects/plot/plot3d/rectangle.rkt b/collects/plot/plot3d/rectangle.rkt
index 3a88495ead..1ba0c8129b 100644
--- a/collects/plot/plot3d/rectangle.rkt
+++ b/collects/plot/plot3d/rectangle.rkt
@@ -24,9 +24,12 @@
 
 (defproc (rectangles3d
           [rects  (listof (vector/c ivl? ivl? ivl?))]
-          [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-          [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) #f]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) #f]
+          [#:y-max y-max (or/c regular-real? #f) #f]
+          [#:z-min z-min (or/c regular-real? #f) #f]
+          [#:z-max z-max (or/c regular-real? #f) #f]
           [#:color color plot-color/c (rectangle-color)]
           [#:style style plot-brush-style/c (rectangle-style)]
           [#:line-color line-color plot-color/c (rectangle-line-color)]
@@ -36,9 +39,9 @@
           [#:label label (or/c string? #f) #f]
           ) renderer3d?
   (match-define (list (vector (ivl x1s x2s) (ivl y1s y2s) (ivl z1s z2s)) ...) rects)
-  (define rxs (filter regular? (append x1s x2s)))
-  (define rys (filter regular? (append y1s y2s)))
-  (define rzs (filter regular? (append z1s z2s)))
+  (define rxs (filter regular-real? (append x1s x2s)))
+  (define rys (filter regular-real? (append y1s y2s)))
+  (define rzs (filter regular-real? (append z1s z2s)))
   (cond
     [(or (empty? rxs) (empty? rys) (empty? rzs))  (renderer3d #f #f #f #f)]
     [else
@@ -77,9 +80,12 @@
 
 (defproc (discrete-histogram3d
           [cat-vals (listof (vector/c any/c any/c real?))]
-          [#:x-min x-min (or/c real? #f) 0] [#:x-max x-max (or/c real? #f) #f]
-          [#:y-min y-min (or/c real? #f) 0] [#:y-max y-max (or/c real? #f) #f]
-          [#:z-min z-min (or/c real? #f) 0] [#:z-max z-max (or/c real? #f) #f]
+          [#:x-min x-min (or/c regular-real? #f) 0]
+          [#:x-max x-max (or/c regular-real? #f) #f]
+          [#:y-min y-min (or/c regular-real? #f) 0]
+          [#:y-max y-max (or/c regular-real? #f) #f]
+          [#:z-min z-min (or/c regular-real? #f) 0]
+          [#:z-max z-max (or/c regular-real? #f) #f]
           [#:gap gap (real-in 0 1) (discrete-histogram-gap)]
           [#:color color plot-color/c (rectangle-color)]
           [#:style style plot-brush-style/c (rectangle-style)]
@@ -92,7 +98,7 @@
           [#:y-far-ticks? y-far-ticks? boolean? #f]
           ) renderer3d?
   (match-define (list (vector cat1s cat2s zs) ...) cat-vals)
-  (define rzs (filter regular? zs))
+  (define rzs (filter regular-real? zs))
   (cond
     [(empty? rzs)  (renderer3d #f #f #f #f)]
     [else
diff --git a/collects/plot/plot3d/surface.rkt b/collects/plot/plot3d/surface.rkt
index 5ff83e1ea4..42c6f0fa4a 100644
--- a/collects/plot/plot3d/surface.rkt
+++ b/collects/plot/plot3d/surface.rkt
@@ -37,9 +37,12 @@
 
 (defproc (surface3d
           [f (real? real? . -> . real?)]
-          [x-min (or/c real? #f) #f] [x-max (or/c real? #f) #f]
-          [y-min (or/c real? #f) #f] [y-max (or/c real? #f) #f]
-          [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+          [x-min (or/c regular-real? #f) #f]
+          [x-max (or/c regular-real? #f) #f]
+          [y-min (or/c regular-real? #f) #f]
+          [y-max (or/c regular-real? #f) #f]
+          [#:z-min z-min (or/c regular-real? #f) #f]
+          [#:z-max z-max (or/c regular-real? #f) #f]
           [#:samples samples (and/c exact-integer? (>=/c 2)) (plot3d-samples)]
           [#:color color plot-color/c (surface-color)]
           [#:style style plot-brush-style/c (surface-style)]
diff --git a/collects/plot/scribblings/plot2d.scrbl b/collects/plot/scribblings/plot2d.scrbl
index d67f0a7220..18f58207b5 100644
--- a/collects/plot/scribblings/plot2d.scrbl
+++ b/collects/plot/scribblings/plot2d.scrbl
@@ -8,8 +8,10 @@
 @title[#:tag "plot2d"]{2D Plot Procedures}
 
 @defproc[(plot [renderer-tree (treeof (or/c renderer2d? non-renderer?))]
-               [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-               [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
+               [#:x-min x-min (or/c regular-real? #f) #f]
+               [#:x-max x-max (or/c regular-real? #f) #f]
+               [#:y-min y-min (or/c regular-real? #f) #f]
+               [#:y-max y-max (or/c regular-real? #f) #f]
                [#:width width exact-positive-integer? (plot-width)]
                [#:height height exact-positive-integer? (plot-height)]
                [#:title title (or/c string? #f) (plot-title)]
diff --git a/collects/plot/scribblings/plot3d.scrbl b/collects/plot/scribblings/plot3d.scrbl
index 5201d541f5..6e786a6c55 100644
--- a/collects/plot/scribblings/plot3d.scrbl
+++ b/collects/plot/scribblings/plot3d.scrbl
@@ -9,9 +9,12 @@
 Each 3D plot procedure corresponds with a @(secref "plot2d") procedure. Each behaves the same way as its corresponding 2D procedure, but takes the additional keyword arguments @(racket #:z-min), @(racket #:z-max), @(racket #:angle), @(racket #:altitude) and @(racket #:z-label).
 
 @defproc[(plot3d [renderer-tree (treeof (or/c renderer3d? non-renderer?))]
-                 [#:x-min x-min (or/c real? #f) #f] [#:x-max x-max (or/c real? #f) #f]
-                 [#:y-min y-min (or/c real? #f) #f] [#:y-max y-max (or/c real? #f) #f]
-                 [#:z-min z-min (or/c real? #f) #f] [#:z-max z-max (or/c real? #f) #f]
+                 [#:x-min x-min (or/c regular-real? #f) #f]
+                 [#:x-max x-max (or/c regular-real? #f) #f]
+                 [#:y-min y-min (or/c regular-real? #f) #f]
+                 [#:y-max y-max (or/c regular-real? #f) #f]
+                 [#:z-min z-min (or/c regular-real? #f) #f]
+                 [#:z-max z-max (or/c regular-real? #f) #f]
                  [#:width width exact-positive-integer? (plot-width)]
                  [#:height height exact-positive-integer? (plot-height)]
                  [#:angle angle real? (plot3d-angle)]