On this page:
7.1 Formatting
digits-for-range
real->plot-label
ivl->plot-label
->plot-label
real->string/  trunc
real->decimal-string*
integer->superscript
7.2 Sampling
linear-seq
linear-seq*
nonlinear-seq
kde
7.3 Plot Colors and Styles
color-seq
color-seq*
->color
->pen-color
->brush-color
->pen-style
->brush-style
color-map-names
color-map-size
register-color-map
7.4 Plot-Specific Math
7.4.1 Real Functions
polar->cartesian
3d-polar->3d-cartesian
ceiling-log/  base
floor-log/  base
maybe-inexact->exact
7.4.2 Vector Functions
v+
v-
vneg
v*
v/
v=
vcross
vcross2
vdot
vmag^2
vmag
vnormalize
vcenter
vrational?
7.4.3 Intervals and Interval Functions
ivl
rational-ivl?
bounds->intervals
clamp-real
7.5 Dates and Times
datetime->real
plot-time
plot-time->seconds
seconds->plot-time
8.1.900.1

7 Plot Utilities

 (require plot/utils) package: plot-lib

7.1 Formatting

procedure

(digits-for-range x-min    
  x-max    
  [base    
  extra-digits])  exact-integer?
  x-min : real?
  x-max : real?
  base : (and/c exact-integer? (>=/c 2)) = 10
  extra-digits : exact-integer? = 3
Given a range, returns the number of decimal places necessary to distinguish numbers in the range. This may return negative numbers for large ranges.

Examples:
> (digits-for-range 0.01 0.02)

5

> (digits-for-range 0 100000)

-2

procedure

(real->plot-label x digits [scientific?])  string?

  x : real?
  digits : exact-integer?
  scientific? : boolean? = #t
Converts a real number to a plot label. Used to format axis tick labels, point-labels, and numbers in legend entries.

Examples:
> (let ([d  (digits-for-range 0.01 0.03)])
    (real->plot-label 0.02555555 d))

".02556"

> (real->plot-label 2352343 -2)

"2352300"

> (real->plot-label 1000000000.0 4)

"1×10⁹"

> (real->plot-label 1000000000.1234 4)

"(1×10⁹)+.1234"

procedure

(ivl->plot-label i [extra-digits])  string?

  i : ivl?
  extra-digits : exact-integer? = 3
Converts an interval to a plot label.

If i = (ivl x-min x-max), the number of digits used is (digits-for-range x-min x-max 10 extra-digits) when both endpoints are rational?. Otherwise, it is unspecified—but will probably remain 15.

Examples:
> (ivl->plot-label (ivl -10.52312 10.99232))

"[-10.52,10.99]"

> (ivl->plot-label (ivl -inf.0 pi))

"[-inf.0,3.141592653589793]"

procedure

(->plot-label a [digits])  string?

  a : any/c
  digits : exact-integer? = 7
Converts a Racket value to a label. Used by discrete-histogram and discrete-histogram3d.

procedure

(real->string/trunc x e)  string?

  x : real?
  e : exact-integer?
Like real->decimal-string, but removes any trailing zeros and any trailing decimal point.

procedure

(real->decimal-string* x    
  min-digits    
  [max-digits])  string?
  x : real?
  min-digits : exact-nonnegative-integer?
  max-digits : exact-nonnegative-integer? = min-digits
Like real->decimal-string, but accepts both a maximum and minimum number of digits.

Examples:
> (real->decimal-string* 1 5 10)

"1.00000"

> (real->decimal-string* 1.123456 5 10)

"1.123456"

> (real->decimal-string* 1.123456789123456 5 10)

"1.1234567891"

Applying (real->decimal-string* x min-digits) yields the same value as (real->decimal-string x min-digits).

procedure

(integer->superscript x)  string?

  x : exact-integer?
Converts an integer into a string of superscript Unicode characters.

Example:
> (integer->superscript -1234567890)

"⁻¹²³⁴⁵⁶⁷⁸⁹⁰"

Systems running some out-of-date versions of Windows XP have difficulty with Unicode superscripts for 4 and up. Because integer->superscript is used by every number formatting function to format exponents, if you have such a system, Plot will apparently not format all numbers with exponents correctly (until you update it).

7.2 Sampling

procedure

(linear-seq start    
  end    
  num    
  [#:start? start?    
  #:end? end?])  (listof real?)
  start : real?
  end : real?
  num : exact-nonnegative-integer?
  start? : boolean? = #t
  end? : boolean? = #t
Returns a list of uniformly spaced real numbers between start and end. If start? is #t, the list includes start. If end? is #t, the list includes end.

This function is used internally to generate sample points.

Examples:
> (linear-seq 0 1 5)

'(0 1/4 1/2 3/4 1)

> (linear-seq 0 1 5 #:start? #f)

'(1/9 1/3 5/9 7/9 1)

> (linear-seq 0 1 5 #:end? #f)

'(0 2/9 4/9 2/3 8/9)

> (linear-seq 0 1 5 #:start? #f #:end? #f)

'(1/10 3/10 1/2 7/10 9/10)

> (define xs (linear-seq -1 1 11))
> (plot (lines (map vector xs (map sqr xs))))

image

procedure

(linear-seq* points    
  num    
  [#:start? start?    
  #:end? end?])  (listof real?)
  points : (listof real?)
  num : exact-nonnegative-integer?
  start? : boolean? = #t
  end? : boolean? = #t
Like linear-seq, but accepts a list of reals instead of a start and end. The #:start? and #:end? keyword arguments work as in linear-seq. This function does not guarantee that each inner value will be in the returned list.

Examples:
> (linear-seq* '(0 1 2) 5)

'(0 1/2 1 3/2 2)

> (linear-seq* '(0 1 2) 6)

'(0 2/5 4/5 6/5 8/5 2)

> (linear-seq* '(0 1 0) 5)

'(0 1/2 1 1/2 0)

procedure

(nonlinear-seq start    
  end    
  num    
  transform    
  [#:start? start?    
  #:end? end?])  (listof real?)
  start : real?
  end : real?
  num : exact-nonnegative-integer?
  transform : axis-transform/c
  start? : boolean? = #t
  end? : boolean? = #t
Generates a list of reals that, if transformed using transform, would be uniformly spaced. This is used to generate samples for transformed axes.

Examples:
> (linear-seq 1 10 4)

'(1 4 7 10)

> (nonlinear-seq 1 10 4 log-transform)

'(1.0 2.154434690031884 4.641588833612779 10.000000000000002)

> (parameterize ([plot-x-transform  log-transform])
    (plot (area-histogram sqr (nonlinear-seq 1 10 4 log-transform))))

image

procedure

(kde xs h [ws])  
(-> real? real?)
(or/c rational? #f)
(or/c rational? #f)
  xs : (listof real?)
  h : (>/c 0)
  ws : (or/c (listof (>=/c 0)) #f) = #f
Given optionally weighted samples and a kernel bandwidth, returns a function representing a kernel density estimate, and bounds, outside of which the density estimate is zero. Used by density.

7.3 Plot Colors and Styles

procedure

(color-seq c1 
  c2 
  num 
  [#:start? start? 
  #:end? end?]) 
  (listof (list/c real? real? real?))
  c1 : color/c
  c2 : color/c
  num : exact-nonnegative-integer?
  start? : boolean? = #t
  end? : boolean? = #t
Interpolates between colors—red, green and blue components separately—using linear-seq. The #:start? and #:end? keyword arguments work as in linear-seq.

Example:
> (plot (contour-intervals (λ (x y) (+ x y)) -2 2 -2 2
                           #:levels 4 #:contour-styles '(transparent)
                           #:colors (color-seq "red" "blue" 5)))

image

procedure

(color-seq* colors 
  num 
  [#:start? start? 
  #:end? end?]) 
  (listof (list/c real? real? real?))
  colors : (listof color/c)
  num : exact-nonnegative-integer?
  start? : boolean? = #t
  end? : boolean? = #t
Interpolates between colors—red, green and blue components separately—using linear-seq*. The #:start? and #:end? keyword arguments work as in linear-seq.

Example:
> (plot (contour-intervals (λ (x y) (+ x y)) -2 2 -2 2
                           #:levels 4 #:contour-styles '(transparent)
                           #:colors (color-seq* '(red white blue) 5)))

image

procedure

(->color c)  (list/c real? real? real?)

  c : color/c
Converts a non-integer plot color to an RGB triplet.

Symbols are converted to strings, and strings are looked up in a color-database<%>. Lists are unchanged, and color% objects are converted straightforwardly.

Examples:
> (->color 'navy)

'(36 36 140)

> (->color "navy")

'(36 36 140)

> (->color '(36 36 140))

'(36 36 140)

> (->color (make-object color% 36 36 140))

'(36 36 140)

This function does not convert integers to RGB triplets, because there is no way for it to know whether the color will be used for a pen or for a brush. Use ->pen-color and ->brush-color to convert integers.

procedure

(->pen-color c)  (list/c real? real? real?)

  c : plot-color/c
Convert a line color to an RGB triplet. Integer colors are looked up in the current plot-pen-color-map, and non-integer colors are converted using ->color. When the integer color is larger than the number of colors in the color map, it will wrap around.

Examples:
> (equal? (->pen-color 0) (->pen-color 8))

#f

> (plot (contour-intervals
         (λ (x y) (+ x y)) -2 2 -2 2
         #:levels 7 #:contour-styles '(transparent)
         #:colors (map ->pen-color (build-list 8 values))))

image

The example above is using the internal color map, with plot-pen-color-map set to #f.

procedure

(->brush-color c)  (list/c real? real? real?)

  c : plot-color/c
Convert a fill color to an RGB triplet. Integer colors are looked up in the current plot-brush-color-map and non-integer colors are converted using ->color. When the integer color is larger than the number of colors in the color map, it will wrap around.

Examples:
> (equal? (->brush-color 0) (->brush-color 8))

#f

> (plot (contour-intervals
         (λ (x y) (+ x y)) -2 2 -2 2
         #:levels 7 #:contour-styles '(transparent)
         #:colors (map ->brush-color (build-list 8 values))))

image

The example above is using the internal color map, with plot-brush-color-map is set to #f. In this example, mapping ->brush-color over the list is actually unnecessary, because contour-intervals uses ->brush-color internally to convert fill colors.

The function-interval function generally plots areas using a fill color and lines using a line color. Both kinds of color have the default value 3. The following example reverses the default behavior; i.e it draws areas using line color 3 and lines using fill color 3:
> (plot (function-interval sin (λ (x) 0) -4 4
                           #:color (->pen-color 3)
                           #:line1-color (->brush-color 3)
                           #:line2-color (->brush-color 3)
                           #:line1-width 4 #:line2-width 4))

image

procedure

(->pen-style s)  symbol?

  s : plot-pen-style/c
Converts a symbolic pen style or a number to a symbolic pen style. Symbols are unchanged. Integer pen styles repeat starting at 5.

Examples:
> (eq? (->pen-style 0) (->pen-style 5))

#t

> (map ->pen-style '(0 1 2 3 4))

'(solid dot long-dash short-dash dot-dash)

procedure

(->brush-style s)  symbol?

  s : plot-brush-style/c
Converts a symbolic brush style or a number to a symbolic brush style. Symbols are unchanged. Integer brush styles repeat starting at 7.

Examples:
> (eq? (->brush-style 0) (->brush-style 7))

#t

> (map ->brush-style '(0 1 2 3))

'(solid bdiagonal-hatch fdiagonal-hatch crossdiag-hatch)

> (map ->brush-style '(4 5 6))

'(horizontal-hatch vertical-hatch cross-hatch)

procedure

(color-map-names)  (listof symbol?)

Return the list of available color map names to be used by plot-pen-color-map and plot-brush-color-map.

Added in version 7.3 of package plot-lib.

procedure

(color-map-size name)  integer?

  name : symbol?
Return the number of colors in the color map name. If name is not a valid color map name, the function will signal an error.

Added in version 7.3 of package plot-lib.

procedure

(register-color-map name color-map)  void

  name : symbol?
  color-map : (vectorof (list byte? byte? byte?))
Register a new color map name with the colors being a vector of RGB triplets. If a color map by that name already exists, it is replaced.

Added in version 7.3 of package plot-lib.

7.4 Plot-Specific Math

7.4.1 Real Functions

procedure

(polar->cartesian θ r)  (vector/c real? real?)

  θ : real?
  r : real?
Converts 2D polar coordinates to 2D cartesian coordinates.

procedure

(3d-polar->3d-cartesian θ ρ r)  (vector/c real? real? real?)

  θ : real?
  ρ : real?
  r : real?
Converts 3D polar coordinates to 3D cartesian coordinates. See parametric3d for an example of use.

procedure

(ceiling-log/base b x)  exact-integer?

  b : (and/c exact-integer? (>=/c 2))
  x : (>/c 0)
Like (ceiling (/ (log x) (log b))), but ceiling-log/base is not susceptible to floating-point error.

Examples:
> (ceiling (/ (log 100) (log 10)))

2.0

> (ceiling-log/base 10 100)

2

> (ceiling (/ (log 1/1000) (log 10)))

-2.0

> (ceiling-log/base 10 1/1000)

-3

Various number-formatting functions use this.

procedure

(floor-log/base b x)  exact-integer?

  b : (and/c exact-integer? (>=/c 2))
  x : (>/c 0)
Like (floor (/ (log x) (log b))), but floor-log/base is not susceptible to floating-point error.

Examples:
> (floor (/ (log 100) (log 10)))

2.0

> (floor-log/base 10 100)

2

> (floor (/ (log 1000) (log 10)))

2.0

> (floor-log/base 10 1000)

3

This is a generalization of order-of-magnitude.

procedure

(maybe-inexact->exact x)  (or/c rational? #f)

  x : (or/c rational? #f)
Returns #f if x is #f; otherwise (inexact->exact x). Use this to convert interval endpoints, which may be #f, to exact numbers.

7.4.2 Vector Functions

procedure

(v+ v1 v2)  (vectorof real?)

  v1 : (vectorof real?)
  v2 : (vectorof real?)

procedure

(v- v1 v2)  (vectorof real?)

  v1 : (vectorof real?)
  v2 : (vectorof real?)

procedure

(vneg v)  (vectorof real?)

  v : (vectorof real?)

procedure

(v* v c)  (vectorof real?)

  v : (vectorof real?)
  c : real?

procedure

(v/ v c)  (vectorof real?)

  v : (vectorof real?)
  c : real?
Vector arithmetic. Equivalent to vector-mapp-ing arithmetic operators over vectors, but specialized so that 2- and 3-vector operations are much faster.

Examples:
> (v+ #(1 2) #(3 4))

'#(4 6)

> (v- #(1 2) #(3 4))

'#(-2 -2)

> (vneg #(1 2))

'#(-1 -2)

> (v* #(1 2 3) 2)

'#(2 4 6)

> (v/ #(1 2 3) 2)

'#(1/2 1 3/2)

procedure

(v= v1 v2)  boolean?

  v1 : (vectorof real?)
  v2 : (vectorof real?)
Like equal? specialized to numeric vectors, but compares elements using =.

Examples:
> (equal? #(1 2) #(1 2))

#t

> (equal? #(1 2) #(1.0 2.0))

#f

> (v= #(1 2) #(1.0 2.0))

#t

procedure

(vcross v1 v2)  (vector/c real? real? real?)

  v1 : (vector/c real? real? real?)
  v2 : (vector/c real? real? real?)
Returns the right-hand vector cross product of v1 and v2.

Examples:
> (vcross #(1 0 0) #(0 1 0))

'#(0 0 1)

> (vcross #(0 1 0) #(1 0 0))

'#(0 0 -1)

> (vcross #(0 0 1) #(0 0 1))

'#(0 0 0)

procedure

(vcross2 v1 v2)  real?

  v1 : (vector/c real? real?)
  v2 : (vector/c real? real?)
Returns the signed area of the 2D parallelogram with sides v1 and v2. Equivalent to (vector-ref (vcross (vector-append v1 #(0)) (vector-append v2 #(0))) 2) but faster.

Examples:
> (vcross2 #(1 0) #(0 1))

1

> (vcross2 #(0 1) #(1 0))

-1

procedure

(vdot v1 v2)  real?

  v1 : (vectorof real?)
  v2 : (vectorof real?)
Returns the dot product of v1 and v2.

procedure

(vmag^2 v)  real?

  v : (vectorof real?)
Returns the squared magnitude of v. Equivalent to (vdot v v).

procedure

(vmag v)  real?

  v : (vectorof real?)
Returns the magnitude of v. Equivalent to (sqrt (vmag^2 v)).

procedure

(vnormalize v)  (vectorof real?)

  v : (vectorof real?)
Returns a normal vector in the same direction as v. If v is a zero vector, returns v.

Examples:
> (vnormalize #(1 1 0))

'#(0.7071067811865475 0.7071067811865475 0)

> (vnormalize #(1 1 1))

'#(0.5773502691896258 0.5773502691896258 0.5773502691896258)

> (vnormalize #(0 0 0.0))

'#(0 0 0.0)

procedure

(vcenter vs)  (vectorof real?)

  vs : (listof (vectorof real?))
Returns the center of the smallest bounding box that contains vs.

Example:
> (vcenter '(#(1 1) #(2 2)))

'#(3/2 3/2)

procedure

(vrational? v)  boolean?

  v : (vectorof real?)
Returns #t if every element of v is rational?.

Examples:
> (vrational? #(1 2))

#t

> (vrational? #(+inf.0 2))

#f

> (vrational? #(#f 1))

vrational?: contract violation

  expected: real?

  given: #f

  in: an element of

      the 1st argument of

      (-> (vectorof real?) any)

  contract from:

      <pkgs>/plot-lib/plot/private/common/math.rkt

  blaming: top-level

   (assuming the contract is correct)

  at: <pkgs>/plot-lib/plot/private/common/math.rkt:304:9

7.4.3 Intervals and Interval Functions

struct

(struct ivl (min max)
    #:extra-constructor-name make-ivl)
  min : real?
  max : real?
Represents a closed interval.

An interval with two real-valued endpoints always contains the endpoints in order:
> (ivl 0 1)

(ivl 0 1)

> (ivl 1 0)

(ivl 0 1)

An interval can have infinite endpoints:
> (ivl -inf.0 0)

(ivl -inf.0 0)

> (ivl 0 +inf.0)

(ivl 0 +inf.0)

> (ivl -inf.0 +inf.0)

(ivl -inf.0 +inf.0)

Functions that return rectangle renderers, such as rectangles and discrete-histogram3d, accept vectors of ivls as arguments. The ivl struct type is also provided by plot so users of such renderers do not have to require plot/utils.

procedure

(rational-ivl? i)  boolean?

  i : any/c
Returns #t if i is an interval and each of its endpoints is rational?.

Example:
> (map rational-ivl? (list (ivl -1 1) (ivl -inf.0 2) 'bob))

'(#t #f #f)

procedure

(bounds->intervals xs)  (listof ivl?)

  xs : (listof real?)
Given a list of points, returns intervals between each pair.

Use this to construct inputs for rectangles and rectangles3d.

Example:
> (bounds->intervals (linear-seq 0 1 5))

(list (ivl 0 1/4) (ivl 1/4 1/2) (ivl 1/2 3/4) (ivl 3/4 1))

procedure

(clamp-real x i)  real?

  x : real?
  i : ivl?

7.5 Dates and Times

Converts various date/time representations into UTC seconds, respecting time zone offsets.

For dates, the value returned is the number of seconds since a system-dependent UTC epoch. See date-ticks for more information.

To plot a time series using dates pulled from an SQL database, simply set the relevant axis ticks (probably plot-x-ticks) to date-ticks, and convert the dates to seconds using datetime->real before passing them to lines. To keep time zone offsets from influencing the plot, set them to 0 first.

struct

(struct plot-time (second minute hour day)
    #:extra-constructor-name make-plot-time)
  second : (and/c (>=/c 0) (</c 60))
  minute : (integer-in 0 59)
  hour : (integer-in 0 23)
  day : exact-integer?
A time representation that accounts for days, negative times (using negative days), and fractional seconds.

Plot (specifically time-ticks) uses plot-time internally to format times, but because renderer-producing functions require only real values, user code should not need it. It is provided just in case.

procedure

(plot-time->seconds t)  real?

  t : plot-time?

procedure

(seconds->plot-time s)  plot-time?

  s : real?
Convert plot-times to real seconds, and vice-versa.

Examples:
> (define (plot-time+ t1 t2)
    (seconds->plot-time (+ (plot-time->seconds t1)
                           (plot-time->seconds t2))))
> (plot-time+ (plot-time 32 0 12 1)
              (plot-time 32 0 14 1))

(plot-time 4 1 2 3)