7 Plot Utilities

▼ |  | Plot: Graph Plotting

1 | Introduction
2 | 2D and 3D Plotting Procedures
3 | 2D Renderers
4 | 3D Renderers
5 | Nonrenderers
6 | Axis Transforms and Ticks
7 | Plot Utilities
8 | Plot and Renderer Parameters
9 | Plot Contracts
10 | Porting From Plot <= 5.1.3
11 | Legacy Typed Interface
12 | Compatibility Module

► | 7 | Plot Utilities

7.1 | Formatting
7.2 | Sampling
7.3 | Plot Colors and Styles
7.4 | Plot-Specific Math
7.5 | Dates and Times

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
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

7.2
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### 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))))

> > 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))))

> > 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)))

> > 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)))

> 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

Converts a line color to an RGB triplet. This function interprets integer colors as darker and more saturated than ->brush-color does.

Non-integer colors are converted using ->color. Integer colors are chosen for good pairwise contrast, especially between neighbors. Integer colors repeat starting with 128.

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))))

> procedure (->brush-color c) → (list/c real? real? real?)
> c : plot-color/c

Converts a fill color to an RGB triplet. This function interprets integer colors as lighter and less saturated than ->pen-color does.

Non-integer colors are converted using ->color. Integer colors are chosen for good pairwise contrast, especially between neighbors. Integer colors repeat starting with 128.

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))))

In the above 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))

> 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)

#### 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

> procedure (datetime->real x) → real?
> x : (or/c plot-time? date? date*? sql-date? sql-time? sql-timestamp?)

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)

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