60 Number Lines and Coordinate Decorations

9.3

Racket

60 Number Lines and Coordinate Decorations🔗ℹ

Number-line Visuals and coordinate-decoration constructors provide grid lines and upright numeric labels derived from an existing coordinate object. These constructors produce immutable snapshots. Changing the source axes or number line later does not update an already constructed grid or label list.

procedure
(number-line range
#:id identifier
[ #:center center
#:rotation rotation
#:scale scale
#:opacity opacity
#:length length
#:stroke stroke
#:stroke-width stroke-width
#:tick-size tick-size
#:tip-length tip-length
#:tip-width tip-width
#:start-tip? start-tip?
#:end-tip? end-tip?]) → number-line-visual?
  range : axis-range?
  identifier : symbol?
  center : vec2? = origin
  rotation : finite-real? = 0
  scale : any/c = 1
  opacity : opacity? = 1
  length : positive-real? = 10
  stroke : string? = "black"
  stroke-width : nonnegative-real? = 2
  tick-size : nonnegative-real? = 1/5
  tip-length : nonnegative-real? = 2/5
  tip-width : nonnegative-real? = 3/10
  start-tip? : boolean? = #f
  end-tip? : boolean? = #f

Constructs a horizontal semantic number line. range must contain zero. The Visual’s reference position is the point representing numeric zero, not necessarily the geometric midpoint of the shaft. length is the local world-unit length of the complete interval.

The regular ticks come from axis-range-tick-values, with zero inserted for the number-line representation. Stroke width is cosmetic. Tick and tip sizes are semantic local geometry and therefore follow affine scale.

procedure
(number-line-visual? value) → boolean?
value : any/c

Returns #t when value is a number-line Visual.

procedure
(number-line-visual-range visual) → axis-range?
visual : number-line-visual?

Returns the numeric range and regular tick step.

procedure
(number-line-visual-length visual) → positive-real?
visual : number-line-visual?

Returns the local shaft length for the complete numeric interval.

procedure
(number-line-visual-stroke visual) → string?
visual : number-line-visual?

Returns the shaft, tick, and tip color name.

procedure
(number-line-visual-stroke-width visual) → nonnegative-real?
visual : number-line-visual?

Returns the cosmetic stroke width.

procedure
(number-line-visual-tick-size visual) → nonnegative-real?
visual : number-line-visual?

Returns the full local length of every regular tick.

procedure
(number-line-visual-tip-length visual) → nonnegative-real?
visual : number-line-visual?

Returns the local length of each enabled triangular tip.

procedure
(number-line-visual-tip-width visual) → nonnegative-real?
visual : number-line-visual?

Returns the full local width of each enabled triangular tip.

procedure
(number-line-visual-start-tip? visual) → boolean?
visual : number-line-visual?

Reports whether the minimum endpoint has a tip.

procedure
(number-line-visual-end-tip? visual) → boolean?
visual : number-line-visual?

Reports whether the maximum endpoint has a tip.

procedure
(number-line-unit-length visual) → positive-real?
visual : number-line-visual?

Returns the local world-unit distance representing one numeric unit.

procedure
(number-line-tick-values visual
[ #:include-zero? include-zero?])
→ (listof finite-real?)
visual : number-line-visual?
include-zero? : boolean? = #t

Returns regular tick values in increasing numeric order. Zero is included by default and can be omitted explicitly.

procedure
(number-line-number->point visual number) → vec2?
visual : number-line-visual?
number : finite-real?

Maps number to the containing coordinate system. The result includes the number line’s complete translation, rotation, and scale. Values outside the visible range are extrapolated.

procedure
(number-line-point->number visual point) → real?
visual : number-line-visual?
point : vec2?

Projects point onto the transformed number line and returns the corresponding numeric value. A point need not lie exactly on the line.

procedure
(number-line-visual-start visual) → vec2?
visual : number-line-visual?

Returns the transformed point at the numeric minimum.

procedure
(number-line-visual-end visual) → vec2?
visual : number-line-visual?

Returns the transformed point at the numeric maximum.

procedure
(axes-grid-lines axes
#:id identifier
[ #:x-grid? x-grid?
#:y-grid? y-grid?
#:include-zero? include-zero?
#:opacity opacity
#:stroke stroke
#:stroke-width stroke-width]) → path-visual?
  axes : axes-visual?
  identifier : symbol?
  x-grid? : boolean? = #t
  y-grid? : boolean? = #t
  include-zero? : boolean? = #f
  opacity : opacity? = 1
  stroke : string? = "lightgray"
  stroke-width : nonnegative-real? = 1

Constructs an ordinary path Visual containing vertical grid lines at x ticks and horizontal grid lines at y ticks. X lines precede y lines in traversal order. Zero is omitted by default because the axes already draw the coordinate axes there. The returned path copies the current axes transform.

procedure
(axes-number-labels axes
#:id-prefix identifier-prefix
[ #:include-zero? include-zero?
#:font-size font-size
#:color color
#:x-gap x-gap
#:y-gap y-gap
#:number->string number->string])
→ (listof text-visual?)
  axes : axes-visual?
  identifier-prefix : symbol?
  include-zero? : boolean? = #f
  font-size : positive-real? = 3/10
  color : string? = "black"
  x-gap : nonnegative-real? = 1/10
  y-gap : nonnegative-real? = 1/10
  number->string : procedure? = number->string

Constructs upright plain-text labels at the current tick positions. X labels come first in increasing value order, followed by y labels. When zero is included, it appears once among the x labels; it is not duplicated on the y axis. The x gap and y gap are semantic distances from the corresponding tick extent to the label anchor.

The formatter is called once per label with the numeric value. It must accept one argument and return exactly one string. It is not retained in the returned Visuals. Child identities have the forms prefix-x-index and prefix-y-index, where each index starts at zero.

procedure
(number-line-number-labels number-line
#:id-prefix identifier-prefix
[ #:include-zero? include-zero?
#:font-size font-size
#:color color
#:gap gap
#:number->string number->string])
→ (listof text-visual?)
  number-line : number-line-visual?
  identifier-prefix : symbol?
  include-zero? : boolean? = #t
  font-size : positive-real? = 3/10
  color : string? = "black"
  gap : nonnegative-real? = 1/10
  number->string : procedure? = number->string

Constructs upright plain-text labels below the current number-line ticks. Values and result order are those of number-line-tick-values. Child identities have the form prefix-number-index. The formatter contract is the same as for axes-number-labels.

Number-line rendering is implemented by converting the model to ordinary semantic path geometry after explicit renderer selection. A custom renderer can therefore override the complete number line. Semantic opacity is applied once after either custom rendering or fallback conversion. Grid lines use the normal path renderer, while labels use the normal plain-text renderer.

Reference · Visuals

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