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Source: vignettes/arcwedges.qmd

Arcs and Wedges

Setup

Packages

Base Plot

To avoid repetitive code, we make a base plot:

my_font <- "Roboto Condensed"
my_font_size <- 20
my_point_size <- 2
my_arrowhead <- arrowheadr::arrow_head_deltoid(2.3, n = 101)

# my_colors <- viridis::viridis(2, begin = .25, end = .5)
my_colors <- c("#3B528B", "#21908C")

bp <- ggdiagram(
  font_family = my_font,
  font_size = my_font_size,
  point_size = my_point_size,
  linewidth = .5,
  theme_function = theme_minimal,
  axis.title.x =  element_text(face = "italic"),
  axis.title.y = element_text(
    face = "italic",
    angle = 0,
    hjust = .5,
    vjust = .5)) +
  scale_x_continuous(labels = signs_centered,
                     limits = c(-4, 4)) +
  scale_y_continuous(labels = signs::signs,
                     limits = c(-4, 4))

Arcs

Just as a segment is part of a line between two points on the line, an arc is part of a circle between two points (on the circle). Thus, an arc has all the properties a circle, with the addition of starting and ending points. For the sake of simplicity, these starting points are specified as angles.

Arc starting and ending points can be specified with any angle unit. If a number is used, it will be interpreted as a degree unit.

ob_arc(center = ob_point(1,2), 
    start = 25, 
    end = 75, 
    radius = 3)
#> <ggdiagram::ob_arc>
#> @ center: <ggdiagram::ob_point>
#>  @ x: num 1
#>  @ y: num 2
#> @ radius: num 3
#> @ start : <ggdiagram::degree>
#>  @ degree: num 25
#> @ end   : <ggdiagram::degree>
#>  @ degree: num 75
#> @ theta : <ggdiagram::degree>
#>  @ degree: num 50
#> Other props: label, type, alpha, arrow_head, arrow_fins,
#>              arrowhead_length, length_head, length_fins, color,
#>              fill, lineend, linejoin, linewidth, linewidth_fins,
#>              linewidth_head, linetype, n, resect, resect_fins,
#>              resect_head, stroke_color, stroke_width, apothem,
#>              arc_length, sagitta, bounding_box, circle, chord,
#>              length, end_point, polygon, start_point, style,
#>              tibble, geom, angle_at, autolabel, hatch, midpoint,
#>              normal_at, place, point_at, tangent_at, aesthetics
Code
ggtext::GeomRichText$default_aes
#> Aesthetic mapping: 
#> * `colour`       -> "black"
#> * `fill`         -> "white"
#> * `size`         -> 7.029196
#> * `angle`        -> 0
#> * `hjust`        -> 0.5
#> * `vjust`        -> 0.5
#> * `alpha`        -> NA
#> * `family`       -> "Roboto Condensed"
#> * `fontface`     -> 1
#> * `lineheight`   -> 1.2
#> * `text.colour`  -> NULL
#> * `label.colour` -> NULL
#> * `label.size`   -> 0.25
bp +
  {p1 <- ob_point(0, 0)} + 
  {a1 <- ob_arc(
    center = p1,
    radius = {r <- 4},
    start = {ang_start <- degree(25)},
    end = {ang_end <- degree(75)}
    )} +
  ob_label(
    label = paste0("Center ", p1@auto_label), 
    center = p1, 
    vjust = 1.1) + 
  connect(
    p1, 
    a1@midpoint(), 
    label = paste0("Radius = ", r)) + 
  ob_label(
    label = ang_start, 
    center = a1@midpoint(0),
    polar_just = ob_polar(ang_start + degree(-90), 1.3), 
    plot_point = TRUE) +
  ob_label(
    label = ang_end, 
    center = a1@midpoint(1), 
    polar_just = ob_polar(ang_end + degree(90), 1), 
    plot_point = TRUE)

Arc with starting and ending angles and center point.

Starting or ending points of arcs

Sometimes you do not know where the center of an arc should be. Instead, you want the arc to start or end at a specific point. For example, you might want to specify the start point or the end point.


p1 <- ob_point(0, 0)

bp +
    ob_arc(start = -45, 
      end = 45, 
      radius = 2,
      color = "orchid4", 
      start_point = p1)  +
  ob_arc(start = -45, 
      end = 45, 
      radius = 2,
      color = "forestgreen", 
      end_point = p1) +
  p1
Figure 1: Fixing the start and end points of an arc

As a example, I used the start_point argument to recreate a fun meme about a “square” object with 4 equal sides that meet at right angles:

little_r <- 1 / (2 * pi - 1)
ggdiagram(font_family = my_font,
          font_size = my_font_size) +
  {p1 <- ob_point(0,0)} +
  {p2 <- ob_point(1,0)} +
  ob_segment(p1, p2) +
  {a1 <- ob_arc(start = 0, end = radian(1), radius = 1 + little_r, start_point = p2)} +
  {p3 <- a1@midpoint(1)} +
  {p4 <- a1@normal_at(radian(1), distance = -1)} +
  ob_segment(p3, p4) + 
  ob_arc(start_point = p4, 
         radius = little_r, 
         start = radian(1), 
         end = turn(1))
Figure 2: A “square” with four equal sizes that meet at right angles.

Midpoints

The midpoint function can find one or more midpoints at different positions. The default position is .5.

bp +
  a1 +
  a1@midpoint()
Figure 3: Default midpoint on a arc

The starting and ending points are at position 0 and 1, respectively.

bp +
  a1 +
  a1@midpoint(position = c(0,1))
Figure 4: Multiple midpoints can be specified

Labelling arcs

By default, the arc label will appear outside the midpoint of the arc

bp +
  ob_arc(radius = 3, 
      start = 20, 
      end = 120, 
      label = ob_label(degree(100)))
Figure 5: A labelled arc

If a label is needed elsewhere, it can be set with the label function’s position property.

bp +
  ob_arc(
    radius = 3,
    start = 20,
    end = 120,
    label = ob_label(
      c("Start", "Middle", "End"),
      position = c(0, .5, 1),
      plot_point = TRUE
    )
  )
Figure 6: Multiple labels on an arc

If the orientation of the label needs to be changed, it can be set with vjust, hjust, or polar_just.

bp +
  ob_arc(
    radius = 3,
    start = 20,
    end = 120,
    label = ob_label(
      "A",
      vjust = 1.2,
      hjust = .75
    )
  )
Figure 7: The arc’s labels can be adjusted.

There are cases where the arc is already created and a label is needed. Although the label can be added after the arc has been created, the position would have to be set manually (otherwise the position will be at 0,0 by default). In such cases, the auto_label function can help place the label correctly. By default, the auto_label will show the the theta property (i.e., end − start).

bp + 
  {a1 <- ob_arc(radius = 3, 
      start = 20, 
      end = 120)} + 
  a1@autolabel()
Figure 8: Using the arc’s autolabel

However, any label can be inserted at any position.

bp + 
  a1 +
  a1@autolabel(label = "Start", 
               position = 0)
Figure 9: Adjusting the arc’s autolabel

Arcs with arrows

The arc object is plotted using ggarrow::arrow. This means that arrows can be placed on either end of an arc.

my_arrow_head <- arrowheadr::arrow_head_deltoid(d = 2.3, n = 100)

bp + 
  ob_arc(radius = 3, 
      start = 0, 
      end = 180, 
      arrow_head = my_arrow_head,
      arrow_fins = my_arrow_head, 
      arrowhead_length = 8)
Figure 10: Arcs with arrowheads

Wedges

The ob_arc function has a @type property that can be set to "arc", "wedge", or "segment". When set to arc, the arc is drawn with geom::arrow so that the arc endpoints can be arrows. Otherwise, when @type is wedge or segment, ob_arc drawn with ggplot2::geom_polygon.

The ob_wedge function is a convenient wrapper function for ob_arc that sets the @type property to wedge.

theta <- c(0, 120, 180, 360)
bp +
  ob_wedge(radius = 3, 
      start = theta[-length(theta)], 
      end = theta[-1], 
      fill = c("dodgerblue4", "orchid4", "darkgreen"), 
      color = "white", 
      linewidth = 1)
Figure 11: Arc wedges

Circular Segments

A circular segment is an arc made into a polygon.

The ob_circular_segment function is a convenient wrapper function for ob_arc that sets the @type property to segment.

ggdiagram() +
  ob_circular_segment(
    start = c(30, 150, 270),
    end = c(150, 270, 390),
    fill = c("dodgerblue4", "orchid4", "darkgreen")
  )
Figure 12: Three circular segments

Objects made with ob_arc, ob_wedge, or ob_circular_segment can return important features of arcs, including the chord, sagitta, and arc_length. In Figure 13, the chord is the ob_segment that connects the endpoints of the arc. The sagitta is ob_segment from the arc’s midpoint to the chord’s midpoint. Not shown in Figure 13, the apothem is the ob_segment from the arc’s center point to the midpoint of the chord. The radius is the sum of the distances spanned by the apothem and the sagitta.


bp +
  {cs <- ob_circular_segment(
      radius = 3,
      start = radian(-acos(1 / 3)),
      end = radian(acos(1 / 3)),
      fill = "dodgerblue3"
    )} +
  ob_arc(
    radius = 3,
    start = cs@end,
    end = cs@start + degree(360),
    linetype = "dashed"
  ) +
  cs@chord@midpoint()@label(
    paste0("Chord Length = ", round(cs@chord@distance, 2)),
    angle = cs@chord@line@angle,
    vjust = -.1,
    color = "black",
    size = 18
  ) +
  cs@sagitta %>% set_props(color = "white") +
  cs@sagitta@midpoint()@label(
    paste0("Sagitta = ", round(cs@sagitta@distance, 2)),
    vjust = 0,
    size = 18,
    fill = NA, 
    color = "white"
  ) +
  ob_path(
    ob_point(
      cs@polygon %>% 
        mutate(id = dplyr::row_number()) %>% 
        arrange(-id) %>% 
        select(x, y)
    ),
    label = ob_label(
      paste0("Arc Length = ", round(cs@arc_length, 2)),
      vjust = -0.1,
      size = 18,
      color = "black"
    ),
    color = "dodgerblue3"
  )
Figure 13: A circular segment and arc and its chord.

Fun fact: Our geometric concepts arc, chord, and sagitta are all archery terms, deriving from the Latin words arcus (bow), chorda (string), and sagitta (arrow).