Introduction
Package ‘ggplot2’ defines its own class system, and function ggplot() can be considered as a constructor.
## [1] "gg" "ggplot"
If we pass no arguments an empty plot is constructed.
The structure of objects of classes "gg" "ggplot" can be explored with R’s method str() as any other structured R object. These allows us to see the different slots of these special type of lists.
## Object size: 3.4 kB
## List of 9
## $ data : list()
## $ layers : list()
## $ scales :Classes 'ScalesList', 'ggproto', 'gg' <ggproto object: Class ScalesList, gg>
## add: function
## clone: function
## find: function
## get_scales: function
## has_scale: function
## input: function
## n: function
## non_position_scales: function
## scales: NULL
## super: <ggproto object: Class ScalesList, gg>
## $ mapping : Named list()
## $ theme : list()
## $ coordinates:Classes 'CoordCartesian', 'Coord', 'ggproto', 'gg' <ggproto object: Class CoordCartesian, Coord, gg>
## aspect: function
## backtransform_range: function
## clip: on
## default: TRUE
## distance: function
## expand: TRUE
## is_free: function
## is_linear: function
## labels: function
## limits: list
## modify_scales: function
## range: function
## render_axis_h: function
## render_axis_v: function
## render_bg: function
## render_fg: function
## setup_data: function
## setup_layout: function
## setup_panel_params: function
## setup_params: function
## transform: function
## super: <ggproto object: Class CoordCartesian, Coord, gg>
## $ facet :Classes 'FacetNull', 'Facet', 'ggproto', 'gg' <ggproto object: Class FacetNull, Facet, gg>
## compute_layout: function
## draw_back: function
## draw_front: function
## draw_labels: function
## draw_panels: function
## finish_data: function
## init_scales: function
## map_data: function
## params: list
## setup_data: function
## setup_params: function
## shrink: TRUE
## train_scales: function
## vars: function
## super: <ggproto object: Class FacetNull, Facet, gg>
## $ plot_env :<environment: R_GlobalEnv>
## $ labels : Named list()
If we pass an argument to parameter data the data is copied into the list slot with name data. As we also map the data to aesthetics, this mapping is stored in slot maaping.
## Object size: 11 kB
## List of 9
## $ data :'data.frame': 100 obs. of 5 variables:
## $ layers : list()
## $ scales :Classes 'ScalesList', 'ggproto', 'gg' <ggproto object: Class ScalesList, gg>
## add: function
## clone: function
## find: function
## get_scales: function
## has_scale: function
## input: function
## n: function
## non_position_scales: function
## scales: NULL
## super: <ggproto object: Class ScalesList, gg>
## $ mapping :List of 3
## $ theme : list()
## $ coordinates:Classes 'CoordCartesian', 'Coord', 'ggproto', 'gg' <ggproto object: Class CoordCartesian, Coord, gg>
## aspect: function
## backtransform_range: function
## clip: on
## default: TRUE
## distance: function
## expand: TRUE
## is_free: function
## is_linear: function
## labels: function
## limits: list
## modify_scales: function
## range: function
## render_axis_h: function
## render_axis_v: function
## render_bg: function
## render_fg: function
## setup_data: function
## setup_layout: function
## setup_panel_params: function
## setup_params: function
## transform: function
## super: <ggproto object: Class CoordCartesian, Coord, gg>
## $ facet :Classes 'FacetNull', 'Facet', 'ggproto', 'gg' <ggproto object: Class FacetNull, Facet, gg>
## compute_layout: function
## draw_back: function
## draw_front: function
## draw_labels: function
## draw_panels: function
## finish_data: function
## init_scales: function
## map_data: function
## params: list
## setup_data: function
## setup_params: function
## shrink: TRUE
## train_scales: function
## vars: function
## super: <ggproto object: Class FacetNull, Facet, gg>
## $ plot_env :<environment: R_GlobalEnv>
## $ labels :List of 3
A summary() method that produces a more compact output is available in recent versions of ‘ggplot2’. However, it does not reveal the internal structure of the objects.
## data: x, y, group, y2, block [100x5]
## mapping: x = ~x, y = ~y, colour = ~group
## faceting: <ggproto object: Class FacetNull, Facet, gg>
## compute_layout: function
## draw_back: function
## draw_front: function
## draw_labels: function
## draw_panels: function
## finish_data: function
## init_scales: function
## map_data: function
## params: list
## setup_data: function
## setup_params: function
## shrink: TRUE
## train_scales: function
## vars: function
## super: <ggproto object: Class FacetNull, Facet, gg>
## -----------------------------------
## geom_point: na.rm = FALSE
## stat_identity: na.rm = FALSE
## position_identity
How does mapping work? Geometries (geoms) and statistics (stats) do not “see” the original variable names, instead the data passed to them is named according to the aesthetics user variables are mapped to. Geoms and stats work in tandem, with geoms doing the actual plotting and stats summarizing or transforming the data. It can be instructive to be able to see what data is received as input by a geom or stat, and what data is returned by a stat.
Both geoms and stats can have either panel- or group functions. Panel functions receive as input the subset of the data that corresponds to a whole panel, mapped to the aesthetics and with factors indicating the grouping (set by the user by mapping to a discrete scale). Group functions receive as input the subset of data corresponding to a single group based on the mapping.
The motivation for writing the “debug” stats and geoms included in package ‘gginnards’ is that at the moment it is in many cases not possible to set breakpoints inside the code of stats and geoms, because frequently nameless panel and group functions are stored in list-like objects used to store the definitions of geoms and stats.
This can make it tedious to analyse how these functions work, as one may need to add print statements to their source code to see the data. I wrote the “debug” stats and geoms as tools to help in the development of my packages ‘ggpmisc’ and ‘ggspectra’, and as a way of learning myself how data are passed around within the different components of a ggplot object when it is printed.
Data input to stats
The code of the stats described in this vignette are very simple and print a summary of their data input by default to the console. However, the default function used to display the data can be substituted by a different one passed as an argument, adding flexibility. The debug stats, in addition return a data frame containing labels suitable for “plotting” debug with geom “text” or geom “label”.
The ‘gginnards’ package defines a "null" geom, which is used as default by the debug stats. Currently this geom is similar to the more recently added ggplot2::geom_blank() and is used as default geom in the stats described in this user guide.
Using as default geom “null” allows to add the debug stats for the side effect of console output without altering the graphic output for the plot when there is at least one other plot layer.
Because of the way ‘ggplot2’ works, the values are listed to the console at the time when the ggplot object is printed. As shown here, no other geom or stat is required, however in the remaining examples we add geom_point() to make the data also visible in the plot.
## [1] "Input 'data' to 'compute_group()':"
## # A tibble: 100 x 4
## x y PANEL group
## <dbl> <dbl> <fct> <int>
## 1 1 -27205. 1 -1
## 2 2 -14243. 1 -1
## 3 3 45791. 1 -1
## 4 4 53731. 1 -1
## 5 5 -8029. 1 -1
## 6 6 102864. 1 -1
## 7 7 -18547. 1 -1
## 8 8 13081. 1 -1
## 9 9 79924. 1 -1
## 10 10 -44711. 1 -1
## # ... with 90 more rows
In the absence of facets or groups we just get the summary from one data frame.
## [1] "Input 'data' to 'compute_group()':"
## # A tibble: 100 x 4
## x y PANEL group
## <dbl> <dbl> <fct> <int>
## 1 1 -27205. 1 -1
## 2 2 -14243. 1 -1
## 3 3 45791. 1 -1
## 4 4 53731. 1 -1
## 5 5 -8029. 1 -1
## 6 6 102864. 1 -1
## 7 7 -18547. 1 -1
## 8 8 13081. 1 -1
## 9 9 79924. 1 -1
## 10 10 -44711. 1 -1
## # ... with 90 more rows
## [1] "Input 'data' to 'compute_panel()':"
## # A tibble: 100 x 4
## x y PANEL group
## <dbl> <dbl> <fct> <int>
## 1 1 -27205. 1 -1
## 2 2 -14243. 1 -1
## 3 3 45791. 1 -1
## 4 4 53731. 1 -1
## 5 5 -8029. 1 -1
## 6 6 102864. 1 -1
## 7 7 -18547. 1 -1
## 8 8 13081. 1 -1
## 9 9 79924. 1 -1
## 10 10 -44711. 1 -1
## # ... with 90 more rows
In the case of grouping then one data frame is summarized for each group in the ggplot object.
## [1] "Input 'data' to 'compute_group()':"
## # A tibble: 50 x 5
## x y colour PANEL group
## <dbl> <dbl> <fct> <fct> <int>
## 1 1 -27205. A 1 1
## 2 3 45791. A 1 1
## 3 5 -8029. A 1 1
## 4 7 -18547. A 1 1
## 5 9 79924. A 1 1
## 6 11 -2824. A 1 1
## 7 13 -78017. A 1 1
## 8 15 -74281. A 1 1
## 9 17 9904. A 1 1
## 10 19 -94023. A 1 1
## # ... with 40 more rows
## [1] "Input 'data' to 'compute_group()':"
## # A tibble: 50 x 5
## x y colour PANEL group
## <dbl> <dbl> <fct> <fct> <int>
## 1 2 -14243. B 1 2
## 2 4 53731. B 1 2
## 3 6 102864. B 1 2
## 4 8 13081. B 1 2
## 5 10 -44711. B 1 2
## 6 12 23840. B 1 2
## 7 14 75602. B 1 2
## 8 16 104677. B 1 2
## 9 18 -68747. B 1 2
## 10 20 -39230. B 1 2
## # ... with 40 more rows
Without facets, we still have only one panel.
## [1] "Input 'data' to 'compute_panel()':"
## # A tibble: 100 x 5
## x y colour PANEL group
## <dbl> <dbl> <fct> <fct> <int>
## 1 1 -27205. A 1 1
## 2 2 -14243. B 1 2
## 3 3 45791. A 1 1
## 4 4 53731. B 1 2
## 5 5 -8029. A 1 1
## 6 6 102864. B 1 2
## 7 7 -18547. A 1 1
## 8 8 13081. B 1 2
## 9 9 79924. A 1 1
## 10 10 -44711. B 1 2
## # ... with 90 more rows
The data are similar, except for the column named after the aesthetic, corresponding to the aesthetics used for grouping.
## [1] "Input 'data' to 'compute_group()':"
## # A tibble: 50 x 5
## x y shape PANEL group
## <dbl> <dbl> <fct> <fct> <int>
## 1 1 -27205. A 1 1
## 2 3 45791. A 1 1
## 3 5 -8029. A 1 1
## 4 7 -18547. A 1 1
## 5 9 79924. A 1 1
## 6 11 -2824. A 1 1
## 7 13 -78017. A 1 1
## 8 15 -74281. A 1 1
## 9 17 9904. A 1 1
## 10 19 -94023. A 1 1
## # ... with 40 more rows
## [1] "Input 'data' to 'compute_group()':"
## # A tibble: 50 x 5
## x y shape PANEL group
## <dbl> <dbl> <fct> <fct> <int>
## 1 2 -14243. B 1 2
## 2 4 53731. B 1 2
## 3 6 102864. B 1 2
## 4 8 13081. B 1 2
## 5 10 -44711. B 1 2
## 6 12 23840. B 1 2
## 7 14 75602. B 1 2
## 8 16 104677. B 1 2
## 9 18 -68747. B 1 2
## 10 20 -39230. B 1 2
## # ... with 40 more rows
Data returned by stats
Next we show how geom_debug() can be used. Simplest but not most important use is to print to the console the data as passed to geoms as input, but this is not that different from what we saw in the previous section with the debug stats.
## colour x y PANEL group
## 1 #F8766D 1 -27205.450 1 1
## 2 #00BFC4 2 -14242.651 1 2
## 3 #F8766D 3 45790.918 1 1
## 4 #00BFC4 4 53731.420 1 2
## 5 #F8766D 5 -8028.578 1 1
## 6 #00BFC4 6 102863.943 1 2
The main use of geom_debug() it to display the data returned by stats and received by the geoms. Not all extensions to ‘ggplot2’ document all the computed variables returned by the stats through data. In addition, when debugging a newly defined stat being able to easily see the output is particularly useful when a bug prevents graphical output from being displayed.
## # A tibble: 160 x 8
## colour x y ymin ymax se PANEL group
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <fct> <int>
## 1 #F8766D 1 -188136. -254711. -121562. 33111. 1 1
## 2 #F8766D 2.24 -176933. -242260. -111606. 32491. 1 1
## 3 #F8766D 3.48 -165730. -229819. -101641. 31875. 1 1
## 4 #F8766D 4.72 -154527. -217387. -91668. 31263. 1 1
## 5 #F8766D 5.96 -143324. -204964. -81684. 30657. 1 1
## 6 #F8766D 7.20 -132121. -192552. -71691. 30055. 1 1
## 7 #F8766D 8.44 -120918. -180150. -61686. 29459. 1 1
## 8 #F8766D 9.68 -109715. -167760. -51670. 28869. 1 1
## 9 #F8766D 10.9 -98512. -155383. -41642. 28285. 1 1
## 10 #F8766D 12.2 -87309. -143019. -31600. 27707. 1 1
## # ... with 150 more rows
## # A tibble: 2 x 7
## colour x group y ymin ymax PANEL
## <chr> <int> <int> <dbl> <dbl> <dbl> <fct>
## 1 #F8766D 1 1 254381. 213599. 295162. 1
## 2 #00BFC4 2 2 278485. 234891. 322079. 1
Grouping and facets
With grouping, for each group the compute_group() function is called with a subset of the data.
## [1] "Input 'data' to 'compute_group()':"
## x y colour PANEL group
## 1 1 -27205.450 A 1 1
## 3 3 45790.918 A 1 1
## 5 5 -8028.578 A 1 1
## [1] "Input 'data' to 'compute_group()':"
## x y colour PANEL group
## 2 2 -14242.65 B 1 2
## 4 4 53731.42 B 1 2
## 6 6 102863.94 B 1 2
In this example with grouping and facets, within each panel the compute_group() function is called for each group, in total four times.
## [1] "Input 'data' to 'compute_group()':"
## [1] 25
## [1] "Input 'data' to 'compute_group()':"
## [1] 25
## [1] "Input 'data' to 'compute_group()':"
## [1] 25
## [1] "Input 'data' to 'compute_group()':"
## [1] 25
With facets, for each panel the compute_panel() function is called with a subset of the data that is not split by groups. For our example, it is called twice.
## [1] "Input 'data' to 'compute_panel()':"
## [1] 50
## [1] "Input 'data' to 'compute_panel()':"
## [1] 50
Controlling the debug output
In the examples above we have demonstrated the use of the stats and geoms using default arguments. Here we show examples of generation of other types of debug output.
Display debug output on the plot
If we use as geom "label" or "text" a debug summary is added to the plot itself, we can use other arguments valid for the geom used, in this case vjust.
## [1] "Input 'data' to 'compute_group()':"
## # A tibble: 50 x 5
## x y shape PANEL group
## <dbl> <dbl> <fct> <fct> <int>
## 1 1 -27205. A 1 1
## 2 3 45791. A 1 1
## 3 5 -8029. A 1 1
## 4 7 -18547. A 1 1
## 5 9 79924. A 1 1
## 6 11 -2824. A 1 1
## 7 13 -78017. A 1 1
## 8 15 -74281. A 1 1
## 9 17 9904. A 1 1
## 10 19 -94023. A 1 1
## # ... with 40 more rows
## [1] "Input 'data' to 'compute_group()':"
## # A tibble: 50 x 5
## x y shape PANEL group
## <dbl> <dbl> <fct> <fct> <int>
## 1 2 -14243. B 1 2
## 2 4 53731. B 1 2
## 3 6 102864. B 1 2
## 4 8 13081. B 1 2
## 5 10 -44711. B 1 2
## 6 12 23840. B 1 2
## 7 14 75602. B 1 2
## 8 16 104677. B 1 2
## 9 18 -68747. B 1 2
## 10 20 -39230. B 1 2
## # ... with 40 more rows
User summaries for debug output
The default, made explicit.
## [1] "Input 'data' to 'compute_group()':"
## # A tibble: 100 x 4
## x y PANEL group
## <dbl> <dbl> <fct> <int>
## 1 1 -27205. 1 -1
## 2 2 -14243. 1 -1
## 3 3 45791. 1 -1
## 4 4 53731. 1 -1
## 5 5 -8029. 1 -1
## 6 6 102864. 1 -1
## 7 7 -18547. 1 -1
## 8 8 13081. 1 -1
## 9 9 79924. 1 -1
## 10 10 -44711. 1 -1
## # ... with 90 more rows
If a different summary function is passed as argument to parameter summary.fun it will be used instead of the default one.
## [1] "Input 'data' to 'compute_group()':"
## x y PANEL group
## Min. : 1.00 Min. : -94023 1:100 Min. :-1
## 1st Qu.: 25.75 1st Qu.: 40345 1st Qu.:-1
## Median : 50.50 Median : 154036 Median :-1
## Mean : 50.50 Mean : 266433 Mean :-1
## 3rd Qu.: 75.25 3rd Qu.: 422069 3rd Qu.:-1
## Max. :100.00 Max. :1077469 Max. :-1
## [1] "Input 'data' to 'compute_group()':"
## x y PANEL group
## 1 1 -27205.450 1 -1
## 2 2 -14242.651 1 -1
## 3 3 45790.918 1 -1
## 4 4 53731.420 1 -1
## 5 5 -8028.578 1 -1
## 6 6 102863.943 1 -1
## [1] "Input 'data' to 'compute_group()':"
## x y PANEL group
## 1 1 -27205.45 1 -1
## 2 2 -14242.65 1 -1
## 3 3 45790.92 1 -1
## [1] "Input 'data' to 'compute_group()':"
## [1] 100
This next chunk showing how to print the whole data frame is not run as its output would be very long as the data set contains 100 observations.
Assign debug output to a variable
In the next example we show how to save the data input of the geom to a variable in the global environment. However, assignment takes place at the time the ggplot object is printed.
pipe_assign <- function(value, name, pos = .GlobalEnv, ...) {
assign(x = name, value = value, inherits = FALSE, pos = pos, ...)
}
ggplot(my.data, aes(x, y, colour = group)) +
geom_point() +
geom_debug(summary.fun = pipe_assign,
summary.fun.args = list(name = "debug_data"),
print.fun = NULL)
debug_data
## colour x y PANEL group
## 1 #F8766D 1 -27205.45039 1 1
## 2 #00BFC4 2 -14242.65108 1 2
## 3 #F8766D 3 45790.91787 1 1
## 4 #00BFC4 4 53731.42037 1 2
## 5 #F8766D 5 -8028.57848 1 1
## 6 #00BFC4 6 102863.94292 1 2
## 7 #F8766D 7 -18547.28227 1 1
## 8 #00BFC4 8 13080.52133 1 2
## 9 #F8766D 9 79924.32504 1 1
## 10 #00BFC4 10 -44711.49916 1 2
## 11 #F8766D 11 -2823.73559 1 1
## 12 #00BFC4 12 23839.55471 1 2
## 13 #F8766D 13 -78016.69001 1 1
## 14 #00BFC4 14 75601.95706 1 2
## 15 #F8766D 15 -74281.23373 1 1
## 16 #00BFC4 16 104676.72111 1 2
## 17 #F8766D 17 9903.67373 1 1
## 18 #00BFC4 18 -68746.93124 1 2
## 19 #F8766D 19 -94022.62267 1 1
## 20 #00BFC4 20 -39230.19259 1 2
## 21 #F8766D 21 40550.54085 1 1
## 22 #00BFC4 22 10961.10296 1 2
## 23 #F8766D 23 12149.63105 1 1
## 24 #00BFC4 24 52254.25671 1 2
## 25 #F8766D 25 9950.24731 1 1
## 26 #00BFC4 26 3101.82898 1 2
## 27 #F8766D 27 23485.44314 1 1
## 28 #00BFC4 28 41668.54023 1 2
## 29 #F8766D 29 -27901.59355 1 1
## 30 #00BFC4 30 -59669.17456 1 2
## 31 #F8766D 31 39726.66001 1 1
## 32 #00BFC4 32 76038.66842 1 2
## 33 #F8766D 33 109169.84766 1 1
## 34 #00BFC4 34 10202.63915 1 2
## 35 #F8766D 35 98481.72725 1 1
## 36 #00BFC4 36 73.97657 1 2
## 37 #F8766D 37 40859.18209 1 1
## 38 #00BFC4 38 104296.43202 1 2
## 39 #F8766D 39 76002.67764 1 1
## 40 #00BFC4 40 146450.81373 1 2
## 41 #F8766D 41 61283.85767 1 1
## 42 #00BFC4 42 151336.13587 1 2
## 43 #F8766D 43 108122.81907 1 1
## 44 #00BFC4 44 38005.48600 1 2
## 45 #F8766D 45 138750.60638 1 1
## 46 #00BFC4 46 105880.33312 1 2
## 47 #F8766D 47 172220.31845 1 1
## 48 #00BFC4 48 166652.15369 1 2
## 49 #F8766D 49 125860.04342 1 1
## 50 #00BFC4 50 128807.63745 1 2
## 51 #F8766D 51 150030.22974 1 1
## 52 #00BFC4 52 156734.97163 1 2
## 53 #F8766D 53 245768.82089 1 1
## 54 #00BFC4 54 293062.82187 1 2
## 55 #F8766D 55 178917.33063 1 1
## 56 #00BFC4 56 288374.87380 1 2
## 57 #F8766D 57 254755.27055 1 1
## 58 #00BFC4 58 123199.36853 1 2
## 59 #F8766D 59 274487.91623 1 1
## 60 #00BFC4 60 222623.20984 1 2
## 61 #F8766D 61 222842.96771 1 1
## 62 #00BFC4 62 241015.87419 1 2
## 63 #F8766D 63 220328.38018 1 1
## 64 #00BFC4 64 318806.51984 1 2
## 65 #F8766D 65 272864.11128 1 1
## 66 #00BFC4 66 265162.41694 1 2
## 67 #F8766D 67 255642.47850 1 1
## 68 #00BFC4 68 322194.31154 1 2
## 69 #F8766D 69 347017.72201 1 1
## 70 #00BFC4 70 359621.14058 1 2
## 71 #F8766D 71 409505.44488 1 1
## 72 #00BFC4 72 295070.27132 1 2
## 73 #F8766D 73 358004.66398 1 1
## 74 #00BFC4 74 459490.18232 1 2
## 75 #F8766D 75 486672.38910 1 1
## 76 #00BFC4 76 409640.42160 1 2
## 77 #F8766D 77 475457.21816 1 1
## 78 #00BFC4 78 508282.47227 1 2
## 79 #F8766D 79 511276.10109 1 1
## 80 #00BFC4 80 459354.48209 1 2
## 81 #F8766D 81 381879.15102 1 1
## 82 #00BFC4 82 594162.52358 1 2
## 83 #F8766D 83 580768.97604 1 1
## 84 #00BFC4 84 718909.76743 1 2
## 85 #F8766D 85 465913.07527 1 1
## 86 #00BFC4 86 680853.27505 1 2
## 87 #F8766D 87 745596.30841 1 1
## 88 #00BFC4 88 620977.11497 1 2
## 89 #F8766D 89 691123.81099 1 1
## 90 #00BFC4 90 739921.53095 1 2
## 91 #F8766D 91 724468.12123 1 1
## 92 #00BFC4 92 720974.71398 1 2
## 93 #F8766D 93 823013.91892 1 1
## 94 #00BFC4 94 829332.45926 1 2
## 95 #F8766D 95 984858.01120 1 1
## 96 #00BFC4 96 977486.03153 1 2
## 97 #F8766D 97 818881.35514 1 1
## 98 #00BFC4 98 1058604.36945 1 2
## 99 #F8766D 99 977556.06367 1 1
## 100 #00BFC4 100 1077468.45449 1 2
## colour x y PANEL group
## 1 #F8766D 1 -27205.45039 1 1
## 2 #00BFC4 2 -14242.65108 1 2
## 3 #F8766D 3 45790.91787 1 1
## 4 #00BFC4 4 53731.42037 1 2
## 5 #F8766D 5 -8028.57848 1 1
## 6 #00BFC4 6 102863.94292 1 2
## 7 #F8766D 7 -18547.28227 1 1
## 8 #00BFC4 8 13080.52133 1 2
## 9 #F8766D 9 79924.32504 1 1
## 10 #00BFC4 10 -44711.49916 1 2
## 11 #F8766D 11 -2823.73559 1 1
## 12 #00BFC4 12 23839.55471 1 2
## 13 #F8766D 13 -78016.69001 1 1
## 14 #00BFC4 14 75601.95706 1 2
## 15 #F8766D 15 -74281.23373 1 1
## 16 #00BFC4 16 104676.72111 1 2
## 17 #F8766D 17 9903.67373 1 1
## 18 #00BFC4 18 -68746.93124 1 2
## 19 #F8766D 19 -94022.62267 1 1
## 20 #00BFC4 20 -39230.19259 1 2
## 21 #F8766D 21 40550.54085 1 1
## 22 #00BFC4 22 10961.10296 1 2
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