--- title: "Metrics" output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{Metrics} %\VignetteEngine{knitr::rmarkdown} %\VignetteEncoding{UTF-8} --- ```{r, include = FALSE} knitr::opts_chunk$set( collapse = TRUE, comment = "#>" ) ``` ## Load Packages The first step is to load the rTwig package. Real Twig works well when paired with packages from the [Tidyverse](https://www.tidyverse.org/), so we will also load the dplyr, tidyr, and ggplot packages to help with data manipulation and visualization, ggpubr for multi-panel plots, and rgl for point cloud plotting. ```{r, eval=FALSE} devtools::install_github("https://github.com/aidanmorales/rTwig") ``` ```{r, message=FALSE, warning=FALSE} # Load rTwig library(rTwig) # Other useful packages library(rgl) library(tidyr) library(dplyr) library(ggplot2) library(ggpubr) ``` ## Run Real Twig & Calculate Metrics Next, let's run Real Twig with `run_rtwig()` and calculate our tree metrics with `tree_metrics()`. ```{r, message=FALSE} # File path to QSM file <- system.file("extdata/QSM.mat", package = "rTwig") # Run Real Twig cylinder <- run_rtwig(file, twig_radius = 4.23, metrics = FALSE) # Calculate detailed tree metrics metrics <- tree_metrics(cylinder) ``` #### Stem Taper ```{r, fig.width=6, fig.height=3, fig.align='center', out.width="100%", echo=FALSE} metrics$stem_taper %>% ggplot(aes(x = height_m, y = diameter_cm)) + geom_point() + stat_smooth(method = "loess", color = "black", formula = y ~ x) + theme_classic() + labs( # title = "Stem Taper", x = "Height (m)", y = "Diameter (cm)" ) ``` #### Tree Metrics ```{r, echo=FALSE} tree_h <- metrics$tree_height_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = height_class_m, y = value, color = height_class_m, fill = height_class_m )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Height Distributions", x = "", y = "", fill = "Height Class (m)", color = "Height Class (m)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} tree_d <- metrics$tree_diameter_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = diameter_class_cm, y = value, color = diameter_class_cm, fill = diameter_class_cm )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Diameter Distributions", x = "", y = "", fill = "Diameter Class (cm)", color = "Diameter Class (cm)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} tree_z <- metrics$tree_zenith_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = zenith_class_deg, y = value, color = zenith_class_deg, fill = zenith_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Zenith Distributions", x = "", y = "", fill = "Zenith Class (deg)", color = "Zenith Class (deg)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} tree_az <- metrics$tree_azimuth_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = azimuth_class_deg, y = value, color = azimuth_class_deg, fill = azimuth_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Azimuth Distributions", x = "", y = "", fill = "Azimuth Class (deg)", color = "Azimuth Class (deg)" ) + theme_classic() + facet_wrap(~type) + theme(legend.position = "right") ``` ```{r, fig.width=12, fig.height=6, fig.align='center', out.width="100%", echo=FALSE} ggarrange(tree_d, tree_h, tree_az, tree_z) # annotate_figure(tree, top = text_grob("Tree Metrics", size = 16, face = "bold")) ``` #### Branch Metrics ```{r, echo=FALSE} branch_d <- metrics$branch_diameter_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = diameter_class_cm, y = value, color = diameter_class_cm, fill = diameter_class_cm )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Branch Diameter Distributions", x = "", y = "", fill = "Diameter Class (cm)", color = "Diameter Class (cm)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} branch_h <- metrics$branch_height_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = height_class_m, y = value, color = height_class_m, fill = height_class_m )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Branch Height Distributions", x = "", y = "", fill = "Height Class (m)", color = "Height Class (m)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} branch_ang <- metrics$branch_angle_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = angle_class_deg, y = value, color = angle_class_deg, fill = angle_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Branch Angle Distributions", x = "", y = "", fill = "Angle Class (deg)", color = "Angle Class (deg)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} branch_z <- metrics$branch_zenith_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = zenith_class_deg, y = value, color = zenith_class_deg, fill = zenith_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Branch Zenith Distributions", x = "", y = "", fill = "Zenith Class (deg)", color = "Zenith Class (deg)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} branch_az <- metrics$branch_azimuth_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = azimuth_class_deg, y = value, color = azimuth_class_deg, fill = azimuth_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Branch Azimuth Distributions", x = "", y = "", fill = "Azimuth Class (deg)", color = "Azimuth Class (deg)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} branch_o <- metrics$branch_order_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = branch_order, y = value, color = branch_order, fill = branch_order )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Branch Order Distributions", x = "", y = "", fill = "Branch Order", color = "Branch Order" ) + facet_wrap(~type) + theme_classic() ``` ```{r, fig.width=12, fig.height=8, out.width="100%", fig.align='center', echo=FALSE} ggarrange(branch_d, branch_h, branch_ang, branch_az, branch_z, branch_o, ncol = 2, nrow = 3) # annotate_figure(branch, top = text_grob("Branch Metrics", size = 16, face = "bold")) ``` #### Segment Metrics ```{r, echo=FALSE} segment_d <- metrics$segment_diameter_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 3:5, names_to = "type") %>% ggplot(aes( x = diameter_class_cm, y = value, color = diameter_class_cm, fill = diameter_class_cm )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Segment Diameter Distributions", x = "", y = "", fill = "Diameter Class (cm)", color = "Diameter Class (cm)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} segment_h <- metrics$segment_height_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = height_class_m, y = value, color = height_class_m, fill = height_class_m )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Segment Height Distributions", x = "", y = "", fill = "Height Class (m)", color = "Height Class (m)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} segment_ang <- metrics$segment_angle_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = angle_class_deg, y = value, color = angle_class_deg, fill = angle_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Segment Angle Distributions", x = "", y = "", fill = "Angle Class (deg)", color = "Angle Class (deg)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} segment_z <- metrics$segment_zenith_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = zenith_class_deg, y = value, color = zenith_class_deg, fill = zenith_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Segment Zenith Distributions", x = "", y = "", fill = "Zenith Class (deg)", color = "Zenith Class (deg)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} segment_az <- metrics$segment_azimuth_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = azimuth_class_deg, y = value, color = azimuth_class_deg, fill = azimuth_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Segment Azimuth Distributions", x = "", y = "", fill = "Azimuth Class (deg)", color = "Azimuth Class (deg)" ) + facet_wrap(~type) + theme_classic() ``` ```{r, echo=FALSE} segment_o <- metrics$segment_order_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 3:5, names_to = "type") %>% ggplot(aes( x = reverse_order, y = value, color = reverse_order, fill = reverse_order )) + geom_bar(stat = "identity", position = "dodge2") + labs( # title = "Reverse Order Distributions", x = "", y = "", fill = "Reverse Order", color = "Reverse Order" ) + facet_wrap(~type) + theme_classic() ``` ```{r, fig.width=12, fig.height=8, out.width="100%", fig.align='center', echo=FALSE} ggarrange(segment_d, segment_h, segment_ang, segment_az, segment_z, segment_o, ncol = 2, nrow = 3) # annotate_figure(segment, top = text_grob("Branch Metrics", size = 16, face = "bold")) ``` #### Spreads ```{r, echo=FALSE, fig.width=6, fig.height=6, out.width="100%"} spreads <- metrics$spreads # Generate colors from red to blue n <- length(unique(spreads$height_class)) colors <- data.frame(r = seq(0, 1, length.out = n), g = 0, b = seq(1, 0, length.out = n)) # Convert colors to hex color_hex <- apply(colors, 1, function(row) { rgb(row[1], row[2], row[3]) }) # Assign colors to height classes height_class_colors <- data.frame( height_class = unique(spreads$height_class), color = color_hex ) spreads %>% left_join(height_class_colors, by = "height_class") %>% ggplot(aes(x = azimuth_deg, y = spread_m, group = height_class, color = color)) + geom_line() + scale_color_identity() + coord_polar(start = 0) + labs(x = "", y = "") + theme_minimal() + theme(axis.text.y = element_blank()) ``` #### Vertical Profile ```{r, fig.width=6, fig.height=3, fig.align='center', out.width="100%", echo=FALSE} metrics$spreads %>% group_by(height_class) %>% summarise( max = max(spread_m), mean = mean(spread_m), min = min(spread_m) ) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes(x = height_class, y = value, color = type)) + geom_line() + labs( x = "Height Class", y = "Spread (m)", color = "" ) + theme_classic() ``` #### Point Cloud We can even plot the simulated point cloud with the rgl library, and look at the cylinder connectivity. ```{r, eval=FALSE} plot_qsm(cylinder, qsm$cylinder, cloud = metrics$cloud, skeleton = TRUE) ``` ## Plotting Code ```{r, eval=FALSE} # Stem Taper ------------------------------------------------------------------- metrics$stem_taper %>% ggplot(aes(x = height_m, y = diameter_cm)) + geom_point() + stat_smooth(method = "loess", color = "black", formula = y ~ x) + theme_classic() + labs( title = "Stem Taper", x = "Height (m)", y = "Diameter (cm)" ) # Tree Metrics ----------------------------------------------------------------- # Tree Height Distributions metrics$tree_height_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = height_class_m, y = value, color = height_class_m, fill = height_class_m )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Height Distributions", x = "", y = "", fill = "Height Class (m)", color = "Height Class (m)" ) + facet_wrap(~type) + theme_classic() # Tree Diameter Distributions metrics$tree_diameter_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = diameter_class_cm, y = value, color = diameter_class_cm, fill = diameter_class_cm )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Diameter Distributions", x = "", y = "", fill = "Diameter Class (cm)", color = "Diameter Class (cm)" ) + facet_wrap(~type) + theme_classic() # Tree Zenith Distributions metrics$tree_zenith_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = zenith_class_deg, y = value, color = zenith_class_deg, fill = zenith_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Zenith Distributions", x = "", y = "", fill = "Zenith Class (deg)", color = "Zenith Class (deg)" ) + facet_wrap(~type) + theme_classic() # Tree azimuth distributions metrics$tree_azimuth_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = azimuth_class_deg, y = value, color = azimuth_class_deg, fill = azimuth_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Azimuth Distributions", x = "", y = "", fill = "Azimuth Class (deg)", color = "Azimuth Class (deg)" ) + theme_classic() + facet_wrap(~type) + theme(legend.position = "right") # Branch Metrics --------------------------------------------------------------- # Branch diameter distributions metrics$branch_diameter_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = diameter_class_cm, y = value, color = diameter_class_cm, fill = diameter_class_cm )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Branch Diameter Distributions", x = "", y = "", fill = "Diameter Class (cm)", color = "Diameter Class (cm)" ) + facet_wrap(~type) + theme_classic() # Branch height distributions metrics$branch_height_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = height_class_m, y = value, color = height_class_m, fill = height_class_m )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Branch Height Distributions", x = "", y = "", fill = "Height Class (m)", color = "Height Class (m)" ) + facet_wrap(~type) + theme_classic() # Branch angle distributions metrics$branch_angle_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = angle_class_deg, y = value, color = angle_class_deg, fill = angle_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Branch Angle Distributions", x = "", y = "", fill = "Angle Class (deg)", color = "Angle Class (deg)" ) + facet_wrap(~type) + theme_classic() # Branch zenith distributions metrics$branch_zenith_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = zenith_class_deg, y = value, color = zenith_class_deg, fill = zenith_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Branch Zenith Distributions", x = "", y = "", fill = "Zenith Class (deg)", color = "Zenith Class (deg)" ) + facet_wrap(~type) + theme_classic() # Branch azimuth distributions metrics$branch_azimuth_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = azimuth_class_deg, y = value, color = azimuth_class_deg, fill = azimuth_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Branch Azimuth Distributions", x = "", y = "", fill = "Azimuth Class (deg)", color = "Azimuth Class (deg)" ) + facet_wrap(~type) + theme_classic() # Branch order distributions metrics$branch_order_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = branch_order, y = value, color = branch_order, fill = branch_order )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Branch Order Distributions", x = "", y = "", fill = "Branch Order", color = "Branch Order" ) + facet_wrap(~type) + # Segment Metrics -------------------------------------------------------------- # Segment diameter distributions metrics$segment_diameter_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 3:5, names_to = "type") %>% ggplot(aes( x = diameter_class_cm, y = value, color = diameter_class_cm, fill = diameter_class_cm )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Segment Diameter Distributions", x = "", y = "", fill = "Diameter Class (cm)", color = "Diameter Class (cm)" ) + facet_wrap(~type) + theme_classic() # Segment height distributions metrics$segment_height_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = height_class_m, y = value, color = height_class_m, fill = height_class_m )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Segment Height Distributions", x = "", y = "", fill = "Height Class (m)", color = "Height Class (m)" ) + facet_wrap(~type) + theme_classic() # Segment angle distributions metrics$segment_angle_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = angle_class_deg, y = value, color = angle_class_deg, fill = angle_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Segment Angle Distributions", x = "", y = "", fill = "Angle Class (deg)", color = "Angle Class (deg)" ) + facet_wrap(~type) + # Segment zenith distributions metrics$segment_zenith_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = zenith_class_deg, y = value, color = zenith_class_deg, fill = zenith_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Segment Zenith Distributions", x = "", y = "", fill = "Zenith Class (deg)", color = "Zenith Class (deg)" ) + facet_wrap(~type) + theme_classic() # Segment azimuth distributions metrics$segment_azimuth_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes( x = azimuth_class_deg, y = value, color = azimuth_class_deg, fill = azimuth_class_deg )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Segment Azimuth Distributions", x = "", y = "", fill = "Azimuth Class (deg)", color = "Azimuth Class (deg)" ) + facet_wrap(~type) + theme_classic() # Segment order distributions metrics$segment_order_dist %>% mutate(volume_L = volume_m3 * 1000) %>% select(-volume_m3) %>% relocate(volume_L, .before = area_m2) %>% pivot_longer(cols = 3:5, names_to = "type") %>% ggplot(aes( x = reverse_order, y = value, color = reverse_order, fill = reverse_order )) + geom_bar(stat = "identity", position = "dodge2") + labs( title = "Reverse Order Distributions", x = "", y = "", fill = "Reverse Order", color = "Reverse Order" ) + facet_wrap(~type) + theme_classic() # Spreads ---------------------------------------------------------------------- spreads <- metrics$spreads # Generate colors from red to blue n <- length(unique(spreads$height_class)) colors <- data.frame(r = seq(0, 1, length.out = n), g = 0, b = seq(1, 0, length.out = n)) # Convert colors to hex color_hex <- apply(colors, 1, function(row) { rgb(row[1], row[2], row[3]) }) # Assign colors to height classes height_class_colors <- data.frame( height_class = unique(spreads$height_class), color = color_hex ) spreads %>% left_join(height_class_colors, by = "height_class") %>% ggplot(aes(x = azimuth_deg, y = spread_m, group = height_class, color = color)) + geom_line() + scale_color_identity() + coord_polar(start = 0) + labs(x = "", y = "") + theme_minimal() + theme(axis.text.y = element_blank()) # Vertical profile ------------------------------------------------------------- metrics$spreads %>% group_by(height_class) %>% summarise( max = max(spread_m), mean = mean(spread_m), min = min(spread_m) ) %>% pivot_longer(cols = 2:4, names_to = "type") %>% ggplot(aes(x = height_class, y = value, color = type)) + geom_line() + labs( x = "Height Class", y = "Spread (m)", color = "" ) + theme_classic() ```