Added the VR-complex figures from the paper and the R code for generation

figures/vietoris_rips_complex_figures/.Rhistory

+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+geom_point()
+# Save plot as pdf
+point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
+ggsave(point_cloud_file_name)
+# fix a proximity for a Vietoris complex
+prox <- c(0.5, 1.0, 1.5)
+# visualize disks of fixed radii
+# Use option theme_void() to get rid of all axis labels
+# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
+p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+geom_point()
+# Save plot as pdf
+# point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
+# ggsave(point_cloud_file_name)
+#  visualize the Vietoris complex for this proximity
+p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+# simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
+# ggsave(simplicial_complex_file_name)
+p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+# overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
+# ggsave(overlay_file_name)
+# combine the plots
+gridExtra::grid.arrange(
+p_d, p_overlay,
+layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+# fix a proximity for a Vietoris complex
+prox <- 0.1
+# visualize disks of fixed radii
+# Use option theme_void() to get rid of all axis labels
+# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
+p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+geom_point()
+# Save plot as pdf
+point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
+ggsave(point_cloud_file_name)
+#  visualize the Vietoris complex for this proximity
+p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
+ggsave(simplicial_complex_file_name)
+p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
+ggsave(overlay_file_name)
+# combine the plots
+gridExtra::grid.arrange(
+p_d, p_overlay,
+layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+# fix a proximity for a Vietoris complex
+prox <- 0.5
+# visualize disks of fixed radii
+# Use option theme_void() to get rid of all axis labels
+# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
+p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+geom_point()
+# Save plot as pdf
+point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
+ggsave(point_cloud_file_name)
+#  visualize the Vietoris complex for this proximity
+p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
+ggsave(simplicial_complex_file_name)
+p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
+ggsave(overlay_file_name)
+# combine the plots
+gridExtra::grid.arrange(
+p_d, p_overlay,
+layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+# fix a proximity for a Vietoris complex
+prox <- 1.0
+# visualize disks of fixed radii
+# Use option theme_void() to get rid of all axis labels
+# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
+p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+geom_point()
+# Save plot as pdf
+point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
+ggsave(point_cloud_file_name)
+#  visualize the Vietoris complex for this proximity
+p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
+ggsave(simplicial_complex_file_name)
+p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
+ggsave(overlay_file_name)
+# combine the plots
+gridExtra::grid.arrange(
+p_d, p_overlay,
+layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+# fix a proximity for a Vietoris complex
+prox <- 1.5
+# visualize disks of fixed radii
+# Use option theme_void() to get rid of all axis labels
+# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
+p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+geom_point()
+# Save plot as pdf
+point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
+ggsave(point_cloud_file_name)
+#  visualize the Vietoris complex for this proximity
+p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
+ggsave(simplicial_complex_file_name)
+p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
+ggsave(overlay_file_name)
+# combine the plots
+gridExtra::grid.arrange(
+p_d, p_overlay,
+layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+# fix a proximity for a Vietoris complex
+prox <- 1.9
+# visualize disks of fixed radii
+# Use option theme_void() to get rid of all axis labels
+# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
+p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+geom_point()
+# Save plot as pdf
+point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
+ggsave(point_cloud_file_name)
+#  visualize the Vietoris complex for this proximity
+p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
+ggsave(simplicial_complex_file_name)
+p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
+ggsave(overlay_file_name)
+# combine the plots
+gridExtra::grid.arrange(
+p_d, p_overlay,
+layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+# fix a proximity for a Vietoris complex
+prox <- 2.0
+# visualize disks of fixed radii
+# Use option theme_void() to get rid of all axis labels
+# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
+p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+geom_point()
+# Save plot as pdf
+point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
+ggsave(point_cloud_file_name)
+#  visualize the Vietoris complex for this proximity
+p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
+ggsave(simplicial_complex_file_name)
+p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
+ggsave(overlay_file_name)
+# combine the plots
+gridExtra::grid.arrange(
+p_d, p_overlay,
+layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+# fix a proximity for a Vietoris complex
+prox <- 1.7
+# visualize disks of fixed radii
+# Use option theme_void() to get rid of all axis labels
+# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
+p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+geom_point()
+# Save plot as pdf
+point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
+ggsave(point_cloud_file_name)
+#  visualize the Vietoris complex for this proximity
+p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
+ggsave(simplicial_complex_file_name)
+p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
+ggsave(overlay_file_name)
+# combine the plots
+gridExtra::grid.arrange(
+p_d, p_overlay,
+layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+# fix a proximity for a Vietoris complex
+prox <- 1.6
+# visualize disks of fixed radii
+# Use option theme_void() to get rid of all axis labels
+# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
+p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+geom_point()
+# Save plot as pdf
+point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
+ggsave(point_cloud_file_name)
+#  visualize the Vietoris complex for this proximity
+p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
+ggsave(simplicial_complex_file_name)
+p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
+theme_bw() +
+theme(axis.title.x=element_blank(),
+axis.text.x=element_blank(),
+axis.ticks.x=element_blank()) +
+theme(axis.title.y=element_blank(),
+axis.text.y=element_blank(),
+axis.ticks.y=element_blank()) +
+coord_fixed() +
+stat_disk(radius = prox/2, fill = "aquamarine3") +
+stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+stat_vietoris1(diameter = prox, alpha = .25) +
+stat_vietoris0()
+# Save plot as pdf
+overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
+ggsave(overlay_file_name)
+# combine the plots
+gridExtra::grid.arrange(
+p_d, p_overlay,
+layout_matrix = matrix(c(1, 2), nrow = 1)
+)

figures/vietoris_rips_complex_figures/ggtda_experiments.Rmd

+---
+title: "R Notebook"
+output: html_notebook
+---
+
+This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code. 
+
+Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Cmd+Shift+Enter*. 
+
+Add a new chunk by clicking the *Insert Chunk* button on the toolbar or by pressing *Cmd+Option+I*.
+
+When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the *Preview* button or press *Cmd+Shift+K* to preview the HTML file). 
+
+The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike *Knit*, *Preview* does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.
+
+
+```{r}
+library(ggplot2)
+# attach *ggtda*
+library(ggtda)
+```
+
+```{r}
+# generate the point cloud data
+n <- 36; sd <- .2
+set.seed(0)
+first_column <- c(1.0, 2.0, 1.0, 2.0)
+second_column <- c(1.0, 1.0, 2.0, 2.0)
+d <- data.frame(
+  first_column,
+  second_column
+)
+# compute the persistent homology
+ph <- as.data.frame(ripserr::vietoris_rips(as.matrix(d), dim = 1))
+print(head(ph, n = 12))
+ph <- transform(ph, dim = as.factor(dimension))
+```
+
+```{r}
+# fix a proximity for a Vietoris complex
+prox <- 1.5
+
+# visualize disks of fixed radii
+# Use option theme_void() to get rid of all axis labels
+# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
+p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
+  theme_bw() +
+  theme(axis.title.x=element_blank(),
+        axis.text.x=element_blank(),
+        axis.ticks.x=element_blank()) +
+  theme(axis.title.y=element_blank(),
+        axis.text.y=element_blank(),
+        axis.ticks.y=element_blank()) +
+  coord_fixed() +
+  stat_disk(radius = prox/2, fill = "aquamarine3") +
+  geom_point()
+# Save plot as pdf
+ggsave("diamonds3.pdf")
+
+#  visualize the Vietoris complex for this proximity
+p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
+  theme_bw() +
+  coord_fixed() +
+  stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+  stat_vietoris1(diameter = prox, alpha = .25) +
+  stat_vietoris0()
+# combine the plots
+gridExtra::grid.arrange(
+  p_d, p_sc,
+  layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+```
+
+```{r}
+# visualize the persistence data, indicating cutoffs at this proximity
+p_bc <- ggplot(ph,
+       aes(start = birth, end = death, colour = dim)) +
+  theme_barcode() +
+  geom_barcode() +
+  labs(x = "Diameter", y = "Homological features") +
+  geom_vline(xintercept = prox, color = "darkgoldenrod", linetype = "dashed")
+p_pd <- ggplot(ph) +
+  theme_persist() +
+  coord_fixed() +
+  stat_persistence(aes(start = birth, end = death, colour = dim, shape = dim)) +
+  geom_abline(intercept = 0, slope = 1, color = "darkgray") +
+  labs(x = "Birth", y = "Death") +
+  lims(x = c(0, 0.8), y = c(0, NA)) +
+  geom_point(data = data.frame(x = prox), aes(x, x),
+             colour = "darkgoldenrod", shape = "diamond", size = 4)
+# combine the plots
+gridExtra::grid.arrange(
+  p_bc, p_pd,
+  layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+```

figures/vietoris_rips_complex_figures/ggtda_template.Rmd

+---
+title: "R Notebook"
+output: html_notebook
+---
+
+This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code. 
+
+Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Cmd+Shift+Enter*. 
+
+Add a new chunk by clicking the *Insert Chunk* button on the toolbar or by pressing *Cmd+Option+I*.
+
+When you save the notebook, an HTML file containing the code and output will be saved alongside it (click the *Preview* button or press *Cmd+Shift+K* to preview the HTML file). 
+
+The preview shows you a rendered HTML copy of the contents of the editor. Consequently, unlike *Knit*, *Preview* does not run any R code chunks. Instead, the output of the chunk when it was last run in the editor is displayed.
+
+
+```{r}
+library(ggplot2)
+# attach *ggtda*
+library(ggtda)
+library(stringr)
+```
+
+```{r}
+# generate the point cloud data
+# noisy circle
+n <- 36; sd <- .2
+set.seed(0)
+t <- stats::runif(n = n, min = 0, max = 2*pi)
+d <- data.frame(
+  first_column = cos(t) + stats::rnorm(n = n, mean = 0, sd = sd),
+  second_column = sin(t) + stats::rnorm(n = n, mean = 0, sd = sd)
+)
+
+# compute the persistent homology
+ph <- as.data.frame(ripserr::vietoris_rips(as.matrix(d), dim = 1))
+print(head(ph, n = 12))
+ph <- transform(ph, dim = as.factor(dimension))
+```
+
+```{r}
+# fix a proximity for a Vietoris complex
+prox <- 1.6
+
+# visualize disks of fixed radii
+# Use option theme_void() to get rid of all axis labels
+# https://stackoverflow.com/questions/35090883/remove-all-of-x-axis-labels-in-ggplot
+p_d <- ggplot(d, aes(x = first_column, y = second_column)) +
+  theme_bw() +
+  theme(axis.title.x=element_blank(),
+        axis.text.x=element_blank(),
+        axis.ticks.x=element_blank()) +
+  theme(axis.title.y=element_blank(),
+        axis.text.y=element_blank(),
+        axis.ticks.y=element_blank()) +
+  coord_fixed() +
+  stat_disk(radius = prox/2, fill = "aquamarine3") +
+  geom_point()
+# Save plot as pdf
+point_cloud_file_name = str_glue('point_cloud_{round(prox, 2)}.pdf')
+ggsave(point_cloud_file_name)
+
+#  visualize the Vietoris complex for this proximity
+p_sc <- ggplot(d, aes(x = first_column, y = second_column)) +
+  theme_bw() +
+  theme(axis.title.x=element_blank(),
+        axis.text.x=element_blank(),
+        axis.ticks.x=element_blank()) +
+  theme(axis.title.y=element_blank(),
+        axis.text.y=element_blank(),
+        axis.ticks.y=element_blank()) +
+  coord_fixed() +
+  stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+  stat_vietoris1(diameter = prox, alpha = .25) +
+  stat_vietoris0()
+# Save plot as pdf
+simplicial_complex_file_name = str_glue('simplicial_complex_{round(prox, 2)}.pdf')
+ggsave(simplicial_complex_file_name)
+
+
+p_overlay <- ggplot(d, aes(x = first_column, y = second_column)) +
+  theme_bw() +
+  theme(axis.title.x=element_blank(),
+        axis.text.x=element_blank(),
+        axis.ticks.x=element_blank()) +
+  theme(axis.title.y=element_blank(),
+        axis.text.y=element_blank(),
+        axis.ticks.y=element_blank()) +
+  coord_fixed() +
+  stat_disk(radius = prox/2, fill = "aquamarine3") +
+  stat_vietoris2(diameter = prox, fill = "darkgoldenrod") +
+  stat_vietoris1(diameter = prox, alpha = .25) +
+  stat_vietoris0()
+# Save plot as pdf
+overlay_file_name = str_glue('overlay_{round(prox, 2)}.pdf')
+ggsave(overlay_file_name)
+
+# combine the plots
+gridExtra::grid.arrange(
+  p_d, p_overlay,
+  layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+```
+
+```{r}
+# visualize the persistence data, indicating cutoffs at this proximity
+p_bc <- ggplot(ph,
+       aes(start = birth, end = death, colour = dim)) +
+  theme_barcode() +
+  geom_barcode() +
+  labs(x = "Diameter", y = "Homological features") +
+  geom_vline(xintercept = prox, color = "darkgoldenrod", linetype = "dashed")
+p_pd <- ggplot(ph) +
+  theme_persist() +
+  coord_fixed() +
+  stat_persistence(aes(start = birth, end = death, colour = dim, shape = dim)) +
+  geom_abline(intercept = 0, slope = 1, color = "darkgray") +
+  labs(x = "Birth", y = "Death") +
+  lims(x = c(0, 0.8), y = c(0, NA)) +
+  geom_point(data = data.frame(x = prox), aes(x, x),
+             colour = "darkgoldenrod", shape = "diamond", size = 4)
+# combine the plots
+gridExtra::grid.arrange(
+  p_bc, p_pd,
+  layout_matrix = matrix(c(1, 2), nrow = 1)
+)
+```