Awesome
<!-- README.md is generated from README.Rmd. Please edit that file -->triangular <img src="man/figures/logo.png" align="right" height=300/>
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triangular decomposes complex polygons into sets of triangles and
works with:
- polygons with holes
- self-intersecting polygons
- polygons with duplicated vertices
Licensing
While the code in this package is licensed under MIT, this package relies heavily on:
- RTriangle which is licensed CC BY-NC-SA 4.0.
- polyclip which is licensed under BSL
Installation
You can install from GitHub with:
# install.package('remotes')
remotes::install_github('coolbutuseless/triangular')
Polygon with a Hole in it
ggplot2 rendering of polygon with a hole in it
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# polygons_df - data.frame of polygon vertices with group/subgroups
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
polygons_df <- df <- data.frame(
x = c(4, 8, 8, 4, 6, 7, 7, 6),
y = c(4, 4, 8, 8, 6, 6, 7, 7),
group = c(1, 1, 1, 1, 1, 1, 1, 1),
subgroup = c(1, 1, 1, 1, 2, 2, 2, 2)
)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# How 'ggplot2' handles this case
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(polygons_df) +
geom_polygon(aes(x, y, group=group, subgroup=subgroup)) +
geom_path(aes(x, y, group = interaction(group, subgroup))) +
theme_bw() +
coord_equal() +
labs(title = "ggplot2 rendering of original polygon(s)")
{triangular} decomposition of a polygon with a hole
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Turn the polygon data.frame into individual triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
triangles_df <- triangular::decompose(polygons_df)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Plot the triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(triangles_df) +
geom_polygon(aes(x, y, fill = as.factor(idx)), colour = 'grey20', size = 0.15) +
theme_bw() +
coord_equal() +
labs(title = "Decomposition into simple tris with {triangular}") +
theme(legend.position = 'none')
Polygon with Two Holes
ggplot2 rendering of polygon with two holes
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# polygon
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
polygons_df <- data.frame(
x = c(4, 8, 8, 4, 6, 7, 7, 6, 4.5, 5, 5, 4.5),
y = c(4, 4, 8, 8, 6, 6, 7, 7, 4.5, 4.5, 5, 5),
group = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1),
subgroup = c(1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3)
)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# "Native" ggplot2 rendering
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(polygons_df) +
geom_polygon(aes(x, y, subgroup = subgroup)) +
theme_bw() +
coord_equal() +
labs(title = "ggplot2 rendering of original polygon(s)")
{triangular} decomposition of a polygon with two holes
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Decompose into triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
triangles_df <- triangular::decompose(polygons_df)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Plot the `triangular` decomposition into triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(triangles_df) +
geom_polygon(aes(x, y, fill = as.factor(idx)), colour = 'grey20', size = 0.15) +
theme_bw() +
coord_equal() +
labs(title = "Decomposition into simple tris with {triangular}") +
theme(legend.position = 'none')
Two Polygons with One Hole Each
ggplot2 rendering of muliple polygons with holes
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Two polygons with one hole each
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
polygons_df <- data.frame(
x = c(1, 4, 4, 1, 2, 3, 3, 2, 5, 8, 8, 5, 6, 7, 7, 6),
y = c(1, 1, 4, 4, 2, 2, 3, 3, 5, 5, 8, 8, 6, 6, 7, 7),
group = c(1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2),
subgroup = c(1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4),
fill = rep(c('tomato', 'skyblue'), each = 8)
)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# "Native" ggplot2 rendering
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(polygons_df) +
geom_polygon(aes(x, y, subgroup = subgroup, fill = I(fill))) +
theme_bw() +
coord_equal() +
labs(title = "ggplot2 rendering of original polygon(s)")
triangular decomposition (Two Polygons with One Hole Each)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Decompose into triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
triangles_df <- triangular::decompose(polygons_df)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Plot the `triangular` decomposition into triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(triangles_df) +
geom_polygon(aes(x, y, fill = I(fill), group = idx), colour = 'grey20', size = 0.15) +
theme_bw() +
coord_equal() +
labs(title = "Decomposition into simple tris with {triangular}") +
theme(legend.position = 'none')
Polygon with duplicated vertex
This happens sometimes with ggplot2::geom_density()
ggplot2 rendering of polygon with duplicated vertices
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Polygon with duplicated vertex
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
polygons_df <- data.frame(
x = c(1, 2, 2, 1, 2, 3, 3, 2),
y = c(1, 1, 2, 2, 2, 2, 3, 3),
group = c(1, 1, 1, 1, 2, 2, 2, 2),
subgroup = 1,
fill = rep(c('tomato', 'skyblue'), each = 4)
)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# "Native" ggplot2 rendering
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(polygons_df) +
geom_polygon(aes(x, y, group = group, fill = I(fill))) +
theme_bw() +
coord_equal() +
labs(title = "ggplot2 rendering of original polygon(s)")
triangular decomposition - (Polygon with duplicated vertex)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Decompose into triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
triangles_df <- triangular::decompose(polygons_df)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Plot the `triangular` decomposition into triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(triangles_df) +
geom_polygon(aes(x, y, fill = I(fill), group = idx), colour = 'grey20', size = 0.15) +
theme_bw() +
coord_equal() +
labs(title = "Decomposition into simple tris with {triangular}") +
theme(legend.position = 'none')
Polygon from Random Points
ggplot2 rendering of a Polygon made from Random Points)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# 10 random points
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
set.seed(1)
polygons_df <- data.frame(
x = runif(10),
y = runif(10),
group = 1,
subgroup = 1
)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# "Native" ggplot2 rendering
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(polygons_df) +
geom_polygon(aes(x, y), fill = 'skyblue') +
geom_path(aes(x, y, group = interaction(group, subgroup))) +
theme_bw() +
coord_equal() +
labs(title = "ggplot2 rendering of original polygon(s)")
triangular decomposition - (Polygon from Random Points)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Decompose into triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
triangles_df <- triangular::decompose(polygons_df)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Plot the `triangular` decomposition into triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(triangles_df) +
geom_polygon(aes(x, y, fill = as.factor(idx)), colour = 'grey20', size = 0.15) +
theme_bw() +
coord_equal() +
labs(title = "Decomposition into simple tris with {triangular}") +
theme(legend.position = 'none')
Triforce
Triforce
d <- sqrt(3)/2
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Single triangle with a triangular hole
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
polygons_df <- df <- data.frame(
x = c(0, 1, 0.5, 0.25, 0.5, 0.75),
y = c(0, 0, d , d/2 , 0 , d/2),
subgroup = c(1, 1, 1 , 2, 2, 2),
group = 1L
)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# "Native" ggplot2 rendering
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(polygons_df) +
geom_polygon(aes(x, y, subgroup = subgroup)) +
geom_path(aes(x, y, group = interaction(group, subgroup))) +
theme_bw() +
coord_equal() +
labs(title = "ggplot2 rendering of original polygon")
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# decompose into simple triangular pieces i.e. without holes or self-intersections
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
triangles_df <- triangular::decompose(polygons_df)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Plot the decomposition into triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(triangles_df) +
geom_polygon(aes(x, y, fill = as.factor(idx)), colour = 'grey20', size = 0.15) +
theme_bw() +
coord_equal() +
labs(title = "{triangular} decomposition of single polygon (with hole)\n into multiple simple polygons") +
theme(legend.position = 'none')
Logo
ggplot2 rendering nested hexagons
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# polygons_df - data.frame of polygon vertices with group/subgroups
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
r <- 5
hex_df <- data.frame(
x = r * cos(seq(30, 360, 60) * pi/180),
y = r * sin(seq(30, 360, 60) * pi/180),
group = 1,
subgroup = 1
)
hole_df <- data.frame(
x = 2 * cos(seq(30, 360, 60) * pi/180) + 1,
y = 2 * sin(seq(30, 360, 60) * pi/180) + 1,
group = 1,
subgroup = 2
)
polygons_df <- rbind(hex_df, hole_df)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# How 'ggplot2' handles this case
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(polygons_df) +
geom_polygon(aes(x, y, group=group, subgroup=subgroup)) +
geom_path(aes(x, y, group = interaction(group, subgroup))) +
theme_bw() +
coord_equal() +
labs(title = "ggplot2 rendering of original polygon(s)")
{triangular} decomposition of nested hexagons
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Turn the polygon data.frame into individual triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
triangles_df <- triangular::decompose(polygons_df)
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Plot the triangles
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
p <- ggplot(triangles_df) +
geom_polygon(aes(x, y, fill = as.factor(idx)), colour = 'grey20', size = 0.15) +
theme_void() +
coord_equal() +
theme(legend.position = 'none') +
scale_fill_viridis_d(option = 'D') +
annotate('text', x = 1, y = 1.4, label = 't\nr i\na n g\nu l a r',
size = 5.5, family = 'mono', fontface = 'bold')
ggsave("man/figures/logo.png", plot = p, width = 5, height = 5)
p
Related Software
- silicate + anglr do all of what triangular does (and more!), with a much more configurable interface (that I did not need)
- decido does fast
ear-cutting triangulation.
Unfortunately, this doesn’t deal nicely with self-intersecting polygons.
Acknowledgements
- Michael Sumner on twitter for his in-depth technical advice on graphics and and triangles in R
- R Core for developing and maintaining such a wonderful language.
- CRAN maintainers, for patiently shepherding packages onto CRAN and maintaining the repository