threed - 3d object transformation library

December 2, 2018 · View on GitHub

threed is a small, dependency-free R library for doing 3d object transformations i.e. translation, scaling, rotation and perspective projection.

The only 3d object format currently supported is the mesh3d format from rgl (as well as some extensions to the mesh3d format to support point and line objects).

Features:

standard translate, scale and rotate transformations
perspective + orthographic projection
as.data.frame.mesh3d
- convert 3d objects into data.frames
- calculates a lot of meta data such as face normals, vertex normals and whether a face is hidden from view.
fortify.mesh3d
- this enables a mesh3d object to be given as the ggplot2 data argument.
Includes some built-in mesh3d objects (see threed::mesh3dobj) e.g.
- cube, icosahedron, teapot, cow, bunny

Vignettes

vignette('drawing-a-cube', package='threed')
- All the ways of drawing a 3d cube using threed in ggplot2
- e.g. hidden line removal, fake light shading etc
vignette('mesh3d', package='threed')
- Adaptations and extensions to the mesh3d format
vignette('animate-in-3d', package='threed')
- Creating a simple 3d animated object in ggplot2

Rendering objects

threed is just a 3d object transformation package and does not include any facility for rendering of objects.
Examples are included below showing how to convert 3d objects to a data.frame and then render with:
- ggplot2 and geom_polygon()
- Base R plotting with polygon()

Installation

# install.packages("devtools")
devtools::install_github("coolbutuseless/threed")

`as.data.frame.mesh3d()`

A mesh3d object can be converted to a data.frame representation using threed::as.data.frame.mesh3d().

Besides the standard x,y,z coordinates, the data.frame also includes:

element_id identifier for each element
element_type indicating how many vertices in an element
vorder the ordering of the vertices to define each element
normal at each vertex - vnx, vny, vnz
normal of each face - fnx, fny, fnz
centroid of each face = fcx, fcy, fcz
vertex global vertex identifier from the mesh3d object
zorder the drawing order of the elements from back to front
hidden whether or not the face is hidden. i.e. fnz < 0

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Convert the object from mesh3d to a data.frame
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
threed::mesh3dobj$cube %>%
  as.data.frame() %>%
  head() %>%
  knitr::kable(caption = "First few rows of the mesh3d cube after conversion to a data.frame")

element_id	element_type	vorder	x	y	z	vertex	vnx	vny	vnz	fny	fnz	fcy	fcz	zorder	zorder_var	hidden
1	4	1	-1	-1	-1	1	-0.5773503	-0.5773503	-0.5773503	0	-1	0	-1	1	-1	TRUE
1	4	2	-1	1	-1	3	-0.5773503	0.5773503	-0.5773503	0	-1	0	-1	1	-1	TRUE
1	4	3	1	1	-1	4	0.5773503	0.5773503	-0.5773503	0	-1	0	-1	1	-1	TRUE
1	4	4	1	-1	-1	2	0.5773503	-0.5773503	-0.5773503	0	-1	0	-1	1	-1	TRUE
2	4	1	-1	1	-1	3	-0.5773503	0.5773503	-0.5773503	1	0	1	0	2	0	FALSE
2	4	2	-1	1	1	7	-0.5773503	0.5773503	0.5773503	1	0	1	0	2	0	FALSE

First few rows of the mesh3d cube after conversion to a data.frame

Drawing a cube in `ggplot2`

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Define camera position and what it's looking at.
# Use the inverse of this to transform all objects in the world
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
camera_to_world <- threed::look_at_matrix(eye = c(3, 4, 5), at = c(0, 0, 0))

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#  - take a cube object
#  - position it in the camera view
#  - perform perspective projection
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
obj <- threed::mesh3dobj$cube %>%
  transform_by(invert_matrix(camera_to_world)) %>%
  perspective_projection()

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Use ggplot to plot the obj
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
ggplot(obj) + 
  geom_polygon(aes(x = x, y = y, group = zorder, fill = 0.5 * fnx + fny), colour = 'black', size = 0.2) +
  theme_minimal() +
  theme(
    legend.position = 'none',
    axis.text       = element_blank()
  ) +
  coord_equal()

Drawing a cube with base plot

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Explicitly convert to data.frame
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
obj_df <- as.data.frame(obj)

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Set up a palette - one entry for each face
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
pal <- colorRampPalette(c('white', 'blue'))(6)

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Initialise a plot of the correct size
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
with(obj_df, plot(x, y, asp = 1, type = 'p', pch = '.', ann = FALSE, axes = FALSE))

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# For each element_id, draw polygons 
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
obj_df %>% 
  split(., .$zorder) %>% 
  purrr::walk(
    ~with(.x, polygon(x, y, col = pal[zorder], density = 300, border = 'black'))
  )

Gallery

Bunny with light shading

camera_to_world <- look_at_matrix(eye = c(-1.5, 1.75, 4), at = c(0, 0, 0))

obj <- threed::mesh3dobj$bunny %>%
  transform_by(invert_matrix(camera_to_world)) %>%
  perspective_projection()

ggplot(obj, aes(x, y, group = element_id)) +
  geom_polygon(aes(fill = fnx + fny, colour = fnx + fny, group = zorder)) +
  theme_minimal() +
  theme(
    legend.position = 'none',
    axis.text       = element_blank()
  ) +
  coord_equal()

Teapot with shading by z-order

camera_to_world <- look_at_matrix(eye = c(1.5, 1.75, 4), at = c(0, 0, 0))

obj <- threed::mesh3dobj$teapot %>%
  transform_by(invert_matrix(camera_to_world)) %>%
  perspective_projection() 

ggplot(obj, aes(x, y, group = zorder)) +
  geom_polygon(aes(fill = zorder, colour = zorder)) +
  theme_minimal() +
  theme(
    legend.position = 'none',
    axis.text       = element_blank()
  ) +
  coord_equal() +
  scale_fill_viridis_d (option = 'A') +
  scale_color_viridis_d(option = 'A')

Dashed hidden lines

camera_to_world <- look_at_matrix(eye = c(1.5, 1.75, 4), at = c(0, 0, 0))

obj <- threed::mesh3dobj$cube %>%
  transform_by(invert_matrix(camera_to_world)) %>%
  perspective_projection()

ggplot(obj, aes(x, y, group = element_id)) +
  geom_polygon(fill = NA, colour='black', aes(linetype = hidden,  size = hidden)) +
  scale_linetype_manual(values = c('TRUE' = "FF", 'FALSE' = 'solid')) +
  scale_size_manual(values = c('TRUE' = 0.2, 'FALSE' = 0.5)) +
  theme_void() +
  theme(legend.position = 'none') +
  coord_equal()

Animated Icosahedron

See vignette('animate-in-3d', package='threed')

Hex logo

threed is used to generate its own hex logo by rendering an orthographic projection of a cube.

camera_to_world <- look_at_matrix(eye = c(4, 4, 4), at = c(0, 0, 0))

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Ensure the output directory is tidy
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
png_files = list.files("~/gganim", "logo.*png", full.names = TRUE)
unlink(png_files)

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Render a cube at a range of angles. Use orthographic projection
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
angles <- tail(seq(0, pi/2, length.out = 15), -1)

for (i in seq_along(angles)) {
  obj <- threed::mesh3dobj$cube %>%
    rotate_by(angle = angles[i], v = c(0, 1, 0)) %>% 
    transform_by(invert_matrix(camera_to_world)) %>%
    orthographic_projection()
  
  p <- ggplot(obj, aes(x, y, group = zorder)) +
    geom_polygon(aes(fill = fnx), colour='black') +
    theme_void() +
    theme(legend.position = 'none') +
    coord_equal(xlim = c(-1.5, 1.5), ylim = c(-1.5, 1.5)) + 
    scale_fill_continuous(limits = c(-1, 1)) 
  
  ggsave(sprintf("~/gganim/logo-%03i.png", i), plot = p, width = 2, height = 2)
}

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Set background to be transparent, and create an animated gif
# Doing this manually in imagemagick to avoid aretfacts that gifski added, 
# and to set a longer delay between loops
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
system("mogrify -transparent white ~/gganim/logo*.png")
system("convert -delay 0 -loop 0 -dispose previous -resize 200x200 ~/gganim/logo*.png figures/logo.gif")
system("convert figures/logo.gif \\( +clone -set delay 500 \\) +swap +delete  figures/logo-with-pause.gif")