Three-Dimensional Object Transformations
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R fixed a bug in how properties in mesh3d converted to data.frame Nov 10, 2018
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DESCRIPTION
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README.Rmd
README.md initial release Nov 8, 2018

README.md

threed - 3d object transformation library

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 fnx fny fnz fcx fcy fcz zorder zorder_var hidden
1 4 1 -1 -1 -1 1 -0.5773503 -0.5773503 -0.5773503 0 0 -1 0 0 -1 1 -1 TRUE
1 4 2 -1 1 -1 3 -0.5773503 0.5773503 -0.5773503 0 0 -1 0 0 -1 1 -1 TRUE
1 4 3 1 1 -1 4 0.5773503 0.5773503 -0.5773503 0 0 -1 0 0 -1 1 -1 TRUE
1 4 4 1 -1 -1 2 0.5773503 -0.5773503 -0.5773503 0 0 -1 0 0 -1 1 -1 TRUE
2 4 1 -1 1 -1 3 -0.5773503 0.5773503 -0.5773503 0 1 0 0 1 0 2 0 FALSE
2 4 2 -1 1 1 7 -0.5773503 0.5773503 0.5773503 0 1 0 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")