In coolbutuseless/threed: Three-Dimensional Object Transformations

suppressPackageStartupMessages({
  library(ggplot2)
  library(magrittr)

  library(threed)
})


knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(ggplot2)

library(threed)

Introduction

Prepare an object for plotting

• Create an object (here the standard 2x2x2 cube is being used)
• Define where camera is located, and where it is looking
• Transform the object into camera space
• Perspective transform the data

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# The `threed` package has some builtin objects in `threed::mesh3dobj`
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
obj <- threed::mesh3dobj$cube

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Define camera 'lookat' matrix i.e. camera-to-world transform
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
camera_to_world <- threed::look_at_matrix(eye = c(1.5, 1.75, 4), at = c(0, 0, 0))

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Transform the object into camera space and do perspective projection
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
obj <- obj %>%
  transform_by(invert_matrix(camera_to_world)) %>%
  perspective_projection()

as.data.frame(obj) %>% knitr::kable()

Plot the points for the vertices of the object

• threed defines a fortify.mesh3d() function.
• If a mesh3d object is given as the data for aggplot2 call, ggplot2 will automatically use fortify() to convert into a data.frame.
• i.e. because threed defines fortify.mesh3d(), we can call ggplot2 directly with a mesh3d object.

ggplot(obj, aes(x, y)) +
  geom_point() +
  theme_void() +
  theme(legend.position = 'none') +
  coord_equal()

Plot the outline of each polygon

• Each element has a unique element_id, and this is used as the group aesthetic to inform ggplot that it should draw one polygon for each element.
• Set fill = NA, colour = 'black' to draw only the borders of each polygon.

ggplot(obj, aes(x, y, group = element_id)) +
  geom_polygon(fill = NA, colour = 'black', size = 0.2) +
  theme_void() +
  theme(legend.position = 'none') +
  coord_equal()

Dotted rendering of hidden lines

• To draw hidden elements in a different way, use the hidden variable.
• hidden is a boolean variable indicating if a triangle or quad element is facing away from the camera.
• Here a different linetype is used for hidden elements

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' = "dotted", 'FALSE' = 'solid')) +
  scale_size_manual(values = c('TRUE' = 0.2, 'FALSE' = 0.5)) +
  theme_void() +
  theme(legend.position = 'none') +
  coord_equal()

Hidden line removal

• Here a zero-width linetype is used for hidden elements to hide them.

ggplot(obj, aes(x, y, group = element_id)) +
  geom_polygon(fill = NA, colour = 'black', aes(size = hidden)) +
  scale_size_manual(values = c('TRUE' = 0, 'FALSE' = 0.5)) +
  theme_void() +
  theme(legend.position = 'none') +
  coord_equal()

Naive Filled Polygons

• When filling polygons, ggplot2 will draw them in the order of the group variable.
• But (as is usually the case), elements drawn in this order will overlap incorrectly with other elements, and the result will look weird - Almost Escher-esque!

ggplot(obj, aes(x, y, group = element_id)) +
  geom_polygon(fill = 'lightblue', colour = 'black', size = 0.2) +
  theme_void() +
  theme(legend.position = 'none') +
  coord_equal()

Filled Polygons - (1) Drop hidden elements so they never get drawn

• First method for drawing filled polygons:
  • drop hidden elements manually
  • Do this by explicitly converting the mesh3d object to a data.frame, and then filtering out the hidden elements.

obj_df <- as.data.frame(obj) 
obj_df <- subset(obj_df, !obj_df$hidden)

ggplot(obj_df, aes(x, y, group = element_id)) +
  geom_polygon(fill = 'lightblue', colour = 'black', size = 0.2) +
  theme_void() +
  theme(legend.position = 'none') +
  coord_equal()

Filled Polygons - (2) Assign hidden elements a fill of NA so they get drawn invisibly

• Second method for drawing filled polygons:
  • draw hidden elements invisibly
  • Do this by explicitly converting the mesh3d object to a data.frame, and then manually setting the variables mapped to fill and colour to be NA for hidden elements

obj_df <- as.data.frame(obj) %>%
  transform(
    shade      = ifelse(hidden, NA, 'lightblue'),
    linecolour = ifelse(hidden, NA, 'black')
  )

ggplot(obj_df, aes(x, y, group = element_id)) +
  geom_polygon(aes(fill = I(shade), colour = I(linecolour)), size = 0.2) +
  theme_void() +
  theme(legend.position = 'none') +
  coord_equal() 

Filled Polygons - (3) Use the zorder variable to control draw order

• Third method for drawing filled polygons:
  • Draw the elements from furtherest to nearest
  • Exploit the fact that elements are drawn in the order of the group variable.
  • When converting a mesh3d to a data.frame, a zorder variable is created starting at 1 for the furtherest element, up to n for the closest element.
  • i.e. change the group variable from element_id to zorder

ggplot(obj, aes(x, y, group = zorder)) +
  geom_polygon(fill = 'lightblue', colour='black', size = 0.2) +
  theme_void() +
  theme(legend.position = 'none') +
  coord_equal() 

Fake-shaded polygon

• The normal to each face is included in the data.frame representation as fnx, fny, fnz
• By calculating dot products to a light source positioned in the scene, the fraction illumination could be calculated for each element.
• Here, the shading is being completely faked by using the sum fny + fnz to shade the polygons.

ggplot(obj, aes(x, y, group = zorder)) +
  geom_polygon(aes(fill = fny + fnz), colour = 'black', size = 0.2) +
  theme_void() +
  theme(legend.position = 'none') +
  coord_equal()

coolbutuseless/threed documentation built on May 5, 2019, 7:08 a.m.