isocubes

isocubes is a voxel renderer using a fixed-view isometric cube as the rendering primitive.

See also

• isocuboids
• oblicubes

What’s in the box

• isocubesGrob() to convert 3d integer coordinates into a grob for plotting
• coord_heightmap() to create coordinates for a heightmap from a matrix and (optional) colour information

Coordinate system

• Left-Handed vs Right-handed

• Flat = xz, yz, xz

• Illustrate location of ‘fill’, ‘fill2’ and ‘fill3’

• Illustrate different lighting locations

Installation

You can install from GitHub with:

# install.package('remotes')
remotes::install_github('coolbutuseless/isocubes')

‘R’ in isocubes

library(grid)
library(purrr)
library(isocubes)

x <- c(9, 8, 7, 6, 5, 4, 3, 2, 10, 9, 3, 2, 11, 10, 3, 2, 11, 10, 
3, 2, 11, 10, 3, 2, 11, 10, 3, 2, 10, 9, 3, 2, 9, 8, 7, 6, 5, 
4, 3, 2, 10, 9, 3, 2, 11, 10, 3, 2, 11, 10, 3, 2, 11, 10, 3, 
2, 11, 10, 3, 2, 11, 10, 3, 2, 11, 10, 3, 2) - 2

y <- c(15, 15, 15, 15, 15, 15, 15, 15, 14, 14, 14, 14, 13, 13, 13, 
13, 12, 12, 12, 12, 11, 11, 11, 11, 10, 10, 10, 10, 9, 9, 9, 
9, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 6, 6, 6, 6, 5, 5, 5, 5, 
4, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1) - 1

coords <- data.frame(x = x, y = y, z = 0)
cubes  <- isocubesGrob(coords, xo = 0.1, yo = 0)
grid.newpage(); grid.draw(cubes)

# Colour the cubes with rainbow
cubes <- isocubesGrob(coords, fill = rainbow(nrow(coords)), size = grid::unit(1/20, 'snpc'), xo = 0.1)
grid.newpage(); grid.draw(cubes)

# VaporWave palette
cubes <- isocubesGrob(coords, fill = '#ff71ce', fill2 = '#01cdfe',
                      fill3 = '#05ffa1', size = grid::unit(5, 'mm'), xo = 0.1)
grid.newpage(); grid.draw(cubes)

# Nightmare palette
cubes <- isocubesGrob(coords, 
                      fill = rainbow(nrow(coords)), 
                      fill2 = 'hotpink',
                      fill3 = viridisLite::inferno(nrow(coords)), 
                      size = unit(5, 'mm'), 
                      xo = 0.1,
                      col = NA)
grid.newpage(); grid.draw(cubes)

Simple isosurface - a sphere

library(grid)
library(isocubes)

N      <- 13
coords <- expand.grid(x=seq(-N, N), y = seq(-N, N), z = seq(-N, N))
keep   <- with(coords, sqrt(x * x + y * y + z * z)) < N
coords <- coords[keep,]

cubes <- isocubesGrob(coords, size = grid::unit(3, 'mm'), xo = 0.5, yo = 0.5)
grid.newpage()
grid.draw(cubes)

Another isosurface

A fancy isosurface by Stephane Laurent

library(grid)
library(isocubes)

A <- cospi(3/4); B <- sinpi(3/4)
f <- function(x, y, z) {
  z^4*B^2 + 4*x*y^2*A*B^2 + x*z^2*A*B^2 - 2*z^4*A - 4*x*y^2*B^2 - x*z^2*B^2 + 
    3*z^2*A*B^2 - 2*z^4 - x*A*B^2 - 2*z^2*A + x*B^2 + A*B^2 + 2*z^2 - B^2
}

N <- 31
x <- y <- z <- seq(-N, N) 
coords <- expand.grid(x = x, y = y, z = z)
keep <- with(
  coords, 
  sqrt(x*x + y*y + z*z) < 10*3 & f(x/10, y/10, z/10) < 0 & f(x/10, y/10, z/10) > -2
) 
coords <- coords[keep,]

fill <- 
  rgb(red = 1 + coords$x/N, 1 + coords$y/N, 1 + coords$z/N, maxColorValue = 2)
cubes <- isocubesGrob(coords, fill, xo = 0.5, yo = 0.5, size = grid::unit(2, 'mm'))
grid.newpage()
grid.draw(cubes)

Random rainbow volume of isocubes

library(isocubes)
set.seed(1)

N      <- 15
coords <- expand.grid(x=0:N, y=0:N, z=0:N)
coords <- coords[sample(nrow(coords), 0.66 * nrow(coords)),]
fill   <- rgb(red = 1 - coords$x / N, coords$y /N, 1 - coords$z/N, maxColorValue = 1)

cubes <- isocubesGrob(coords, fill, size = grid::unit(4, 'mm'))
grid.newpage(); grid.draw(cubes)

Heightmap as isocubes

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Prepare a matrix of values
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
mat <- volcano

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# An optional matrix of colours
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
val <- as.vector(mat)
val <- round(255 * (val - min(val)) / diff(range(val)))
col <- viridisLite::viridis(256)[val + 1L]
dim(col) <- dim(mat) 

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Find the (integer) coordiinates of the cubes in the heightmap
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
coords <- coords_heightmap(mat - min(mat), col = col, scale = 0.3)

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Convert the coordinates into a grob
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
cubes  <- isocubesGrob(coords, size = grid::unit(1.5, 'mm'), fill = coords$col, xo = 0.65)
grid.newpage(); grid.draw(cubes)

Image as isocubes

• Treat image to a heightmap

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Load image and convert to a matrix of heights
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
img <- png::readPNG("man/figures/Rlogo-small-blur.png")
ht        <- round( 10 * (1 - img[,,2]) ) # Use Green channel intensity as height
ht[,1]    <- 0 # image editing to remove some artefacts

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# A matrix of colours extracted from the image
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
col       <- rgb(img[,,1], img[,,2], img[,,3])
dim(col)  <- dim(ht) 

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# convert to cubes and draw
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
coords <- coords_heightmap(ht, col = col, ground = 'xy')
cubes  <- isocubesGrob(coords, size = grid::unit(1.3, 'mm'), fill = coords$col, xo = 0.1, col = NA, light = 'right-top')
grid.newpage(); grid.draw(cubes)

Terrain with ambient

library(grid)
library(ggplot2)
library(dplyr)
library(ambient)

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Create some perlin noise on an NxN grid
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
set.seed(3)
N <- 60

dat <- long_grid(x = seq(0, 10, length.out = N), y = seq(0, 10, length.out = N)) %>% 
  mutate(
    noise = 
      gen_perlin(x, y, frequency = 0.3) + 
      gen_perlin(x, y, frequency = 2) / 10
  ) 

hm <- dat %>%
  mutate(
    x = x * 4,
    z = y * 4,
    y = noise * 4
  )

pal  <- topo.colors(11)
sy   <- as.integer(10 * (hm$y - min(hm$y)) / diff(range(hm$y))) + 1
cols <- pal[sy]

cubes  <- isocubesGrob(hm, size = grid::unit(3.5, 'mm'), fill = cols, col = NA)

grid.newpage(); grid.draw(cubes)

Bitmap font rendering

library(grid)
library(isocubes)
library(lofifonts)

coords <- lofifonts::bitmap_text_coords('I\u2764#RStats')
coords$z <- 0

cols <- rainbow(nrow(coords))

cubes  <- isocubesGrob(coords, xo = 0, size = grid::unit(2, 'mm'), fill = cols)
grid.newpage(); 
grid.draw(cubes)

Technical Notes

Cube sort

Arrange cubes by -x, -z then y to ensure cubes are drawn in the correct ordering such that cubes in front are drawn over the top of cubes which are behind.

grob

All the faces of all the cubes are then calculated as polygons - each with 4 vertices.

The data for all polygons is then concatenated into a single polygonGrob() call with an appropiate vector for id.lengths to split the data.