Rpolyhedra

Introduction

This package is a curation made based on the poly package found on https://netlib.org/polyhedra/ (Original Help message), and the polyhedra database found on http://dmccooey.com/polyhedra/, both of which provide polyhedra databases on its own format. As such, Rpolyhedra provides with the following:

1. A module to scrape the polyhedra for the different sources found with features for incremental correction of issues found and to be found in scraping process.
2. A database of the scraped polyhedra.
3. An R6 polyhedron representation with ‘rgl’ package visualizing capabilities.

Usage

For final users, the package provides a common interface for accessing public polyhedra databases, analyze properties, compare and visualize them with RGL.

For advanced users, the package provides a simplified set of R6 objects to scrape and compare polyhedra databases.

Get available polyhedra

Once the original files had been processed, a simple call to getAvailablePolyhedra() retrieves a list of the available polyhedra with properties and status in the polyhedra database:

#show only the first 10 polyhedra.
head(getAvailablePolyhedra(), n = 10)

##    source                      scraped.name            symbol vertices faces
## 1  netlib                       tetrahedron {3,3}\t@Y sub 3 @        4     4
## 31 netlib               square pyramid (j1)      \t@Y sub 4 @        5     5
## 42 netlib        triangular dipyramid (j12)      \t@Y sub 3 @        5     6
## 9  netlib                  triangular prism      \t@P sub 3 @        6     5
## 32 netlib           pentagonal pyramid (j2)      \t@Y sub 5 @        6     6
## 3  netlib                        octahedron {3,4}\t@S sub 3 @        6     8
## 37 netlib elongated triangular pyramid (j7)      \t@Y sub 3 @        7     7
## 74 netlib  augmented triangular prism (j49)      \t@Y sub 4 @        7     8
## 43 netlib        pentagonal dipyramid (j13)      \t@Y sub 5 @        7    10
## 2  netlib                              cube {4,3}\t@P sub 4 @        8     6
##     status
## 1  scraped
## 31 scraped
## 42 scraped
## 9  scraped
## 32 scraped
## 3  scraped
## 37 scraped
## 74 scraped
## 43 scraped
## 2  scraped

Retrieve a polyhedron

The access to a particular polyhedron can be done with a call to getPolyhedron(<<source>>, <<polyhedron.name>>), which returns a Polyhedron object. For example, to retrieve a cube from the netlib database, the call would be:

cube <- getPolyhedron(source = "netlib", polyhedron.name = "cube")

A demo

To try package functionality, a simple demo can be executed which shows the 5 regular polyhedra.

# 1.  Obtain 5 regular solids
polyhedra.2.draw <- getAvailablePolyhedra(source = "netlib")
polyhedra.2.draw <- polyhedra.2.draw %>%
                        filter(scraped.name %in%
                            c("tetrahedron", "octahedron", "cube",
                               "icosahedron", "dodecahedron"))

# 2. Setup colors and scales
n <- nrow(polyhedra.2.draw)
polyhedron.colors <- rainbow(n)
polyhedron.scale <- 5

# 3. Open and setup RGL window
open3d()

## null 
##    2

par3d(FOV = 1)
rgl.bg( sphere =FALSE, fogtype = "none", color=c("black"))

## Warning in rgl.bg(sphere = FALSE, fogtype = "none", color = c("black")): 'rgl.bg' is deprecated.
## Use 'bg3d' instead.
## See help("Deprecated")

rgl.viewpoint(theta = 0, phi=0, zoom=0.8, fov=1)

## Warning in rgl.viewpoint(theta = 0, phi = 0, zoom = 0.8, fov = 1): 'rgl.viewpoint' is deprecated.
## Use 'view3d' instead.
## See help("Deprecated")

# 4. For each polyhedron, setup rotation, position and render
for (i in seq_len(n)) {
  # Obtain polyhedron
  polyhedron.row <- polyhedra.2.draw[i,]
  polyhedron.name <- polyhedron.row$scraped.name
  polyhedron <- getPolyhedron(source = polyhedron.row$source, polyhedron.name)

  # Setup angles, position into transformationMatrix
  current.angle <- i/n * 2 * pi
  tm <- rotationMatrix(current.angle, 1, 0, 0)
  x.pos <- round(polyhedron.scale * sin(current.angle), 2)
  y.pos <- round(polyhedron.scale * cos(current.angle), 2)
  tm <- tm %*% translationMatrix(x.pos, y.pos, 0)

  # Render
  print(paste("Drawing ", polyhedron.name, " rotated ", round(current.angle, 2),
              " in (1,0,0) axis. Translated to (", x.pos, ",", y.pos, ",0)",
              " with color ", polyhedron.colors[i], sep = ""))
  shape.rgl <- polyhedron$getRGLModel(transformation.matrix = tm)
  shade3d(shape.rgl, color = polyhedron.colors[i])
}

## [1] "Drawing tetrahedron rotated 1.26 in (1,0,0) axis. Translated to (4.76,1.55,0) with color #FF0000"
## [1] "Drawing octahedron rotated 2.51 in (1,0,0) axis. Translated to (2.94,-4.05,0) with color #CCFF00"
## [1] "Drawing cube rotated 3.77 in (1,0,0) axis. Translated to (-2.94,-4.05,0) with color #00FF66"
## [1] "Drawing icosahedron rotated 5.03 in (1,0,0) axis. Translated to (-4.76,1.55,0) with color #0066FF"
## [1] "Drawing dodecahedron rotated 6.28 in (1,0,0) axis. Translated to (0,5,0) with color #CC00FF"