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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()
## glX 
##   1
par3d(FOV = 1)
rgl.bg( sphere =FALSE, fogtype = "none", color=c("black"))
rgl.viewpoint(theta = 0, phi=0, zoom=0.8, fov=1)

# 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"

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.