inst/essais/translated_icosahedra.R

In stla/gyro: Hyperbolic Geometry

####~~ translated icosahedra ~~####
library(gyro)
library(rgl)
library(Morpho)
library(Rvcg)

# draw hyperbolic polyhedron ####
hpolyhedron <- function(vertices, faces, edges, s){
  Gtriangles <- vector("list", nrow(faces))
  for(i in 1:nrow(faces)){
    idx <- faces[i,]
    Gtriangles[[i]] <- gyrotriangle(
      vertices[idx[1],], vertices[idx[2],], vertices[idx[3],], s = s
    )
  }
  mesh <- vcgClean(mergeMeshes(Gtriangles), sel = 0)
  shade3d(mesh, color = "royalblue")
  for(i in 1:nrow(edges)){
    idx <- edges[i,]
    A <- vertices[idx[1],]; B <- vertices[idx[2],]
    tube <- gyrotube(A, B, s = s, n = 100, radius = 0.03)
    shade3d(tube, color = "powderblue")
  }
  spheres3d(vertices, radius = 0.05, color = "powderblue")
}

# vertices ####
icosahedron <- icosahedron3d()
vertices <- t(icosahedron$vb[-4, ])

# faces ####
faces <- t(icosahedron$it)

# edges ####
edges <- as.matrix(vcgGetEdge(icosahedron)[, c("vert1", "vert2")])

# plot ####
open3d(windowRect = c(50, 50, 562, 562))
view3d(0, 0, zoom = 0.9)
s <- 0.5
h <- 1.5
hpolyhedron(
  sweep(vertices, 2, c(h, 0, 0), "+"), faces, edges, s = s
)
hpolyhedron(
  sweep(vertices, 2, c(h*cos(2*pi/3), h*sin(2*pi/3), 0), "+"),
  faces, edges, s = s
)
hpolyhedron(
  sweep(vertices, 2, c(h*cos(4*pi/3), h*sin(4*pi/3), 0), "+"),
  faces, edges, s = s
)

# animation ####
M <- par3d("userMatrix")
movie3d(
  par3dinterp(
    time = seq(0, 1, len = 9),
    userMatrix = list(
      M,
      rotate3d(M, pi, 1, 0, 0),
      rotate3d(M, pi, 1, 1, 0),
      rotate3d(M, pi, 1, 1, 1),
      rotate3d(M, pi, 0, 1, 1),
      rotate3d(M, pi, 0, 1, 0),
      rotate3d(M, pi, 1, 0, 1),
      rotate3d(M, pi, 0, 0, 1),
      M
    )
  ),
  fps = 120,
  duration = 1,
  dir = ".",
  movie = "zzpic",
  convert = FALSE,
  clean = FALSE,
  webshot = FALSE
)

command <- "gifski --fps=10 --frames=zzpic*.png -o translatedIcosahedra.gif"
system(command)