Higher-dimensional stuff with 'rgl' (R)

.gitignore

zzpic*
.Rproj.user
*.Rproj
.Rhistory

ICN5D_anim01.R

library(rgl)
library(rmarchingcubes)

a <- 0

# f <- function(x, y, z, a, t){
#   (((x*cos(t)-a*sin(t))^2+y^2+z^2+(x*sin(t)+a*cos(t))^2+145/3)^2-4*(9*z^2+16*(x*sin(t)+a*cos(t))^2))^2*(((x*cos(t)-a*sin(t))^2+y^2+z^2+(x*sin(t)+a*cos(t))^2+145/3)^2+296*((x*cos(t)-a*sin(t))^2+y^2)-4*(9*z^2+16*(x*sin(t)+a*cos(t))^2)) -16*((x*cos(t)-a*sin(t))^2+y^2)*((x*cos(t)-a*sin(t))^2+y^2+z^2+(x*sin(t)+a*cos(t))^2+145/3)^2*(37*((x*cos(t)-a*sin(t))^2+y^2+z^2+(x*sin(t)+a*cos(t))^2+145/3)^2-1369*((x*cos(t)-a*sin(t))^2+y^2)-7*(225*z^2+448*(x*sin(t)+a*cos(t))^2)) -16*sqrt(3)/9*((x*cos(t)-a*sin(t))^3-3*(x*cos(t)-a*sin(t))*y^2)*(110*((x*cos(t)-a*sin(t))^2+y^2+z^2+(x*sin(t)+a*cos(t))^2+145/3)^3 -148*((x*cos(t)-a*sin(t))^2+y^2+z^2+(x*sin(t)+a*cos(t))^2+145/3)*(110*(x*cos(t)-a*sin(t))^2+110*y^2-297*z^2+480*(x*sin(t)+a*cos(t))^2)) -64*((x*cos(t)-a*sin(t))^2+y^2)*(3*(729*z^4+4096*(x*sin(t)+a*cos(t))^4)+168*((x*cos(t)-a*sin(t))^2+y^2)*(15*z^2-22*(x*sin(t)+a*cos(t))^2)) +64*(12100/27*((x*cos(t)-a*sin(t))^3-3*(x*cos(t)-a*sin(t))*y^2)^2 -7056*(3*(x*cos(t)-a*sin(t))^2*y-y^3)^2) -592240896*z^2*(x*sin(t)+a*cos(t))^2
# }
# since a = 0
f <- function(x, y, z, t){
  (((x*cos(t))^2+y^2+z^2+(x*sin(t))^2+145/3)^2-4*(9*z^2+16*(x*sin(t))^2))^2*(((x*cos(t))^2+y^2+z^2+(x*sin(t))^2+145/3)^2+296*((x*cos(t))^2+y^2)-4*(9*z^2+16*(x*sin(t))^2)) -16*((x*cos(t))^2+y^2)*((x*cos(t))^2+y^2+z^2+(x*sin(t))^2+145/3)^2*(37*((x*cos(t))^2+y^2+z^2+(x*sin(t))^2+145/3)^2-1369*((x*cos(t))^2+y^2)-7*(225*z^2+448*(x*sin(t))^2)) -16*sqrt(3)/9*((x*cos(t))^3-3*(x*cos(t))*y^2)*(110*((x*cos(t))^2+y^2+z^2+(x*sin(t))^2+145/3)^3 -148*((x*cos(t))^2+y^2+z^2+(x*sin(t))^2+145/3)*(110*(x*cos(t))^2+110*y^2-297*z^2+480*(x*sin(t))^2)) -64*((x*cos(t))^2+y^2)*(3*(729*z^4+4096*(x*sin(t))^4)+168*((x*cos(t))^2+y^2)*(15*z^2-22*(x*sin(t))^2)) +64*(12100/27*((x*cos(t))^3-3*(x*cos(t))*y^2)^2 -7056*(3*(x*cos(t))^2*y-y^3)^2) -592240896*z^2*(x*sin(t))^2
}

nx <- 200; ny <- 200; nz <- 200
x <- seq(-8, 9, length.out = nx)
y <- seq(-9, 9, length.out = ny)
z <- seq(-6, 6, length.out = nz)
G <- expand.grid(x = x, y = y, z = z)

userMatrix <- rbind(
  c( 0.69, -0.71, 0.12, 0),
  c( 0.00,  0.16, 0.99, 0),
  c(-0.72, -0.68, 0.11, 0),
  c( 0.00,  0.00, 0.00, 1)
)

t_ <- seq(0, pi, length.out = 100)

for(i in seq_along(t_)){
  # run the marching cubes algorithm ####
  voxel <- array(with(G, f(x, y, z, t_[i])), dim = c(nx, ny, nz))
  cont <- contour3d(
    voxel, level = 0, x = x, y = y, z = z
  )
  # make the mesh
  mesh <- tmesh3d(
    vertices = t(cont$vertices),
    indices  = t(cont$triangles),
    normals  = cont$normals,
    homogeneous = FALSE
  )
  # plot
  open3d(windowRect = c(50, 50, 562, 562))
  bg3d(
    sphere = FALSE, texture = "SpaceBackground.png", col = "white"
  )
  par3d(userMatrix = userMatrix, zoom = 0.85)
  shade3d(mesh, color = "turquoise4")
  rgl.snapshot(sprintf("zzzpic%03d.png", i))
  close3d()
}

# animation
command <-
  "magick convert -dispose previous -delay 1x10 -duplicate 1,-2-1 zzzpic*.png ICN5D_anim01.gif"
system(command)

pngs <- list.files(".", pattern = "^zzzpic", full.names = TRUE)
file.remove(pngs)


# https://thumbs.gfycat.com/SnoopyDeliciousGuineapig-size_restricted.gif

deformedTorus.gif

deformedTorus.R

ICN5D_anim01.gif

ICN5D_anim01_isoclinic.gif

ICN5D_anim01_isoclinic.R

slices4Dtorus.gif

slices4Dtorus.R

SpaceBackground.png

tiger01.gif

tiger01.R

tiger01bis.gif

Toratope7D_anim2.gif

Toratope7D_anim2.R

Toratope7D_anim2_U_anim3.gif

Toratope7D_anim2_U_anim3.R

Toratope7D_anim3.gif

Toratope7D_anim3.R

toroidalHyperboloid.R