Twenty Hopf tori with rgl

HopfTwentyTori.md

HopfTwentyTori.R

source('HopfTorusMesh.R') # https://gist.github.com/stla/85224a6639ccf165f11fa1a2bf987f16#file-hopftorus_mesh3d-r
source('ConeMesh00.R') # https://gist.github.com/stla/b3db4a593c9b030567bde701d45fa385
library(rgl)

Reorient_Trans <- function(Axis1, Axis2){
  vX1 <- Axis1 / sqrt(c(crossprod(Axis1)))
  vX2 <- Axis2 / sqrt(c(crossprod(Axis2)))
  Y <- rgl:::xprod(vX1, vX2)
  vY <- Y / sqrt(c(crossprod(Y)))
  Z1 <- rgl:::xprod(vX1, vY)
  vZ1 <- Z1 / sqrt(c(crossprod(Z1)))
  Z2 <- rgl:::xprod(vX2, vY)
  vZ2 <- Z2 / sqrt(c(crossprod(Z2)))
  M1 <- cbind(vX1, vY, vZ1)
  M2 <- rbind(vX2, vY, vZ2)
  M <- M1 %*% M2
  rbind(cbind(M, c(0,0,0)), c(0,0,0,1))
}

# vertices ####
phi <- (1+sqrt(5))/2
a <- 1/sqrt(3)
b <- a/phi 
c <- a*phi
vertices <- 
  rbind(
    c( a,  a,  a), 
    c( a,  a, -a),
    c( a, -a,  a),
    c(-a, -a,  a),
    c(-a,  a, -a),
    c(-a,  a,  a),
    c( 0,  b, -c), 
    c( 0, -b, -c), 
    c( 0, -b,  c),
    c( c,  0, -b),
    c(-c,  0, -b),
    c(-c,  0,  b),
    c( b,  c,  0),
    c( b, -c,  0),
    c(-b, -c,  0),
    c(-b,  c,  0),
    c( 0,  b,  c),
    c( a, -a, -a),
    c( c,  0,  b),
    c(-a, -a, -a)
  )

# Hopf mesh
HTmesh0 <- hmesh(200, 200)

# rgl ####
colors <- randomcoloR::distinctColorPalette(20)

sc <- 0.035
HTmesh <- scale3d(HTmesh0, sc, sc, sc)

open3d(windowRect=c(50,50,550,550))
bg3d(rgb(54,57,64, maxColorValue = 255))

for(i in 1:20){
    v <- vertices[i,]
    M <- Reorient_Trans(c(0,0,1), v)
    obj <- transform3d(HTmesh, M)
    obj <- translate3d(obj, v[1], v[2], v[3])
    shade3d(obj, color=colors[i])
    shade3d(Cmesh(c(0,0,0), 0, v, 0.05, 6, 40, color="brown"))
}