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using Meshes
using MeshViz
using GLMakie
using LinearAlgebra
using Makie
using Printf

# image of circle (center, radius) by the inversion 
#   with center c and power k
function iotaCircle(c, k, center, radius)

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using Meshes
using MeshViz
using LinearAlgebra
using GLMakie
using Makie
using ColorSchemes
using Printf

# parameterization of the Hopf torus
function HopfTorus(u, v, nlobes, A)

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using Meshes
using Rotations
import TransformsBase as TB
using MeshViz
using GLMakie

function HopfFiber(q, t)
  [
    q[1]*cos(t) + q[2]*sin(t),
    sin(t)*(1 + q[3]),

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using MarchingCubes
import Meshes
using MeshViz
using GLMakie
using Makie
using Printf

# isosurface function f=0
phi = (1 + sqrt(5)) / 2
function f(x, y, z)

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using Meshes
using MeshViz
using GLMakie

function HopfTorus(u, nlobes, A)
  t = [0, pi / 2, pi]
  cos_v = cos.(t)
  sin_v = sin.(t)
  B = pi / 2 - (pi / 2 - A) * cos(u * nlobes)
  C = u + A * sin(2 * u * nlobes)

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library(rgl) 

#~~ Torus passing by three points ~~####

## cross-product ###
crossProduct <- function(u, v) {
  c(
    u[2L]*v[3L] - u[3L]*v[2L],
    u[3L]*v[1L] - u[1L]*v[3L],
    u[1L]*v[2L] - u[2L]*v[1L]

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library(rgl)

# tetrahedra vertices
r <- 3*sqrt(3)/10
theta <- acos(-2/3)
h <- 1/sqrt(10)
n <- 20
i <- 1:n
p <- cbind(r*cos(i*theta), r*sin(i*theta), i*h)

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library(rgl)
library(cgalMeshes)

# trefoil (2,3) ####
p <- function(theta, phi) {
  c(
    cos(theta)*cos(phi), cos(theta)*sin(phi), 
    sin(theta)*cos(1.5*phi), sin(theta)*sin(1.5*phi)
  )
}

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library(rgl)
library(cgalMeshes)

p <- function(theta, phi) {
  c(
    cos(theta)*cos(phi), cos(theta)*sin(phi), 
    sin(theta)*cos(phi), sin(theta)*sin(phi)
  )
}

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library(rgl)
library(cgalMeshes)

# Hopf fiber
HopfFiber <- function(p, t) { 
  c(
    p[3L] * cos(t) + p[2L] * sin(t),
    p[2L] * cos(t) - p[3L] * sin(t),
    sin(t) * (1 + p[1L]),
    cos(t) * (1 + p[1L])