cgalMeshes (version 2.2.0)

torusMesh: Torus mesh

Description

Triangle mesh of a torus.

Usage

torusMesh(R, r, p1 = NULL, p2 = NULL, p3 = NULL, nu = 50, nv = 30)

Value

A triangle rgl mesh (class mesh3d).

Arguments

R, r

major and minor radii, positive numbers; R is ignored if p1, p2 and p3 are given

p1, p2, p3

three points or NULL; if not NULL, the function returns a mesh of the torus whose equator passes through these three points and with minor radius r; if NULL, the torus has equatorial plane z=0 and the z-axis as revolution axis

nu, nv

numbers of subdivisions, integers (at least 3)

Examples

library(cgalMeshes)
library(rgl)
mesh <- torusMesh(R = 3, r = 1)
open3d(windowRect = 50 + c(0, 0, 512, 512))
view3d(0, 0, zoom = 0.75)
shade3d(mesh, color = "green")
wire3d(mesh)

# Villarceau circles ####
Villarceau <- function(beta, theta0, phi) {
  c(
    cos(theta0 + beta) * cos(phi),
    sin(theta0 + beta) * cos(phi),
    cos(beta) * sin(phi)
  ) / (1 - sin(beta) * sin(phi))
}
ncircles <- 30
if(require("randomcoloR")) {
  colors <- 
    randomColor(ncircles, hue = "random", luminosity = "dark")
} else {
  colors <- rainbow(ncircles)
}
theta0_ <- seq(0, 2*pi, length.out = ncircles+1)[-1L]
phi <- 0.7
open3d(windowRect = 50 + c(0, 0, 512, 512), zoom = 0.8)
for(i in seq_along(theta0_)) {
  theta0 <- theta0_[i]
  p1 <- Villarceau(0, theta0, phi)
  p2 <- Villarceau(2, theta0, phi)
  p3 <- Villarceau(4, theta0, phi)
  rmesh <- torusMesh(r = 0.05, p1 = p1, p2 = p2, p3 = p3)
  shade3d(rmesh, color = colors[i])
}