cgalMeshes (version 2.2.0)

gyroTriangle: Hyperbolic triangle

Description

Mesh of a hyperbolic triangle.

Usage

gyroTriangle(A, B, C, s, iterations = 3)

Value

A cgalMesh object.

Arguments

A, B, C

the vertices of the triangle

s

hyperbolic curvature, a positive number

iterations

number of iterations used to construct the mesh, at least 1

Examples

library(cgalMeshes)
library(rgl)
mesh <- gyroTriangle(
  c(0, 0, 1), c(1, 0, 0), c(0, 1, 0), s = 0.7
)
mesh$computeNormals()
rmesh <- mesh$getMesh()
open3d(windowRect = 50 + c(0, 0, 512, 512))
view3d(20, 20)
shade3d(rmesh, color = "green")
wire3d(rmesh)

# hyperbolic icosahedron ####
library(cgalMeshes)
library(rgl)
icosahedron <- icosahedron3d()
vertices    <- icosahedron[["vb"]][-4L, ]
faces       <- icosahedron[["it"]]
colors <- hcl.colors(ncol(faces), palette = "Plasma")
open3d(windowRect = 50 + c(0, 0, 512, 512))
view3d(15, -60, zoom = 0.7)
for(i in 1L:ncol(faces)) {
  triangle <- faces[, i]
  A <- vertices[, triangle[1L]]
  B <- vertices[, triangle[2L]]
  C <- vertices[, triangle[3L]]
  mesh <- gyroTriangle(A, B, C, s = 0.6)
  mesh$computeNormals()
  rmesh <- mesh$getMesh()
  shade3d(rmesh, color = colors[i])
  wire3d(rmesh)
}