gyrotriangle {gyro}

Gyrotriangle in 3D space

Description

3D gyrotriangle as a mesh.

Usage

gyrotriangle(
  A,
  B,
  C,
  s = 1,
  model = "U",
  iterations = 5,
  palette = NULL,
  bias = 1,
  interpolate = "linear",
  g = identity
)

Arguments

A, B, C

three distinct 3D points

s

positive number, the radius of the Poincaré ball if model="M", otherwise, if model="U", this number defines the hyperbolic curvature (the smaller, the more curved)

model

the hyperbolic model, either "M" (Möbius model, i.e. Poincaré model) or "U" (Ungar model, i.e. hyperboloid model)

iterations

the gyrotriangle is constructed by iterated subdivisions, this argument is the number of iterations

palette

a vector of colors to decorate the triangle, or NULL if you don't want to use a color palette

bias, interpolate

if palette is not NULL, these arguments are passed to colorRamp

g

a function from [0,1] to [0,1]; if palette is not NULL, this function is applied to the scalars defining the colors (the normalized gyrodistances to the gyrocentroid of the gyrotriangle)

Value

A mesh3d object.

Examples

library(gyro)
library(rgl)
A <- c(1, 0, 0); B <- c(0, 1, 0); C <- c(0, 0, 1)
ABC <- gyrotriangle(A, B, C, s = 0.3)
open3d(windowRect = c(50, 50, 562, 562))
view3d(30, 30, zoom = 0.75)
shade3d(ABC, color = "navy", specular = "cyan")

# using a color palette ####
if(require("trekcolors")) {
  pal <- trek_pal("klingon")
} else {
  pal <- hcl.colors(32L, palette = "Rocket")
}
ABC <- gyrotriangle(
  A, B, C, s = 0.5,
  palette = pal, bias = 1.5, interpolate = "spline"
)
open3d(windowRect = c(50, 50, 562, 562))
view3d(zoom = 0.75)
shade3d(ABC)

# hyperbolic icosahedron ####
library(rgl)
library(Rvcg) # to get the edges with the `vcgGetEdge` function
icosahedron <- icosahedron3d() # mesh with 12 vertices, 20 triangles
vertices <- t(icosahedron$vb[-4, ])
triangles <- t(icosahedron$it)
edges <- as.matrix(vcgGetEdge(icosahedron)[, c("vert1", "vert2")])
s <- 0.3
open3d(windowRect = c(50, 50, 562, 562))
view3d(zoom = 0.75)
for(i in 1:nrow(triangles)){
  triangle <- triangles[i, ]
  A <- vertices[triangle[1], ]
  B <- vertices[triangle[2], ]
  C <- vertices[triangle[3], ]
  gtriangle <- gyrotriangle(A, B, C, s)
  shade3d(gtriangle, color = "midnightblue")
}
for(i in 1:nrow(edges)){
  edge <- edges[i, ]
  A <- vertices[edge[1], ]
  B <- vertices[edge[2], ]
  gtube <- gyrotube(A, B, s, radius = 0.03)
  shade3d(gtube, color = "lemonchiffon")
}
spheres3d(vertices, radius = 0.05, color = "lemonchiffon")