plotGyrohull3d {gyro}

Plot hyperbolic convex hull

Description

Plot the hyperbolic convex hull of a set of 3D points.

Usage

plotGyrohull3d(
  points,
  s = 1,
  model = "U",
  iterations = 5,
  n = 100,
  edgesAsTubes = TRUE,
  verticesAsSpheres = edgesAsTubes,
  edgesColor = "yellow",
  spheresColor = edgesColor,
  tubesRadius = 0.03,
  spheresRadius = 0.05,
  facesColor = "navy",
  bias = 1,
  interpolate = "linear",
  g = identity
)

Arguments

points

matrix of 3D points, one point per row

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

argument passed to gyrotriangle

n

argument passed to gyrotube or gyrosegment, the number of points for each edge

edgesAsTubes

Boolean, whether to represent tubular edges

verticesAsSpheres

Boolean, whether to represent the vertices as spheres

edgesColor

a color for the edges

spheresColor

a color for the spheres, if verticesAsSpheres = TRUE

tubesRadius

radius of the tubes, if edgesAsTubes = TRUE

spheresRadius

radius of the spheres, if verticesAsSpheres = TRUE

facesColor

this argument sets the color of the faces; it can be either a single color or a color palette, i.e. a vector of colors; if it is a color palette, it will be passed to the argument palette of gyrotriangle

bias, interpolate, g

these arguments are passed to gyrotriangle in the case when facesColor is a color palette

Value

No value, called for plotting.

Examples

library(gyro)
library(rgl)
# Triangular orthobicopula ####
points <- rbind(
  c(1, -1/sqrt(3), sqrt(8/3)),
  c(1, -1/sqrt(3), -sqrt(8/3)),
  c(-1, -1/sqrt(3), sqrt(8/3)),
  c(-1, -1/sqrt(3), -sqrt(8/3)),
  c(0, 2/sqrt(3), sqrt(8/3)),
  c(0, 2/sqrt(3), -sqrt(8/3)),
  c(1, sqrt(3), 0),
  c(1, -sqrt(3), 0),
  c(-1, sqrt(3), 0),
  c(-1, -sqrt(3), 0),
  c(2, 0, 0),
  c(-2, 0, 0)
)
open3d(windowRect = c(50, 50, 562, 562))
view3d(zoom = 0.7)
plotGyrohull3d(points, s = 0.4)

# a non-convex polyhedron with triangular faces ####
vertices <- rbind(
  c(-2.1806973249, -2.1806973249, -2.1806973249),
  c(-3.5617820682, 0.00000000000, 0.00000000000),
  c(0.00000000000, -3.5617820682, 0.00000000000),
  c(0.00000000000, 0.00000000000, -3.5617820682),
  c(-2.1806973249, -2.1806973249, 2.18069732490),
  c(0.00000000000, 0.00000000000, 3.56178206820),
  c(-2.1806973249, 2.18069732490, -2.1806973249),
  c(0.00000000000, 3.56178206820, 0.00000000000),
  c(-2.1806973249, 2.18069732490, 2.18069732490),
  c(2.18069732490, -2.1806973249, -2.1806973249),
  c(3.56178206820, 0.00000000000, 0.00000000000),
  c(2.18069732490, -2.1806973249, 2.18069732490),
  c(2.18069732490, 2.18069732490, -2.1806973249),
  c(2.18069732490, 2.18069732490, 2.18069732490))
triangles <- 1 + rbind(
  c(3, 2, 0),
  c(0, 1, 3),
  c(2, 1, 0),
  c(4, 2, 5),
  c(5, 1, 4),
  c(4, 1, 2),
  c(6, 7, 3),
  c(3, 1, 6),
  c(6, 1, 7),
  c(5, 7, 8),
  c(8, 1, 5),
  c(7, 1, 8),
  c(9, 2, 3),
  c(3, 10, 9),
  c(9, 10, 2),
  c(5, 2, 11),
  c(11, 10, 5),
  c(2, 10, 11),
  c(3, 7, 12),
  c(12, 10, 3),
  c(7, 10, 12),
  c(13, 7, 5),
  c(5, 10, 13),
  c(13, 10, 7))
edges0 <- do.call(c, lapply(1:nrow(triangles), function(i){
  face <- triangles[i, ]
  list(
    sort(c(face[1], face[2])),
    sort(c(face[1], face[3])),
    sort(c(face[2], face[3]))
  )
}))
edges <- do.call(rbind, edges0)
edges <- edges[!duplicated(edges), ]
s <- 2
library(rgl)
open3d(windowRect = c(50, 50, 1074, 562))
mfrow3d(1, 2)
view3d(zoom = 0.65)
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 = "violetred")
}
for(i in 1:nrow(edges)){
  edge <- edges[i, ]
  A <- vertices[edge[1], ]
  B <- vertices[edge[2], ]
  gtube <- gyrotube(A, B, s, radius = 0.06)
  shade3d(gtube, color = "darkviolet")
}
spheres3d(vertices, radius = 0.09, color = "deeppink")
# now plot the hyperbolic convex hull
next3d()
view3d(zoom = 0.65)
plotGyrohull3d(vertices, s)

# an example of color palette ####
if(require("trekcolors")) {
  pal <- trek_pal("lcars_series")
} else {
  pal <- hcl.colors(32L, palette = "Rocket")
}
set.seed(666) # 50 random points on sphere
if(require("uniformly")) {
  points <- runif_on_sphere(50L, d = 3L)
} else {
  points <- matrix(rnorm(50L * 3L), nrow = 50L, ncol = 3L)
  points <- points / sqrt(apply(points, 1L, crossprod))
}
open3d(windowRect = c(50, 50, 562, 562))
plotGyrohull3d(
  points, edgesColor = "brown",
  facesColor = pal, g = function(u) 1-u^2
)