Package 'sphereTessellation'

Spherical Delaunay triangulation

Description

Computes a spherical Delaunay triangulation.

Usage

DelaunayOnSphere(vertices, radius = 1, center = c(0, 0, 0), iterations = 5L)

Arguments

vertices	vertices, a numeric matrix with three columns
radius	radius of the sphere, a positive number; the vertices will be projected on this sphere
center	center of the sphere, a numeric vector of length three; the vertices will be projected on this sphere
iterations	positive integer, the number of iterations used to construct the meshes of the spherical faces

Details

See 2D Triangulations on the Sphere.

Value

A named list with four fields:

• vertices, the matrix of vertices obtained by projecting the original vertices to the sphere;

• faces, an integer matrix providing by row the indices of the faces of the triangulation;

• solidFaces, an integer vector providing the indices of the solid faces; faces are either solid faces or ghost faces, see details

• meshes, a list of meshes of the solid faces used for plotting in plotDelaunayOnSphere.

See Also

plotDelaunayOnSphere

Examples

library(sphereTessellation)
library(rgl)

if(require(cooltools)) {
vertices <- fibonaccisphere(30L)
del <- DelaunayOnSphere(vertices)
open3d(windowRect = 50 + c(0, 0, 512, 512), zoom = 0.8)
plotDelaunayOnSphere(del)
}

if(require(uniformly)) {
# sample vertices on a hemisphere, so there will be some ghost faces
set.seed(421L)
vertices <- rphong_on_hemisphere(6L)
del <- DelaunayOnSphere(vertices)
# the ghost faces are not plotted
open3d(windowRect = 50 + c(0, 0, 512, 512), zoom = 0.8)
plotDelaunayOnSphere(del)
}

---

Icosphere

Description

Returns the mesh of an icosphere.

Usage

icosphereMesh(x = 0, y = 0, z = 0, r = 1, iterations = 3L)

Arguments

x, y, z	coordinates of the center
r	radius
iterations	number of iterations (the icosphere is obtained by iteratively subdividing the faces of an icosahedron)

Value

A rgl mesh (class mesh3d).

Examples

library(sphereTessellation)
library(rgl)
mesh <- icosphereMesh()
open3d(windowRect = 50 + c(0, 0, 512, 512))
shade3d(mesh, color = "navy")

---

Plot spherical Delaunay triangulation

Description

Plot a spherical Delaunay triangulation.

Usage

plotDelaunayOnSphere(
  del,
  colors = "random",
  distinctArgs = list(seedcolors = c("#ff0000", "#00ff00", "#0000ff")),
  randomArgs = list(hue = "random", luminosity = "bright"),
  edges = FALSE,
  vertices = FALSE,
  ecolor = "black",
  lwd = 3,
  vcolor = "black",
  vradius = NA,
  ...
)

Arguments

del	an output of DelaunayOnSphere
colors	controls the filling colors of the triangles, either NA for no color, or a single color, or "random" to get multiple colors with randomColor, or "distinct" to get multiple colors with createPalette
distinctArgs	if colors = "distinct", a list of arguments passed to createPalette
randomArgs	if colors = "random", a list of arguments passed to randomColor
edges	Boolean, whether to plot the edges
vertices	Boolean, whether to plot the vertices
ecolor	a color for the edges
lwd	line width for the edges, if they are plotted
vcolor	a color for the vertices
vradius	a radius for the vertices, which are plotted as spheres (if they are plotted); NA for a default value
...	arguments passed to shade3d to plot the spherical triangles

Value

No value is returned.

Examples

library(sphereTessellation)
library(rgl)

vertices <- t(cuboctahedron3d()$vb[-4L, ])
del <- DelaunayOnSphere(vertices, radius = sqrt(2))

open3d(windowRect = 50 + c(0, 0, 512, 512), zoom = 0.8)
plotDelaunayOnSphere(del)

---

Plot spherical Voronoï tessellation

Description

Plot a spherical Voronoï tessellation.

Usage

plotVoronoiOnSphere(
  vor,
  colors = "gradient",
  distinctArgs = list(seedcolors = c("#ff0000", "#00ff00", "#0000ff")),
  randomArgs = list(hue = "random", luminosity = "bright"),
  palette = "Rocket",
  bias = 1,
  edges = FALSE,
  sites = FALSE,
  ecolor = "black",
  lwd = 3,
  scolor = "black",
  sradius = NA,
  ...
)

Arguments

vor	an output of VoronoiOnSphere
colors	controls the filling colors of the triangles, either NA for no color, or a single color, or "random" to get multiple colors with randomColor, or "distinct" to get multiple colors with createPalette, or "gradient"
distinctArgs	if colors = "distinct", a list of arguments passed to createPalette
randomArgs	if colors = "random", a list of arguments passed to randomColor
palette	this argument is used only when colors="gradient"; it can be either a character vector of colors, or the name of a palette which will be passed to the palette argument of the function hcl.colors
bias	this argument is used only when colors="gradient"; it is passed to the bias argument of the function colorRamp
edges	Boolean, whether to plot the edges
sites	Boolean, whether to plot the Voronoï sites
ecolor	a color for the edges
lwd	graphical parameter for the edges, if they are plotted
scolor	a color for the sites
sradius	a radius for the sites, which are plotted as spheres (if they are plotted); NA for a default value
...	arguments passed to shade3d to plot the spherical faces

Value

No value is returned.

Examples

library(sphereTessellation)
library(rgl)
# take the vertices of the cuboctahedron and Voronoïze
vertices <- t(cuboctahedron3d()$vb[-4L, ])
vor <- VoronoiOnSphere(vertices)
# plot
open3d(windowRect = 50 + c(0, 0, 512, 512), zoom = 0.8)
plotVoronoiOnSphere(vor, specular = "black", edges = TRUE)

# effect of the `bias` argument ###
library(sphereTessellation)
library(rgl)
vertices <- t(cuboctahedron3d()$vb[-4L, ])
vor <- VoronoiOnSphere(vertices)
open3d(windowRect = 50 + c(0, 0, 900, 300), zoom = 0.8)
mfrow3d(1, 3)
plotVoronoiOnSphere(vor, palette = "Viridis", bias = 0.5)
next3d()
plotVoronoiOnSphere(vor, palette = "Viridis", bias = 0.8)
next3d()
plotVoronoiOnSphere(vor, palette = "Viridis", bias = 1.1)

---

Spherical Voronoï tessellation

Description

Computes a spherical Voronoï tessellation.

Usage

VoronoiOnSphere(vertices, radius = 1, center = c(0, 0, 0), iterations = 5L)

Arguments

vertices	vertices, a numeric matrix with three columns
radius	radius of the sphere, a positive number; the vertices will be projected on this sphere
center	center of the sphere, a numeric vector of length three; the vertices will be projected on this sphere
iterations	positive integer, the number of iterations used to construct the meshes of the spherical faces

Details

First the Delaunay triangulation is computed, then the Voronoï tessellation is obtained by duality.

Value

An unnamed list whose each element corresponds to a Voronoï face and is a named list with three fields:

• site, the coordinates of the Voronoï site of the face;

• cell, a numeric matrix providing the coordinates of the vertices of the face;

• mesh, a mesh of the face used for plotting in the function plotVoronoiOnSphere.

See Also

plotVoronoiOnSphere

Examples

library(sphereTessellation)
library(rgl)
if(require(cooltools)) {
vertices <- fibonaccisphere(150L)
vor <- VoronoiOnSphere(vertices)
open3d(windowRect = 50 + c(0, 0, 512, 512), zoom = 0.8)
plotVoronoiOnSphere(vor, colors = "random")
}

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