---
title: "Update of 'gyro'"
author: "Stéphane Laurent"
date: '2022-06-04'
tags: geometry, R, graphics
rbloggers: yes
output:
  md_document:
    variant: markdown
    preserve_yaml: true
  html_document:
    highlight: kate
    keep_md: no
highlighter: pandoc-solarized
---

I updated the **gyro** package (soon on CRAN). Here are the new features.


## Hyperbolic polyhedra in the Poincaré model

The previous version of the package only dealt with hyperbolic polyhedra in 
the Minkowski model. Now it is possible to get hyperbolic polyhedra in the 
Poincaré model. I don't provide some example, because they look similar 
to the polyhedra in the Minkowski model (see 
[this post](https://laustep.github.io/stlahblog/posts/hyperbolicPolyhedra.html)). 
I prefer the Minkowski model because one can change the hyperbolic curvature 
in this model.


## Hyperbolic tilings of the Poincaré disk

The package now provides the `tiling` function, which draws a hyperbolic 
tiling of the Poincaré disk.

```r
library(gyro)
tiling(7, 4, depth = 4, border = "darkred", lwd = 2)
```

![](./figures/htiling_7-4.png)


## Hyperbolic Delaunay tessellations

The package now provides the `hdelaunay` function, which constructs a hyperbolic 
Delaunay triangulation in the Poincaré disk thanks to the C++ library **CGAL**, 
and the `plotHdelaunay` function, which plots such a triangulation.

Unfortunately, this new feature will not be included in the CRAN version, 
because of a C++ issue spotted by Valgrind. If you want to use it, you have to 
install the **hdelaunay** branch of the Github repo:

```r
remotes::install_github("stla/gyro@hdelaunay", build_vignettes = TRUE)
```

Here is a first example:

```r
library(gyro)
library(uniformly)
set.seed(666)
points <- runif_in_sphere(50L, d = 2)
hdel <- hdelaunay(points)
plotHdelaunay(hdel, color="random", luminosity="bright")
```

![](./figures/hdelaunay1.png)

Actually the faces of the hyperbolic Delaunay triangulation are the same as 
the ones of the Euclidean Delaunay triangulation, except that they are 
hyperbolic, up to this point: as you can see on the above plot, there are some 
edges without incident face; this occurs when the circumcircle of the 
missing Euclidean Delaunay face is not contained in the unit disk. 

Here is a second example, not random:

```r
library(gyro)
library(trekcolors)
phi <- (1 + sqrt(5)) / 2
theta <- head(seq(0, pi/2, length.out = 11L), -1L)
a <- phi^((2*theta/pi)^0.8 - 1)
u <- a * cos(theta)
v <- a * sin(theta)
x <- c(0, u, -v, -u, v)
y <- c(0, v, u, -v, -u)
pts <- cbind(x, y) / 1.03
hdel <- hdelaunay(pts, centroids = TRUE, exact = TRUE)
fcolor <- function(t){
	RGB <- colorRamp(trek_pal("klingon"))(t)
	rgb(RGB[, 1L], RGB[, 2L], RGB[, 3L], maxColorValue = 255)
}
plotHdelaunay(
		hdel, vertices = FALSE, circle = FALSE, color = fcolor
)
```

![](./figures/hdelaunay2.png)