---
title: "Gyrotriangle (aka hyperbolic triangle) with moving colors"
author: "Stéphane Laurent"
date: '2022-02-05'
tags: R, maths, geometry, graphics, rgl
rbloggers: yes
output:
  md_document:
    variant: markdown
    preserve_yaml: true
  html_document:
    highlight: kate
    keep_md: no
highlighter: pandoc-solarized
---

My package [gyro](https://github.com/stla/gyro) has been freshly released on 
CRAN. I implemented the ideas given in 
[this blog post](https://laustep.github.io/stlahblog/posts/hyperbolicPolyhedra.html) 
in this package. It has a short 
[vignette](https://cran.r-project.org/web/packages/gyro/vignettes/getstarted.html).

The `gyrodemos` function provides some examples. But none of them explains how 
I did the moving colors on this polyhedra that you can see on the Github repo:

![](https://raw.githubusercontent.com/stla/gyro/main/inst/images/icosahedron_dynamic_colors.gif)

So I will explain here. In fact, this is similar to the method I presented 
[here](https://laustep.github.io/stlahblog/posts/PyVistaDynamicCmap.html) 
for **PyVista** and 
[here](https://laustep.github.io/stlahblog/posts/HopfTorusDynamicColors.html) 
for **rgl**.

The `gyrotriangle` function of the **gyro** package has a `palette` argument, 
in which the user provides a vector of colors. Here is an example:

```{r, eval=FALSE}
library(gyro)
library(rgl)

s <- 0.6 # hyperbolic curvature
A <- c(1, 0, 0); B <- c(0, 1, 0); C <- c(0, 0, 1)
ABC <- gyrotriangle(
  A, B, C, s = s,
  palette = hcl.colors(n = 256, palette = "Berlin")
)

open3d(windowRect = c(50, 50, 562, 562))
material3d(lit = FALSE)
view3d(10, 40, zoom = 0.8)
shade3d(ABC)
```

![](figures/gyrotriangle.png)

Under the hood, the `gyrotriangle` function uses the 
[colorRamp](https://www.rdocumentation.org/packages/grDevices/versions/3.6.2/topics/colorRamp) 
with the vector of colors passed to the `palette` argument. This creates a 
function, let's call it `fpalette`, that assigns a color to each number in the 
interval $[0, 1]$. Then, `gyrotriangle` calculates all the distances from the 
points in the mesh forming the triangle to the gyrocentroid of the triangle. 
Finally, it linearly normalizes these distances to the interval $[0, 1]$, and 
it applies the `fpalette` function to the normalized distances.

Now, the `gyrotriangle` function has a `g` argument. This is the key to make 
the moving colors. This argument `g` must be a function from $[0, 1]$ to 
$[0, 1]$, by default it is the `identity` function, and `fpalette` is actually 
applied to the normalized distances transformed by `g`. 

So, here is how we can do to get some moving colors:

```{r, eval=FALSE}
shift_ <- seq(0, 1, length.out = 61)[-1]
for(i in seq_along(shift_)){
  ABC <- gyrotriangle(
    A, B, C, s,
    palette = hcl.colors(n = 256, palette = "Berlin"), 
    g = function(u) (sin(2*pi*(u - shift_[i])) + 1) / 2
  )
  open3d(windowRect = c(50, 50, 562, 562))
  material3d(lit = FALSE)
  view3d(10, 40, zoom = 0.8)
  shade3d(ABC)
  rgl.snapshot(sprintf("snapshot%03d", i))
  close3d()
}

library(gifski)
pngs <- list.files(pattern = "^snapshot")
gifski(
  pngs,
  gif_file = "gyrotriangle.gif",
  width = 512,
  height = 512,
  delay = 1/8
)

file.remove(pngs)
```

![](figures/gyrotriangle.gif)
