---
author: Stéphane Laurent
date: '2018-08-16'
highlighter: kate
linenums: True
output:
  html_document:
    keep_md: False
  md_document:
    preserve_yaml: True
    variant: markdown
prettify: True
prettifycss: 'twitter-bootstrap'
tags: 'R, graphics, plotly'
title: Triangulated surfaces with plotly in R
---

The `plotly` package for R has a type `mesh3d` allowing to draw
triangulated surfaces. We will give some examples.

From a `mesh3d` object: icosahedron example
-------------------------------------------

``` {.r}
tmesh <- rgl::icosahedron3d()
plot_ly(
  x = tmesh$vb[1,], y = tmesh$vb[2,], z = tmesh$vb[3,],
  i = tmesh$it[1,]-1, j = tmesh$it[2,]-1, k = tmesh$it[3,]-1,
  facecolor = toRGB(viridisLite::inferno(20)),
  type = "mesh3d"
) %>% layout(scene = list(aspectmode = "data"))
```

![](figures/icosahedron.png)

Drawing a parametric surface : cyclide example
----------------------------------------------

``` {.r}
a = 0.94; d = 0.56; c = 0.34; b = sqrt(a^2-c^2)
fx <- function(u,v){
  (d*(c-a*cos(u)*cos(v))+b^2*cos(u)) / (a-c*cos(u)*cos(v))
}
fy <- function(u,v){
  (b*sin(u)*(a-d*cos(v))) / (a-c*cos(u)*cos(v))
}
fz <- function(u,v){
  (b*sin(v)*(c*cos(u)-d)) / (a-c*cos(u)*cos(v))
}

library(misc3d)
tris <- parametric3d(fx, fy, fz, 
                     umin=0, umax=2*pi, vmin=0, vmax=2*pi, 
                     n=100, engine="none")

n <- nrow(tris$v1)
cont <- matrix(NA_real_, ncol=3, nrow=3*n)
cont[3*(1:n)-2,] <- tris$v1
cont[3*(1:n)-1,] <- tris$v2
cont[3*(1:n),] <- tris$v3
idx <- matrix(0:(3*n-1), ncol=3, byrow=TRUE)

plot_ly(
  x = cont[,1], y = cont[,2], z = cont[,3],
  i = idx[,1], j = idx[,2], k = idx[,3],
  type = "mesh3d"
) %>% layout(scene = list(aspectmode = "data"))
```

![](figures/cyclide_parametric.png)

We can add some colors:

``` {.r}
midpoints <- (tris$v1 + tris$v2 + tris$v3)/3
distances <- apply(midpoints, 1, crossprod)
intervals <- cut(distances, 256)
colorsPalette <- viridisLite::viridis(256)
colors <- colorsPalette[as.integer(intervals)]

plot_ly(
  x = cont[,1], y = cont[,2], z = cont[,3],
  i = idx[,1], j = idx[,2], k = idx[,3],
  type = "mesh3d",
  facecolor = toRGB(colors)
) %>% layout(scene = list(aspectmode = "data"))
```

![](figures/cyclide_parametric_colored.png)

Drawing an isosurface: cyclide again
------------------------------------

I like cyclides...

``` {.r}
a = 0.94; mu = 0.56; c = 0.34
f <- function(x, y, z, a, c, mu){
  b <- sqrt(a^2-c^2)
  (x^2+y^2+z^2-mu^2+b^2)^2 - 4*(a*x-c*mu)^2 - 4*b^2*y^2
}

x <- seq(-c-mu-a, abs(mu-c)+a, length=100) 
y <- seq(-mu-a, mu+a, length=100)
z <- seq(-mu-c, mu+c, length=50) 
g <- expand.grid(x=x, y=y, z=z)
voxel <- array(with(g, f(x,y,z,a,c,mu)), c(100,100,50))
library(misc3d)
cont <- computeContour3d(voxel, level=0, x=x, y=y, z=z)

idx <- matrix(0:(nrow(cont)-1), ncol=3, byrow=TRUE)

plot_ly(
  x = cont[,1], y = cont[,2], z = cont[,3],
  i = idx[,1], j = idx[,2], k = idx[,3],
  type = "mesh3d"
) %>% layout(scene = list(aspectmode = "data"))
```

![](figures/cyclide_isosurface.png)