3D Biplot in plotly - R - r

Question

I want to build a 3D PCA bi-plot using plotly package because the graph is nice and interactive in html format (something that I need).
My difficulty is to add the loading. I want the loading to be presented as straight lines from the point (0,0,0) (i.e. the equivalent to 2D biplots)
So all in all I don't know how to add straight lines starting from the centre of the 3D graph.
I have calculated the scores and loading using the PCA function;
pca1 <- PCA (dat1, graph = F)
for scores:
ind1 <- pca1$ind$coord[,1:3]
x <- ind1[,1] ; y <- ind1[,2] ; z <- ind1[,3]
for loadings:
var1 <- pca1$var$coord[,1:3]
xl <- var1[,1] ; yl <- var1[,2] ; zl <- var1[,3]
and using the code bellow the 3D score plot is generated;
p <- plot_ly( x=x, y=y, z=z,
marker = list(opacity = 0.7, color=y , colorscale = c('#FFE1A1', '#683531'), showscale = F)) %>%
layout(title = "3D Prefmap",
scene = list(
xaxis = list(title = "PC 1"),
yaxis = list(title = "PC 2"),
zaxis = list(title = "PC 3")))

Answer 1

Here are some ideas that could be useful for the development of a 3D biplot.
# Data generating process
library(MASS)
set.seed(6543)
n <- 500
mu <- c(1,-2,3,-1,3,4)
Sigma <- diag(rep(1,length(mu)))
Sigma[3,1] <- Sigma[1,3] <- 0.1
Sigma[4,6] <- Sigma[6,4] <- 0.1
X <- as.data.frame(mvrnorm(n, mu=mu, Sigma=Sigma))
# PCA
pca <- princomp(X, scores=T, cor=T)
# Scores
scores <- pca$scores
x <- scores[,1]
y <- scores[,2]
z <- scores[,3]
# Loadings
loads <- pca$loadings
# Scale factor for loadings
scale.loads <- 5
# 3D plot
library(plotly)
p <- plot_ly() %>%
add_trace(x=x, y=y, z=z,
type="scatter3d", mode="markers",
marker = list(color=y,
colorscale = c("#FFE1A1", "#683531"),
opacity = 0.7))
for (k in 1:nrow(loads)) {
x <- c(0, loads[k,1])*scale.loads
y <- c(0, loads[k,2])*scale.loads
z <- c(0, loads[k,3])*scale.loads
p <- p %>% add_trace(x=x, y=y, z=z,
type="scatter3d", mode="lines",
line = list(width=8),
opacity = 1)
}
print(p)