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I've been trying to reproduce this matrix scatter plots, and understand them. For instance, I had trouble calling the multiple plots with the curves around points of the grouping categorical variable:

> levels(sa.groups.area)
[1] "Lower"  "Middle" "Upper" 

Finally, though, I got a practically identical plot with this code:

library(compositions)
data(SimulatedAmounts)
colors = c(rgb(red=0.3, green=0.3,  blue=.3, alpha=1),
           rgb(red=0.9, green=0,    blue=0, alpha=0.7),
           rgb(red=0,   green=.9,   blue=0, alpha=0.7))

tt = acomp(sa.groups5)
plot(tt, col = rgb(0,0,0,0), bg = colors[as.numeric(sa.groups.area)], pch = 21, cex = .9)

strata = sa.groups5.area
temp = cbind(sa.groups5,strata)

a = acomp(temp[temp[ , 6] == 1, ][,1:5])
ellipses(mean(a), var(a), r = 2, col = colors[1])

b = acomp(temp[temp[ , 6] == 2, ][,1:5])
ellipses(mean(b), var(b), r = 2, col = colors[2])

c = acomp(temp[temp[ , 6] == 3, ][,1:5])
ellipses(mean(c), var(c), r = 2, col = colors[3])

In Analyzing Compositional Data with R By K. Gerald van den Boogaart, Raimon Tolosana-Delgado the following plot can be found with a telling caption:

and (minimally) paraphrasing:

in which the radius of the lines contain 95% of the probability assuming a normal model for the composition and a known variance.

The code of this latter plot likely includes the lines:

r = sqrt(qchisq(p = .095, df = 2))
mm = mean(tt)
vr = var(tt)
ellipses(mean = mm, var = vr, r = r)

... and ?ellipses describes the r parameter in the function ellipses as:

r      a scaling of the half-diameters

The remaining question is:

What are the meaning and mathematics behind these deformed circles (lines or curves) generated by the function ellipses?

The question is:

What are the meaning and mathematics behind these deformed circles (lines or curves) generated by the function ellipses, and how to generate them?

library(compositions)
data(SimulatedAmounts)
colors = c(rgb(red=0.3, green=0.3,  blue=.3, alpha=1),
           rgb(red=0.9, green=0,    blue=0, alpha=0.7),
           rgb(red=0,   green=.9,   blue=0, alpha=0.7))
           
tt = acomp(sa.groups5)
plot(tt, col = rgb(0,0,0,0), bg = colors[as.numeric(sa.groups.area)], pch = 21, cex = .9)
ellipses(mean(tt), var(tt), r = 2, col = "peru")

strata = sa.groups5.area
temp = cbind(sa.groups5,strata)

a = acomp(temp[temp[ , 6] == 1, ][,1:5])
ellipses(mean(a), var(a), r = 2, col = colors[1])

b = acomp(temp[temp[ , 6] == 2, ][,1:5])
ellipses(mean(b), var(b), r = 2, col = colors[2])

c = acomp(temp[temp[ , 6] == 3, ][,1:5])
ellipses(mean(c), var(c), r = 2, col = colors[3])

library(compositions)
data(SimulatedAmounts)
colors = c(rgb(red=0.3, green=0.3,  blue=.3, alpha=1),
           rgb(red=0.9, green=0,    blue=0, alpha=0.7),
           rgb(red=0,   green=.9,   blue=0, alpha=0.7))

tt = acomp(sa.groups5)
plot(tt, col = rgb(0,0,0,0), bg = colors[as.numeric(sa.groups.area)], pch = 21, cex = .9)

strata = sa.groups5.area
temp = cbind(sa.groups5,strata)

a = acomp(temp[temp[ , 6] == 1, ][,1:5])
ellipses(mean(a), var(a), r = 2, col = colors[1])

b = acomp(temp[temp[ , 6] == 2, ][,1:5])
ellipses(mean(b), var(b), r = 2, col = colors[2])

c = acomp(temp[temp[ , 6] == 3, ][,1:5])
ellipses(mean(c), var(c), r = 2, col = colors[3])

So I've been trying to reproduce this matrix scatter plots, and understand them. For instance I am having trouble calling the multiple plots with the curves around points of the grouping categorical variable:

Here is my code and the output:

library(compositions)
data(SimulatedAmounts)
colors = c(rgb(red=0.3, green=0.3,  blue=.3, alpha=1),
           rgb(red=0.9, green=0,    blue=0, alpha=0.7),
           rgb(red=0,   green=.9,   blue=0, alpha=0.7))
           
tt = acomp(sa.groups5)
plot(tt, col = rgb(0,0,0,0), bg = colors[as.numeric(sa.groups.area)], pch = 21, cex = .9)
ellipses(mean(tt), var(tt), r = 2, col = "peru")

yielding only one curve per ternary diagram.

in which the radius of the lines contain 95% of the probability assuming a normal model for the composition and a known variance.

and there is a clarifying comment as to the meaning of $*$:

margin = "acomp" (or nothing, the default) computes the third part as the geometric of all components except those two from row and colum (symbolized with "*").

What are the color-coded (black, red and green) lines on the (first) plot? And, if at all possible - I understand this second part is code-specific - how can they be generated?

The "mystery" asterisk $(*)$ is clarified in this passage in Analyzing Compositional Data with R By K. Gerald van den Boogaart, Raimon Tolosana-Delgado

margin = "acomp" (or nothing, the default) computes the third part as the geometric of all components except those two from row and colum (symbolized with "*").

I've been trying to reproduce this matrix scatter plots, and understand them. For instance, I had trouble calling the multiple plots with the curves around points of the grouping categorical variable:

Finally, though, I got a practically identical plot with this code:

library(compositions)
data(SimulatedAmounts)
colors = c(rgb(red=0.3, green=0.3,  blue=.3, alpha=1),
           rgb(red=0.9, green=0,    blue=0, alpha=0.7),
           rgb(red=0,   green=.9,   blue=0, alpha=0.7))
           
tt = acomp(sa.groups5)
plot(tt, col = rgb(0,0,0,0), bg = colors[as.numeric(sa.groups.area)], pch = 21, cex = .9)
ellipses(mean(tt), var(tt), r = 2, col = "peru")

strata = sa.groups5.area
temp = cbind(sa.groups5,strata)

a = acomp(temp[temp[ , 6] == 1, ][,1:5])
ellipses(mean(a), var(a), r = 2, col = colors[1])

b = acomp(temp[temp[ , 6] == 2, ][,1:5])
ellipses(mean(b), var(b), r = 2, col = colors[2])

c = acomp(temp[temp[ , 6] == 3, ][,1:5])
ellipses(mean(c), var(c), r = 2, col = colors[3])

and (minimally) paraphrasing:

in which the radius of the lines contain 95% of the probability assuming a normal model for the composition and a known variance.

... and ?ellipses describes the r parameter in the function ellipses as:

r      a scaling of the half-diameters

What are the meaning and mathematics behind these deformed circles (lines or curves) generated by the function ellipses?