ggtern: intersection between line (geom_segment) and smoothed data (geom_smooth_tern)

Question

im currently working on visualization of an evaporation experiment. I've plotted a ternary phase diagram (NaCl-Na2SO4-H2O) with ggtern and data based on phreeqc simulation. Phase boundaries (red/blue) are smoothed data points (geom_smooth_tern).

> geom_smooth_tern(data=dataTernNaCl, aes(x=NaCl, y=H2O, z=Na2SO4), method = loess, se = FALSE, color = "blue")

#Dataframe
> select(dataTernNaCl, NaCl, Na2SO4, H2O)[324:329,]
# A tibble: 6 x 3
   NaCl     Na2SO4       H2O
  <dbl>      <dbl>     <dbl>
1 0.2503361 0.03098092 0.7186830
2 0.2502058 0.03123192 0.7185623
3 0.2500746 0.03148678 0.7184386
4 0.2499421 0.03174650 0.7183114
5 0.2498056 0.03201021 0.7181842
6 0.2496680 0.03227777 0.7180542

Given that phase diagram, I want to visualize the evaporation path (reduction of H2O) from a certain point P1 (based on experimental data).

Straight reduction of H2O is perfectly describable as a line between 2 points. Im using geom_segment.

I need to find the intersection of the evaporation line with the phase boundaries to finally draw the line from P1 to the point of intersection.

Plot

Greetings, Christian

To be able to find the intersection we must have the two equations. Check [here](https://stackoverflow.com/questions/50087814/how-to-find-an-intersection-of-curve-and-circle/50089155#50089155) whether this helps — Onyambu, May 03 '18 at 05:40
Thank you for your response. Sadly I can't get the predict() to work yet. — Christian S., May 03 '18 at 15:42
how did you graph the red line or blue line? Waht are their equations? — Onyambu, May 03 '18 at 18:20
I used ggplots: geom_smooth_tern (data=dataTernNaCl, aes(x=NaCl, y=H2O, z=Na2SO4), method = loess, se = FALSE, color = "blue") + — Christian S., May 03 '18 at 18:55
dataTernNaCl is a dataframe obtained by simulation with "phreeqc" programm - giving me around 2k-3k NaCl, H2O, Na2SO4 pairs — Christian S., May 03 '18 at 19:00

score 1 · Accepted Answer · answered May 05 '18 at 12:42

Based on @Onyambu advise:

key was to limit optimise() inside the range of the data im giving to the model for the blue line (modelPhaseboundaryNaCl).

#function evaporation line between from starting point | input = NaCl
funEvapLine = function(x){
y <- messwerteTern
m <- (y$Ausgang_Na2SO4Ende-y$Ausgang_Na2SO4)/(y$Ausgang_NaClEnde-y$Ausgang_NaCl)
n <- y$Ausgang_Na2SO4/(y$Ausgang_NaCl * m)
m*x+n-1
  }

#function NaCl phase boundary | only works in NaCl range | input = NaCl
modelPhaseBoundaryNaCl <- loess(Na2SO4 ~ NaCl, data=dataTernNaCl)
funNaClBorder <- function(x)predict(modelPhaseBoundaryNaCl, data.frame(NaCl = x))

#function Intersection EvapLine and NaCl phase boundary | input = NaCl | output = NaCl
NaClmin <- min(dataTernNaCl$NaCl)
NaClmax <- max(dataTernNaCl$NaCl)
g <- function(x)(funNaClBorder(x) - funEvapLine(x))
intersectionNaCl <- optimise(function(x)abs(g(x)), c(NaClmin,NaClmax))$min
intersectionNa2SO4 <- funEvapLine(intersectionNa2SO4)
intersectionH2O <- 1-(intersectionNaCl+intersectionNa2SO4)

ggtern: intersection between line (geom_segment) and smoothed data (geom_smooth_tern)

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