R: Draw lines which "fit" the same shape as a reference line - r

Question

I'm currently working on a project were I need to indentify lines which have the same kind of shape, e.g:
yrefer = c(0.2900,0.3189,0.4097,0.3609,0.3762,0.5849,0.7144)
For example take a look at the following plot, I want R to recognize these two red lines for example as a fitting shape, also if there is a little deviation(say 0.05 from the reference line(in blue)).
So I want to write a code which checks based on a list of y coördinates if these y coördinates fit the yrefer line, were a deviation of 0.05 is permitted.
I'm not sure if this is possible in R, but if it is I know there are people here that can help me out.
notice: What I mean with the deviation of 0.05:
let's say we have a line which is:
1.2900 1.3189 1.4097 1.3609 1.3762 1.5849 1.7144
this would be exactly the same line but then 1 higher then the yrefer line, but with the deviation of 0.05 I mean that if some y coördinates differ 0.05 from what you would expect them to be, so in this example I should expect them to be 1 higher for ever yRefer coördinate, but if one of them is 0.98 higher I would still accept this as a "fitting" line, because it's devation is < 0.05.
To clarify I drawed some possiblities(there are a lot more of course!) which should be accepted as correct for the first y-value:
I hope it's clear, if not let me know!

Answer 1

I don't think Johannes' answer generalizes, e.g:
y_ref = c(0, 0, 0)
y_test = c(.03,.03, -.06) #then test_line fails even though, let:
y_test = y_test +.011
abs(y_test - y_ref) #never outside the .05 range
test_line(y_test) #failed
I think you want something like:
n = length(y_test)
d1 = y_test[-1] - y_test[-n]
d2 = y_ref[-1] - y_ref[-n]
max(cumsum(d2 - d1)) - min(cumsum(d2 - d1)) #shouldn't be >= .1

Answer 2

Just account for the different y mean.
newline<- c(1.25, 1.3189, 1.4097, 1.4609, 1.3762, 1.5249, 1.7144)
newline2<-newline+mean(yrefer)-mean(newline)
sd(newline2-yrefer) #Can use var or whatever you want here.
This can all be packed into a function like.
lindev<- function(x){
newline2<-x+mean(yrefer)-mean(x)
return(sd(newline2-yrefer))}
lindev(c(1.25, 1.3189, 1.4097, 1.4609, 1.3762, 1.5249, 1.7144))
Note this will only work if the x coordinates are the same.

Answer 3

y_ref <- c(0.2900,0.3189,0.4097,0.3609,0.3762,0.5849,0.7144)
y_test_1 <- c(1.2900, 1.3187, 1.4097, 1.3609, 1.3762, 1.5849, 1.7144)
y_test_2 <- c(1.2900, 1.2189, 1.4097, 1.3609, 1.3762, 1.5849, 1.7144)
test_line <- function(y_test) {
overall_deviation <- mean(y_test - y_ref)
residuals <- y_test - y_ref - overall_deviation
if (any(abs(residuals) > 0.05)) message("Failed")
else message("Passed")
}
test_line(y_test_1)
test_line(y_test_2)