Get the row in a CSV where xyz coordinates stop changing

Question

I have a measurement of an object with xyz coordinates and a timeline in ms. My CSV looks like this:

TimeInSec  X.6   Y.6  Z.6
0.000000    -1.383422   -0.058891   0.023290    
0.004167    -1.387636   -0.058947   0.023584
0.008333    -1.391491   -0.058972   0.023989
...

I want to find the row in my dataset where the xyz coordinates stop changing (within a threshold). The key feature I want is a time from row 0 to the stop point of my object.

My Code:

dummy.data <- read.csv (file="D:\\tmp\\dummy.csv", header = TRUE, skip = 6
dummy.data %>%
  gather(key,value, X.6, X.7, X.8, Y.6, Y.7, Y.8, Z.6, Z.7, Z.8) %>%
  ggplot(aes(x=Time..Seconds., y=value, colour=key)) +
  geom_line()

Many Thanks for your help!

Sample Graph: Sample Graph

Here is the link to the RawData CSV RawData

Answer 1

Here's an updated example that uses exactly the same code as before but now I made some dummy data that shows different offsets and the data settles to a constant value eventually. The point is that successive points will get closer and closer so a Euclidean distance (think of this as the actual distance) between successive points will get smaller. Once below the threshold, we declare the points to have settled.

library(tidyverse)
library(ggplot2)
numberofpoints <- 100
threshold <- 0.01
set.seed(1)
dummy.data <- # make some dummy data with offsets
    data.frame(
        X.6=runif(numberofpoints), X.7=runif(numberofpoints), X.8=runif(numberofpoints),
        Y.6=runif(numberofpoints), Y.7=runif(numberofpoints), Y.8=runif(numberofpoints),
        Z.6=runif(numberofpoints), Z.7=runif(numberofpoints), Z.8=runif(numberofpoints)) %>%
    mutate(
        X.6=3+X.6/row_number(), X.7=1+X.7/row_number(), X.8=2+X.8/row_number(),
        Y.6=4+Y.6/row_number(), Y.7=6+Y.7/row_number(), Y.8=9+Y.8/row_number(),
        Z.6=5+Z.6/row_number(), Z.7=7+Z.7/row_number(), Z.8=10+Z.8/row_number()
    )

distances <- dist(dummy.data)  # find distances between all pairs of readings (will be slow for large data)
distances.matrix <- as.matrix(distances)
# distances between adjacent readings
distancechange <- c(NA,unlist(sapply(1:numberofpoints-1, function(r) distances.matrix[r,r+1])))
# the first point below the threshold
changebelowthreshold <- min(which(distancechange < threshold))

# Plot something
dummy.data$Time <- 1:nrow(dummy.data)
thresholdtime <- dummy.data$Time[changebelowthreshold]
plotdata <- dummy.data %>% pivot_longer(cols=c(X.6, X.7, X.8, Y.6, Y.7, Y.8, Z.6, Z.7, Z.8))
gg <- ggplot(plotdata, aes(x=Time, y=value, colour=name)) + geom_line() + geom_vline(xintercept = thresholdtime)

This makes the following plot.

The vertical line shows where the data is below a threshold.