doc: show screenshots in readme

doc: minor tweaks
doc: include screenshots
2026-01-22 00:37:47 +01:00 · 2026-01-21 22:42:00 +01:00 · 2026-01-21 22:31:12 +01:00 · 2026-01-21 22:21:24 +01:00 · 2026-01-21 16:02:00 +01:00 · 2026-01-21 15:57:57 +01:00
10 changed files with 1920 additions and 60 deletions
--- a/README.md
+++ b/README.md
@@ -14,6 +14,12 @@ Develop an R-based software, which will perform the following tasks:

 6.  In the final project report, describe the problem, describe the method and the developed software support in the R environment, present and interpret the results, and form a conclusion.

+## Demo
+![Departures View](doc/web-departures.png)
+![Single Flight View](doc/web-single.png)
+![Statistics View](doc/web-stats.png)
+![Interpretation View](doc/web-interpretation.png)
+
 ## Resources

 1.  [The OpenSky Network. (2025). Internet archive of observed aircraft trajectories.](https://opensky-network.org/datasets/states/)
--- a/doc/slides.Rmd
+++ b/doc/slides.Rmd
@@ -23,11 +23,22 @@ Develop an R-based software, which will perform the following tasks:

 ## Methodology

-1. acquire data using the OpenSky API
+1. acquire data using the OpenSky API bindings in the `openSkies` R package

-2. use 
+2. use `tcltk` and `shiny` for GUI and Web Interface
+
+3. show an interactive map using leaflet
+
+4. calculate required parameters using `trajr`
+
+5. calculate descriptive statistics

 ## Contribution

- extended functionality of the `openSkies` R package and created a merge request
+- extended functionality of the `openSkies` R package and created a merge request in the original repository

+- created a web app to display stats, density functions and boxplots
+
+---
+
+![web interface](web-single.png)
--- a/doc/web-departures.png
+++ b/doc/web-departures.png
--- a/doc/web-interpretation.png
+++ b/doc/web-interpretation.png
--- a/doc/web-single.png
+++ b/doc/web-single.png
--- a/doc/web-stats.png
+++ b/doc/web-stats.png
--- a/doc/web-stats_full.png
+++ b/doc/web-stats_full.png
--- a/renv.lock
+++ b/renv.lock
--- a/src/app.Rmd
+++ b/src/app.Rmd
@@ -0,0 +1,301 @@
+```{r backend, include=FALSE}
+# Load all functions from main.Rmd
+knitr::purl("./main.Rmd", output = tempfile(), quiet = TRUE) |> source()
+```
+
+# Web Interface
+```{r shiny}
+# Flight Trajectory Analysis - Shiny GUI Application
+# This app allows interactive selection of flights and displays trajectory analysis
+# All core functions are loaded from main.Rmd
+
+# UI Definition
+ui <- fluidPage(
+  titlePanel("Flight Trajectory Analysis - GUI"),
+  
+  sidebarLayout(
+    sidebarPanel(
+      width = 3,
+      
+      h4("OpenSky Credentials"),
+      textInput("client_id", "Client ID:", value = Sys.getenv('OPENSKY_CLIENT_ID')),
+      passwordInput("client_secret", "Client Secret:", value = Sys.getenv('OPENSKY_CLIENT_SECRET')),
+      
+      hr(),
+      
+      h4("Airport Selection"),
+      textInput("airport_code", "Airport ICAO Code:", value = "EDDF"),
+      sliderInput("hours_back", "Hours back from now:", min = 1, max = 12, value = 1),
+      
+      actionButton("load_departures", "Load Departures", class = "btn-primary"),
+      
+      hr(),
+      
+      h4("Flight Selection"),
+      selectInput("selected_flight", "Select Flight:", choices = NULL),
+      
+      actionButton("analyze_flight", "Analyze Selected Flight", class = "btn-success"),
+      
+      hr(),
+      
+      h4("Batch Analysis"),
+      numericInput("batch_size", "Days of flights to analyze:", value = 5, min = 1, max = 30),
+      actionButton("batch_analyze", "Run Batch Analysis", class = "btn-warning"),
+      
+      hr(),
+      
+      verbatimTextOutput("status_text")
+    ),
+    
+    mainPanel(
+      width = 9,
+      
+      tabsetPanel(
+        id = "main_tabs",
+        
+        tabPanel("Departures List",
+                 h4("Available Departures"),
+                 tableOutput("departures_table")
+        ),
+        
+        tabPanel("Single Flight Analysis",
+                 fluidRow(
+                   column(6, leafletOutput("route_plot", height = "400px")),
+                   column(6, plotOutput("altitude_plot", height = "400px"))
+                 ),
+                 fluidRow(
+                   column(6, plotOutput("trajectory_plot", height = "400px")),
+                   column(6, 
+                          h4("Trajectory Characteristics"),
+                          tableOutput("characteristics_table"))
+                 )
+        ),
+        
+        tabPanel("Statistical Analysis",
+                 h4("Multiple Trajectory Statistics"),
+                 tableOutput("stats_summary_table"),
+                 hr(),
+                 fluidRow(
+                   column(12, plotOutput("boxplots", height = "500px"))
+                 ),
+                 fluidRow(
+                   column(12, plotOutput("density_plots", height = "500px"))
+                 ),
+                 fluidRow(
+                   column(12, plotOutput("histograms", height = "500px"))
+                 )
+        ),
+        
+        tabPanel("Interpretation",
+                 h4("Analysis Interpretation"),
+                 verbatimTextOutput("interpretation_text")
+        )
+      )
+    )
+  )
+)
+
+# Server Logic
+server <- function(input, output, session) {
+  
+  # Reactive values to store data
+  rv <- reactiveValues(
+    creds = NULL,
+    departures = NULL,
+    departures_df = NULL,
+    current_route = NULL,
+    current_trj = NULL,
+    current_icao = NULL,
+    trajectory_stats_df = NULL
+  )
+  
+  # Status message
+  status <- reactiveVal("Ready. Enter credentials and load departures.")
+  
+  output$status_text <- renderText({
+    status()
+  })
+  
+  # Load departures
+  observeEvent(input$load_departures, {
+    req(input$client_id, input$client_secret, input$airport_code)
+    
+    status("Loading departures...")
+    
+    tryCatch({
+      # Use getCredentials from main.Rmd
+      rv$creds <- getCredentials(
+        client_id = input$client_id,
+        client_secret = input$client_secret
+      )
+      
+      time_now <- Sys.time()
+      rv$departures <- getAirportDepartures(
+        airport = input$airport_code,
+        startTime = time_now - hours(input$hours_back),
+        endTime = time_now,
+        credentials = rv$creds
+      )
+      
+      if (length(rv$departures) > 0) {
+        # Create departures dataframe for display
+        departures_list <- lapply(seq_along(rv$departures), function(i) {
+          dep <- rv$departures[[i]]
+          data.frame(
+            Index = i,
+            ICAO24 = dep[["ICAO24"]] %||% NA,
+            #FIXME Callsign, Origin, Destination
+            Callsign = dep[["callsign"]] %||% NA,
+            Origin = dep[["estDepartureAirport"]] %||% NA,
+            Destination = dep[["estArrivalAirport"]] %||% NA,
+            DepartureTime = as.POSIXct(dep[["departure_time"]] %||% NA, origin = "1970-01-01"),
+            stringsAsFactors = FALSE
+          )
+        })
+        rv$departures_df <- do.call(rbind, departures_list)
+        
+        # Update flight selection dropdown
+        choices <- setNames(
+          seq_along(rv$departures),
+          paste(rv$departures_df$ICAO24, "-", rv$departures_df$Callsign, 
+                "(", rv$departures_df$Destination, ")")
+        )
+        updateSelectInput(session, "selected_flight", choices = choices)
+        
+        status(paste("Loaded", length(rv$departures), "departures from", input$airport_code))
+      } else {
+        status("No departures found for the selected time period.")
+      }
+      
+    }, error = function(e) {
+      status(paste("Error loading departures:", e$message))
+    })
+  })
+  
+  # Display departures table
+  output$departures_table <- renderTable({
+    req(rv$departures_df)
+    rv$departures_df
+  })
+  
+  # Analyze selected flight
+  observeEvent(input$analyze_flight, {
+    req(rv$departures, input$selected_flight, rv$creds)
+    
+    status("Analyzing selected flight...")
+    
+    tryCatch({
+      idx <- as.integer(input$selected_flight)
+      dep <- rv$departures[[idx]]
+      icao24 <- dep[["ICAO24"]]
+      dep_time <- dep[["departure_time"]]
+      
+      rv$current_icao <- icao24
+      
+      # Use getAircraftTrack from main.Rmd
+      route_df <- getAircraftTrack(icao24, dep_time, rv$creds)
+      
+      if (is.null(route_df) || nrow(route_df) < 2) {
+        status(paste("No path data available for", icao24))
+        return()
+      }
+      
+      rv$current_route <- route_df
+      
+      # Use getTrajFromRoute from main.Rmd
+      rv$current_trj <- getTrajFromRoute(route_df)
+      status(paste("Successfully analyzed", icao24, "with", nrow(route_df), "points"))
+      
+      # Switch to analysis tab
+      updateTabsetPanel(session, "main_tabs", selected = "Single Flight Analysis")
+      
+    }, error = function(e) {
+      status(paste("Error analyzing flight:", e$message))
+    })
+  })
+  
+  # Route plot
+  output$route_plot <- renderLeaflet({
+    req(rv$current_route)
+    createInteractiveMap(rv$current_route)
+  })
+  
+  # Altitude plot
+  output$altitude_plot <- renderPlot({
+    req(rv$current_route)
+    plot(rv$current_route$time, rv$current_route$alt, type = "l", col = "red", lwd = 2,
+         main = paste("Altitude Profile of", rv$current_icao),
+         xlab = "Time (Unix)", ylab = "Altitude (m)")
+  })
+  
+  # Trajectory plot
+  output$trajectory_plot <- renderPlot({
+    req(rv$current_trj)
+    plot(rv$current_trj, main = paste("Trajectory of", rv$current_icao))
+  })
+  
+  # Characteristics table
+  output$characteristics_table <- renderTable({
+    req(rv$current_trj)
+    calculateTrajectoryStats(rv$current_trj, format = "table")
+  })
+  
+  # Batch analysis
+  observeEvent(input$batch_analyze, {
+    req(rv$departures, rv$creds)
+    
+    status("Running batch analysis...")
+    
+    tryCatch({
+      
+      withProgress(message = 'Analyzing flights', value = 0, {
+        all_trajectories <- getAircraftTrajectories(rv$current_icao, time = Sys.time(), creds, days = input$batch_size)
+      })
+      
+      if (length(all_trajectories) > 0) {
+        rv$trajectory_stats_df <- do.call(rbind, all_trajectories)
+        status(paste("Batch analysis complete:", nrow(rv$trajectory_stats_df), "trajectories analyzed"))
+        updateTabsetPanel(session, "main_tabs", selected = "Statistical Analysis")
+      } else {
+        status("No trajectory data collected in batch analysis")
+      }
+      
+    }, error = function(e) {
+      status(paste("Error in batch analysis:", e$message))
+    })
+  })
+  
+  # Statistics summary table - use calculateStatsSummary from main.Rmd
+  output$stats_summary_table <- renderTable({
+    req(rv$trajectory_stats_df)
+    calculateStatsSummary(rv$trajectory_stats_df)
+  })
+  
+  # Boxplots - use createBoxplots from main.Rmd
+  output$boxplots <- renderPlot({
+    req(rv$trajectory_stats_df)
+    createBoxplots(rv$trajectory_stats_df)
+  })
+  
+  # Density plots - use createDensityPlots from main.Rmd
+  output$density_plots <- renderPlot({
+    req(rv$trajectory_stats_df)
+    createDensityPlots(rv$trajectory_stats_df)
+  })
+  
+  # Histograms - use createHistograms from main.Rmd
+  output$histograms <- renderPlot({
+    req(rv$trajectory_stats_df)
+    createHistograms(rv$trajectory_stats_df)
+  })
+  
+  # Interpretation text - use generateInterpretation from main.Rmd
+  output$interpretation_text <- renderText({
+    req(rv$trajectory_stats_df)
+    generateInterpretation(rv$trajectory_stats_df)
+  })
+}
+
+# Run the application
+shinyApp(ui = ui, server = server)
+```
--- a/src/main.Rmd
+++ b/src/main.Rmd
@@ -1,5 +1,5 @@
 ---
-title: "Topic 8"
+title: "Topic 8 - Flight Trajectory Analysis"
 output:
  pdf_document: default
  html_document: default
@@ -8,87 +8,635 @@ date: "`r Sys.Date()`"

 ```{r setup, include=FALSE}
 knitr::opts_chunk$set(echo = TRUE)
+# include `eval=isArtifact()` to check if pdf/html is being produced
+isArtifact <- function(){
+  isOutput <-knitr::is_html_output() || knitr::is_latex_output()
+  return(isOutput)
+}
 ```

+# Abstract
+
+This project implements an R-based application for the retrieval, processing, and statistical analysis of aircraft trajectories. Flight data is obtained from the OpenSky Network API, transformed into analyzable trajectory objects using the `trajr` package, and subsequently characterized using established movement ecology metrics. The methodology enables quantitative comparison of flight paths through parameters such as path length, straightness index, and fractal dimension.
+
+# Introduction
+
+## Background
+
+The analysis of movement trajectories constitutes a fundamental aspect of spatial data science, with applications ranging from animal behavior studies to transportation network optimization. In the context of aviation, trajectory analysis provides insights into flight efficiency, airspace utilization, and routing patterns.
+
+## Objectives
+
+The primary objectives of this project are:
+
+1. **Data Acquisition**: Implement robust methods for retrieving real-time flight trajectory data from the OpenSky Network
+2. **Trajectory Characterization**: Apply established metrics from movement ecology to quantify flight path properties
+3. **Statistical Analysis**: Perform comparative analysis across multiple flights to identify patterns and distributions
+
+## Theoretical Framework
+
+The `trajr` package, originally developed for animal movement analysis, provides a comprehensive toolkit for trajectory characterization. Key metrics employed in this analysis include:
+
+- **Path Length**: Total distance traveled along the trajectory
+- **Diffusion Distance**: Euclidean displacement from origin to destination
+- **Straightness Index**: Ratio of diffusion distance to path length (range 0-1)
+- **Fractal Dimension**: Measure of path complexity (1 = straight line, approaching 2 = space-filling curve)
+
+# Methodology
+
+## Data Source
+
+Flight trajectory data is obtained from the OpenSky Network, a community-based receiver network providing open access to air traffic surveillance data. The API provides:
+
+- Aircraft state vectors (position, velocity, heading)
+- Historical flight tracks
+- Airport departure and arrival information
+
+## Data Processing Pipeline
+
+The analysis workflow consists of the following stages:
+
+1. **Authentication**: Establish connection to OpenSky API using credentials
+2. **Data Acquisition**: Retrieve departure information for specified airport and time window
+3. **Track Retrieval**: Obtain detailed waypoint data for individual flights
+4. **Coordinate Transformation**: Convert geographic coordinates to metric distances
+5. **Trajectory Construction**: Create `trajr` trajectory objects for analysis
+6. **Statistical Computation**: Calculate trajectory metrics and aggregate statistics
+
+## Libraries
+The following libraries were included for convenience and backend handling. 
+The packages more central to the task, such as `openSkies` and `trajr` are explicitly mentioned in the text.
 ```{r preamble, message=FALSE}
-# Load Libraries
 library(dplyr)
 library(lubridate)
 library(readr)
 library(utils)
-library(openSkies)
 library(dotenv)
 library(httr)
 library(jsonlite)
-library(trajr)
+library(shiny)
 ```

-# Download flights 
-```{r opensky}
+# Implementation
+
+The following section will demonstrate the implementation of the methodology using R code snippets.
+
+The full analysis is also available in the `shiny` web interface.
+
+## API Authentication
+
+Authentication with https://opensky-network.org/ was supposed to be provided by the `openSkies` R package.
+The API provider however had deprecated username + password authentication for the API in 2025-03, leading us to first work with the
+REST API manually.
+While working on the manual API code, we however already forked the original package at [Rafael-Ayala/openSkies](https://github.com/Rafael-Ayala/openSkies)
+to [eneller/openSkies](https://github.com/eneller/openSkies/) and made several
+[changes](https://github.com/Rafael-Ayala/openSkies/issues/3) that were later included in a
+[pull request](https://github.com/Rafael-Ayala/openSkies/pull/4).
+Our contributions include refactoring and streamlining authenticated requests to use the `makeAuthenticatedRequest()` function used below
+and store the token obtained by initial authentication in a `credentials` object obtained from the new `getCredentials()` function.
+
+We further adjusted the front-facing functions to accept either _username + password_ or _client ID + secret_
+where applicable using the new credentials object.
+
+```{r auth, include=FALSE}
+library(openSkies)
+# Openskies API Functions 

-time_now <- Sys.time()
 creds <- getCredentials(
  client_id = Sys.getenv('OPENSKY_CLIENT_ID'),
  client_secret = Sys.getenv('OPENSKY_CLIENT_SECRET'))

-# get departures from Frankfurt airport
-departures <- getAirportDepartures(airport = "EDDF", startTime = time_now - hours(1), endTime = time_now, credentials = creds )
+```

+## Data Acquisition
+In the code below, the new `makeAuthenticatedRequests()` is also used to make requests to the `tracks/all` endpoint for which no
+official function is provided by `openSkies` as that endpoint is still considered experimental at the time of writing.
+We use this endpoint in `getAircraftTrack()` to obtain the track data that is used for all further trajectory calculations.
+
+In order to request the track from the API, we first need to get a list of flights for an aircraft using 
+`openSkies::getAircraftFlights()` in our convenience function `getFlights()`.
+
+```{r get-data}
+# Get flights for a specific aircraft from OpenSky API
 getFlights <- function(icao, time, creds){
  flights <-getAircraftFlights(icao, startTime =  time - days(1), endTime = time, credentials = creds )
  return(flights)
 }
-icao <- departures[[1]][["ICAO24"]]
-flights <- getFlights(icao,Sys.time(), creds)
-# TODO map from all available flights to tracks
-query <- list(icao24= icao, time=as.numeric(flights[[1]][["departure_time"]]))

-# can get tracks for up to 30 days in the past
-response <-makeAuthenticatedRequest('tracks/all',query, creds)
-track_data <- fromJSON(content(response, as = "text", encoding = "UTF-8"))
-if (!is.null(track_data$path) && length(track_data$path) > 0) {
-    
+# Get aircraft track from OpenSky API
+getAircraftTrack <- function(icao, time, creds) {
+  query <- list(icao24 = icao, time = as.numeric(time))
+  response <- makeAuthenticatedRequest('tracks/all', query, creds)
+  track_data <- fromJSON(content(response, as = "text", encoding = "UTF-8"))
+  if (!is.null(track_data$path) && length(track_data$path) > 0) {
    route_df <- as.data.frame(track_data$path)
    colnames(route_df) <- c("time", "lat", "lon", "alt", "heading", "on_ground")
-    
-    message("Loading of route successfull! Points: ", nrow(route_df))
-    
-    plot(route_df$lon, route_df$lat, type="o", pch=20, col="blue", 
-         main=paste("Geographic route of", icao),
-         xlab="Longitude", ylab="Latitude")
-    
-    plot(route_df$time, route_df$alt, type="l", col="red", lwd=2,
-         main=paste("Altitude profile of", icao),
-         xlab="Time (Unix)", ylab="Height (Meter)")
-    
-  } else {
-    print("No path points from api")
+    return(route_df)
  }
-```
-
-# GUI selection
-```{r gui}
-icaos <- lapply(departures, function(x) x[["ICAO24"]])
-options <- unlist(icaos) # tcltk needs a character vector
-
-# Create a GUI list selection
-listSelect <- function(options){
-  selected_option <- NULL
-  tryCatch({
-    selected_option <- select.list(
-      title = "Select an aircraft",
-      choices = options,
-      preselect = NULL,
-      multiple = FALSE,
-      graphics = TRUE
-    )
-  }, error = function(w) {
-    message('No GUI available')
-    }
-  )
-  if (nzchar(selected_option)){
-    return(selected_option)
-  }
-  return(options[1])
+  return(NULL)
 }
 ```
+## Parameter Calculation
+We then calculate several basic parameters from the route, such as time and distance, that are then used to
+construct an object in `getTrajFromRoute()` that can later be used with `trajr`.
+
+```{r trajectory-functions}
+library(trajr)
+
+# Trajectory Conversion Functions
+
+# Convert route to distance in meters
+getRouteDistance <- function(route_df) {
+  lat_ref <- route_df$lat[1]
+  lon_ref <- route_df$lon[1]
+  meters_per_deg_lat <- 111320
+  meters_per_deg_lon <- 111320 * cos(lat_ref * pi / 180)
+  x_meters <- (route_df$lon - lon_ref) * meters_per_deg_lon
+  y_meters <- (route_df$lat - lat_ref) * meters_per_deg_lat
+  return(list('x' = x_meters, 'y' = y_meters))
+}
+
+# Get time in seconds from start
+getRouteTime <- function(route_df) {
+  return(route_df$time - route_df$time[1])
+}
+
+# Create trajr object from route
+getTrajFromRoute <- function(route_df) {
+  meters <- getRouteDistance(route_df)
+  time <- getRouteTime(route_df)
+  trj <- TrajFromCoords(
+    data.frame(x = meters$x, y = meters$y, time = time),
+    xCol = "x", yCol = "y", timeCol = "time"
+  )
+  return(trj)
+}
+
+```
+
+The altitude profile reveals distinct flight phases: climb, cruise, and descent. This temporal representation provides insight into vertical movement patterns.
+
+```{r demo-altitude-plot, fig.width=7, fig.height=4, purl=FALSE, echo=FALSE}
+time_now <- Sys.time()
+departures <- getAirportDepartures(
+  airport = "EDDF",
+  startTime = time_now - hours(2),
+  endTime = time_now - hours(1),
+  credentials = creds
+)
+cat("Departures retrieved:", length(departures), "\n")
+route_df <- NULL
+icao <- "N/A"
+
+if (length(departures) > 0) {
+  for (i in seq_along(departures)) {
+    icao <- departures[[i]][["ICAO24"]]
+    dep_time <- departures[[i]][["departure_time"]]
+    route_df <- getAircraftTrack(icao, dep_time, creds)
+    if (!is.null(route_df) && nrow(route_df) >= 3) {
+      cat("Aircraft ICAO24:", icao, "\n")
+      cat("Track points acquired:", nrow(route_df), "\n")
+      break
+    }
+    Sys.sleep(1)
+  }
+}
+
+if (!is.null(route_df)) {
+  time_minutes <- (route_df$time - route_df$time[1]) / 60
+  plot(time_minutes, route_df$alt, type = "l", col = "red", lwd = 2,
+       main = paste("Altitude Profile -", icao),
+       xlab = "Elapsed Time (min)", ylab = "Barometric Altitude (m)")
+  grid()
+} else {
+  cat("Insufficient data for altitude analysis\n")
+}
+```
+
+# Results
+
+## Trajectory Metrics
+For each obtained trajectory, we first calculate the following metrics:
+duration, length, diffusion distance, straightness index, mean velocity and fractal dimension.
+```{r trajectory-metrics}
+# Calculate trajectory characteristics
+# Input: either route_df (data.frame with lat/lon) or trj (trajr object)
+# format: "row" for batch analysis (one row per flight), "table" for single flight display
+calculateTrajectoryStats <- function(input, icao = NULL, format = "row") {
+  # Determine if input is route_df or trj
+  if (inherits(input, "Trajectory")) {
+    trj <- input
+  } else {
+    trj <- getTrajFromRoute(input)
+  }
+  
+  # Calculate all metrics
+  duration <- TrajDuration(trj)
+  path_length <- TrajLength(trj)
+  diffusion_distance <- TrajDistance(trj)
+  straightness <- TrajStraightness(trj)
+  mean_velocity <- path_length / duration
+  
+  fractal_dim <- tryCatch({
+    min_step <- path_length / 100
+    max_step <- path_length / 2
+    if (min_step > 0 && max_step > min_step) {
+      step_sizes <- exp(seq(log(min_step), log(max_step), length.out = 10))
+      TrajFractalDimension(trj, stepSizes = step_sizes)
+    } else {
+      NA
+    }
+  }, error = function(e) NA)
+  
+  # Return format based on use case
+  if (format == "table") {
+    # For single flight display (Parameter | Value)
+    return(data.frame(
+      Parameter = c(
+        "Duration (s)", "Duration (min)",
+        "Path Length (km)",
+        "Diffusion Distance (m)",
+        "Diffusion Distance (km)",
+        "Straightness Index",
+        "Mean Velocity (km/h)",
+        "Fractal Dimension"
+      ),
+      Value = c(
+        round(duration, 2),
+        round(duration / 60, 2),
+        round(path_length / 1000, 2),
+        round(diffusion_distance, 2),
+        round(diffusion_distance / 1000, 2),
+        round(straightness, 4),
+        round(mean_velocity * 3.6, 2),
+        round(fractal_dim, 4)
+      )
+    ))
+  } else {
+    # For batch analysis (one row per flight)
+    return(data.frame(
+      icao24 = icao,
+      diffusion_distance_km = diffusion_distance / 1000,
+      path_length_km = path_length / 1000,
+      straightness = straightness,
+      duration_min = duration / 60,
+      mean_velocity_kmh = mean_velocity * 3.6,
+      fractal_dimension = fractal_dim
+    ))
+  }
+}
+
+# Calculate trajectory parameters for a single flight
+calculate_trajectory_params <- function(icao, departure_time, creds) {
+  tryCatch({
+    route_df <- getAircraftTrack(icao, departure_time, creds)
+    
+    if (is.null(route_df) || nrow(route_df) < 3) return(NULL)
+    
+    return(calculateTrajectoryStats(route_df, icao = icao, format = "row"))
+    
+  }, error = function(e) {
+    message("Error processing ", icao, ": ", e$message)
+    return(NULL)
+  })
+}
+
+getAircraftTrajectories <- function(icao, time, creds, days = 5){
+  tracks <- list()
+  for (i in 0: (days-1)) {
+    flights <- getFlights(icao,time - days(i),creds)
+    for (f in flights){
+      track <- calculate_trajectory_params(icao, f[["departure_time"]], creds)
+      if (!is.null(track)){
+        tracks[[length(tracks)+1]] <- track
+      }
+      Sys.sleep(0.5) # API courtesy
+    }
+  }
+  return(tracks)
+}
+```
+
+```{r demo-multiple-tracks, purl=FALSE, echo=FALSE, include=FALSE}
+flight_data <- list()
+successful_flights <- 0
+
+if (length(departures) > 0) {
+  max_attempts <- min(10, length(departures))
+  
+  for (i in seq_len(max_attempts)) {
+    icao_temp <- departures[[i]][["ICAO24"]]
+    dep_time_temp <- departures[[i]][["departure_time"]]
+    
+    route_df_temp <- getAircraftTrack(icao_temp, dep_time_temp, creds)
+    
+    if (!is.null(route_df_temp) && nrow(route_df_temp) >= 3) {
+      stats <- calculateTrajectoryStats(route_df_temp, icao = icao_temp, format = "row")
+      if (!is.null(stats)) {
+        flight_data[[length(flight_data) + 1]] <- stats
+        successful_flights <- successful_flights + 1
+        cat("Flight", successful_flights, "| ICAO:", icao_temp, 
+            "| Waypoints:", nrow(route_df_temp), "\n")
+      }
+    }
+    
+    if (successful_flights >= 5) break
+  }
+  
+  if (length(flight_data) > 0) {
+    all_flights_stats <- do.call(rbind, flight_data)
+    cat("\nSample size (n):", nrow(all_flights_stats), "flights\n")
+  } else {
+    all_flights_stats <- NULL
+    cat("No valid trajectories obtained\n")
+  }
+} else {
+  all_flights_stats <- NULL
+  cat("No departure data available\n")
+}
+```
+
+
+The following table presents computed metrics for all successfully analyzed flights.
+
+```{r demo-all-stats-table, purl=FALSE, echo=FALSE}
+# FIXME we should display several flights from the same aircraft as stated in the requirements
+# not different aircraft's flights
+if (!is.null(all_flights_stats)) {
+  display_stats <- all_flights_stats
+  display_stats$diffusion_distance_km <- round(display_stats$diffusion_distance_km, 2)
+  display_stats$path_length_km <- round(display_stats$path_length_km, 2)
+  display_stats$straightness <- round(display_stats$straightness, 4)
+  display_stats$duration_min <- round(display_stats$duration_min, 1)
+  display_stats$mean_velocity_kmh <- round(display_stats$mean_velocity_kmh, 1)
+  display_stats$fractal_dimension <- round(display_stats$fractal_dimension, 4)
+  
+  knitr::kable(display_stats, caption = "Computed Trajectory Metrics",
+               col.names = c("ICAO24", "Displacement (km)", "Path Length (km)", 
+                           "Straightness", "Duration (min)", "Velocity (km/h)", "Fractal Dim."))
+} else {
+  cat("No data available for tabulation\n")
+}
+```
+
+## Trajectory Statistics
+To enable statistical inference, trajectory data is collected for multiple flights.
+We then calculate basic descriptive statistics for the metrics we obtained earlier,
+such as
+- mean
+- median
+- standard deviation
+- interquartile range
+```{r trajectory-summary}
+getTrajectoryParams <- function() {
+  list(
+    params = c("diffusion_distance_km", "straightness", "duration_min", 
+               "mean_velocity_kmh", "fractal_dimension"),
+    labels = c("Diffusion Distance (km)", "Straightness", "Duration (min)", 
+               "Mean Velocity (km/h)", "Fractal Dimension")
+  )
+}
+
+# Calculate statistics summary table
+calculateStatsSummary <- function(trajectory_stats_df) {
+  p <- getTrajectoryParams()
+  
+  stats_list <- lapply(seq_along(p$params), function(i) {
+    x <- trajectory_stats_df[[p$params[i]]]
+    x <- x[!is.na(x)]
+    if (length(x) < 2) return(NULL)
+    
+    data.frame(
+      Parameter = p$labels[i],
+      N = length(x),
+      Mean = round(mean(x), 1),
+      Variance = round(var(x), 1),
+      Std_Dev = round(sd(x), 1),
+      Q1 = round(quantile(x, 0.25), 1),
+      Median = round(median(x), 1),
+      Q3 = round(quantile(x, 0.75), 1)
+    )
+  })
+  
+  do.call(rbind, stats_list[!sapply(stats_list, is.null)])
+}
+```
+
+
+The `calculateStatsSummary()` function computes central tendency and dispersion measures for each trajectory parameter.
+
+```{r demo-summary-stats, purl=FALSE, echo=FALSE}
+# FIXME first table column broken
+if (!is.null(all_flights_stats) && nrow(all_flights_stats) >= 2) {
+  summary_stats <- calculateStatsSummary(all_flights_stats)
+  knitr::kable(summary_stats, caption = "Descriptive Statistics Summary")
+} else {
+  cat("Minimum sample size (n >= 2) not met\n")
+}
+```
+
+## Visualisation
+Boxplots provide a robust visualization of parameter distributions, displaying median, interquartile range, and potential outliers. The red diamond indicates the arithmetic mean.
+
+```{r vis-boxplot}
+createBoxplots <- function(trajectory_stats_df) {
+  p <- getTrajectoryParams()
+  
+  par(mfrow = c(2, 3))
+  for (i in seq_along(p$params)) {
+    data <- trajectory_stats_df[[p$params[i]]][!is.na(trajectory_stats_df[[p$params[i]]])]
+    if (length(data) >= 2) {
+      boxplot(data, main = p$labels[i], ylab = p$labels[i], col = "lightblue", border = "darkblue")
+      points(1, mean(data), pch = 18, col = "red", cex = 1.5)
+    }
+  }
+  par(mfrow = c(1, 1))
+}
+```
+
+```{r demo-boxplot, fig.width=10, fig.height=8, purl=FALSE, echo=FALSE}
+if (!is.null(all_flights_stats) && nrow(all_flights_stats) >= 2) {
+  createBoxplots(all_flights_stats)
+} else {
+  cat("Minimum sample size (n >= 2) not met\n")
+}
+```
+
+
+Density plots employ kernel density estimation to approximate the probability distribution of each parameter. Vertical lines indicate mean (red, dashed) and median (green, dotted).
+
+```{r vis-density}
+createDensityPlots <- function(trajectory_stats_df) {
+  p <- getTrajectoryParams()
+  
+  par(mfrow = c(2, 3))
+  for (i in seq_along(p$params)) {
+    data <- trajectory_stats_df[[p$params[i]]][!is.na(trajectory_stats_df[[p$params[i]]])]
+    if (length(data) >= 3) {
+      dens <- density(data)
+      plot(dens, main = paste("Density:", p$labels[i]), xlab = p$labels[i], col = "darkblue", lwd = 2)
+      polygon(dens, col = rgb(0, 0, 1, 0.3), border = "darkblue")
+      abline(v = mean(data), col = "red", lwd = 2, lty = 2)
+      abline(v = median(data), col = "green", lwd = 2, lty = 3)
+    }
+  }
+  par(mfrow = c(1, 1))
+}
+```
+
+```{r demo-density, fig.width=10, fig.height=8, purl=FALSE, echo=FALSE}
+if (!is.null(all_flights_stats) && nrow(all_flights_stats) >= 3) {
+  createDensityPlots(all_flights_stats)
+} else {
+  cat("Minimum sample size (n >= 3) not met for density estimation\n")
+}
+```
+
+Histograms with overlaid density curves provide an alternative visualization of parameter distributions.
+
+```{r vis-histogram}
+createHistograms <- function(trajectory_stats_df) {
+  p <- getTrajectoryParams()
+  
+  par(mfrow = c(2, 3))
+  for (i in seq_along(p$params)) {
+    data <- trajectory_stats_df[[p$params[i]]][!is.na(trajectory_stats_df[[p$params[i]]])]
+    if (length(data) >= 3) {
+      hist(data, probability = TRUE, main = paste("Histogram:", p$labels[i]),
+           xlab = p$labels[i], col = "lightgray", border = "darkgray")
+      lines(density(data), col = "red", lwd = 2)
+    }
+  }
+  par(mfrow = c(1, 1))
+}
+```
+
+```{r demo-histogram, fig.width=10, fig.height=8, purl=FALSE, echo=FALSE}
+if (!is.null(all_flights_stats) && nrow(all_flights_stats) >= 3) {
+  createHistograms(all_flights_stats)
+} else {
+  cat("Minimum sample size (n >= 3) not met for histogram analysis\n")
+}
+```
+
+
+The `generateInterpretation()` function provides contextual analysis of the computed trajectory metrics.
+
+```{r vis-interpretation, include=FALSE}
+generateInterpretation <- function(trajectory_stats_df) {
+  df <- trajectory_stats_df
+  
+  text <- "========== INTERPRETATION OF TRAJECTORY PARAMETERS ==========\n\n"
+  
+  dd <- df$diffusion_distance_km[!is.na(df$diffusion_distance_km)]
+  if (length(dd) >= 2) {
+    text <- paste0(text, "1. DIFFUSION DISTANCE (Net Displacement):\n")
+    text <- paste0(text, "   - Mean: ", round(mean(dd), 2), " km\n")
+    text <- paste0(text, "   - Represents straight-line distance from origin to destination.\n")
+    text <- paste0(text, "   - Variance: ", round(var(dd), 2), " (indicates diversity in flight distances)\n\n")
+  }
+  
+  st <- df$straightness[!is.na(df$straightness)]
+  if (length(st) >= 2) {
+    text <- paste0(text, "2. STRAIGHTNESS INDEX:\n")
+    text <- paste0(text, "   - Mean: ", round(mean(st), 4), " (range 0-1, where 1 = perfectly straight)\n")
+    text <- paste0(text, "   - Values close to 1 indicate efficient, direct flight paths.\n")
+    text <- paste0(text, "   - Lower values suggest deviations due to weather, airspace, or routing.\n\n")
+  }
+  
+  dur <- df$duration_min[!is.na(df$duration_min)]
+  if (length(dur) >= 2) {
+    text <- paste0(text, "3. DURATION OF TRAVEL:\n")
+    text <- paste0(text, "   - Mean: ", round(mean(dur), 2), " minutes\n")
+    text <- paste0(text, "   - Range: ", round(min(dur), 2), " - ", round(max(dur), 2), " minutes\n")
+    text <- paste0(text, "   - IQR: ", round(IQR(dur), 2), " minutes (middle 50% of flights)\n\n")
+  }
+  
+  vel <- df$mean_velocity_kmh[!is.na(df$mean_velocity_kmh)]
+  if (length(vel) >= 2) {
+    text <- paste0(text, "4. MEAN TRAVEL VELOCITY:\n")
+    text <- paste0(text, "   - Mean: ", round(mean(vel), 2), " km/h\n")
+    text <- paste0(text, "   - Typical commercial aircraft cruise: 800-900 km/h\n")
+    text <- paste0(text, "   - Lower values may include taxi, takeoff, and landing phases.\n\n")
+  }
+  
+  fd <- df$fractal_dimension[!is.na(df$fractal_dimension)]
+  if (length(fd) >= 2) {
+    text <- paste0(text, "5. FRACTAL DIMENSION:\n")
+    text <- paste0(text, "   - Mean: ", round(mean(fd), 4), "\n")
+    text <- paste0(text, "   - Value of 1.0 = perfectly straight line\n")
+    text <- paste0(text, "   - Values closer to 2.0 = more complex, space-filling paths\n")
+    text <- paste0(text, "   - Aircraft typically show low fractal dimension (efficient paths).\n\n")
+  }
+  
+  text <- paste0(text, "========== END OF ANALYSIS ==========")
+  text
+}
+```
+
+```{r demo-interpretation, purl=FALSE, echo=TRUE}
+if (!is.null(all_flights_stats) && nrow(all_flights_stats) >= 2) {
+  interpretation <- generateInterpretation(all_flights_stats)
+  cat(interpretation)
+} else {
+  cat("Minimum sample size (n >= 2) not met for interpretation\n")
+}
+```
+
+We also include an interactive map using `leaflet` to provide an intuitive display for the route of the aircraft.
+```{r vis-map}
+library(leaflet)
+createInteractiveMap <- function(route) {
+  leaflet(route) %>%
+    addTiles() %>%
+    addPolylines(lng=~lon, lat=~lat, color="blue", weight=3, opacity=0.8) %>%
+    addCircleMarkers(
+    lng = ~lon[1],
+    lat = ~lat[1],
+    color = "green",
+    radius = 6,
+    popup = "Origin"
+  ) %>%
+  addCircleMarkers(
+    lng = ~lon[nrow(route)],
+    lat = ~lat[nrow(route)],
+    color = "red",
+    radius = 6,
+    popup = "Destination"
+  )
+}
+```
+![Departures View](../doc/web-departures.png)
+![Single Flight View](../doc/web-single.png)
+![Statistics View](../doc/web-stats.png)
+![Interpretation View](../doc/web-interpretation.png)
+
+# Discussion
+
+## Key Findings
+
+The trajectory analysis reveals several characteristics typical of commercial aviation:
+
+1. **High Straightness Values**: Commercial flights generally exhibit straightness indices approaching 1.0, indicating efficient direct routing between waypoints.
+
+2. **Low Fractal Dimension**: Values close to 1.0 confirm that flight paths approximate straight lines, consistent with fuel-efficient routing principles.
+
+3. **Velocity Patterns**: Mean velocities below typical cruise speeds (800-900 km/h) reflect the inclusion of departure and arrival phases in the trajectory data.
+
+## Limitations
+
+- **Temporal Resolution**: Track data granularity varies based on ADS-B receiver coverage
+- **Sample Size**: Statistical inference is limited by the number of available flights with complete track data
+
+# Conclusion
+
+This project demonstrates the successful application of movement ecology metrics to aviation trajectory analysis. The implemented R framework provides a reproducible methodology for flight path characterization and statistical comparison. The `trajr` package proves suitable for aircraft trajectory analysis, offering robust metrics originally developed for biological movement studies.
+
+# References
+
+1.  [The OpenSky Network. (2025). Internet archive of observed aircraft trajectories.](https://opensky-network.org/datasets/states/)
+2.  [Schäfer, M, Strohmeier, M, Lenders, V, Martinovic, I, Wilhelm, M. (2014). Bringing Up OpenSky: A Large-scale ADS-B Sensor Network for Research. In Proceedings of the 13th IEEE/ACM International Symposium on Information Processing in Sensor Networks (IPSN), pages 83-94.](https://opensky-network.org/files/publications/ipsn2014.pdf)
+3.  [Zheng, Y. (2015). Trajectory Data Mining: An Overview. ACM Transactions on Intelligent Systems and Technology, 61(3), 1–41.](https://doi.org/10.1145/2743025)
+4.  [Thulin, M. (2025). Modern Statistics with R: From wrangling and exploring data to inference and predictive modelling. CRC Press. Boca Raton, Fl.](https://modernstatisticswithr.com/)
+5.  [McLean, D J, and Skowron Volponi, M A. (2018). trajr: An R package for characterisation of animal trajectories. Ethology, 124, 440–448.](https://doi.org/10.1111/eth.12739)
+
Author	SHA1	Message	Date
eneller	c1541c693a	doc: show screenshots in readme	2026-01-22 00:37:47 +01:00
eneller	1ab649f25f	doc: minor tweaks	2026-01-21 22:42:00 +01:00
eneller	137ddb197b	doc: include screenshots	2026-01-21 22:31:12 +01:00
eneller	5d129f1498	doc: finalize report	2026-01-21 22:21:24 +01:00
eneller	010345ae03	move doc	2026-01-21 16:02:00 +01:00
eneller	595388e413	build: add webshot for pdf screenshots	2026-01-21 15:57:57 +01:00
eneller	20270f5816	Create Web UI using shiny commit `3de1345642` Merge: `9106db3` `f4955af` Author: eneller <erikneller@gmx.de> Date: Wed Jan 21 15:14:32 2026 +0100 Merge branch 'feat/trajectories-and-alternative-gui' into feat/add-osm-for-trajectory commit `9106db35a9` Author: eneller <erikneller@gmx.de> Date: Wed Jan 21 15:13:28 2026 +0100 build: lock renv commit `f4955af7f4` Author: eneller <erikneller@gmx.de> Date: Wed Jan 21 13:13:23 2026 +0100 build: exclude demo chunks from purl commit `2757a86383` Author: lukasadrion <lukas.adrion@uni-ulm.de> Date: Wed Jan 21 13:12:34 2026 +0100 🐛 add getAircraftTrajectories function commit `133827c2bd` Author: lukasadrion <lukas.adrion@uni-ulm.de> Date: Wed Jan 21 12:54:03 2026 +0100 add interactive map with leaflet commit `a7aa5025ea` Merge: `74292bd` `93f4e3e` Author: eneller <erikneller@gmx.de> Date: Wed Jan 21 12:22:42 2026 +0100 Merge remote-tracking branch 'refs/remotes/origin/feat/trajectories-and-alternative-gui' into feat/trajectories-and-alternative-gui commit `93f4e3e81d` Author: lukasadrion <lukas.adrion@uni-ulm.de> Date: Wed Jan 21 00:21:50 2026 +0100 📝 add more documentation commit `74292bd0ec` Merge: `ec51069` `86a9e41` Author: eneller <erikneller@gmx.de> Date: Wed Jan 21 00:09:16 2026 +0100 Merge remote-tracking branch 'origin/feat/trajectories-and-alternative-gui' into feat/trajectories-and-alternative-gui commit `ec51069f1d` Author: eneller <erikneller@gmx.de> Date: Tue Jan 20 23:49:51 2026 +0100 wip: fix: trajectory stats for single aircraft commit `86a9e4163f` Author: lukasadrion <lukas.adrion@uni-ulm.de> Date: Tue Jan 20 23:36:07 2026 +0100 🐛 fixed the credentials bug for documentation commit `387e1caa7f` Author: lukasadrion <lukas.adrion@uni-ulm.de> Date: Tue Jan 20 23:10:08 2026 +0100 📝 add documentation to main commit `696f52eda3` Author: lukasadrion <lukas.adrion@uni-ulm.de> Date: Tue Jan 20 16:53:19 2026 +0100 ♻️ refactor all logic to main.rmd commit `eb49746268` Author: lukasadrion <lukas.adrion@uni-ulm.de> Date: Tue Jan 20 16:13:41 2026 +0100 🩹 fix small issues in main commit `f491345ea0` Author: eneller <erikneller@gmx.de> Date: Tue Jan 20 15:46:26 2026 +0100 refactor: consolidate main.Rmd statistics commit `aacdc12638` Author: lukasadrion <lukas.adrion@uni-ulm.de> Date: Tue Jan 20 15:31:21 2026 +0100 ♻️ refactor app.Rmd commit `e4c7ce4977` Author: eneller <erikneller@gmx.de> Date: Tue Jan 20 13:48:49 2026 +0100 chore: move app from R to Rmd commit `d9a33a5d2b` Author: eneller <erikneller@gmx.de> Date: Mon Jan 19 17:45:35 2026 +0100 build: add dependencies commit `d8dd920d6b` Author: Patrik M <57401452+Patrik157@users.noreply.github.com> Date: Mon Jan 19 17:25:18 2026 +0100 Added trajectories and alternative GUI	2026-01-21 15:38:17 +01:00
eneller	e2699640ca	doc: slides	2026-01-20 18:10:55 +01:00