C#-Code

using System;
using System.Collections.Generic;
using System.Linq;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Media;
using System.Windows.Shapes;

namespace WpfKonvexeHuellkurve
{
    /// <summary>
    /// Interaktionslogik für MainWindow.xaml
    /// </summary>
    public partial class MainWindow : Window
    {
        private static readonly Random rnd = new Random();
        private List<Point> points;

        const int size = 6;
        const int padding = 20;
        private readonly Brush brush = Brushes.Blue;
        public MainWindow()
        {
            InitializeComponent();
        }

        private void DrawRandomPoints(int n)
        {
            points = new List<Point>();

            listBoxPoints.Items.Clear();
            canvasDraw.Children.Clear();
            canvasDraw.UpdateLayout();
            int width = (int)canvasDraw.ActualWidth;
            int height = (int)canvasDraw.ActualHeight;

            for (int i = 0; i < n; i++)
            {
                int x = rnd.Next(padding, width - padding);
                int y = rnd.Next(padding, height - padding);
                points.Add(new Point(x, y));

                Ellipse ell = new Ellipse() { Width = size, Height = size, Stroke = brush, StrokeThickness = double.Epsilon, Fill = brush };
                Canvas.SetLeft(ell, x - size / 2);
                Canvas.SetTop(ell, y - size / 2);

                canvasDraw.Children.Add(ell);

                listBoxPoints.Items.Add($"X: {x} | Y: {y}");
            }
        }

        private void buttonDrawRandom_Click(object sender, RoutedEventArgs e)
        {
            int n;
            if (int.TryParse(textBoxNumber.Text, out n))
            {
                if (n >= 3)
                {
                    DrawRandomPoints(n);
                }
            }
        }

        private void DrawConvexLine()
        {
            PointCollection points = new PointCollection(GetPoints().Distinct());
            Polygon convex = new Polygon() { Points = points, Stroke = Brushes.Red, StrokeThickness = 2 };
            canvasDraw.Children.Add(convex);
        }

        private IEnumerable<Point> GetPoints()
        {
            var westernmost = points.Where(b => b.X == points.Min(a => a.X)).OrderByDescending(a => a.Y);
            var northernmost = points.Where(b => b.Y == points.Min(a => a.Y)).OrderBy(a => a.X);
            var easternmost = points.Where(b => b.X == points.Max(a => a.X)).OrderBy(a => a.Y);
            var southernmost = points.Where(b => b.Y == points.Max(a => a.Y)).OrderByDescending(a => a.X);

            Point west = westernmost.First();
            Point north = northernmost.First();
            Point east = easternmost.First();
            Point south = southernmost.First();
            Point start = new Point(west.X, west.Y);

            foreach (var point in westernmost)
            {
                west = point;
                yield return west;
            }

            while (west != north)
            {
                west = GetNextPointWest(west);
                yield return west;
            }

            foreach (var point in northernmost)
            {
                north = point;
                yield return north;
            }

            while (north != east)
            {
                north = GetNextPointNorth(north);
                yield return north;
            }

            foreach (var point in easternmost)
            {
                east = point;
                yield return east;
            }
            
            while (east != south)
            {
                east = GetNextPointEast(east);
                yield return east;
            }

            foreach (var point in southernmost)
            {
                south = point;
                yield return south;
            }
            
            while (south != start)
            {
                south = GetNextPointSouth(south);
                yield return south;
            }
        }

        private Point GetNextPointWest(Point west)
        {
            var northern = points.Where(p => p.X > west.X && p.Y < west.Y);

            foreach (Point p in northern)
            {
                Vector r = p - west;
                Vector s = new Vector(west.X, west.Y);

                double m = r.Y / r.X;
                double c = west.Y - (m * west.X);

                if (!northern.Any(a => Math.Round((a.X * m + c)) > a.Y))
                {
                    return p;
                }
            }

            return default(Point);
        }

        private Point GetNextPointNorth(Point north)
        {
            var eastern = points.Where(p => p.Y > north.Y && p.X > north.X);

            foreach (Point p in eastern)
            {
                Vector r = p - north;
                Vector s = new Vector(north.X, north.Y);

                double m = r.Y / r.X;
                double c = north.Y - (m * north.X);

                if (!eastern.Any(a => Math.Round((a.X * m + c)) > a.Y))
                {
                    return p;
                }
            }

            return default(Point);
        }

        private Point GetNextPointEast(Point east)
        {
            var southern = points.Where(p => p.X < east.X && p.Y > east.Y);

            foreach (Point p in southern)
            {
                Vector r = p - east;
                Vector s = new Vector(east.X, east.Y);

                double m = r.Y / r.X;
                double c = east.Y - (m * east.X);

                if (!southern.Any(a => Math.Round((a.X * m + c)) < a.Y))
                {
                    return p;
                }
            }

            return default(Point);
        }

        private Point GetNextPointSouth(Point south)
        {
            var western = points.Where(p => p.Y < south.Y && p.X < south.X);

            foreach (Point p in western)
            {
                Vector r = p - south;
                Vector s = new Vector(south.X, south.Y);

                double m = r.Y / r.X;
                double c = south.Y - (m * south.X);

                if (!western.Any(a => Math.Round((a.X * m + c)) < a.Y))
                {
                    return p;
                }
            }

            return default(Point);
        }

        private void buttonDrawConvex_Click(object sender, RoutedEventArgs e)
        {
            DrawConvexLine();
        }
    }
}

XML-Code

<Window x:Class="WpfKonvexeHuellkurve.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:WpfKonvexeHuellkurve"
        mc:Ignorable="d"
        Title="MainWindow" Height="610" Width="755" ResizeMode="CanMinimize">
    <Grid>
        <Border BorderBrush="Black" BorderThickness="2" Width="504" Height="504" Margin="10,10,0,0" HorizontalAlignment="Left" VerticalAlignment="Top">
            <Canvas x:Name="canvasDraw" Background="#FF08F48E" Width="500" Height="500" Margin="0"/>
        </Border>
        <ListBox x:Name="listBoxPoints" Width="218" Height="504" Margin="519,10,0,0" HorizontalAlignment="Left" VerticalAlignment="Top"/>
        <Button x:Name="buttonDrawRandom" Content="Zufällige Punkte zeichnen" HorizontalAlignment="Left" Margin="10,548,0,0" VerticalAlignment="Top" Width="161" Click="buttonDrawRandom_Click"/>
        <TextBlock x:Name="textBlock" HorizontalAlignment="Left" Margin="10,522,0,0" TextWrapping="Wrap" Text="Anzahl" VerticalAlignment="Top"/>
        <TextBox x:Name="textBoxNumber" HorizontalAlignment="Left" Height="24" Margin="51,519,0,0" TextWrapping="Wrap" Text="20" VerticalAlignment="Top" Width="120" TextAlignment="Center"/>
        <Button x:Name="buttonDrawConvex" Content="Konvexe Hüllkurve zeichnen" HorizontalAlignment="Left" Margin="176,548,0,0" VerticalAlignment="Top" Width="172" Click="buttonDrawConvex_Click"/>


    </Grid>
</Window>