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Delaunay Triangulation - currently with DelaunatorSharp - VoronoiDiagram work in progress

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ti_mo
2025-10-21 15:51:37 +02:00
parent 4f5530c87e
commit 22aaca545f
4 changed files with 362 additions and 45 deletions
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DelauneyTriangulation/DelauneyTriangulation.csproj
+2
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@@ -20,5 +20,7 @@
<!--Condition below is needed to remove Avalonia.Diagnostics package from build output in Release configuration.-->
<PackageReference Condition="'$(Configuration)' == 'Debug'" Include="Avalonia.Diagnostics" Version="11.3.6"/>
<PackageReference Include="CommunityToolkit.Mvvm" Version="8.2.1"/>
<PackageReference Include="Delaunator" Version="1.0.11" />
<PackageReference Include="Xaml.Behaviors.Interactions" Version="11.3.6.5" />
</ItemGroup>
</Project>
DelauneyTriangulation/Models/Geometries.cs
+39 -5
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@@ -1,19 +1,44 @@
using System;
using System.Collections.Generic;
using Avalonia.Media;
using CommunityToolkit.Mvvm.Input;
namespace DelauneyTriangulation.Models;
public static class Geometries
{
public sealed class Point(double x, double y, double z = 3)
public sealed class Point(double x, double y, double r = 3, Color? color = null)
{
public double X { get; } = x;
public double Y { get; } = y;
public double R { get; } = z;
public double R { get; } = r;
public Color Color { get; set; } = color ?? new Color(255, 255, 255, 255);
public double Left => X - R;
public double Top => Y - R;
public double Top => Y - R;
public double Size => 2 * R;
}
public sealed class PointComparer : IComparer<Point>
{
public static readonly PointComparer Instance = new();
public int Compare(Point? a, Point? b)
{
if (ReferenceEquals(a, b)) return 0;
if (a is null) return -1;
if (b is null) return 1;
int c = a.X.CompareTo(b.X);
if (c != 0) return c;
c = a.Y.CompareTo(b.Y);
if (c != 0) return c;
return a.R.CompareTo(b.R);
}
}
public sealed class Edge(double x1, double y1, double x2, double y2)
{
@@ -23,7 +48,7 @@ public static class Geometries
public double Y2 { get; } = y2;
public Avalonia.Point Start => new(X1, Y1);
public Avalonia.Point End => new(X2, Y2);
public Avalonia.Point End => new(X2, Y2);
}
public sealed class Circle(double x, double y, double r)
@@ -33,7 +58,16 @@ public static class Geometries
public double R { get; } = r;
public double Left => X - R;
public double Top => Y - R;
public double Top => Y - R;
public double Diameter => 2 * R;
}
public sealed class Triangle(Point p1, Point p2, Point p3)
{
public Avalonia.Point X { get; } = new(p1.X, p1.Y);
public Avalonia.Point Y { get; } = new(p2.X, p2.Y);
public Avalonia.Point Z { get; } = new(p3.X, p3.Y);
public IReadOnlyList<Avalonia.Point> Vertices => [ X, Y, Z ];
}
}
DelauneyTriangulation/ViewModels/MainWindowViewModel.cs
+215 -17
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@@ -1,50 +1,248 @@
using System;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.ComponentModel;
using System.Globalization;
using System.Linq;
using System.Threading;
using System.Threading.Tasks;
using Avalonia.Media;
using Avalonia.Rendering.Composition.Animations;
using CommunityToolkit.Mvvm.ComponentModel;
using CommunityToolkit.Mvvm.Input;
using DelaunatorSharp;
using DelauneyTriangulation.Models;
namespace DelauneyTriangulation.ViewModels;
public partial class MainWindowViewModel : ViewModelBase
{
private int _pointCount = 20;
[ObservableProperty] private int _pointCount = 20;
[ObservableProperty] private int _minPointDistance = 5;
[ObservableProperty] private double _panX;
[ObservableProperty] private double _panY;
[ObservableProperty] private double _zoom = 1.0;
[ObservableProperty] private bool _pointsVisible = true;
[ObservableProperty] private bool _edgesVisible = false;
[ObservableProperty] private bool _circlesVisible = false;
[ObservableProperty] private bool _trianglesVisible = false;
[ObservableProperty] private int _generationDelay = 20;
private CancellationTokenSource? _genCts;
public double Width { get; set; } = 1280;
public double Height { get; set; } = 720;
public int PointCount
{
get => _pointCount;
set
{
_pointCount = value;
OnPropertyChanged(nameof(PointCount));
GenerateRandomPoints(value);
}
}
private double LeftOffset => Width / 4;
private double TopOffset => Height - 50;
public ObservableCollection<Geometries.Point> Points { get; } = new();
public ObservableCollection<Geometries.Point> Points { get; set; } = new();
public ObservableCollection<Geometries.Edge> Edges { get; } = new();
public ObservableCollection<Geometries.Circle> Circles { get; } = new();
public ObservableCollection<Geometries.Edge> VoronoiDiagram { get; } = new();
public ObservableCollection<Geometries.Triangle> Triangles { get; } = new();
void GenerateRandomPoints(int count)
public IAsyncRelayCommand GenerateCommand { get; }
// gets distance of a and b edge to calc hypotenuse aka dist of two points
double PointDistance(Geometries.Point p1, Geometries.Point p2) => Math.Sqrt(Math.Pow(p1.X - p2.X, 2) + Math.Pow(p1.Y - p2.Y, 2));
async Task GenerateRandomPoints(int count, CancellationToken ct)
{
bool CheckAdd(Geometries.Point p1, IList<Geometries.Point> p) => !p.Any(x => PointDistance(p1, x) <= MinPointDistance);
Points.Clear();
var rand = new Random();
var rgb = (byte)(255 - PointCount);
const byte a = 255;
var color = new Color(rgb, rgb, rgb, a);
List<Geometries.Point> l = new();
int retry = 0;
for (var i = 0; i < PointCount; i++)
{
var x = rand.NextDouble() * Width;
var y = rand.NextDouble() * Height;
Points.Add(new Geometries.Point(x, y));
ct.ThrowIfCancellationRequested();
if (retry == 10) break;
var x = rand.NextDouble() * (Width - LeftOffset) + LeftOffset;
var y = rand.NextDouble() * (Height - TopOffset * 2) + TopOffset;
var p = new Geometries.Point(x, y);
if (CheckAdd(p, l))
{
p.Color = color;
rgb++;
color = new Color(rgb, rgb, rgb, a);
l.Add(p);
retry = 0;
}
else
{
i--;
retry++;
};
}
l.Sort(Geometries.PointComparer.Instance);
foreach (var p in l)
{
ct.ThrowIfCancellationRequested();
Points.Add(p);
await DelayAsync(ct);
}
}
void ConnectPoint(Geometries.Point p1, Geometries.Point p2) => Edges.Add(new Geometries.Edge(p1.X, p1.Y, p2.X, p2.Y));
async Task ConnectPoints(CancellationToken ct)
{
if(Points.Count == 0) return;
Edges.Clear();
var toConnect = Points.ToList();
var p1 = toConnect[0];
while (toConnect.Count > 0)
{
ct.ThrowIfCancellationRequested();
var p2 = toConnect.MinBy(x => PointDistance(p1, x));
if (p2 is null) continue;
ConnectPoint(p1, p2);
toConnect.Remove(p1);
p1 = p2;
await DelayAsync(ct);
}
}
void AddTriangle(Geometries.Point p1, Geometries.Point p2, Geometries.Point p3) => Triangles.Add(new(p1, p2, p3));
async Task Triangulate(CancellationToken ct)
{
Triangles.Clear();
if (Points.Count < 3) return;
var toTriangulate = Points.ToList();
var p1 = toTriangulate[0];
var p2 = toTriangulate.Where(x => !ReferenceEquals(x, p1)).MinBy(x => PointDistance(p1, x));
if (p2 is null) return;
static double TwiceArea(Geometries.Point a, Geometries.Point b, Geometries.Point c) => Math.Abs((b.X - a.X) * (c.Y - a.Y) - (b.Y - a.Y) * (c.X - a.X));
while (toTriangulate.Count >= 3)
{
ct.ThrowIfCancellationRequested();
var candidates = toTriangulate.Where(x => !ReferenceEquals(x, p1) && !ReferenceEquals(x, p2));
Geometries.Point? p3 = null;
foreach (var c in candidates.OrderBy(x => PointDistance(p1, x) + PointDistance(p2, x)))
{
if (TwiceArea(p1, p2, c) > 1e-6) p3 = c; break;
}
if (p3 is null) break;
AddTriangle(p1, p2, p3);
toTriangulate.Remove(p1);
p1 = p2;
p2 = p3;
await DelayAsync(ct);
}
}
async Task DelaunayTriangulateAsync(CancellationToken ct)
{
Triangles.Clear();
Edges.Clear();
var pts = Points
.Select(p => (DelaunatorSharp.IPoint)new DelaunatorSharp.Point(p.X, p.Y))
.ToArray();
var d = new Delaunator(pts);
// Delaunay Triangle Extraction
for (int i = 0; i < d.Triangles.Length; i += 3)
{
ct.ThrowIfCancellationRequested();
int i0 = d.Triangles[i];
int i1 = d.Triangles[i + 1];
int i2 = d.Triangles[i + 2];
var p0 = Points[i0];
var p1 = Points[i1];
var p2 = Points[i2];
Triangles.Add(new Geometries.Triangle(p0, p1, p2));
await DelayAsync(ct);
}
// Konvex Hull Extraction
var hullPoints = d.GetHullPoints();
var first = hullPoints.First();
var last = hullPoints.Last();
var p1h = hullPoints[0];
for (int h = 1; h < d.Hull.Length; h++)
{
var p2h = hullPoints[h];
Edges.Add(new Geometries.Edge(p1h.X, p1h.Y, p2h.X, p2h.Y));
p1h = p2h;
await DelayAsync(ct);
}
Edges.Add(new Geometries.Edge(first.X, first.Y, last.X, last.Y));
/*
// Voronoi Diagram Extraction
foreach (var cell in d.GetVoronoiCellsBasedOnCircumcenters())
{
ct.ThrowIfCancellationRequested();
var f = cell.Points[0];
for (int i = 1; i < cell.Points.Length; i++)
{
var s = cell.Points[i];
VoronoiDiagram.Add(new Geometries.Edge(f.X, f.Y, s.X, s.Y));
f = s;
await DelayAsync(ct);
}
}
*/
}
private Task DelayAsync(CancellationToken ct) => GenerationDelay > 0 ? Task.Delay(GenerationDelay, ct) : Task.CompletedTask;
async Task RunGenerateAsync()
{
_genCts?.CancelAsync();
_genCts = new CancellationTokenSource();
try { await Generate(_genCts.Token); }
catch (OperationCanceledException) { }
}
private async Task Generate(CancellationToken ct)
{
Points.Clear();
Edges.Clear();
Circles.Clear();
Triangles.Clear();
VoronoiDiagram.Clear();
await GenerateRandomPoints(_pointCount, ct);
// await ConnectPoints(ct);
// await Triangulate(ct);
await DelaunayTriangulateAsync(ct);
}
private bool CanGenerate() => true;
public MainWindowViewModel()
{
GenerateRandomPoints(_pointCount);
GenerateCommand = new AsyncRelayCommand(RunGenerateAsync, CanGenerate);
}
}
DelauneyTriangulation/Views/MainWindow.axaml
+106 -23
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@@ -15,8 +15,8 @@
ExtendClientAreaTitleBarHeightHint="32"
TransparencyLevelHint="AcrylicBlur, Blur, Transparent"
Background="Transparent"
Width="{Binding Width}"
Height="{Binding Height}"
Width="{Binding Width, Mode=TwoWay}"
Height="{Binding Height, Mode=TwoWay}"
>
<Design.DataContext>
@@ -42,24 +42,61 @@
</Border>
<Grid Grid.Row="1" ZIndex="1000" Margin="20">
<Grid.ColumnDefinitions>
<ColumnDefinition Width="Auto"/>
<ColumnDefinition Width="auto"/>
<ColumnDefinition Width="*"/>
</Grid.ColumnDefinitions>
<Border Classes="InnerCard">
<Border.Effect>
<DropShadowEffect BlurRadius="20" Color="#aa000000" OffsetX="5" OffsetY="5"/>
</Border.Effect>
<StackPanel Orientation="Vertical">
<Border Classes="InnerCard">
<TextBlock Text="Delaunay Triangulation" FontSize="18" Foreground="White"/>
</Border>
<Border Classes="InnerCard">
<Grid ColumnDefinitions="4*,1*">
<Slider Grid.Column="0" Value="{Binding PointCount, Mode=TwoWay}" Margin="5" Minimum="20" Maximum="500"/>
<TextBox Grid.Column="1" Text="{Binding PointCount, Mode=TwoWay}" FontSize="18" Foreground="White" Background="#30ffffff" HorizontalContentAlignment="Center" VerticalContentAlignment="Center"/>
</Grid>
</Border>
</StackPanel>
<Grid RowDefinitions="*, auto">
<StackPanel Orientation="Vertical">
<Border Classes="InnerCard">
<TextBlock Text="Delaunay Triangulation" FontSize="18" Foreground="White"/>
</Border>
<Border Classes="InnerCard">
<StackPanel Orientation="Vertical">
<TextBlock Text="Maximal Point Count" Foreground="White"/>
<Grid ColumnDefinitions="4*,1*">
<Slider Grid.Column="0" Value="{Binding PointCount, Mode=TwoWay}" Margin="5" Minimum="20" Maximum="200"/>
<TextBox Grid.Column="1" Text="{Binding PointCount, Mode=TwoWay}" FontSize="18" Foreground="White" Background="#30ffffff" HorizontalContentAlignment="Center" VerticalContentAlignment="Center"/>
</Grid>
</StackPanel>
</Border>
<Border Classes="InnerCard">
<StackPanel Orientation="Vertical">
<TextBlock Text="Minimal Point Distance" Foreground="White"/>
<Grid ColumnDefinitions="4*,1*">
<Slider Grid.Column="0" Value="{Binding MinPointDistance, Mode=TwoWay}" Margin="5" Minimum="1" Maximum="10"/>
<TextBox Grid.Column="1" Text="{Binding MinPointDistance, Mode=TwoWay}" FontSize="18" Foreground="White" Background="#30ffffff" HorizontalContentAlignment="Center" VerticalContentAlignment="Center"/>
</Grid>
</StackPanel>
</Border>
<Border Classes="InnerCard">
<StackPanel Orientation="Vertical">
<TextBlock Text="Genearation Speed" Foreground="White"/>
<Grid ColumnDefinitions="4*,1*">
<Slider Grid.Column="0" Value="{Binding GenerationDelay, Mode=TwoWay}" Margin="5" Minimum="0" Maximum="1000"/>
<TextBox Grid.Column="1" Text="{Binding GenerationDelay, Mode=TwoWay}" FontSize="18" Foreground="White" Background="#30ffffff" HorizontalContentAlignment="Center" VerticalContentAlignment="Center"/>
</Grid>
</StackPanel>
</Border>
<Border Classes="InnerCard">
<StackPanel Orientation="Vertical">
<TextBlock Text="Enabled Visuals:" Foreground="White"/>
<StackPanel Orientation="Horizontal">
<CheckBox Content="Points" IsChecked="{Binding PointsVisible}" Foreground="White" Margin="10,0"/>
<CheckBox Content="Convex Hull" IsChecked="{Binding EdgesVisible}" Foreground="White" Margin="10,0"/>
</StackPanel>
<StackPanel Orientation="Horizontal">
<CheckBox Content="Circles" IsChecked="{Binding CirclesVisible}" Foreground="White" Margin="10,0"/>
<CheckBox Content="Triangles" IsChecked="{Binding TrianglesVisible}" Foreground="White" Margin="10,0"/>
</StackPanel>
</StackPanel>
</Border>
</StackPanel>
<Button Grid.Row="1" Foreground="White" VerticalAlignment="Bottom" HorizontalAlignment="Stretch" HorizontalContentAlignment="Center" VerticalContentAlignment="Center" Content="Generate" Command="{Binding GenerateCommand}"/>
</Grid>
</Border>
</Grid>
<Canvas Grid.Row="0" Grid.RowSpan="2"
@@ -84,14 +121,19 @@
IsHitTestVisible="False">
<ItemsControl.ItemsPanel>
<ItemsPanelTemplate>
<Canvas/>
<Canvas IsVisible="{Binding EdgesVisible}"/>
</ItemsPanelTemplate>
</ItemsControl.ItemsPanel>
<ItemsControl.ItemTemplate>
<DataTemplate x:DataType="models:Geometries+Edge">
<Line StartPoint="{Binding Start}"
EndPoint="{Binding End}"
Stroke="LightGray" StrokeThickness="1"/>
Stroke="GreenYellow" StrokeThickness="2"
>
<Line.RenderTransform>
<TranslateTransform X="{Binding Start}" Y="{Binding End}"/>
</Line.RenderTransform>
</Line>
</DataTemplate>
</ItemsControl.ItemTemplate>
</ItemsControl>
@@ -101,7 +143,7 @@
IsHitTestVisible="False">
<ItemsControl.ItemsPanel>
<ItemsPanelTemplate>
<Canvas/>
<Canvas IsVisible="{Binding CirclesVisible}"/>
</ItemsPanelTemplate>
</ItemsControl.ItemsPanel>
<ItemsControl.ItemTemplate>
@@ -109,9 +151,33 @@
<Ellipse Stroke="DarkOrange" StrokeThickness="1.5"
Width="{Binding Diameter}"
Height="{Binding Diameter}"
Canvas.Left="{Binding Left}"
Canvas.Top="{Binding Top}"
/>
>
<Ellipse.RenderTransform>
<TranslateTransform X="{Binding Left}" Y="{Binding Top}"/>
</Ellipse.RenderTransform>
</Ellipse>
</DataTemplate>
</ItemsControl.ItemTemplate>
</ItemsControl>
<ItemsControl ItemsSource="{Binding VoronoiDiagram}"
Width="{Binding Bounds.Width, ElementName=Scene}"
Height="{Binding Bounds.Height, ElementName=Scene}"
IsHitTestVisible="False">
<ItemsControl.ItemsPanel>
<ItemsPanelTemplate>
<Canvas IsVisible="{Binding CirclesVisible}"/>
</ItemsPanelTemplate>
</ItemsControl.ItemsPanel>
<ItemsControl.ItemTemplate>
<DataTemplate x:DataType="models:Geometries+Edge">
<Line StartPoint="{Binding Start}"
EndPoint="{Binding End}"
Stroke="GreenYellow" StrokeThickness="2"
>
<Line.RenderTransform>
<TranslateTransform X="{Binding Start}" Y="{Binding End}"/>
</Line.RenderTransform>
</Line>
</DataTemplate>
</ItemsControl.ItemTemplate>
</ItemsControl>
@@ -122,23 +188,40 @@
>
<ItemsControl.ItemsPanel>
<ItemsPanelTemplate>
<Canvas/>
<Canvas IsVisible="{Binding PointsVisible}"/>
</ItemsPanelTemplate>
</ItemsControl.ItemsPanel>
<ItemsControl.ItemTemplate>
<DataTemplate x:DataType="models:Geometries+Point">
<Ellipse Fill="White" Stroke="Black" StrokeThickness="1"
<Ellipse Fill="Transparent" Stroke="White" StrokeThickness="1"
Width="{Binding Size}"
Height="{Binding Size}"
>
<Ellipse.RenderTransform>
<!-- Nutze Left/Top aus dem VM (oder X/Y, wenn das deine Top-Left-Koords sind) -->
<TranslateTransform X="{Binding Left}" Y="{Binding Top}"/>
</Ellipse.RenderTransform>
</Ellipse>
</DataTemplate>
</ItemsControl.ItemTemplate>
</ItemsControl>
<ItemsControl ItemsSource="{Binding Triangles}"
Width="{Binding Bounds.Width, ElementName=Scene}"
Height="{Binding Bounds.Height, ElementName=Scene}"
IsHitTestVisible="False"
>
<ItemsControl.ItemsPanel>
<ItemsPanelTemplate>
<Canvas IsVisible="{Binding TrianglesVisible}"/>
</ItemsPanelTemplate>
</ItemsControl.ItemsPanel>
<ItemsControl.ItemTemplate>
<DataTemplate x:DataType="models:Geometries+Triangle">
<Canvas>
<Polygon Points="{Binding Vertices}" Stroke="CornflowerBlue" StrokeThickness="1" Fill="Transparent"/>
</Canvas>
</DataTemplate>
</ItemsControl.ItemTemplate>
</ItemsControl>
</Canvas>
</Canvas>
</Grid>