Delaunay Triangulation - currently with DelaunatorSharp - VoronoiDiagram work in progress
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ti_mo
@@ -1,50 +1,248 @@
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using System;
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using System.Collections.Generic;
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using System.Collections.ObjectModel;
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using System.ComponentModel;
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using System.Globalization;
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using System.Linq;
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using System.Threading;
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using System.Threading.Tasks;
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using Avalonia.Media;
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using Avalonia.Rendering.Composition.Animations;
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using CommunityToolkit.Mvvm.ComponentModel;
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using CommunityToolkit.Mvvm.Input;
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using DelaunatorSharp;
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using DelauneyTriangulation.Models;
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namespace DelauneyTriangulation.ViewModels;
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public partial class MainWindowViewModel : ViewModelBase
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{
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private int _pointCount = 20;
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[ObservableProperty] private int _pointCount = 20;
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[ObservableProperty] private int _minPointDistance = 5;
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[ObservableProperty] private double _panX;
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[ObservableProperty] private double _panY;
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[ObservableProperty] private double _zoom = 1.0;
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[ObservableProperty] private bool _pointsVisible = true;
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[ObservableProperty] private bool _edgesVisible = false;
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[ObservableProperty] private bool _circlesVisible = false;
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[ObservableProperty] private bool _trianglesVisible = false;
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[ObservableProperty] private int _generationDelay = 20;
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private CancellationTokenSource? _genCts;
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public double Width { get; set; } = 1280;
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public double Height { get; set; } = 720;
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public int PointCount
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{
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get => _pointCount;
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set
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{
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_pointCount = value;
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OnPropertyChanged(nameof(PointCount));
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GenerateRandomPoints(value);
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}
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}
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private double LeftOffset => Width / 4;
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private double TopOffset => Height - 50;
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public ObservableCollection<Geometries.Point> Points { get; } = new();
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public ObservableCollection<Geometries.Point> Points { get; set; } = new();
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public ObservableCollection<Geometries.Edge> Edges { get; } = new();
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public ObservableCollection<Geometries.Circle> Circles { get; } = new();
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public ObservableCollection<Geometries.Edge> VoronoiDiagram { get; } = new();
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public ObservableCollection<Geometries.Triangle> Triangles { get; } = new();
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void GenerateRandomPoints(int count)
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public IAsyncRelayCommand GenerateCommand { get; }
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// gets distance of a and b edge to calc hypotenuse aka dist of two points
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double PointDistance(Geometries.Point p1, Geometries.Point p2) => Math.Sqrt(Math.Pow(p1.X - p2.X, 2) + Math.Pow(p1.Y - p2.Y, 2));
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async Task GenerateRandomPoints(int count, CancellationToken ct)
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{
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bool CheckAdd(Geometries.Point p1, IList<Geometries.Point> p) => !p.Any(x => PointDistance(p1, x) <= MinPointDistance);
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Points.Clear();
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var rand = new Random();
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var rgb = (byte)(255 - PointCount);
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const byte a = 255;
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var color = new Color(rgb, rgb, rgb, a);
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List<Geometries.Point> l = new();
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int retry = 0;
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for (var i = 0; i < PointCount; i++)
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{
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var x = rand.NextDouble() * Width;
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var y = rand.NextDouble() * Height;
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Points.Add(new Geometries.Point(x, y));
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ct.ThrowIfCancellationRequested();
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if (retry == 10) break;
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var x = rand.NextDouble() * (Width - LeftOffset) + LeftOffset;
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var y = rand.NextDouble() * (Height - TopOffset * 2) + TopOffset;
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var p = new Geometries.Point(x, y);
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if (CheckAdd(p, l))
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{
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p.Color = color;
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rgb++;
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color = new Color(rgb, rgb, rgb, a);
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l.Add(p);
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retry = 0;
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}
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else
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{
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i--;
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retry++;
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};
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}
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l.Sort(Geometries.PointComparer.Instance);
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foreach (var p in l)
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{
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ct.ThrowIfCancellationRequested();
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Points.Add(p);
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await DelayAsync(ct);
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}
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}
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void ConnectPoint(Geometries.Point p1, Geometries.Point p2) => Edges.Add(new Geometries.Edge(p1.X, p1.Y, p2.X, p2.Y));
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async Task ConnectPoints(CancellationToken ct)
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{
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if(Points.Count == 0) return;
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Edges.Clear();
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var toConnect = Points.ToList();
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var p1 = toConnect[0];
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while (toConnect.Count > 0)
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{
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ct.ThrowIfCancellationRequested();
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var p2 = toConnect.MinBy(x => PointDistance(p1, x));
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if (p2 is null) continue;
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ConnectPoint(p1, p2);
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toConnect.Remove(p1);
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p1 = p2;
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await DelayAsync(ct);
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}
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}
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void AddTriangle(Geometries.Point p1, Geometries.Point p2, Geometries.Point p3) => Triangles.Add(new(p1, p2, p3));
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async Task Triangulate(CancellationToken ct)
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{
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Triangles.Clear();
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if (Points.Count < 3) return;
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var toTriangulate = Points.ToList();
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var p1 = toTriangulate[0];
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var p2 = toTriangulate.Where(x => !ReferenceEquals(x, p1)).MinBy(x => PointDistance(p1, x));
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if (p2 is null) return;
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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));
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while (toTriangulate.Count >= 3)
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{
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ct.ThrowIfCancellationRequested();
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var candidates = toTriangulate.Where(x => !ReferenceEquals(x, p1) && !ReferenceEquals(x, p2));
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Geometries.Point? p3 = null;
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foreach (var c in candidates.OrderBy(x => PointDistance(p1, x) + PointDistance(p2, x)))
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{
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if (TwiceArea(p1, p2, c) > 1e-6) p3 = c; break;
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}
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if (p3 is null) break;
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AddTriangle(p1, p2, p3);
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toTriangulate.Remove(p1);
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p1 = p2;
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p2 = p3;
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await DelayAsync(ct);
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}
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}
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async Task DelaunayTriangulateAsync(CancellationToken ct)
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{
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Triangles.Clear();
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Edges.Clear();
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var pts = Points
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.Select(p => (DelaunatorSharp.IPoint)new DelaunatorSharp.Point(p.X, p.Y))
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.ToArray();
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var d = new Delaunator(pts);
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// Delaunay Triangle Extraction
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for (int i = 0; i < d.Triangles.Length; i += 3)
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{
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ct.ThrowIfCancellationRequested();
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int i0 = d.Triangles[i];
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int i1 = d.Triangles[i + 1];
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int i2 = d.Triangles[i + 2];
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var p0 = Points[i0];
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var p1 = Points[i1];
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var p2 = Points[i2];
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Triangles.Add(new Geometries.Triangle(p0, p1, p2));
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await DelayAsync(ct);
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}
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// Konvex Hull Extraction
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var hullPoints = d.GetHullPoints();
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var first = hullPoints.First();
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var last = hullPoints.Last();
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var p1h = hullPoints[0];
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for (int h = 1; h < d.Hull.Length; h++)
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{
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var p2h = hullPoints[h];
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Edges.Add(new Geometries.Edge(p1h.X, p1h.Y, p2h.X, p2h.Y));
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p1h = p2h;
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await DelayAsync(ct);
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}
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Edges.Add(new Geometries.Edge(first.X, first.Y, last.X, last.Y));
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/*
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// Voronoi Diagram Extraction
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foreach (var cell in d.GetVoronoiCellsBasedOnCircumcenters())
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{
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ct.ThrowIfCancellationRequested();
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var f = cell.Points[0];
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for (int i = 1; i < cell.Points.Length; i++)
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{
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var s = cell.Points[i];
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VoronoiDiagram.Add(new Geometries.Edge(f.X, f.Y, s.X, s.Y));
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f = s;
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await DelayAsync(ct);
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}
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}
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*/
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}
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private Task DelayAsync(CancellationToken ct) => GenerationDelay > 0 ? Task.Delay(GenerationDelay, ct) : Task.CompletedTask;
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async Task RunGenerateAsync()
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{
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_genCts?.CancelAsync();
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_genCts = new CancellationTokenSource();
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try { await Generate(_genCts.Token); }
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catch (OperationCanceledException) { }
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}
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private async Task Generate(CancellationToken ct)
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{
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Points.Clear();
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Edges.Clear();
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Circles.Clear();
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Triangles.Clear();
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VoronoiDiagram.Clear();
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await GenerateRandomPoints(_pointCount, ct);
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// await ConnectPoints(ct);
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// await Triangulate(ct);
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await DelaunayTriangulateAsync(ct);
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}
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private bool CanGenerate() => true;
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public MainWindowViewModel()
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{
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GenerateRandomPoints(_pointCount);
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GenerateCommand = new AsyncRelayCommand(RunGenerateAsync, CanGenerate);
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}
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}
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