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Moved to BowyerWatson Algorithm

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Ano-sys
2025-11-04 21:56:39 +01:00
parent f3475011dc
commit c82cc25703
2 changed files with 266 additions and 48 deletions
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DelauneyTriangulation/Models/Geometries.cs
+47 -4
View File
@@ -1,4 +1,5 @@
using System;
using System.Collections;
using System.Collections.Generic;
using Avalonia.Media;
using CommunityToolkit.Mvvm.Input;
@@ -49,17 +50,59 @@ public static class Geometries
public Avalonia.Point Start => new(X1, Y1);
public Avalonia.Point End => new(X2, Y2);
private static bool Almost(double a, double b, double eps = 1e-9) => Math.Abs(a - b) <= eps;
public bool EqualsUndirected(Edge other, double eps = 1e-9)
{
bool same = Almost(X1, other.X1, eps) && Almost(Y1, other.Y1, eps) &&
Almost(X2, other.X2, eps) && Almost(Y2, other.Y2, eps);
bool swapped = Almost(X1, other.X2, eps) && Almost(Y1, other.Y2, eps) &&
Almost(X2, other.X1, eps) && Almost(Y2, other.Y1, eps);
return same || swapped;
}
}
public sealed class Circle(double x, double y, double r)
public sealed class Circle
{
public double X { get; } = x;
public double Y { get; } = y;
public double R { get; } = r;
public double X { get; }
public double Y { get; }
public double R { get; }
public double Left => X - R;
public double Top => Y - R;
public double Diameter => 2 * R;
public Circle(double x, double y, double r)
{
X = x;
Y = y;
R = r;
}
public Circle(Point p1, Point p2, Point p3)
{
double x1 = p1.X, y1 = p1.Y;
double x2 = p2.X, y2 = p2.Y;
double x3 = p3.X, y3 = p3.Y;
var d = 2.0 * (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2));
if (Math.Abs(d) < 1e-12) throw new ArgumentException("Points are collinear; circumcircle undefined.");
var x1p = x1 * x1 + y1 * y1;
var x2p = x2 * x2 + y2 * y2;
var x3p = x3 * x3 + y3 * y3;
var ux = (x1p * (y2 - y3) + x2p * (y3 - y1) + x3p * (y1 - y2)) / d;
var uy = (x1p * (x3 - x2) + x2p * (x1 - x3) + x3p * (x2 - x1)) / d;
X = ux;
Y = uy;
R = Math.Sqrt((ux - x1) * (ux - x1) + (uy - y1) * (uy - y1));
}
}
public sealed class Triangle(Point p1, Point p2, Point p3)
DelauneyTriangulation/ViewModels/MainWindowViewModel.cs
+187 -12
View File
@@ -49,11 +49,53 @@ public partial class MainWindowViewModel : ViewModelBase
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));
double PointDistance(Geometries.Point p1, Geometries.Point p2) =>
Math.Sqrt(Math.Pow(p1.X - p2.X, 2) + Math.Pow(p1.Y - p2.Y, 2));
static bool Almost(double a, double b, double eps = 1e-9) => Math.Abs(a - b) <= eps;
bool IsPointInCircumcircle(Geometries.Triangle t, Geometries.Point p)
{
var a = new Geometries.Point(t.X.X, t.X.Y);
var b = new Geometries.Point(t.Y.X, t.Y.Y);
var c = new Geometries.Point(t.Z.X, t.Z.Y);
var circ = new Geometries.Circle(a, b, c);
var d = PointDistance(new(circ.X, circ.Y), p);
return d <= circ.R + 1e-9;
}
static bool UsesVertex(Geometries.Triangle t, Geometries.Point v)
{
bool isV(Avalonia.Point q) => Math.Abs(q.X - v.X) <= 1e-9 && Math.Abs(q.Y - v.Y) <= 1e-9;
return isV(t.X) || isV(t.Y) || isV(t.Z);
}
(Geometries.Point A, Geometries.Point B, Geometries.Point C) BuildSuperTriangle()
{
var minX = Points.Min(p => p.X);
var minY = Points.Min(p => p.Y);
var maxX = Points.Max(p => p.X);
var maxY = Points.Max(p => p.Y);
var dx = maxX - minX;
var dy = maxY - minY;
var delta = Math.Max(dx, dy);
var cx = (minX + maxX) * 0.5;
var cy = (minY + maxY) * 0.5;
var A = new Geometries.Point(cx - 2 * delta, cy - delta * 3);
var B = new Geometries.Point(cx, cy + 3 * delta);
var C = new Geometries.Point(cx + 2 * delta, cy - delta * 3);
return (A, B, C);
}
async Task GenerateRandomPoints(int count, CancellationToken ct)
{
bool CheckAdd(Geometries.Point p1, IList<Geometries.Point> p) => !p.Any(x => PointDistance(p1, x) <= MinPointDistance);
bool CheckAdd(Geometries.Point p1, IList<Geometries.Point> p) =>
!p.Any(x => PointDistance(p1, x) <= MinPointDistance);
Points.Clear();
var rand = new Random();
@@ -85,7 +127,9 @@ public partial class MainWindowViewModel : ViewModelBase
{
i--;
retry++;
};
}
;
}
l.Sort(Geometries.PointComparer.Instance);
@@ -97,7 +141,8 @@ public partial class MainWindowViewModel : ViewModelBase
}
}
void ConnectPoint(Geometries.Point p1, Geometries.Point p2) => Edges.Add(new Geometries.Edge(p1.X, p1.Y, p2.X, p2.Y));
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)
{
@@ -122,6 +167,7 @@ public partial class MainWindowViewModel : ViewModelBase
}
void AddTriangle(Geometries.Point p1, Geometries.Point p2, Geometries.Point p3) => Triangles.Add(new(p1, p2, p3));
async Task Triangulate(CancellationToken ct)
{
Triangles.Clear();
@@ -133,7 +179,8 @@ public partial class MainWindowViewModel : ViewModelBase
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));
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)
{
@@ -144,7 +191,8 @@ public partial class MainWindowViewModel : ViewModelBase
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 (TwiceArea(p1, p2, c) > 1e-6) p3 = c;
break;
}
if (p3 is null) break;
@@ -159,6 +207,125 @@ public partial class MainWindowViewModel : ViewModelBase
}
}
List<Geometries.Edge> ExtractTriangleEdges(Geometries.Triangle t)
{
var e1 = new Geometries.Edge(t.X.X, t.X.Y, t.Y.X, t.Y.Y);
var e2 = new Geometries.Edge(t.Y.X, t.Y.Y, t.Z.X, t.Z.Y);
var e3 = new Geometries.Edge(t.Z.X, t.Z.Y, t.X.X, t.X.Y);
return [e1, e2, e3];
}
static string CanonKey(Geometries.Edge e)
{
var abFirst = (e.X1 < e.X2) || (Almost(e.X1, e.X2) && e.Y1 <= e.Y2);
var ax = abFirst ? e.X1 : e.X2;
var ay = abFirst ? e.Y1 : e.Y2;
var bx = abFirst ? e.X2 : e.X1;
var by = abFirst ? e.Y2 : e.Y1;
static double Q(double v) => Math.Round(v, 9, MidpointRounding.AwayFromZero);
return $"{Q(ax)},{Q(ay)}|{Q(bx)},{Q(by)}";
}
void DrawCircles(IEnumerable<Geometries.Triangle> triangles, Geometries.Point superA, Geometries.Point superB,
Geometries.Point superC)
{
Circles.Clear();
foreach (var t in triangles)
{
if (UsesVertex(t, superA) || UsesVertex(t, superB) || UsesVertex(t, superC)) continue;
try
{
var a = new Geometries.Point(t.X.X, t.X.Y);
var b = new Geometries.Point(t.Y.X, t.Y.Y);
var c = new Geometries.Point(t.Z.X, t.Z.Y);
var cc = new Geometries.Circle(a, b, c);
if (double.IsFinite(cc.X) && double.IsFinite(cc.Y) && double.IsFinite(cc.R) && cc.R > 0)
Circles.Add(cc);
}
catch (ArgumentException)
{
}
}
}
async Task BowyerWatson(CancellationToken ct)
{
Triangles.Clear();
if (Points.Count < 3) return;
var (sa, sb, sc) = BuildSuperTriangle();
Triangles.Add(new Geometries.Triangle(sa, sb, sc));
await DelayAsync(ct);
foreach (var p in Points)
{
ct.ThrowIfCancellationRequested();
var bad = new List<Geometries.Triangle>();
foreach (var t in Triangles)
{
try
{
if (IsPointInCircumcircle(t, p)) bad.Add(t);
}
catch (ArgumentException)
{
// kollinear -> explicit ignore
}
}
DrawCircles(bad, sa, sb, sc);
await DelayAsync(ct);
var edgeCount = new Dictionary<string, Geometries.Edge>();
var counter = new Dictionary<string, int>();
foreach (var bt in bad)
{
foreach (var e in ExtractTriangleEdges(bt))
{
string key = CanonKey(e);
if (!edgeCount.ContainsKey(key)) edgeCount[key] = e;
counter.TryGetValue(key, out int c);
counter[key] = c + 1;
}
}
var polygon = new List<Geometries.Edge>();
foreach (var kv in counter)
if (kv.Value == 1)
polygon.Add(edgeCount[kv.Key]);
// remove bad triangles form triangulation
foreach (var bt in bad) Triangles.Remove(bt);
// re-triangulate the polygonal hole
foreach (var e in polygon)
{
var a = new Geometries.Point(e.X1, e.Y1);
var b = new Geometries.Point(e.X2, e.Y2);
Triangles.Add(new Geometries.Triangle(a, b, p));
await DelayAsync(ct);
}
}
// remove triangles containing super triangle vertex
var toRemove = new List<Geometries.Triangle>();
foreach (var t in Triangles)
{
if (UsesVertex(t, sa) || UsesVertex(t, sb) || UsesVertex(t, sc)) toRemove.Add(t);
}
foreach (var t in toRemove) Triangles.Remove(t);
DrawCircles(Triangles, sa, sb, sc);
await DelayAsync(ct);
}
async Task DelaunayTriangulateAsync(CancellationToken ct)
{
Triangles.Clear();
@@ -198,6 +365,7 @@ public partial class MainWindowViewModel : ViewModelBase
p1h = p2h;
await DelayAsync(ct);
}
Edges.Add(new Geometries.Edge(first.X, first.Y, last.X, last.Y));
// Voronoi Diagram Extraction
@@ -209,7 +377,8 @@ public partial class MainWindowViewModel : ViewModelBase
{
var s = cell.Points[i];
VoronoiDiagram.Add(new Geometries.Edge(f.X, f.Y, s.X, s.Y));
Circles.Add(new Geometries.Circle(f.X, f.Y, Points.Min(x => PointDistance(new Geometries.Point(f.X, f.Y), x))));
Circles.Add(new Geometries.Circle(f.X, f.Y,
Points.Min(x => PointDistance(new Geometries.Point(f.X, f.Y), x))));
f = s;
await DelayAsync(ct);
@@ -217,15 +386,20 @@ public partial class MainWindowViewModel : ViewModelBase
}
}
private Task DelayAsync(CancellationToken ct) => GenerationDelay > 0 ? Task.Delay(GenerationDelay ?? 0, ct) : Task.CompletedTask;
private Task DelayAsync(CancellationToken ct) =>
GenerationDelay > 0 ? Task.Delay(GenerationDelay ?? 0, ct) : Task.CompletedTask;
async Task RunGenerateAsync()
{
_genCts?.CancelAsync();
_genCts = new CancellationTokenSource();
try { await Generate(_genCts.Token); }
catch (OperationCanceledException) { }
try
{
await Generate(_genCts.Token);
}
catch (OperationCanceledException)
{
}
}
private async Task Generate(CancellationToken ct)
@@ -239,7 +413,8 @@ public partial class MainWindowViewModel : ViewModelBase
await GenerateRandomPoints(PointCount ?? 20, ct);
// await ConnectPoints(ct);
// await Triangulate(ct);
await DelaunayTriangulateAsync(ct);
// await DelaunayTriangulateAsync(ct);
await BowyerWatson(ct);
}
private bool CanGenerate() => true;