/// <summary>
/// Converts all <see cref="DelaunayEdges"/> to a planar <see cref="Subdivision"/>, using
/// the specified clipping bounds.</summary>
/// <param name="bounds">
/// A <see cref="RectD"/> that indicates the clipping bounds for all <see
/// cref="DelaunayEdges"/>.</param>
/// <param name="addRegions">
/// <c>true</c> to add all <see cref="VoronoiRegions"/> with the corresponding <see
/// cref="GeneratorSites"/> to the <see cref="Subdivision.VertexRegions"/> collection of the
/// new <see cref="Subdivision"/>; otherwise, <c>false</c>.</param>
/// <returns>
/// A new <see cref="Subdivision"/> whose <see cref="Subdivision.Edges"/> correspond to the
/// <see cref="DelaunayEdges"/> of the <see cref="VoronoiResults"/>.</returns>
/// <remarks><para>
/// The specified <paramref name="bounds"/> determine the subset of <see
/// cref="GeneratorSites"/> and <see cref="DelaunayEdges"/> that is stored in the new <see
/// cref="Subdivision"/>, as described in <see cref="ClipDelaunayEdges"/>.
/// </para><para>
/// If <paramref name="addRegions"/> is <c>true</c>, the polygons added to the <see
/// cref="Subdivision.VertexRegions"/> collection are also clipped the specified <paramref
/// name="bounds"/>.</para></remarks>
public Subdivision ToDelaunySubdivision(RectD bounds, bool addRegions = false)
{
LineD[] edges = ClipDelaunayEdges(bounds);
Subdivision division = Subdivision.FromLines(edges);
if (addRegions)
{
for (int i = 0; i < GeneratorSites.Length; i++)
{
PointD site = GeneratorSites[i];
if (!bounds.Contains(site))
{
continue;
}
PointD[] region;
if (bounds.Intersect(VoronoiRegions[i], out region))
{
division.VertexRegions.Add(site, region);
}
}
}
return(division);
}
public static Subdivision CreateSquareStar(bool test)
{
PointD[] points =
{
new PointD(), new PointD(-1, -2), new PointD(-1, 2), new PointD(1, 2), new PointD(1, -2)
};
LineD[] lines =
{
new LineD(points[1], points[2]), new LineD(points[2], points[3]),
new LineD(points[4], points[3]), new LineD(points[1], points[4]),
new LineD(points[0], points[1]), new LineD(points[0], points[2]),
new LineD(points[0], points[3]), new LineD(points[0], points[4])
};
var division = Subdivision.FromLines(lines);
division.Validate();
if (!test)
{
return(division);
}
var edges = division.Edges.Values;
var faces = division.Faces.Values;
Assert.AreEqual(16, edges.Count);
Assert.AreEqual(5, faces.Count);
CollectionAssert.AreEqual(new[] {
new SubdivisionEdge(0, points[1], edges[1], faces[0], edges[2], edges[7]),
new SubdivisionEdge(1, points[2], edges[0], faces[1], edges[9], edges[10]),
new SubdivisionEdge(2, points[2], edges[3], faces[0], edges[5], edges[0]),
new SubdivisionEdge(3, points[3], edges[2], faces[2], edges[11], edges[12]),
new SubdivisionEdge(4, points[4], edges[5], faces[3], edges[13], edges[14]),
new SubdivisionEdge(5, points[3], edges[4], faces[0], edges[7], edges[2]),
new SubdivisionEdge(6, points[1], edges[7], faces[4], edges[15], edges[8]),
new SubdivisionEdge(7, points[4], edges[6], faces[0], edges[0], edges[5]),
new SubdivisionEdge(8, points[0], edges[9], faces[4], edges[6], edges[15]),
new SubdivisionEdge(9, points[1], edges[8], faces[1], edges[10], edges[1]),
new SubdivisionEdge(10, points[0], edges[11], faces[1], edges[1], edges[9]),
new SubdivisionEdge(11, points[2], edges[10], faces[2], edges[12], edges[3]),
new SubdivisionEdge(12, points[0], edges[13], faces[2], edges[3], edges[11]),
new SubdivisionEdge(13, points[3], edges[12], faces[3], edges[14], edges[4]),
new SubdivisionEdge(14, points[0], edges[15], faces[3], edges[4], edges[13]),
new SubdivisionEdge(15, points[4], edges[14], faces[4], edges[8], edges[6]),
}, edges);
var cycles = division.GetZeroAreaCycles();
Assert.AreEqual(0, cycles.Count);
return(division);
}
/// <overloads>
/// Converts all <see cref="DelaunayEdges"/> to a planar <see cref="Subdivision"/>.
/// </overloads>
/// <summary>
/// Converts all <see cref="DelaunayEdges"/> to a planar <see cref="Subdivision"/>, using
/// the default <see cref="ClippingBounds"/>.</summary>
/// <param name="addRegions">
/// <c>true</c> to add all <see cref="VoronoiRegions"/> with the corresponding <see
/// cref="GeneratorSites"/> to the <see cref="Subdivision.VertexRegions"/> collection of the
/// new <see cref="Subdivision"/>; otherwise, <c>false</c>.</param>
/// <returns>
/// A new <see cref="Subdivision"/> whose <see cref="Subdivision.Edges"/> correspond to the
/// <see cref="DelaunayEdges"/> of the <see cref="VoronoiResults"/>.</returns>
public Subdivision ToDelaunySubdivision(bool addRegions = false)
{
Subdivision division = Subdivision.FromLines(DelaunayEdges);
if (addRegions)
{
for (int i = 0; i < GeneratorSites.Length; i++)
{
division.VertexRegions.Add(GeneratorSites[i], VoronoiRegions[i]);
}
}
return(division);
}
public void IGraph2DTest()
{
PointD[] points =
{
new PointD(0, 0), new PointD(-1, -2),
new PointD(-1, 2), new PointD(1, 2),new PointD(1, -2)
};
LineD[] lines =
{
new LineD(points[0], points[1]), new LineD(points[0], points[2]),
new LineD(points[0], points[3]), new LineD(points[4], points[0])
};
var division = Subdivision.FromLines(lines);
division.Validate();
var graph = division as IGraph2D <PointD>;
Assert.AreEqual(4, graph.Connectivity);
Assert.AreEqual(5, graph.NodeCount);
foreach (PointD node in graph.Nodes)
{
CollectionAssert.Contains(points, node);
}
foreach (PointD point in points)
{
Assert.IsTrue(graph.Contains(point));
Assert.AreEqual(point, graph.GetWorldLocation(point));
PointD near = new PointD(point.X + 0.1, point.Y - 0.1);
Assert.IsFalse(graph.Contains(near));
Assert.AreEqual(point, graph.GetNearestNode(near));
}
var center = new[] { points[0] };
var neighbors = new PointD[points.Length - 1];
double distance = Math.Sqrt(5.0);
for (int i = 1; i < points.Length; i++)
{
Assert.AreEqual(distance, graph.GetDistance(points[0], points[i]));
CollectionAssert.AreEquivalent(center, graph.GetNeighbors(points[i]));
neighbors[i - 1] = points[i];
}
CollectionAssert.AreEquivalent(neighbors, graph.GetNeighbors(points[0]));
}
private SubdivisionSearch CheckSearch(params LineD[] lines)
{
Subdivision division = Subdivision.FromLines(lines);
division.Validate();
SubdivisionSearch search = new SubdivisionSearch(division);
search.Validate();
CheckVertices(search);
CheckEdges(search);
PointD[] points = new[] {
new PointD(+1, +1), new PointD(+1, -1),
new PointD(-1, +1), new PointD(-1, -1)
};
if (division.Faces.Count == 1)
{
foreach (PointD point in points)
{
Assert.IsTrue(search.Find(point).IsUnboundedFace);
Assert.IsTrue(division.Find(point).IsUnboundedFace);
}
}
else
{
var element = new SubdivisionElement(division.Faces[1]);
foreach (PointD point in points)
{
Assert.AreEqual(element, search.Find(point));
Assert.AreEqual(element, division.Find(point));
}
}
points = new[] {
new PointD(+10, +10), new PointD(+10, -10),
new PointD(-10, +10), new PointD(-10, -10)
};
foreach (PointD point in points)
{
Assert.IsTrue(search.Find(point).IsUnboundedFace);
Assert.IsTrue(division.Find(point).IsUnboundedFace);
}
return(search);
}
public void FindEdgeEpsilon()
{
PointD[] points =
{
new PointD(0, 0), new PointD(-1, -2),
new PointD(-1, 2), new PointD(1, 2),new PointD(1, -2)
};
LineD[] lines =
{
new LineD(points[1], points[0]), new LineD(points[0], points[2]),
new LineD(points[0], points[3]), new LineD(points[4], points[0])
};
var division = Subdivision.FromLines(lines, 0.2);
division.Validate();
// check all existing half-edges
PointD offset = new PointD(0.1, -0.1);
foreach (SubdivisionEdge edge in division.Edges.Values)
{
Assert.AreSame(edge, division.FindEdge(edge.Origin, edge.Destination));
Assert.AreSame(edge, division.FindEdge(
edge.Origin.Add(offset), edge.Destination.Add(offset)));
}
for (int i = 0; i < points.Length; i++)
{
// check half-edges including one non-existing vertex
Assert.IsNull(division.FindEdge(points[i], new PointD(1, 0)));
Assert.IsNull(division.FindEdge(new PointD(1, 0), points[i]));
// check nonexistent half-edges between vertices
if (i == 0)
{
continue;
}
for (int j = 1; j < points.Length; j++)
{
if (j != i)
{
Assert.IsNull(division.FindEdge(points[i], points[j]));
}
}
}
}
public void FromLinesVertical()
{
PointD[] points =
{
new PointD(-1, -2), new PointD(-1, 2), new PointD(1, -2), new PointD(1, 2)
};
LineD[] lines =
{
new LineD(points[0], points[1]), new LineD(points[2], points[3])
};
var division = Subdivision.FromLines(lines);
division.Validate();
CollectionAssert.AreEquivalent(lines, division.ToLines());
var edges = division.Edges.Values;
var faces = division.Faces.Values;
CollectionAssert.AreEqual(new[] {
new VertexPair(points[0], edges[0]),
new VertexPair(points[2], edges[2]),
new VertexPair(points[1], edges[1]),
new VertexPair(points[3], edges[3]),
}, division.Vertices);
CollectionAssert.AreEqual(new[] {
new SubdivisionEdge(0, points[0], edges[1], faces[0], edges[1], edges[1]),
new SubdivisionEdge(1, points[1], edges[0], faces[0], edges[0], edges[0]),
new SubdivisionEdge(2, points[2], edges[3], faces[0], edges[3], edges[3]),
new SubdivisionEdge(3, points[3], edges[2], faces[0], edges[2], edges[2]),
}, edges);
CollectionAssert.AreEqual(new[] {
new SubdivisionFace(division, 0, null, new[] { edges[0], edges[2] }),
}, faces);
CheckFace(edges[0], new[] { points[0], points[1] }, 0, PointD.Empty);
CheckFace(edges[2], new[] { points[2], points[3] }, 0, PointD.Empty);
var cycles = division.GetZeroAreaCycles();
Assert.AreEqual(2, cycles.Count);
Assert.AreEqual(edges[0], cycles[0]);
Assert.AreEqual(edges[2], cycles[1]);
}
public void FromLinesSquare()
{
PointD[] points =
{
new PointD(-1, -2), new PointD(-1, 2), new PointD(1, 2), new PointD(1, -2)
};
LineD[] lines =
{
new LineD(points[0], points[1]), new LineD(points[1], points[2]),
new LineD(points[3], points[2]), new LineD(points[0], points[3])
};
var division = Subdivision.FromLines(lines);
division.Validate();
CollectionAssert.AreEquivalent(lines, division.ToLines());
CheckLinesSquare(points, division);
}
private void PasteCommandExecuted(object sender, ExecutedRoutedEventArgs args)
{
args.Handled = true;
try {
string text = Clipboard.GetText();
LineD[] lines = XmlSerialization.Deserialize <LineD[]>(text);
Subdivision division = Subdivision.FromLines(lines);
DrawSubdivision(division);
}
catch (Exception e) {
MessageDialog.Show(this,
"An error occurred while attempting to\n" +
"paste a new subdivision from the clipboard.",
Strings.ClipboardPasteError, e, MessageBoxButton.OK,
WindowsUtility.GetSystemBitmap(MessageBoxImage.Error));
}
}
public void FromLinesSquareEpsilon()
{
PointD[] points =
{
new PointD(-1, -2), new PointD(-1, 2), new PointD(1, 2), new PointD(1, -2)
};
LineD[] lines =
{
new LineD(points[0], points[1]),
new LineD(new PointD(-1.1, 1.9),points[2]),
new LineD(points[3], new PointD(0.9, 2.1)),
new LineD(new PointD(-0.9, -2.1),new PointD(1.1, -1.9))
};
var division = Subdivision.FromLines(lines, 0.2);
division.Validate();
CollectionAssert.AreNotEquivalent(lines, division.ToLines());
CheckLinesSquare(points, division);
}
/// <summary>
/// Creates a random <see cref="Subdivision"/> with the specified number of full edges and
/// comparison epsilon.</summary>
/// <param name="size">
/// The number of full edges, i.e. half the number of <see cref="Subdivision.Edges"/>, in
/// the returned <see cref="Subdivision"/>.</param>
/// <param name="epsilon">
/// The maximum absolute difference at which two coordinates should be considered equal.
/// </param>
/// <returns>
/// A new random <see cref="Subdivision"/> with the specified <paramref name="size"/> and
/// <paramref name="epsilon"/>.</returns>
private static Subdivision CreateSubdivision(int size, double epsilon)
{
LineD[] lines = new LineD[size];
for (int i = 0; i < size; i++)
{
lines[i] = GeoAlgorithms.RandomLine(0, 0, 1000, 1000);
}
// split random set into non-intersecting line segments
var crossings = MultiLineIntersection.FindSimple(lines, epsilon);
var splitLines = MultiLineIntersection.Split(lines, crossings);
Array.Copy(splitLines, lines, size);
// re-randomize lines to eliminate split ordering
CollectionsUtility.Randomize(lines);
Subdivision division = Subdivision.FromLines(lines);
division.Validate();
return(division);
}
private void OnIntersect(object sender, RoutedEventArgs args)
{
args.Handled = true;
RectD bounds = OutputBounds;
double x = bounds.Left + (double)LeftUpDown.Value;
double y = bounds.Top + (double)TopUpDown.Value;
double dx = (double)WidthUpDown.Value;
double dy = (double)HeightUpDown.Value;
Subdivision rectangle;
if (sender == RectangleButton)
{
rectangle = Subdivision.FromLines(new LineD[] {
new LineD(x, y, x + dx, y),
new LineD(x + dx, y, x + dx, y + dy),
new LineD(x + dx, y + dy, x, y + dy),
new LineD(x, y + dy, x, y)
});
}
else if (sender == DiamondButton)
{
rectangle = Subdivision.FromLines(new LineD[] {
new LineD(x + dx / 2, y, x + dx, y + dy / 2),
new LineD(x + dx, y + dy / 2, x + dx / 2, y + dy),
new LineD(x + dx / 2, y + dy, x, y + dy / 2),
new LineD(x, y + dy / 2, x + dx / 2, y)
});
}
else
{
return;
}
rectangle.Validate();
_division = Subdivision.Intersection(_division, rectangle, out _faceKeys);
_division.Validate();
SubdivisionTest.DrawSubdivision(OutputBox, FontSize, _division);
}
public void FromLinesDiamond()
{
PointD[] points =
{
new PointD(0, -4), new PointD(-6, 0), new PointD(-3, 0),
new PointD(3, 0), new PointD(6, 0), new PointD(0, 4)
};
LineD[] lines =
{
new LineD(points[0], points[1]), new LineD(points[1], points[5]),
new LineD(points[0], points[2]), new LineD(points[2], points[5]),
new LineD(points[0], points[3]), new LineD(points[3], points[5]),
new LineD(points[0], points[4]), new LineD(points[4], points[5])
};
var division = Subdivision.FromLines(lines);
division.Validate();
CollectionAssert.AreEquivalent(lines, division.ToLines());
var edges = division.Edges.Values;
var faces = division.Faces.Values;
CollectionAssert.AreEqual(new[] {
new VertexPair(points[0], edges[0]),
new VertexPair(points[1], edges[1]),
new VertexPair(points[2], edges[5]),
new VertexPair(points[3], edges[9]),
new VertexPair(points[4], edges[13]),
new VertexPair(points[5], edges[3]),
}, division.Vertices);
CollectionAssert.AreEqual(new[] {
new SubdivisionEdge(0, points[0], edges[1], faces[0], edges[2], edges[13]),
new SubdivisionEdge(1, points[1], edges[0], faces[1], edges[4], edges[3]),
new SubdivisionEdge(2, points[1], edges[3], faces[0], edges[15], edges[0]),
new SubdivisionEdge(3, points[5], edges[2], faces[1], edges[1], edges[6]),
new SubdivisionEdge(4, points[0], edges[5], faces[1], edges[6], edges[1]),
new SubdivisionEdge(5, points[2], edges[4], faces[2], edges[8], edges[7]),
new SubdivisionEdge(6, points[2], edges[7], faces[1], edges[3], edges[4]),
new SubdivisionEdge(7, points[5], edges[6], faces[2], edges[5], edges[10]),
new SubdivisionEdge(8, points[0], edges[9], faces[2], edges[10], edges[5]),
new SubdivisionEdge(9, points[3], edges[8], faces[3], edges[12], edges[11]),
new SubdivisionEdge(10, points[3], edges[11], faces[2], edges[7], edges[8]),
new SubdivisionEdge(11, points[5], edges[10], faces[3], edges[9], edges[14]),
new SubdivisionEdge(12, points[0], edges[13], faces[3], edges[14], edges[9]),
new SubdivisionEdge(13, points[4], edges[12], faces[0], edges[0], edges[15]),
new SubdivisionEdge(14, points[4], edges[15], faces[3], edges[11], edges[12]),
new SubdivisionEdge(15, points[5], edges[14], faces[0], edges[13], edges[2]),
}, edges);
CollectionAssert.AreEqual(new[] {
new SubdivisionFace(division, 0, null, new[] { edges[0] }),
new SubdivisionFace(division, 1, edges[1], null),
new SubdivisionFace(division, 2, edges[5], null),
new SubdivisionFace(division, 3, edges[9], null),
}, faces);
CheckFace(edges[0], new[] { points[0], points[1], points[5], points[4] }, -48, PointD.Empty);
CheckFace(edges[1], new[] { points[1], points[0], points[2], points[5] }, +12, new PointD(-3, 0));
CheckFace(edges[5], new[] { points[2], points[0], points[3], points[5] }, +24, PointD.Empty);
CheckFace(edges[9], new[] { points[3], points[0], points[4], points[5] }, +12, new PointD(3, 0));
var cycles = division.GetZeroAreaCycles();
Assert.AreEqual(0, cycles.Count);
}
public static Subdivision CreateTriforce(bool test)
{
PointD[] points =
{
new PointD(-5, -4), new PointD(0, 6), new PointD(5, -4),
new PointD(0, 0), new PointD(-1, 2), new PointD(1, 2)
};
LineD[] lines =
{
new LineD(points[0], points[1]), new LineD(points[2], points[1]),
new LineD(points[0], points[2]), new LineD(points[3], points[4]),
new LineD(points[3], points[5]), new LineD(points[4], points[5])
};
Subdivision division = Subdivision.FromLines(lines);
division.Validate();
if (!test)
{
return(division);
}
CollectionAssert.AreEquivalent(lines, division.ToLines());
var edges = division.Edges.Values;
var faces = division.Faces.Values;
CollectionAssert.AreEqual(new[] {
new VertexPair(points[0], edges[0]),
new VertexPair(points[2], edges[2]),
new VertexPair(points[3], edges[6]),
new VertexPair(points[4], edges[7]),
new VertexPair(points[5], edges[9]),
new VertexPair(points[1], edges[1]),
}, division.Vertices);
CollectionAssert.AreEqual(new[] {
new SubdivisionEdge(0, points[0], edges[1], faces[0], edges[3], edges[5]),
new SubdivisionEdge(1, points[1], edges[0], faces[1], edges[4], edges[2]),
new SubdivisionEdge(2, points[2], edges[3], faces[1], edges[1], edges[4]),
new SubdivisionEdge(3, points[1], edges[2], faces[0], edges[5], edges[0]),
new SubdivisionEdge(4, points[0], edges[5], faces[1], edges[2], edges[1]),
new SubdivisionEdge(5, points[2], edges[4], faces[0], edges[0], edges[3]),
new SubdivisionEdge(6, points[3], edges[7], faces[1], edges[10], edges[9]),
new SubdivisionEdge(7, points[4], edges[6], faces[2], edges[8], edges[11]),
new SubdivisionEdge(8, points[3], edges[9], faces[2], edges[11], edges[7]),
new SubdivisionEdge(9, points[5], edges[8], faces[1], edges[6], edges[10]),
new SubdivisionEdge(10, points[4], edges[11], faces[1], edges[9], edges[6]),
new SubdivisionEdge(11, points[5], edges[10], faces[2], edges[7], edges[8]),
}, edges);
CollectionAssert.AreEqual(new[] {
new SubdivisionFace(division, 0, null, new[] { edges[0] }),
new SubdivisionFace(division, 1, edges[1], new[] { edges[6] }),
new SubdivisionFace(division, 2, edges[7], null),
}, faces);
PointD centroid = new PointD(0, -2 / 3.0);
CheckFace(edges[0], new[] { points[0], points[1], points[2] }, -50, centroid);
CheckFace(edges[1], new[] { points[1], points[0], points[2] }, +50, centroid);
centroid = new PointD(0, 4 / 3.0);
CheckFace(edges[6], new[] { points[3], points[4], points[5] }, -2, centroid);
CheckFace(edges[7], new[] { points[4], points[3], points[5] }, +2, centroid);
var cycles = division.GetZeroAreaCycles();
Assert.AreEqual(0, cycles.Count);
return(division);
}