// Improve the random set of points with Lloyd Relaxation.
private void ImprovePoints()
{
// We'd really like to generate "blue noise". Algorithms:
// 1. Poisson dart throwing: check each new point against all
// existing points, and reject it if it's too close.
// 2. Start with a hexagonal grid and randomly perturb points.
// 3. Lloyd Relaxation: move each point to the centroid of the
// generated Voronoi polygon, then generate Voronoi again.
// 4. Use force-based layout algorithms to push points away.
// 5. More at http://www.cs.virginia.edu/~gfx/pubs/antimony/
// Option 3 is implemented here. If it's run for too many iterations,
// it will turn into a grid, but convergence is very slow, and we only
// run it a few times.
var newPoints = new List <Vector>();
foreach (var key in _provinces.Keys)
{
var provincePoints = _provinces[key];
var newpoint = new Vector(2);
foreach (var point in provincePoints)
{
newpoint.Add(point);
}
newpoint[0] /= provincePoints.Count;
newpoint[1] /= provincePoints.Count;
newpoint[0] = (newpoint[0] + key[0]) / 2;
newpoint[1] = (newpoint[1] + key[1]) / 2;
newPoints.Add(newpoint);
}
var height = Convert.ToInt32(txtHeight.Value);
var width = Convert.ToInt32(txtWidth.Value);
var points = Convert.ToInt32(txtPoints.Value);
OrderedPoints = newPoints
.Select(WrapVector)
.OrderBy(v => String.Format("{0:000000000}{1:000000000}", height - (int)v[1], (int)v[0]))
.ToList();
for (var x = -1; x <= 1; x++)
{
for (var y = -1; y <= 1; y++)
{
if (x == 0 && y == 0)
{
continue;
}
for (var i = 0; i < points; i++)
{
var point = newPoints[i];
newPoints.Add(new Vector(point[0] + (x * width), point[1] + (y * height)));
}
}
}
_pointList = newPoints;
//Text = _pointList.Count.ToString();
_provinces = null;
picDiagram.Image = new Bitmap(width, height);
Map.Neighbours = new MultiValueDictionary <int, int>();
}
private void GenerateProvinces()
{
_rightMatrix = new Matrix();
_rightMatrix.Translate(Width(), 0);
_leftMatric = new Matrix();
_leftMatric.Translate(-1 * Width(), 0);
_downMatrix = new Matrix();
_downMatrix.Translate(0, Height());
_upMatrix = new Matrix();
_upMatrix.Translate(0, -1 * Height());
Map = new Dominons3Map();
Map.MapImage = picDiagram.Image;
Map.Title = "Test Map";
Map.Filename = "TestMap";
Map.IsWrapAround = true;
Map.Description = "Description of Dom 3 Map.";
Map.ProvinceCount = OrderedPoints.Count;
var neighbours = new MultiValueDictionary <Vector, Vector>();
_provinces = new MultiValueDictionary <Vector, Vector>();
var height = Convert.ToInt32(txtHeight.Value);
var width = Convert.ToInt32(txtWidth.Value);
_indexToPath.Clear();
MapBounds = new Rectangle(0, 0, Width(), Height());
_borderPointX = new PointF(Width(), 0);
_borderPointEdge = new PointF(Width(), Height());
_borderPointY = new PointF(0, Height());
var visibleEdges = _graph.Edges
.Cast <VoronoiEdge>()
.Where(edge => IsVertexValid(edge.VVertexA) && IsVertexValid(edge.VVertexB) && (MapBounds.ContainsEdge(edge) || MapBounds.IntersectsEdge(edge)))
.ToArray();
foreach (var edge in visibleEdges)
{
var segmentId = GetSegmentId(edge);
if (!_indexToPath.ContainsKey(segmentId))
{
_indexToPath[segmentId] = GenerateJaggedSegment(edge);
}
}
foreach (VoronoiEdge edge1 in _graph.Edges)
{
if (!IsOutofBounds(height, width, edge1.LeftData) && !IsOutofBounds(height, width, edge1.RightData))
{
neighbours.Add(edge1.LeftData, edge1.RightData);
neighbours.Add(edge1.RightData, edge1.LeftData);
var leftProvinceId = OrderedPoints.IndexOf(edge1.LeftData) + 1;
var rightProvinceId = OrderedPoints.IndexOf(edge1.RightData) + 1;
Map.Neighbours.Add(leftProvinceId, rightProvinceId);
Map.Neighbours.Add(rightProvinceId, leftProvinceId);
}
if (!IsOutofBounds(height, width, edge1.LeftData) && IsOutofBounds(height, width, edge1.RightData))
{
var leftProvinceId = OrderedPoints.IndexOf(edge1.LeftData) + 1;
var rightProvinceId = OrderedPoints.IndexOf(WrapVector(edge1.RightData)) + 1;
Map.Neighbours.Add(leftProvinceId, rightProvinceId);
Map.Neighbours.Add(rightProvinceId, leftProvinceId);
}
if (IsOutofBounds(height, width, edge1.LeftData) && !IsOutofBounds(height, width, edge1.RightData))
{
var leftProvinceId = OrderedPoints.IndexOf(WrapVector(edge1.LeftData)) + 1;
var rightProvinceId = OrderedPoints.IndexOf(edge1.RightData) + 1;
Map.Neighbours.Add(leftProvinceId, rightProvinceId);
Map.Neighbours.Add(rightProvinceId, leftProvinceId);
}
if (!IsOutofBounds(height, width, edge1.LeftData))
{
_provinces.Add(edge1.LeftData, edge1.VVertexA);
_provinces.Add(edge1.LeftData, edge1.VVertexB);
}
if (!IsOutofBounds(height, width, edge1.RightData))
{
_provinces.Add(edge1.RightData, edge1.VVertexA);
_provinces.Add(edge1.RightData, edge1.VVertexB);
}
}
for (int i = 0; i < OrderedPoints.Count; i++)
{
var provinceId = i + 1;
Map.TerrainTypes[provinceId] = 0;
}
using (var g = Graphics.FromImage(picDiagram.Image))
{
foreach (var key in _provinces.Keys.ToList())
{
var list = _provinces[key];
var f = list.First();
Vector key1 = key;
var points = list
.Select(v => new { angle = GetAngle(f, key1, v), v })
.OrderBy(a => a.angle)
.Select(a => a.v)
.ToList();
_provinces[key] = new HashSet <Vector>(points);
var randomBrush = GetRandomBrush();
g.FillPolygon(randomBrush, points.Select(v => v.ToPointF()).ToArray());
g.FillPolygon(randomBrush, points.Select(v => new PointF((float)v[0] + width, (float)v[1])).ToArray());
g.FillPolygon(randomBrush, points.Select(v => new PointF((float)v[0] - width, (float)v[1])).ToArray());
g.FillPolygon(randomBrush, points.Select(v => new PointF((float)v[0], (float)v[1] + height)).ToArray());
g.FillPolygon(randomBrush, points.Select(v => new PointF((float)v[0], (float)v[1] - height)).ToArray());
var provId = OrderedPoints.IndexOf(key);
g.DrawString(provId.ToString(), _provFont, Brushes.Black, (float)key[0] + 5f, (float)key[1] + 5f);
}
}
picDiagram.Invalidate();
}