public static List <Polyline> DelaunayTriangulation(List <Point> points, Plane plane = null, double tolerance = Tolerance.Distance)
{
//Preform check all inputs that triangulation can be done
if (points == null || points.Count < 3)
{
Base.Compute.RecordError("Insufficient points for triangulation. Please provide at least 3 Points.");
return(new List <Polyline>());
}
if (points.IsCollinear(tolerance))
{
Base.Compute.RecordError("Points are colinear and can not be triangulated.");
return(new List <Polyline>());
}
//Basic edge case, simply create a triangle
if (points.Count == 3)
{
Polyline pLine = new Polyline {
ControlPoints = points
};
pLine.ControlPoints.Add(points[0]);
return(new List <Polyline> {
pLine
});
}
//Try fit plane if no is provided
if (plane == null)
{
plane = points.FitPlane(tolerance);
}
if (plane == null)
{
Engine.Base.Compute.RecordError("Could not fit a plane through the Points and no plane was provided.");
return(new List <Polyline>());
}
//Check all points within distance of the plane
if (points.Any(x => x.Distance(plane) > tolerance))
{
BH.Engine.Base.Compute.RecordError("Can only handle coplanar points. Please make sure all your points lie in the same plane.");
return(new List <Polyline>());
}
//Calculate the local coordinates
Vector localX = points[1] - points[0];
Vector localY = plane.Normal.CrossProduct(localX);
Point min = points.Min();
Point refPt = new Point {
X = min.X, Y = min.Y
};
Cartesian localSystem = Create.CartesianCoordinateSystem(min, localX, localY);
Cartesian globalSystem = Create.CartesianCoordinateSystem(refPt, Vector.XAxis, Vector.YAxis);
//Transform to xy-plane
List <Point> xyPoints = points.Select(x => x.Orient(localSystem, globalSystem)).ToList();
//Convert to TringleNet vertecies
List <TriangleNet.Geometry.Vertex> vertecies = xyPoints.Select(p => new TriangleNet.Geometry.Vertex(p.X, p.Y)).ToList();
// Triangulate
TriangleNet.Meshing.ITriangulator triangulator = new TriangleNet.Meshing.Algorithm.Dwyer();
TriangleNet.Configuration config = new TriangleNet.Configuration();
TriangleNet.Mesh mesh = (TriangleNet.Mesh)triangulator.Triangulate(vertecies, config);
// Convert triangulations back to BHoM geometry
List <Polyline> translatedPolylines = new List <Polyline>();
foreach (var face in mesh.Triangles)
{
// List points defining the triangle
List <Point> pts = new List <Point>();
pts.Add(BH.Engine.Geometry.Create.Point(face.GetVertex(0).X, face.GetVertex(0).Y));
pts.Add(BH.Engine.Geometry.Create.Point(face.GetVertex(1).X, face.GetVertex(1).Y));
pts.Add(BH.Engine.Geometry.Create.Point(face.GetVertex(2).X, face.GetVertex(2).Y));
pts.Add(pts.First());
translatedPolylines.Add(BH.Engine.Geometry.Create.Polyline(pts));
}
return(translatedPolylines.Select(x => x.Orient(globalSystem, localSystem)).ToList());
}
public static List <Polyline> VoronoiRegions(List <Point> points, Plane plane = null, double boundarySize = -1, double tolerance = Tolerance.Distance)
{
List <Point> uniquePoints = points.CullDuplicates(tolerance);
if (points.Count != uniquePoints.Count)
{
Base.Compute.RecordError("Some points are overlapping with others. Duplicates need to be culled out to create voronoi regions.");
return(new List <Polyline>());
}
//Preform check all inputs that triangulation can be done
if (points == null || points.Count < 2)
{
Base.Compute.RecordError("Insuffient points for generating the diagram. Please provide at least 2 Points.");
return(new List <Polyline>());
}
//Special case for colinear points. No need to triangulate
if (points.IsCollinear(tolerance))
{
return(ColinearVoronoiRegions(points, plane, boundarySize, tolerance));
}
//Try fit plane if no is provided
if (plane == null)
{
plane = points.FitPlane(tolerance);
}
if (plane == null)
{
Engine.Base.Compute.RecordError("Could not fit a plane through the Points and no plane was provided.");
return(new List <Polyline>());
}
//Check all points within distance of the plane
if (points.Any(x => x.Distance(plane) > tolerance))
{
BH.Engine.Base.Compute.RecordError("Can only handle coplanar points. Please make sure all your points lie in the same plane.");
return(new List <Polyline>());
}
//Calculate the local coordinates
Vector localX = points[1] - points[0];
Vector localY = plane.Normal.CrossProduct(localX);
Point min = points.Min();
Point refPt = new Point {
X = min.X, Y = min.Y
};
Cartesian localSystem = Create.CartesianCoordinateSystem(min, localX, localY);
Cartesian globalSystem = Create.CartesianCoordinateSystem(refPt, Vector.XAxis, Vector.YAxis);
//Transform to xy-plane
List <Point> xyPoints = points.Select(x => x.Orient(localSystem, globalSystem)).ToList();
//Add point at all corners. This is to try to handle weirdness at the boundaries
BoundingBox bounds = xyPoints.Bounds();
double lengthX;
double lengthY;
//If boundary size is or equal to 0, calculate based on the bounds
if (boundarySize <= 0)
{
lengthX = (bounds.Max.X - bounds.Min.X);
lengthY = (bounds.Max.X - bounds.Min.X);
}
else
{
//if positive, use value provided
lengthX = boundarySize;
lengthY = boundarySize;
}
double minX = bounds.Min.X - lengthX;
double minY = bounds.Min.Y - lengthY;
double maxX = bounds.Max.X + lengthX;
double maxY = bounds.Max.Y + lengthY;
xyPoints.Add(new Point {
X = minX, Y = minY
});
xyPoints.Add(new Point {
X = minX, Y = maxY
});
xyPoints.Add(new Point {
X = maxX, Y = maxY
});
xyPoints.Add(new Point {
X = maxX, Y = minY
});
//Convert to TringleNet vertecies
List <TriangleNet.Geometry.Vertex> vertecies = xyPoints.Select(p => new TriangleNet.Geometry.Vertex(p.X, p.Y)).ToList();
// Triangulate
TriangleNet.Meshing.ITriangulator triangulator = new TriangleNet.Meshing.Algorithm.Dwyer();
TriangleNet.Configuration config = new TriangleNet.Configuration();
TriangleNet.Mesh mesh = (TriangleNet.Mesh)triangulator.Triangulate(vertecies, config);
TriangleNet.Voronoi.StandardVoronoi voronoi = new TriangleNet.Voronoi.StandardVoronoi(mesh);
List <Polyline> translatedPolylines = new List <Polyline>();
double sqTol = tolerance * tolerance;
// Convert regions to BHoMGeometry. Skip the last 4 faces as they correspond to the added boundary points.
for (int i = 0; i < voronoi.Faces.Count - 4; i++)
{
var face = voronoi.Faces[i];
try
{
// List points defining the region
List <Point> pts = new List <Point>();
HashSet <int> visitedIds = new HashSet <int>();
int bailOut = 100000;
int counter = 0;
TriangleNet.Topology.DCEL.HalfEdge halfEdge = face.Edge;
int nextId;
do
{
visitedIds.Add(halfEdge.ID);
Point pt = new Point {
X = halfEdge.Origin.X, Y = halfEdge.Origin.Y
};
//Make sure two of the same points are not added. This could maybe be done in a more cleaver way with the half edge
if (pts.Count == 0 || pt.SquareDistance(pts.Last()) > sqTol)
{
pts.Add(pt);
}
halfEdge = halfEdge.Next;
if (halfEdge == null)
{
break;
}
nextId = halfEdge.ID;
counter++;
} while (!visitedIds.Contains(nextId) && counter < bailOut);
if (pts.Count > 0 && pts.First().SquareDistance(pts.Last()) > sqTol)
{
pts.Add(pts.First());
}
translatedPolylines.Add(BH.Engine.Geometry.Create.Polyline(pts));
}
catch (Exception)
{
Engine.Base.Compute.RecordWarning("Failed to generate the region for at least one cell. An empty polyline as been added in its place.");
translatedPolylines.Add(new Polyline());
}
}
//Orient back the regions to the local plane
return(translatedPolylines.Select(x => x.Orient(globalSystem, localSystem)).ToList());
}
