/// <summary>
/// Initializes a new instance of the <see cref="Segment" /> class.
/// </summary>
public Segment(Vertex v0, Vertex v1, int label)
{
this.v0 = v0;
this.v1 = v1;
this.label = label;
}
/// <summary>
/// Read vertex information of the given line.
/// </summary>
/// <param name="data">The input geometry.</param>
/// <param name="index">The current vertex index.</param>
/// <param name="line">The current line.</param>
/// <param name="attributes">Number of point attributes</param>
/// <param name="marks">Number of point markers (0 or 1)</param>
static void ReadVertex(List<Vertex> data, int index, string[] line, int attributes, int marks)
{
double x = double.Parse(line[1], nfi);
double y = double.Parse(line[2], nfi);
var v = new Vertex(x, y);
// Read a vertex marker.
if (marks > 0 && line.Length > 3 + attributes)
{
v.Label = int.Parse(line[3 + attributes]);
}
if (attributes > 0)
{
#if USE_ATTRIBS
var attribs = new double[attributes];
// Read the vertex attributes.
for (int j = 0; j < attributes; j++)
{
if (line.Length > 3 + j)
{
attribs[j] = double.Parse(line[3 + j], nfi);
}
}
v.attributes = attribs;
#endif
}
data.Add(v);
}
/// <summary>
/// Enumerate all vertices adjacent to given vertex.
/// </summary>
/// <param name="vertex">The center vertex.</param>
/// <returns></returns>
public IEnumerable<Vertex> EnumerateVertices(Vertex vertex)
{
BuildCache(vertex, true);
foreach (var item in cache)
{
yield return item.Dest();
}
}
public VoronoiRegion(Vertex generator)
{
this.id = generator.id;
this.generator = generator;
this.vertices = new List<Point>();
this.bounded = true;
this.neighbors = new Dictionary<int, VoronoiRegion>();
}
/// <summary>
/// Enumerate all triangles adjacent to given vertex.
/// </summary>
/// <param name="vertex">The center vertex.</param>
/// <returns></returns>
public IEnumerable<ITriangle> EnumerateTriangles(Vertex vertex)
{
BuildCache(vertex, false);
foreach (var item in cache)
{
yield return item.tri;
}
}
/// <summary>
/// Case 2: edge origin lies outside the domain.
/// </summary>
private void HandleCase2(HalfEdge edge, TVertex v1, TVertex v2)
{
// The vertices of the infinite edge.
var p1 = (Point)edge.origin;
var p2 = (Point)edge.twin.origin;
// The two edges leaving p1, pointing into the mesh.
var e1 = edge.twin.next;
var e2 = e1.twin.next;
// Check if the neighboring cell was closed before.
if (edge.twin.id != edge.twin.face.edge.id)
{
edge.twin.face.edge.next = e1;
}
else
{
// If the cell isn't closed yet, make sure to update the faces edge pointer.
e1.face.edge = e1;
}
// Find the two intersections with boundary edge.
IntersectionHelper.IntersectSegments(v1, v2, e1.origin, e1.twin.origin, ref p2);
IntersectionHelper.IntersectSegments(v1, v2, e2.origin, e2.twin.origin, ref p1);
// The infinite edge will now lie on the boundary. Update pointers:
e1.twin.next = edge.twin;
edge.twin.next = e2;
edge.twin.face = e2.face;
e1.origin = edge.twin.origin;
// Dissolve edge from other edges (origin and face stay the same).
edge.twin.twin = null;
edge.twin = null;
// Close the cell.
var gen = factory.CreateVertex(v1.x, v1.y);
var he = factory.CreateHalfEdge(gen, edge.face);
gen.leaving = he;
edge.next = he;
he.next = edge.face.edge;
e2.twin.next = edge;
// Let the face edge point to the edge leaving at generator.
edge.face.edge = he;
base.edges.Add(he);
he.id = base.edges.Count;
gen.id = offset++;
base.vertices.Add(gen);
}
void KruskalsMinimumSpanningTree()
{
//triangles = new List<Triangle>();
tmpConnections = new List <KruskalsEdge>();
connections = new List <KruskalsEdge>();
//triangles = DelaunayTriangulation.TriangulateByFlippingEdges(points);
List <int> vertices = new List <int>();
int index = 0;
int index2 = 0;
foreach (var edge in mesh.Edges)
{
TriangleNet.Geometry.Vertex v0 = mesh.vertices[edge.P0];
TriangleNet.Geometry.Vertex v1 = mesh.vertices[edge.P1];
Vector3 p0 = new Vector3((float)v0.x, 0.0f, (float)v0.y);
Vector3 p1 = new Vector3((float)v1.x, 0.0f, (float)v1.y);
int tmp = 0;
foreach (var point in Rooms)
{
if (p0 == point.Position)
{
index = tmp;
break;
}
tmp++;
}
tmp = 0;
foreach (var point in Rooms)
{
if (p1 == point.Position)
{
index2 = tmp;
break;
}
tmp++;
}
tmpConnections.Add(new KruskalsEdge()
{
Vertex1 = edge.P0, Room1 = Rooms[index], Vertex2 = edge.P1, Room2 = Rooms[index2], Weight = (Vector3.Distance(p0, p1)) * (Rooms[index].weight / 20)
});
if (!vertices.Contains(edge.P0))
{
vertices.Add(edge.P0);
}
if (!vertices.Contains(edge.P1))
{
vertices.Add(edge.P1);
}
}
connections = KruskalsAlgorithm.Kruskals_MST(tmpConnections, vertices, false, connectivityPercentage);
}
/// <summary>
/// Find a new location for a Steiner point.
/// </summary>
/// <param name="org"></param>
/// <param name="dest"></param>
/// <param name="apex"></param>
/// <param name="xi"></param>
/// <param name="eta"></param>
/// <param name="offcenter"></param>
/// <param name="badotri"></param>
/// <returns></returns>
public Point FindLocation(Vertex org, Vertex dest, Vertex apex,
ref double xi, ref double eta, bool offcenter, Otri badotri)
{
// Based on using -U switch, call the corresponding function
if (behavior.MaxAngle == 0.0)
{
return FindNewLocationWithoutMaxAngle(org, dest, apex, ref xi, ref eta, true, badotri);
}
// With max angle
return FindNewLocation(org, dest, apex, ref xi, ref eta, true, badotri);
}
private void BuildCache(Vertex vertex, bool vertices)
{
cache.Clear();
Otri init = vertex.tri;
Otri next = default(Otri);
Otri prev = default(Otri);
init.Copy(ref next);
// Move counter-clockwise around the vertex.
while (next.tri.id != Mesh.DUMMY)
{
cache.Add(next);
next.Copy(ref prev);
next.Onext();
if (next.Equals(init))
{
break;
}
}
if (next.tri.id == Mesh.DUMMY)
{
// We reached the boundary. To get all adjacent triangles, start
// again at init triangle and now move clockwise.
init.Copy(ref next);
if (vertices)
{
// Don't forget to add the vertex lying on the boundary.
prev.Lnext();
cache.Add(prev);
}
next.Oprev();
while (next.tri.id != Mesh.DUMMY)
{
cache.Insert(0, next);
next.Oprev();
if (next.Equals(init))
{
break;
}
}
}
}
public static void GenerateOffSet(IslandNetMesh islandNetMesh, float skylandDeclinePrecent, float skylandRadius)
{
IEnumerator <TriangleNet.Geometry.Vertex> vertexEnum = islandNetMesh.netMesh.Vertices.GetEnumerator();
for (int i = 0; i < islandNetMesh.netMesh.vertices.Count; i++)
{
if (!vertexEnum.MoveNext())
{
break;
}
TriangleNet.Geometry.Vertex current = vertexEnum.Current;
float precentDistanceFromTheEdge = 1 - Mathf.Sqrt(Mathf.Pow((float)current.x, 2) + Mathf.Pow((float)current.y, 2)) / (float)skylandRadius;
current.x += (perlinNoise.GetNoise((float)current.x * 10, (float)current.y * 10)) * 5;
current.y += (perlinNoise.GetNoise((float)current.x * 10, (float)current.y * 10)) * 5;
}
}
/// <summary>
/// Impose alternating cuts on given vertex array.
/// </summary>
/// <param name="array">The vertex array.</param>
/// <param name="length">The number of vertices to sort.</param>
/// <param name="seed">Random seed used for pivoting.</param>
public static void Alternate(Vertex[] array, int length, int seed = RANDOM_SEED)
{
var qs = new VertexSorter(array, seed);
int divider = length >> 1;
// Re-sort the array of vertices to accommodate alternating cuts.
if (length - divider >= 2)
{
if (divider >= 2)
{
qs.AlternateAxes(0, divider - 1, 1);
}
qs.AlternateAxes(divider, length - 1, 1);
}
}
void CreateMap(TriangleNet.Mesh m, float maxz, float yOffset)
{
Dictionary <int, TriangleNet.Geometry.Vertex> id2vert = new Dictionary <int, TriangleNet.Geometry.Vertex>();
List <TriangleNet.Geometry.Vertex> vertices = new List <TriangleNet.Geometry.Vertex>();
List <ISegment> segments = new List <ISegment>();
foreach (TriangleNet.Geometry.Vertex v in m.Vertices)
{
id2vert[v.id] = v;
vertices.Add(v);
}
foreach (Edge e in m.Edges)
{
TriangleNet.Geometry.Vertex v1 = id2vert[e.P0];
TriangleNet.Geometry.Vertex v2 = id2vert[e.P1];
segments.Add(new Segment(v1, v2));
}
CreateMap(vertices, segments, maxz, yOffset);
}
/// <summary>
/// Case 2: edge origin lies outside the domain.
/// </summary>
private void HandleCase2(HalfEdge edge, TVertex v1, TVertex v2)
{
// The vertices of the infinite edge.
var p1 = (Point)edge.origin;
var p2 = (Point)edge.twin.origin;
// The two edges leaving p1, pointing into the mesh.
var e1 = edge.twin.next;
var e2 = e1.twin.next;
// Find the two intersections with boundary edge.
IntersectionHelper.IntersectSegments(v1, v2, e1.origin, e1.twin.origin, ref p2);
IntersectionHelper.IntersectSegments(v1, v2, e2.origin, e2.twin.origin, ref p1);
// The infinite edge will now lie on the boundary. Update pointers:
e1.twin.next = edge.twin;
edge.twin.next = e2;
edge.twin.face = e2.face;
e1.origin = edge.twin.origin;
edge.twin.twin = null;
edge.twin = null;
// Close the cell.
var gen = factory.CreateVertex(v1.x, v1.y);
var he = factory.CreateHalfEdge(gen, edge.face);
edge.next = he;
he.next = edge.face.edge;
// Let the face edge point to the edge leaving at generator.
edge.face.edge = he;
base.edges.Add(he);
he.id = base.edges.Count;
gen.id = offset++;
base.vertices.Add(gen);
}
/// <summary>
/// Linear interpolation of vertex attributes.
/// </summary>
/// <param name="vertex">The interpolation vertex.</param>
/// <param name="triangle">The triangle containing the vertex.</param>
/// <param name="n">The number of vertex attributes.</param>
/// <remarks>
/// The vertex is expected to lie inside the triangle.
/// </remarks>
public static void InterpolateAttributes(Vertex vertex, ITriangle triangle, int n)
{
Vertex org = triangle.GetVertex(0);
Vertex dest = triangle.GetVertex(1);
Vertex apex = triangle.GetVertex(2);
double xdo, ydo, xao, yao;
double denominator;
double dx, dy;
double xi, eta;
// Compute the circumcenter of the triangle.
xdo = dest.x - org.x;
ydo = dest.y - org.y;
xao = apex.x - org.x;
yao = apex.y - org.y;
denominator = 0.5 / (xdo * yao - xao * ydo);
//dx = (yao * dodist - ydo * aodist) * denominator;
//dy = (xdo * aodist - xao * dodist) * denominator;
dx = vertex.x - org.x;
dy = vertex.y - org.y;
// To interpolate vertex attributes for the new vertex inserted at
// the circumcenter, define a coordinate system with a xi-axis,
// directed from the triangle's origin to its destination, and
// an eta-axis, directed from its origin to its apex.
// Calculate the xi and eta coordinates of the circumcenter.
xi = (yao * dx - xao * dy) * (2.0 * denominator);
eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
for (int i = 0; i < n; i++)
{
// Interpolate the vertex attributes.
vertex.attributes[i] = org.attributes[i]
+ xi * (dest.attributes[i] - org.attributes[i])
+ eta * (apex.attributes[i] - org.attributes[i]);
}
}
void CreateMap(VoronoiBase sv, float maxz, float yOffset)
{
Dictionary <int, TriangleNet.Geometry.Vertex> id2vert = new Dictionary <int, TriangleNet.Geometry.Vertex>();
List <TriangleNet.Geometry.Vertex> vertices = new List <TriangleNet.Geometry.Vertex>();
List <ISegment> segments = new List <ISegment>();
foreach (TriangleNet.Topology.DCEL.Vertex v in sv.Vertices)
{
TriangleNet.Geometry.Vertex new_v = new TriangleNet.Geometry.Vertex(v.x, v.y);
id2vert[v.id] = new_v;
vertices.Add(new_v);
}
foreach (Edge e in sv.Edges)
{
TriangleNet.Geometry.Vertex v1 = id2vert[e.P0];
TriangleNet.Geometry.Vertex v2 = id2vert[e.P1];
segments.Add(new Segment(v1, v2));
}
CreateMap(vertices, segments, maxz, yOffset);
}
/// <summary>
/// Case 1: edge origin lies inside the domain.
/// </summary>
private void HandleCase1(HalfEdge edge, TVertex v1, TVertex v2)
{
//int mark = GetBoundaryMark(v1);
// The infinite vertex.
var v = (Point)edge.twin.origin;
// The half-edge is the bisector of v1 and v2, so the projection onto the
// boundary segment is actually its midpoint.
v.x = (v1.x + v2.x) / 2.0;
v.y = (v1.y + v2.y) / 2.0;
// Close the cell connected to edge.
var gen = factory.CreateVertex(v1.x, v1.y);
var h1 = factory.CreateHalfEdge(edge.twin.origin, edge.face);
var h2 = factory.CreateHalfEdge(gen, edge.face);
edge.next = h1;
h1.next = h2;
h2.next = edge.face.edge;
gen.leaving = h2;
// Let the face edge point to the edge leaving at generator.
edge.face.edge = h2;
base.edges.Add(h1);
base.edges.Add(h2);
int count = base.edges.Count;
h1.id = count;
h2.id = count + 1;
gen.id = offset++;
base.vertices.Add(gen);
}
/// <summary>
/// Case 1: edge origin lies inside the domain.
/// </summary>
private void HandleCase1(HalfEdge edge, TVertex v1, TVertex v2)
{
//int mark = GetBoundaryMark(v1);
// The infinite vertex.
var v = (Point)edge.twin.origin;
// The half-edge is the bisector of v1 and v2, so the projection onto the
// boundary segment is actually its midpoint.
v.x = (v1.x + v2.x) / 2.0;
v.y = (v1.y + v2.y) / 2.0;
// Close the cell connected to edge.
var gen = factory.CreateVertex(v1.x, v1.y);
var h1 = factory.CreateHalfEdge(edge.twin.origin, edge.face);
var h2 = factory.CreateHalfEdge(gen, edge.face);
edge.next = h1;
h1.next = h2;
h2.next = edge.face.edge;
gen.leaving = h2;
// Let the face edge point to the edge leaving at generator.
edge.face.edge = h2;
base.edges.Add(h1);
base.edges.Add(h2);
int count = base.edges.Count;
h1.id = count;
h2.id = count + 1;
gen.id = offset++;
base.vertices.Add(gen);
}
/// <summary>
/// Set the origin of the segment that includes the subsegment.
/// </summary>
internal void SetSegOrg(Vertex vertex)
{
seg.vertices[2 + orient] = vertex;
}
/// <summary>
/// Set destination of a subsegment.
/// </summary>
internal void SetDest(Vertex vertex)
{
seg.vertices[1 - orient] = vertex;
}
/// <summary>
/// Set the origin or destination of a subsegment.
/// </summary>
internal void SetOrg(Vertex vertex)
{
seg.vertices[orient] = vertex;
}
/// <summary>
/// Case 2: edge origin lies outside the domain.
/// </summary>
private void HandleCase2(HalfEdge edge, TVertex v1, TVertex v2)
{
// The vertices of the infinite edge.
var p1 = (Point)edge.origin;
var p2 = (Point)edge.twin.origin;
// The two edges leaving p1, pointing into the mesh.
var e1 = edge.twin.next;
var e2 = e1.twin.next;
// Find the two intersections with boundary edge.
IntersectionHelper.IntersectSegments(v1, v2, e1.origin, e1.twin.origin, ref p2);
IntersectionHelper.IntersectSegments(v1, v2, e2.origin, e2.twin.origin, ref p1);
// The infinite edge will now lie on the boundary. Update pointers:
e1.twin.next = edge.twin;
edge.twin.next = e2;
edge.twin.face = e2.face;
e1.origin = edge.twin.origin;
edge.twin.twin = null;
edge.twin = null;
// Close the cell.
var gen = factory.CreateVertex(v1.x, v1.y);
var he = factory.CreateHalfEdge(gen, edge.face);
edge.next = he;
he.next = edge.face.edge;
// Let the face edge point to the edge leaving at generator.
edge.face.edge = he;
base.edges.Add(he);
he.id = base.edges.Count;
gen.id = offset++;
base.vertices.Add(gen);
}
/// <summary>
/// Set Destination
/// </summary>
internal void SetDest(Vertex v)
{
tri.vertices[minus1Mod3[orient]] = v;
}
/// <summary>
/// Finds the star of a given point.
/// </summary>
/// <param name="badotri"></param>
/// <param name="p"></param>
/// <param name="q"></param>
/// <param name="r"></param>
/// <param name="whichPoint"></param>
/// <param name="points">List of points on the star of the given point.</param>
/// <returns>Number of points on the star of the given point.</returns>
private int GetStarPoints(Otri badotri, Vertex p, Vertex q, Vertex r,
int whichPoint, ref double[] points)
{
Otri neighotri = default(Otri); // for return value of the function
Otri tempotri; // for temporary usage
double first_x = 0, first_y = 0; // keeps the first point to be considered
double second_x = 0, second_y = 0; // for determining the edge we will begin
double third_x = 0, third_y = 0; // termination
double[] returnPoint = new double[2]; // for keeping the returned point
int numvertices = 0; // for keeping number of surrounding vertices
// first determine which point to be used to find its neighbor triangles
switch (whichPoint)
{
case 1:
first_x = p.x; // point at the center
first_y = p.y;
second_x = r.x; // second vertex of first edge to consider
second_y = r.y;
third_x = q.x; // for terminating the search
third_y = q.y;
break;
case 2:
first_x = q.x; // point at the center
first_y = q.y;
second_x = p.x; // second vertex of first edge to consider
second_y = p.y;
third_x = r.x; // for terminating the search
third_y = r.y;
break;
case 3:
first_x = r.x; // point at the center
first_y = r.y;
second_x = q.x; // second vertex of first edge to consider
second_y = q.y;
third_x = p.x; // for terminating the search
third_y = p.y;
break;
}
tempotri = badotri;
// add first point as the end of first edge
points[numvertices] = second_x;
numvertices++;
points[numvertices] = second_y;
numvertices++;
// assign as dummy value
returnPoint[0] = second_x; returnPoint[1] = second_y;
// until we reach the third point of the beginning triangle
do
{
// find the neighbor's third point where it is incident to given edge
if (!GetNeighborsVertex(tempotri, first_x, first_y, second_x, second_y, ref returnPoint, ref neighotri))
{
// go to next triangle
tempotri = neighotri;
// now the second point is the neighbor's third vertex
second_x = returnPoint[0];
second_y = returnPoint[1];
// add a new point to the list of surrounding points
points[numvertices] = returnPoint[0];
numvertices++;
points[numvertices] = returnPoint[1];
numvertices++;
}
else
{
numvertices = 0;
break;
}
} while (!((Math.Abs(returnPoint[0] - third_x) <= EPS) &&
(Math.Abs(returnPoint[1] - third_y) <= EPS)));
return numvertices / 2;
}
/// <summary>
/// Add a vertex to the polygon.
/// </summary>
/// <param name="vertex">The vertex to insert.</param>
public void Add(Vertex vertex)
{
this.points.Add(vertex);
}
private void OnDrawGizmos()
{
if (Rooms == null)
{
return;
}
if (ShowBestPointsOnly)
{
foreach (var point in bestRooms)
{
Gizmos.color = Color.black;
Gizmos.DrawWireCube(point.Position, point.Size);
}
}
else
{
foreach (var point in Rooms)
{
Gizmos.color = Color.black;
Gizmos.color = new Color(point.weight / 20, Gizmos.color.g, Gizmos.color.b, Gizmos.color.a);
Gizmos.DrawWireCube(point.Position, point.Size);
//Handles.Label(point.Position, point.Position.ToString());
}
}
if (mesh == null)
{
return;
}
if (!showConections)
{
Gizmos.color = Color.green;
foreach (var edge in mesh.Edges)
{
TriangleNet.Geometry.Vertex v0 = mesh.vertices[edge.P0];
TriangleNet.Geometry.Vertex v1 = mesh.vertices[edge.P1];
Vector3 p0 = new Vector3((float)v0.x, 0.0f, (float)v0.y);
Vector3 p1 = new Vector3((float)v1.x, 0.0f, (float)v1.y);
Gizmos.DrawLine(p0, p1);
}
}
if (connections == null)
{
return;
}
if (showConections)
{
foreach (var connection in connections)
{
Gizmos.color = Color.magenta;
Gizmos.DrawLine(connection.Room1.Position, connection.Room2.Position);
}
}
if (showRoomConections)
{
foreach (var room in bestRooms)
{
Gizmos.color = Color.cyan;
foreach (var connection in room.connections)
{
Gizmos.DrawLine(room.Position, connection.Position);
}
}
}
}
public override List <SubdividableEdgeLoop <CityEdge> > GetChildren(SubdividableEdgeLoop <CityEdge> parent)
{
Vector2[] parentPoints = parent.GetPoints();
Polygon parentPoly = parent.GetPolygon();
//generate points of interest
List <RoadDestination> pointsOfInterest = new List <RoadDestination>();
Vector2 centroid = parent.GetCenter();
//parent.EnumerateEdges((EdgeLoopEdge edge) =>
//{
// pointsOfInterest.Add(new RoadDestination(Vector2.Lerp(edge.a.pt, edge.b.pt, Random.Range(0.2f, 0.8f)), 1, false, true));
//});
Rect bounds = parent.GetBounds();
bounds.width = bounds.width * 2;
bounds.height = bounds.height * 2;
int potentialRoadPointsRt = Mathf.CeilToInt(Mathf.Sqrt(potentialRoadPoints));
float approxDiameter = Mathf.Sqrt(parentPoly.area);
float minimumPerimeterDistance = approxDiameter / 4f;
for (int x = 0; x < potentialRoadPointsRt; x++)
{
for (int y = 0; y < potentialRoadPointsRt; y++)
{
Vector2 point = new Vector2((x / (float)potentialRoadPointsRt) * bounds.width + bounds.xMin,
(y / (float)potentialRoadPointsRt) * bounds.height + bounds.yMin);
float distBtwnPts = (bounds.width + bounds.height) / (potentialRoadPoints * 2);
point = point + new Vector2(Random.Range(-1f, 1f), Random.Range(-1, 1f)) * distBtwnPts * 3f;
if (parentPoly.ContainsPoint(point)) // && parent.DistToPerimeter(point) > minimumPerimeterDistance)
{
pointsOfInterest.Add(new RoadDestination(point, 0, false, false));
}
}
}
pointsOfInterest.Add(new RoadDestination(bounds.center + new Vector2(bounds.width * 100, bounds.height * 100), 0, false, false));
pointsOfInterest.Add(new RoadDestination(bounds.center + new Vector2(bounds.width * 100, -bounds.height * 100), 0, false, false));
pointsOfInterest.Add(new RoadDestination(bounds.center + new Vector2(-bounds.width * 100, -bounds.height * 100), 0, false, false));
pointsOfInterest.Add(new RoadDestination(bounds.center + new Vector2(-bounds.width * 100, bounds.height * 100), 0, false, false));
//triangulate points of interest to get potential road segments
TriangleNet.Geometry.Polygon polygon = new TriangleNet.Geometry.Polygon();
Dictionary <TriangleNet.Geometry.Vertex, RoadDestination> vertexDestMap = new Dictionary <TriangleNet.Geometry.Vertex, RoadDestination>();
foreach (RoadDestination dest in pointsOfInterest)
{
TriangleNet.Geometry.Vertex vert = new TriangleNet.Geometry.Vertex(dest.point.x, dest.point.y);
vertexDestMap.Add(vert, dest);
polygon.Add(vert);
}
TriangleNet.Meshing.ConstraintOptions options =
new TriangleNet.Meshing.ConstraintOptions()
{
ConformingDelaunay = true
};
TriangleNet.Meshing.GenericMesher mesher = new TriangleNet.Meshing.GenericMesher();
TriangleNet.Meshing.IMesh mesh = mesher.Triangulate(polygon);
TriangleNet.Voronoi.StandardVoronoi voronoi = new TriangleNet.Voronoi.StandardVoronoi((TriangleNet.Mesh)mesh);
IEnumerable <TriangleNet.Geometry.IEdge> voronoiEdges = voronoi.Edges;
List <TriangleNet.Topology.DCEL.Vertex> voronoiVerts = voronoi.Vertices;
List <DividingEdge> dividingEdges = new List <DividingEdge>();
ILinkedGraphEdgeFactory <CityEdge> factory = new CityEdgeFactory();
foreach (TriangleNet.Geometry.IEdge edge in voronoiEdges)
{
Vector2 a = new Vector2((float)voronoiVerts[edge.P0].X, (float)voronoiVerts[edge.P0].Y);
Vector2 b = new Vector2((float)voronoiVerts[edge.P1].X, (float)voronoiVerts[edge.P1].Y);
dividingEdges.Add(new DividingEdge(a, b, factory, factoryParams));
}
//get vertices as list
//ICollection<TriangleNet.Geometry.Vertex> vertices = mesh.Vertices;
//TriangleNet.Geometry.Vertex[] vertexList = new TriangleNet.Geometry.Vertex[vertices.Count];
//vertices.CopyTo(vertexList, 0);
//IEnumerable<TriangleNet.Geometry.Edge> meshEdges = mesh.Edges;
//build a list of dividing edges and pass it to the child collector
//foreach (TriangleNet.Geometry.Edge edge in meshEdges) {
// //if (vertConnections[edge.P0] > 4)
// //{
// // vertConnections[edge.P0]--;
// // continue;
// //}
// //if (vertConnections[edge.P1] > 4)
// //{
// // vertConnections[edge.P1]--;
// // continue;
// //}
// Vector2 a = new Vector2((float)vertexList[edge.P0].X, (float)vertexList[edge.P0].Y);
// Vector2 b = new Vector2((float)vertexList[edge.P1].X, (float)vertexList[edge.P1].Y);
// dividingEdges.Add(new DividingEdge(a, b, factory, CityEdgeType.LandPath));
//}
return(CollectChildren(parent, dividingEdges));
}
/// <summary>
/// Split all the encroached subsegments.
/// </summary>
/// <param name="triflaws">A flag that specifies whether one should take
/// note of new bad triangles that result from inserting vertices to repair
/// encroached subsegments.</param>
/// <remarks>
/// Each encroached subsegment is repaired by splitting it - inserting a
/// vertex at or near its midpoint. Newly inserted vertices may encroach
/// upon other subsegments; these are also repaired.
/// </remarks>
private void SplitEncSegs(bool triflaws)
{
Otri enctri = default(Otri);
Otri testtri = default(Otri);
Osub testsh = default(Osub);
Osub currentenc = default(Osub);
BadSubseg seg;
Vertex eorg, edest, eapex;
Vertex newvertex;
InsertVertexResult success;
double segmentlength, nearestpoweroftwo;
double split;
double multiplier, divisor;
bool acuteorg, acuteorg2, acutedest, acutedest2;
// Note that steinerleft == -1 if an unlimited number
// of Steiner points is allowed.
while (badsubsegs.Count > 0)
{
if (mesh.steinerleft == 0)
{
break;
}
seg = badsubsegs.Dequeue();
currentenc = seg.subseg;
eorg = currentenc.Org();
edest = currentenc.Dest();
// Make sure that this segment is still the same segment it was
// when it was determined to be encroached. If the segment was
// enqueued multiple times (because several newly inserted
// vertices encroached it), it may have already been split.
if (!Osub.IsDead(currentenc.seg) && (eorg == seg.org) && (edest == seg.dest))
{
// To decide where to split a segment, we need to know if the
// segment shares an endpoint with an adjacent segment.
// The concern is that, if we simply split every encroached
// segment in its center, two adjacent segments with a small
// angle between them might lead to an infinite loop; each
// vertex added to split one segment will encroach upon the
// other segment, which must then be split with a vertex that
// will encroach upon the first segment, and so on forever.
// To avoid this, imagine a set of concentric circles, whose
// radii are powers of two, about each segment endpoint.
// These concentric circles determine where the segment is
// split. (If both endpoints are shared with adjacent
// segments, split the segment in the middle, and apply the
// concentric circles for later splittings.)
// Is the origin shared with another segment?
currentenc.Pivot(ref enctri);
enctri.Lnext(ref testtri);
testtri.Pivot(ref testsh);
acuteorg = testsh.seg.hash != Mesh.DUMMY;
// Is the destination shared with another segment?
testtri.Lnext();
testtri.Pivot(ref testsh);
acutedest = testsh.seg.hash != Mesh.DUMMY;
// If we're using Chew's algorithm (rather than Ruppert's)
// to define encroachment, delete free vertices from the
// subsegment's diametral circle.
if (!behavior.ConformingDelaunay && !acuteorg && !acutedest)
{
eapex = enctri.Apex();
while ((eapex.type == VertexType.FreeVertex) &&
((eorg.x - eapex.x) * (edest.x - eapex.x) +
(eorg.y - eapex.y) * (edest.y - eapex.y) < 0.0))
{
mesh.DeleteVertex(ref testtri);
currentenc.Pivot(ref enctri);
eapex = enctri.Apex();
enctri.Lprev(ref testtri);
}
}
// Now, check the other side of the segment, if there's a triangle there.
enctri.Sym(ref testtri);
if (testtri.tri.id != Mesh.DUMMY)
{
// Is the destination shared with another segment?
testtri.Lnext();
testtri.Pivot(ref testsh);
acutedest2 = testsh.seg.hash != Mesh.DUMMY;
acutedest = acutedest || acutedest2;
// Is the origin shared with another segment?
testtri.Lnext();
testtri.Pivot(ref testsh);
acuteorg2 = testsh.seg.hash != Mesh.DUMMY;
acuteorg = acuteorg || acuteorg2;
// Delete free vertices from the subsegment's diametral circle.
if (!behavior.ConformingDelaunay && !acuteorg2 && !acutedest2)
{
eapex = testtri.Org();
while ((eapex.type == VertexType.FreeVertex) &&
((eorg.x - eapex.x) * (edest.x - eapex.x) +
(eorg.y - eapex.y) * (edest.y - eapex.y) < 0.0))
{
mesh.DeleteVertex(ref testtri);
enctri.Sym(ref testtri);
eapex = testtri.Apex();
testtri.Lprev();
}
}
}
// Use the concentric circles if exactly one endpoint is shared
// with another adjacent segment.
if (acuteorg || acutedest)
{
segmentlength = Math.Sqrt((edest.x - eorg.x) * (edest.x - eorg.x) +
(edest.y - eorg.y) * (edest.y - eorg.y));
// Find the power of two that most evenly splits the segment.
// The worst case is a 2:1 ratio between subsegment lengths.
nearestpoweroftwo = 1.0;
while (segmentlength > 3.0 * nearestpoweroftwo)
{
nearestpoweroftwo *= 2.0;
}
while (segmentlength < 1.5 * nearestpoweroftwo)
{
nearestpoweroftwo *= 0.5;
}
// Where do we split the segment?
split = nearestpoweroftwo / segmentlength;
if (acutedest)
{
split = 1.0 - split;
}
}
else
{
// If we're not worried about adjacent segments, split
// this segment in the middle.
split = 0.5;
}
// Create the new vertex (interpolate coordinates).
newvertex = new Vertex(
eorg.x + split * (edest.x - eorg.x),
eorg.y + split * (edest.y - eorg.y),
currentenc.seg.boundary
#if USE_ATTRIBS
, mesh.nextras
#endif
);
newvertex.type = VertexType.SegmentVertex;
newvertex.hash = mesh.hash_vtx++;
newvertex.id = newvertex.hash;
mesh.vertices.Add(newvertex.hash, newvertex);
#if USE_ATTRIBS
// Interpolate attributes.
for (int i = 0; i < mesh.nextras; i++)
{
newvertex.attributes[i] = eorg.attributes[i]
+ split * (edest.attributes[i] - eorg.attributes[i]);
}
#endif
if (!Behavior.NoExact)
{
// Roundoff in the above calculation may yield a 'newvertex'
// that is not precisely collinear with 'eorg' and 'edest'.
// Improve collinearity by one step of iterative refinement.
multiplier = predicates.CounterClockwise(eorg, edest, newvertex);
divisor = ((eorg.x - edest.x) * (eorg.x - edest.x) +
(eorg.y - edest.y) * (eorg.y - edest.y));
if ((multiplier != 0.0) && (divisor != 0.0))
{
multiplier = multiplier / divisor;
// Watch out for NANs.
if (!double.IsNaN(multiplier))
{
newvertex.x += multiplier * (edest.y - eorg.y);
newvertex.y += multiplier * (eorg.x - edest.x);
}
}
}
// Check whether the new vertex lies on an endpoint.
if (((newvertex.x == eorg.x) && (newvertex.y == eorg.y)) ||
((newvertex.x == edest.x) && (newvertex.y == edest.y)))
{
logger.Error("Ran out of precision: I attempted to split a"
+ " segment to a smaller size than can be accommodated by"
+ " the finite precision of floating point arithmetic.",
"Quality.SplitEncSegs()");
throw new Exception("Ran out of precision");
}
// Insert the splitting vertex. This should always succeed.
success = mesh.InsertVertex(newvertex, ref enctri, ref currentenc, true, triflaws);
if ((success != InsertVertexResult.Successful) && (success != InsertVertexResult.Encroaching))
{
logger.Error("Failure to split a segment.", "Quality.SplitEncSegs()");
throw new Exception("Failure to split a segment.");
}
if (mesh.steinerleft > 0)
{
mesh.steinerleft--;
}
// Check the two new subsegments to see if they're encroached.
CheckSeg4Encroach(ref currentenc);
currentenc.Next();
CheckSeg4Encroach(ref currentenc);
}
// Set subsegment's origin to NULL. This makes it possible to detect dead
// badsubsegs when traversing the list of all badsubsegs.
seg.org = null;
}
}
/// <summary>
/// Find a new location for a Steiner point.
/// </summary>
/// <param name="torg"></param>
/// <param name="tdest"></param>
/// <param name="tapex"></param>
/// <param name="circumcenter"></param>
/// <param name="xi"></param>
/// <param name="eta"></param>
/// <param name="offcenter"></param>
/// <param name="badotri"></param>
private Point FindNewLocationWithoutMaxAngle(Vertex torg, Vertex tdest, Vertex tapex,
ref double xi, ref double eta, bool offcenter, Otri badotri)
{
double offconstant = behavior.offconstant;
// for calculating the distances of the edges
double xdo, ydo, xao, yao, xda, yda;
double dodist, aodist, dadist;
// for exact calculation
double denominator;
double dx, dy, dxoff, dyoff;
////////////////////////////// HALE'S VARIABLES //////////////////////////////
// keeps the difference of coordinates edge
double xShortestEdge = 0, yShortestEdge = 0, xMiddleEdge, yMiddleEdge, xLongestEdge, yLongestEdge;
// keeps the square of edge lengths
double shortestEdgeDist = 0, middleEdgeDist = 0, longestEdgeDist = 0;
// keeps the vertices according to the angle incident to that vertex in a triangle
Point smallestAngleCorner, middleAngleCorner, largestAngleCorner;
// keeps the type of orientation if the triangle
int orientation = 0;
// keeps the coordinates of circumcenter of itself and neighbor triangle circumcenter
Point myCircumcenter, neighborCircumcenter;
// keeps if bad triangle is almost good or not
int almostGood = 0;
// keeps the cosine of the largest angle
double cosMaxAngle;
bool isObtuse; // 1: obtuse 0: nonobtuse
// keeps the radius of petal
double petalRadius;
// for calculating petal center
double xPetalCtr_1, yPetalCtr_1, xPetalCtr_2, yPetalCtr_2, xPetalCtr, yPetalCtr, xMidOfShortestEdge, yMidOfShortestEdge;
double dxcenter1, dycenter1, dxcenter2, dycenter2;
// for finding neighbor
Otri neighborotri = default(Otri);
double[] thirdPoint = new double[2];
//int neighborNotFound = -1;
bool neighborNotFound;
// for keeping the vertices of the neighbor triangle
Vertex neighborvertex_1;
Vertex neighborvertex_2;
Vertex neighborvertex_3;
// dummy variables
double xi_tmp = 0, eta_tmp = 0;
//vertex thirdVertex;
// for petal intersection
double vector_x, vector_y, xMidOfLongestEdge, yMidOfLongestEdge, inter_x, inter_y;
double[] p = new double[5], voronoiOrInter = new double[4];
bool isCorrect;
// for vector calculations in perturbation
double ax, ay, d;
double pertConst = 0.06; // perturbation constant
double lengthConst = 1; // used at comparing circumcenter's distance to proposed point's distance
double justAcute = 1; // used for making the program working for one direction only
// for smoothing
int relocated = 0;// used to differentiate between calling the deletevertex and just proposing a steiner point
double[] newloc = new double[2]; // new location suggested by smoothing
double origin_x = 0, origin_y = 0; // for keeping torg safe
Otri delotri; // keeping the original orientation for relocation process
// keeps the first and second direction suggested points
double dxFirstSuggestion, dyFirstSuggestion, dxSecondSuggestion, dySecondSuggestion;
// second direction variables
double xMidOfMiddleEdge, yMidOfMiddleEdge;
////////////////////////////// END OF HALE'S VARIABLES //////////////////////////////
Statistic.CircumcenterCount++;
// Compute the circumcenter of the triangle.
xdo = tdest.x - torg.x;
ydo = tdest.y - torg.y;
xao = tapex.x - torg.x;
yao = tapex.y - torg.y;
xda = tapex.x - tdest.x;
yda = tapex.y - tdest.y;
// keeps the square of the distances
dodist = xdo * xdo + ydo * ydo;
aodist = xao * xao + yao * yao;
dadist = (tdest.x - tapex.x) * (tdest.x - tapex.x) +
(tdest.y - tapex.y) * (tdest.y - tapex.y);
// checking if the user wanted exact arithmetic or not
if (Behavior.NoExact)
{
denominator = 0.5 / (xdo * yao - xao * ydo);
}
else
{
// Use the counterclockwise() routine to ensure a positive (and
// reasonably accurate) result, avoiding any possibility of
// division by zero.
denominator = 0.5 / predicates.CounterClockwise(tdest, tapex, torg);
// Don't count the above as an orientation test.
Statistic.CounterClockwiseCount--;
}
// calculate the circumcenter in terms of distance to origin point
dx = (yao * dodist - ydo * aodist) * denominator;
dy = (xdo * aodist - xao * dodist) * denominator;
// for debugging and for keeping circumcenter to use later
// coordinate value of the circumcenter
myCircumcenter = new Point(torg.x + dx, torg.y + dy);
delotri = badotri; // save for later
///////////////// FINDING THE ORIENTATION OF TRIANGLE //////////////////
// Find the (squared) length of the triangle's shortest edge. This
// serves as a conservative estimate of the insertion radius of the
// circumcenter's parent. The estimate is used to ensure that
// the algorithm terminates even if very small angles appear in
// the input PSLG.
// find the orientation of the triangle, basically shortest and longest edges
orientation = LongestShortestEdge(aodist, dadist, dodist);
//printf("org: (%f,%f), dest: (%f,%f), apex: (%f,%f)\n",torg[0],torg[1],tdest[0],tdest[1],tapex[0],tapex[1]);
/////////////////////////////////////////////////////////////////////////////////////////////
// 123: shortest: aodist // 213: shortest: dadist // 312: shortest: dodist //
// middle: dadist // middle: aodist // middle: aodist //
// longest: dodist // longest: dodist // longest: dadist //
// 132: shortest: aodist // 231: shortest: dadist // 321: shortest: dodist //
// middle: dodist // middle: dodist // middle: dadist //
// longest: dadist // longest: aodist // longest: aodist //
/////////////////////////////////////////////////////////////////////////////////////////////
switch (orientation)
{
case 123: // assign necessary information
/// smallest angle corner: dest
/// largest angle corner: apex
xShortestEdge = xao; yShortestEdge = yao;
xMiddleEdge = xda; yMiddleEdge = yda;
xLongestEdge = xdo; yLongestEdge = ydo;
shortestEdgeDist = aodist;
middleEdgeDist = dadist;
longestEdgeDist = dodist;
smallestAngleCorner = tdest;
middleAngleCorner = torg;
largestAngleCorner = tapex;
break;
case 132: // assign necessary information
/// smallest angle corner: dest
/// largest angle corner: org
xShortestEdge = xao; yShortestEdge = yao;
xMiddleEdge = xdo; yMiddleEdge = ydo;
xLongestEdge = xda; yLongestEdge = yda;
shortestEdgeDist = aodist;
middleEdgeDist = dodist;
longestEdgeDist = dadist;
smallestAngleCorner = tdest;
middleAngleCorner = tapex;
largestAngleCorner = torg;
break;
case 213: // assign necessary information
/// smallest angle corner: org
/// largest angle corner: apex
xShortestEdge = xda; yShortestEdge = yda;
xMiddleEdge = xao; yMiddleEdge = yao;
xLongestEdge = xdo; yLongestEdge = ydo;
shortestEdgeDist = dadist;
middleEdgeDist = aodist;
longestEdgeDist = dodist;
smallestAngleCorner = torg;
middleAngleCorner = tdest;
largestAngleCorner = tapex;
break;
case 231: // assign necessary information
/// smallest angle corner: org
/// largest angle corner: dest
xShortestEdge = xda; yShortestEdge = yda;
xMiddleEdge = xdo; yMiddleEdge = ydo;
xLongestEdge = xao; yLongestEdge = yao;
shortestEdgeDist = dadist;
middleEdgeDist = dodist;
longestEdgeDist = aodist;
smallestAngleCorner = torg;
middleAngleCorner = tapex;
largestAngleCorner = tdest;
break;
case 312: // assign necessary information
/// smallest angle corner: apex
/// largest angle corner: org
xShortestEdge = xdo; yShortestEdge = ydo;
xMiddleEdge = xao; yMiddleEdge = yao;
xLongestEdge = xda; yLongestEdge = yda;
shortestEdgeDist = dodist;
middleEdgeDist = aodist;
longestEdgeDist = dadist;
smallestAngleCorner = tapex;
middleAngleCorner = tdest;
largestAngleCorner = torg;
break;
case 321: // assign necessary information
default: // TODO: is this safe?
/// smallest angle corner: apex
/// largest angle corner: dest
xShortestEdge = xdo; yShortestEdge = ydo;
xMiddleEdge = xda; yMiddleEdge = yda;
xLongestEdge = xao; yLongestEdge = yao;
shortestEdgeDist = dodist;
middleEdgeDist = dadist;
longestEdgeDist = aodist;
smallestAngleCorner = tapex;
middleAngleCorner = torg;
largestAngleCorner = tdest;
break;
}// end of switch
// check for offcenter condition
if (offcenter && (offconstant > 0.0))
{
// origin has the smallest angle
if (orientation == 213 || orientation == 231)
{
// Find the position of the off-center, as described by Alper Ungor.
dxoff = 0.5 * xShortestEdge - offconstant * yShortestEdge;
dyoff = 0.5 * yShortestEdge + offconstant * xShortestEdge;
// If the off-center is closer to destination than the
// circumcenter, use the off-center instead.
/// doubleLY BAD CASE ///
if (dxoff * dxoff + dyoff * dyoff <
(dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo))
{
dx = xdo + dxoff;
dy = ydo + dyoff;
}
/// ALMOST GOOD CASE ///
else
{
almostGood = 1;
}
// destination has the smallest angle
}
else if (orientation == 123 || orientation == 132)
{
// Find the position of the off-center, as described by Alper Ungor.
dxoff = 0.5 * xShortestEdge + offconstant * yShortestEdge;
dyoff = 0.5 * yShortestEdge - offconstant * xShortestEdge;
// If the off-center is closer to the origin than the
// circumcenter, use the off-center instead.
/// doubleLY BAD CASE ///
if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy)
{
dx = dxoff;
dy = dyoff;
}
/// ALMOST GOOD CASE ///
else
{
almostGood = 1;
}
// apex has the smallest angle
}
else
{//orientation == 312 || orientation == 321
// Find the position of the off-center, as described by Alper Ungor.
dxoff = 0.5 * xShortestEdge - offconstant * yShortestEdge;
dyoff = 0.5 * yShortestEdge + offconstant * xShortestEdge;
// If the off-center is closer to the origin than the
// circumcenter, use the off-center instead.
/// doubleLY BAD CASE ///
if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy)
{
dx = dxoff;
dy = dyoff;
}
/// ALMOST GOOD CASE ///
else
{
almostGood = 1;
}
}
}
// if the bad triangle is almost good, apply our approach
if (almostGood == 1)
{
/// calculate cosine of largest angle ///
cosMaxAngle = (middleEdgeDist + shortestEdgeDist - longestEdgeDist) / (2 * Math.Sqrt(middleEdgeDist) * Math.Sqrt(shortestEdgeDist));
if (cosMaxAngle < 0.0)
{
// obtuse
isObtuse = true;
}
else if (Math.Abs(cosMaxAngle - 0.0) <= EPS)
{
// right triangle (largest angle is 90 degrees)
isObtuse = true;
}
else
{
// nonobtuse
isObtuse = false;
}
/// RELOCATION (LOCAL SMOOTHING) ///
/// check for possible relocation of one of triangle's points ///
relocated = DoSmoothing(delotri, torg, tdest, tapex, ref newloc);
/// if relocation is possible, delete that vertex and insert a vertex at the new location ///
if (relocated > 0)
{
Statistic.RelocationCount++;
dx = newloc[0] - torg.x;
dy = newloc[1] - torg.y;
origin_x = torg.x; // keep for later use
origin_y = torg.y;
switch (relocated)
{
case 1:
//printf("Relocate: (%f,%f)\n", torg[0],torg[1]);
mesh.DeleteVertex(ref delotri);
break;
case 2:
//printf("Relocate: (%f,%f)\n", tdest[0],tdest[1]);
delotri.Lnext();
mesh.DeleteVertex(ref delotri);
break;
case 3:
//printf("Relocate: (%f,%f)\n", tapex[0],tapex[1]);
delotri.Lprev();
mesh.DeleteVertex(ref delotri);
break;
}
}
else
{
// calculate radius of the petal according to angle constraint
// first find the visible region, PETAL
// find the center of the circle and radius
petalRadius = Math.Sqrt(shortestEdgeDist) / (2 * Math.Sin(behavior.MinAngle * Math.PI / 180.0));
/// compute two possible centers of the petal ///
// finding the center
// first find the middle point of smallest edge
xMidOfShortestEdge = (middleAngleCorner.x + largestAngleCorner.x) / 2.0;
yMidOfShortestEdge = (middleAngleCorner.y + largestAngleCorner.y) / 2.0;
// two possible centers
xPetalCtr_1 = xMidOfShortestEdge + Math.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (middleAngleCorner.y -
largestAngleCorner.y) / Math.Sqrt(shortestEdgeDist);
yPetalCtr_1 = yMidOfShortestEdge + Math.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (largestAngleCorner.x -
middleAngleCorner.x) / Math.Sqrt(shortestEdgeDist);
xPetalCtr_2 = xMidOfShortestEdge - Math.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (middleAngleCorner.y -
largestAngleCorner.y) / Math.Sqrt(shortestEdgeDist);
yPetalCtr_2 = yMidOfShortestEdge - Math.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (largestAngleCorner.x -
middleAngleCorner.x) / Math.Sqrt(shortestEdgeDist);
// find the correct circle since there will be two possible circles
// calculate the distance to smallest angle corner
dxcenter1 = (xPetalCtr_1 - smallestAngleCorner.x) * (xPetalCtr_1 - smallestAngleCorner.x);
dycenter1 = (yPetalCtr_1 - smallestAngleCorner.y) * (yPetalCtr_1 - smallestAngleCorner.y);
dxcenter2 = (xPetalCtr_2 - smallestAngleCorner.x) * (xPetalCtr_2 - smallestAngleCorner.x);
dycenter2 = (yPetalCtr_2 - smallestAngleCorner.y) * (yPetalCtr_2 - smallestAngleCorner.y);
// whichever is closer to smallest angle corner, it must be the center
if (dxcenter1 + dycenter1 <= dxcenter2 + dycenter2)
{
xPetalCtr = xPetalCtr_1; yPetalCtr = yPetalCtr_1;
}
else
{
xPetalCtr = xPetalCtr_2; yPetalCtr = yPetalCtr_2;
}
/// find the third point of the neighbor triangle ///
neighborNotFound = GetNeighborsVertex(badotri, middleAngleCorner.x, middleAngleCorner.y,
smallestAngleCorner.x, smallestAngleCorner.y, ref thirdPoint, ref neighborotri);
/// find the circumcenter of the neighbor triangle ///
dxFirstSuggestion = dx; // if we cannot find any appropriate suggestion, we use circumcenter
dyFirstSuggestion = dy;
// if there is a neighbor triangle
if (!neighborNotFound)
{
neighborvertex_1 = neighborotri.Org();
neighborvertex_2 = neighborotri.Dest();
neighborvertex_3 = neighborotri.Apex();
// now calculate neighbor's circumcenter which is the voronoi site
neighborCircumcenter = predicates.FindCircumcenter(neighborvertex_1, neighborvertex_2, neighborvertex_3,
ref xi_tmp, ref eta_tmp);
/// compute petal and Voronoi edge intersection ///
// in order to avoid degenerate cases, we need to do a vector based calculation for line
vector_x = (middleAngleCorner.y - smallestAngleCorner.y);//(-y, x)
vector_y = smallestAngleCorner.x - middleAngleCorner.x;
vector_x = myCircumcenter.x + vector_x;
vector_y = myCircumcenter.y + vector_y;
// by intersecting bisectors you will end up with the one you want to walk on
// then this line and circle should be intersected
CircleLineIntersection(myCircumcenter.x, myCircumcenter.y, vector_x, vector_y,
xPetalCtr, yPetalCtr, petalRadius, ref p);
/// choose the correct intersection point ///
// calculate middle point of the longest edge(bisector)
xMidOfLongestEdge = (middleAngleCorner.x + smallestAngleCorner.x) / 2.0;
yMidOfLongestEdge = (middleAngleCorner.y + smallestAngleCorner.y) / 2.0;
// we need to find correct intersection point, since line intersects circle twice
isCorrect = ChooseCorrectPoint(xMidOfLongestEdge, yMidOfLongestEdge, p[3], p[4],
myCircumcenter.x, myCircumcenter.y, isObtuse);
// make sure which point is the correct one to be considered
if (isCorrect)
{
inter_x = p[3];
inter_y = p[4];
}
else
{
inter_x = p[1];
inter_y = p[2];
}
/// check if there is a Voronoi vertex between before intersection ///
// check if the voronoi vertex is between the intersection and circumcenter
PointBetweenPoints(inter_x, inter_y, myCircumcenter.x, myCircumcenter.y,
neighborCircumcenter.x, neighborCircumcenter.y, ref voronoiOrInter);
/// determine the point to be suggested ///
if (p[0] > 0.0)
{ // there is at least one intersection point
// if it is between circumcenter and intersection
// if it returns 1.0 this means we have a voronoi vertex within feasible region
if (Math.Abs(voronoiOrInter[0] - 1.0) <= EPS)
{
if (IsBadTriangleAngle(middleAngleCorner.x, middleAngleCorner.y, largestAngleCorner.x, largestAngleCorner.y, neighborCircumcenter.x, neighborCircumcenter.y))
{
// go back to circumcenter
dxFirstSuggestion = dx;
dyFirstSuggestion = dy;
}
else
{ // we are not creating a bad triangle
// neighbor's circumcenter is suggested
dxFirstSuggestion = voronoiOrInter[2] - torg.x;
dyFirstSuggestion = voronoiOrInter[3] - torg.y;
}
}
else
{ // there is no voronoi vertex between intersection point and circumcenter
if (IsBadTriangleAngle(largestAngleCorner.x, largestAngleCorner.y, middleAngleCorner.x, middleAngleCorner.y, inter_x, inter_y))
{
// if it is inside feasible region, then insert v2
// apply perturbation
// find the distance between circumcenter and intersection point
d = Math.Sqrt((inter_x - myCircumcenter.x) * (inter_x - myCircumcenter.x) +
(inter_y - myCircumcenter.y) * (inter_y - myCircumcenter.y));
// then find the vector going from intersection point to circumcenter
ax = myCircumcenter.x - inter_x;
ay = myCircumcenter.y - inter_y;
ax = ax / d;
ay = ay / d;
// now calculate the new intersection point which is perturbated towards the circumcenter
inter_x = inter_x + ax * pertConst * Math.Sqrt(shortestEdgeDist);
inter_y = inter_y + ay * pertConst * Math.Sqrt(shortestEdgeDist);
if (IsBadTriangleAngle(middleAngleCorner.x, middleAngleCorner.y, largestAngleCorner.x, largestAngleCorner.y, inter_x, inter_y))
{
// go back to circumcenter
dxFirstSuggestion = dx;
dyFirstSuggestion = dy;
}
else
{
// intersection point is suggested
dxFirstSuggestion = inter_x - torg.x;
dyFirstSuggestion = inter_y - torg.y;
}
}
else
{
// intersection point is suggested
dxFirstSuggestion = inter_x - torg.x;
dyFirstSuggestion = inter_y - torg.y;
}
}
/// if it is an acute triangle, check if it is a good enough location ///
// for acute triangle case, we need to check if it is ok to use either of them
if ((smallestAngleCorner.x - myCircumcenter.x) * (smallestAngleCorner.x - myCircumcenter.x) +
(smallestAngleCorner.y - myCircumcenter.y) * (smallestAngleCorner.y - myCircumcenter.y) >
lengthConst * ((smallestAngleCorner.x - (dxFirstSuggestion + torg.x)) *
(smallestAngleCorner.x - (dxFirstSuggestion + torg.x)) +
(smallestAngleCorner.y - (dyFirstSuggestion + torg.y)) *
(smallestAngleCorner.y - (dyFirstSuggestion + torg.y))))
{
// use circumcenter
dxFirstSuggestion = dx;
dyFirstSuggestion = dy;
}// else we stick to what we have found
}// intersection point
}// if it is on the boundary, meaning no neighbor triangle in this direction, try other direction
/// DO THE SAME THING FOR THE OTHER DIRECTION ///
/// find the third point of the neighbor triangle ///
neighborNotFound = GetNeighborsVertex(badotri, largestAngleCorner.x, largestAngleCorner.y,
smallestAngleCorner.x, smallestAngleCorner.y, ref thirdPoint, ref neighborotri);
/// find the circumcenter of the neighbor triangle ///
dxSecondSuggestion = dx; // if we cannot find any appropriate suggestion, we use circumcenter
dySecondSuggestion = dy;
// if there is a neighbor triangle
if (!neighborNotFound)
{
neighborvertex_1 = neighborotri.Org();
neighborvertex_2 = neighborotri.Dest();
neighborvertex_3 = neighborotri.Apex();
// now calculate neighbor's circumcenter which is the voronoi site
neighborCircumcenter = predicates.FindCircumcenter(neighborvertex_1, neighborvertex_2, neighborvertex_3,
ref xi_tmp, ref eta_tmp);
/// compute petal and Voronoi edge intersection ///
// in order to avoid degenerate cases, we need to do a vector based calculation for line
vector_x = (largestAngleCorner.y - smallestAngleCorner.y);//(-y, x)
vector_y = smallestAngleCorner.x - largestAngleCorner.x;
vector_x = myCircumcenter.x + vector_x;
vector_y = myCircumcenter.y + vector_y;
// by intersecting bisectors you will end up with the one you want to walk on
// then this line and circle should be intersected
CircleLineIntersection(myCircumcenter.x, myCircumcenter.y, vector_x, vector_y,
xPetalCtr, yPetalCtr, petalRadius, ref p);
/// choose the correct intersection point ///
// calcuwedgeslate middle point of the longest edge(bisector)
xMidOfMiddleEdge = (largestAngleCorner.x + smallestAngleCorner.x) / 2.0;
yMidOfMiddleEdge = (largestAngleCorner.y + smallestAngleCorner.y) / 2.0;
// we need to find correct intersection point, since line intersects circle twice
// this direction is always ACUTE
isCorrect = ChooseCorrectPoint(xMidOfMiddleEdge, yMidOfMiddleEdge, p[3], p[4],
myCircumcenter.x, myCircumcenter.y, false/*(isObtuse+1)%2*/);
// make sure which point is the correct one to be considered
if (isCorrect)
{
inter_x = p[3];
inter_y = p[4];
}
else
{
inter_x = p[1];
inter_y = p[2];
}
/// check if there is a Voronoi vertex between before intersection ///
// check if the voronoi vertex is between the intersection and circumcenter
PointBetweenPoints(inter_x, inter_y, myCircumcenter.x, myCircumcenter.y,
neighborCircumcenter.x, neighborCircumcenter.y, ref voronoiOrInter);
/// determine the point to be suggested ///
if (p[0] > 0.0)
{ // there is at least one intersection point
// if it is between circumcenter and intersection
// if it returns 1.0 this means we have a voronoi vertex within feasible region
if (Math.Abs(voronoiOrInter[0] - 1.0) <= EPS)
{
if (IsBadTriangleAngle(middleAngleCorner.x, middleAngleCorner.y, largestAngleCorner.x, largestAngleCorner.y, neighborCircumcenter.x, neighborCircumcenter.y))
{
// go back to circumcenter
dxSecondSuggestion = dx;
dySecondSuggestion = dy;
}
else
{ // we are not creating a bad triangle
// neighbor's circumcenter is suggested
dxSecondSuggestion = voronoiOrInter[2] - torg.x;
dySecondSuggestion = voronoiOrInter[3] - torg.y;
}
}
else
{ // there is no voronoi vertex between intersection point and circumcenter
if (IsBadTriangleAngle(middleAngleCorner.x, middleAngleCorner.y, largestAngleCorner.x, largestAngleCorner.y, inter_x, inter_y))
{
// if it is inside feasible region, then insert v2
// apply perturbation
// find the distance between circumcenter and intersection point
d = Math.Sqrt((inter_x - myCircumcenter.x) * (inter_x - myCircumcenter.x) +
(inter_y - myCircumcenter.y) * (inter_y - myCircumcenter.y));
// then find the vector going from intersection point to circumcenter
ax = myCircumcenter.x - inter_x;
ay = myCircumcenter.y - inter_y;
ax = ax / d;
ay = ay / d;
// now calculate the new intersection point which is perturbated towards the circumcenter
inter_x = inter_x + ax * pertConst * Math.Sqrt(shortestEdgeDist);
inter_y = inter_y + ay * pertConst * Math.Sqrt(shortestEdgeDist);
if (IsBadTriangleAngle(middleAngleCorner.x, middleAngleCorner.y, largestAngleCorner.x, largestAngleCorner.y, inter_x, inter_y))
{
// go back to circumcenter
dxSecondSuggestion = dx;
dySecondSuggestion = dy;
}
else
{
// intersection point is suggested
dxSecondSuggestion = inter_x - torg.x;
dySecondSuggestion = inter_y - torg.y;
}
}
else
{
// intersection point is suggested
dxSecondSuggestion = inter_x - torg.x;
dySecondSuggestion = inter_y - torg.y;
}
}
/// if it is an acute triangle, check if it is a good enough location ///
// for acute triangle case, we need to check if it is ok to use either of them
if ((smallestAngleCorner.x - myCircumcenter.x) * (smallestAngleCorner.x - myCircumcenter.x) +
(smallestAngleCorner.y - myCircumcenter.y) * (smallestAngleCorner.y - myCircumcenter.y) >
lengthConst * ((smallestAngleCorner.x - (dxSecondSuggestion + torg.x)) *
(smallestAngleCorner.x - (dxSecondSuggestion + torg.x)) +
(smallestAngleCorner.y - (dySecondSuggestion + torg.y)) *
(smallestAngleCorner.y - (dySecondSuggestion + torg.y))))
{
// use circumcenter
dxSecondSuggestion = dx;
dySecondSuggestion = dy;
}// else we stick on what we have found
}
}// if it is on the boundary, meaning no neighbor triangle in this direction, the other direction might be ok
if (isObtuse)
{
//obtuse: do nothing
dx = dxFirstSuggestion;
dy = dyFirstSuggestion;
}
else
{ // acute : consider other direction
if (justAcute * ((smallestAngleCorner.x - (dxSecondSuggestion + torg.x)) *
(smallestAngleCorner.x - (dxSecondSuggestion + torg.x)) +
(smallestAngleCorner.y - (dySecondSuggestion + torg.y)) *
(smallestAngleCorner.y - (dySecondSuggestion + torg.y))) >
(smallestAngleCorner.x - (dxFirstSuggestion + torg.x)) *
(smallestAngleCorner.x - (dxFirstSuggestion + torg.x)) +
(smallestAngleCorner.y - (dyFirstSuggestion + torg.y)) *
(smallestAngleCorner.y - (dyFirstSuggestion + torg.y)))
{
dx = dxSecondSuggestion;
dy = dySecondSuggestion;
}
else
{
dx = dxFirstSuggestion;
dy = dyFirstSuggestion;
}
}// end if obtuse
}// end of relocation
}// end of almostGood
Point circumcenter = new Point();
if (relocated <= 0)
{
circumcenter.x = torg.x + dx;
circumcenter.y = torg.y + dy;
}
else
{
circumcenter.x = origin_x + dx;
circumcenter.y = origin_y + dy;
}
xi = (yao * dx - xao * dy) * (2.0 * denominator);
eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
return circumcenter;
}
/// <summary>
/// Set Apex
/// </summary>
internal void SetApex(Vertex v)
{
tri.vertices[orient] = v;
}
/// <summary>
/// Set the destination of the segment that includes the subsegment.
/// </summary>
internal void SetSegDest(Vertex vertex)
{
seg.vertices[3 - orient] = vertex;
}
void GenMap()
{
/*
* <settings>
*/
int starsAm = 10000;
// What percentage of space is taken up by stars.
int starDensity = 20;
// Minimal corridor length relative to maximal star size.
float minCorridorLengthCoeff = 3.0f;
// What percentage of space is taken up by corridors.
int corridorDensity = 60;
float maxz = 3.0f;
/*
* </settings>
*/
float max_star_size = Mathf.Max(pos_star_sizes);
Debug.Log("Max star size: " + max_star_size);
float min_corridor_length = max_star_size * minCorridorLengthCoeff;
float min_corridor_length_squared = Mathf.Pow(min_corridor_length, 2);
int starsx = Mathf.RoundToInt(Mathf.Sqrt(starsAm));
int starsy = starsx;
float width = (starsx * max_star_size) + ((starsx - 1) * min_corridor_length);
float height = (starsy * max_star_size) + ((starsy - 1) * min_corridor_length);
background.transform.localScale = new Vector3(width * 0.11f, 1.0f, height * 0.11f);
background.GetComponent <MeshRenderer>().material.SetTextureScale("_MainTex", new Vector2(width / 70.0f, height / 70.0f));
Debug.Log("Dimensions: " + width + ", " + height);
float minx = width * -0.5f;
float miny = height * -0.5f;
float maxx = width * 0.5f;
float maxy = height * 0.5f;
float max_offset_x = (width / starsx) - ((min_corridor_length - max_star_size) * 0.5f);
float max_offset_y = (height / starsy) - ((min_corridor_length - max_star_size) * 0.5f);
Debug.Log("Offsets: " + max_offset_x + ", " + max_offset_y);
Rectangle bounds = new Rectangle(minx, miny, width, height);
TriangleNet.Mesh mesh = (TriangleNet.Mesh)GenericMesher.StructuredMesh(bounds, starsx - 1, starsy - 1);
List <TriangleNet.Geometry.Vertex> stars = new List <TriangleNet.Geometry.Vertex>();
List <TriangleNet.Geometry.Vertex> shuffled_verts = new List <TriangleNet.Geometry.Vertex>(mesh.Vertices);
shuffled_verts.Shuffle();
int stars_amount = 0;
foreach (TriangleNet.Geometry.Vertex v in shuffled_verts)
{
if (stars_amount > 3 && Random.Range(0, 101) > starDensity)
{
continue;
}
stars.Add(v);
stars_amount++;
}
GenericMesher gm = new GenericMesher(new SweepLine());
mesh = (TriangleNet.Mesh)gm.Triangulate(stars);
StandardVoronoi sv = new StandardVoronoi(mesh);
Polygon final = new Polygon(sv.Vertices.Count);
Dictionary <int, TriangleNet.Geometry.Vertex> good_stars = new Dictionary <int, TriangleNet.Geometry.Vertex>();
Dictionary <int, int> bad2goodstar = new Dictionary <int, int>();
List <int> outBoundStars = new List <int>();
foreach (TriangleNet.Topology.DCEL.Vertex v in sv.Vertices)
{
if (v.x < minx || v.x > maxx || v.y < miny || v.y > maxy)
{
outBoundStars.Add(v.id);
continue;
}
bool invalid = false;
foreach (TriangleNet.Geometry.Vertex other in good_stars.Values)
{
Vector2 v1 = new Vector2((float)v.x, (float)v.y);
Vector2 v2 = new Vector2((float)other.x, (float)other.y);
if ((v2 - v1).sqrMagnitude < min_corridor_length_squared)
{
invalid = true;
bad2goodstar[v.id] = other.id;
}
}
if (invalid)
{
continue;
}
TriangleNet.Geometry.Vertex new_v = new TriangleNet.Geometry.Vertex(v.x, v.y);
new_v.id = v.id;
good_stars[v.id] = new_v;
final.Add(new_v);
}
List <Segment> good_segments = new List <Segment>();
foreach (Edge e in sv.Edges)
{
if (outBoundStars.Contains(e.P0) || outBoundStars.Contains(e.P1))
{
continue;
}
int P0_id;
int P1_id;
if (bad2goodstar.ContainsKey(e.P0))
{
P0_id = bad2goodstar[e.P0];
}
else
{
P0_id = e.P0;
}
if (bad2goodstar.ContainsKey(e.P1))
{
P1_id = bad2goodstar[e.P1];
}
else
{
P1_id = e.P1;
}
if (P0_id == P1_id)
{
continue;
}
good_segments.Add(new Segment(good_stars[P0_id], good_stars[P1_id]));
}
Dictionary <int, List <int> > connected_stars = new Dictionary <int, List <int> >();
foreach (Segment s in good_segments)
{
if (!connected_stars.ContainsKey(s.P0))
{
connected_stars[s.P0] = new List <int>();
}
connected_stars[s.P0].Add(s.P1);
if (!connected_stars.ContainsKey(s.P1))
{
connected_stars[s.P1] = new List <int>();
}
connected_stars[s.P1].Add(s.P0);
}
Debug.Log("Currently edges: " + good_segments.Count);
List <Segment> temp_segments = new List <Segment>(good_segments);
temp_segments.Shuffle();
foreach (Segment s in temp_segments)
{
if (Random.Range(0, 101) > corridorDensity && RemovalConnectionsCheck(connected_stars, s.P0, s.P1))
{
connected_stars[s.P0].Remove(s.P1);
connected_stars[s.P1].Remove(s.P0);
good_segments.Remove(s);
}
}
foreach (Segment s in good_segments)
{
final.Add(s);
}
Debug.Log("Stars after everything: " + final.Points.Count);
Debug.Log("Corridors after everything: " + good_segments.Count);
CreateMap(final, maxz, 0.0f);
}
public static Mesh GetTriangulationMesh(Vector3[] verts, HashSet <int> borderVerts, Polygon boundary)
{
TriangleNet.Geometry.Polygon polygon = new TriangleNet.Geometry.Polygon();
//Dictionary<TriangleNet.Geometry.Vertex, float> vertexElevMap = new Dictionary<TriangleNet.Geometry.Vertex, float>();
foreach (Vector3 vert in verts)
{
TriangleNet.Geometry.Vertex triangulationVert = new TriangleNet.Geometry.Vertex(vert.x, vert.z);
//vertexElevMap.Add(triangulationVert, vert.y);
polygon.Add(triangulationVert);
}
TriangleNet.Meshing.ConstraintOptions options =
new TriangleNet.Meshing.ConstraintOptions()
{
ConformingDelaunay = true
};
TriangleNet.Meshing.GenericMesher mesher = new TriangleNet.Meshing.GenericMesher();
TriangleNet.Meshing.IMesh mesh = mesher.Triangulate(polygon);
Vector3[] meshVerts = new Vector3[mesh.Vertices.Count];
List <int> meshTriangles = new List <int>();
Dictionary <TriangleNet.Geometry.Vertex, int> vertexIndexMap = new Dictionary <TriangleNet.Geometry.Vertex, int>();
int v = 0;
foreach (TriangleNet.Geometry.Vertex triangulatorVert in mesh.Vertices)
{
meshVerts[v] = new Vector3((float)triangulatorVert.X, verts[v].y, (float)triangulatorVert.Y);
vertexIndexMap[triangulatorVert] = v;
v++;
}
//for (int i = 0; i < vertexList.Length; i ++)
//{
// TriangleNet.Geometry.Vertex triangulatorVert = vertexList[i];
// meshVerts[i] = new Vector3((float)triangulatorVert.X, vertexElevMap[triangulatorVert], (float)triangulatorVert.Y);
// vertexIndexMap[triangulatorVert] = i;
//}
foreach (TriangleNet.Topology.Triangle tri in mesh.Triangles)
{
int ind1 = vertexIndexMap[tri.GetVertex(0)];
int ind2 = vertexIndexMap[tri.GetVertex(2)];
int ind3 = vertexIndexMap[tri.GetVertex(1)];
Vector2 center = new Vector2((float)(tri.GetVertex(0).X + tri.GetVertex(1).X + tri.GetVertex(2).X) / 3f, (float)(tri.GetVertex(0).Y + tri.GetVertex(1).Y + tri.GetVertex(2).Y) / 3f);
if (!(borderVerts.Contains(ind1) && borderVerts.Contains(ind2) && borderVerts.Contains(ind3)) || (boundary.ContainsPoint(center) && !boundary.PermiterContainsPoint(center)))
{
meshTriangles.Add(ind1);
meshTriangles.Add(ind2);
meshTriangles.Add(ind3);
}
}
Mesh unityMesh = new Mesh();
unityMesh.vertices = meshVerts;
unityMesh.triangles = meshTriangles.ToArray();
unityMesh.RecalculateBounds();
unityMesh.RecalculateNormals();
return(unityMesh);
}
/// <summary>
/// Deallocate space for a vertex, marking it dead.
/// </summary>
/// <param name="dyingvertex"></param>
internal void VertexDealloc(Vertex dyingvertex)
{
// Mark the vertex as dead. This makes it possible to detect dead
// vertices when traversing the list of all vertices.
dyingvertex.type = VertexType.DeadVertex;
vertices.Remove(dyingvertex.hash);
}
/// <summary>
/// Checks if smothing is possible for a given bad triangle.
/// </summary>
/// <param name="badotri"></param>
/// <param name="torg"></param>
/// <param name="tdest"></param>
/// <param name="tapex"></param>
/// <param name="newloc">The new location for the point, if somothing is possible.</param>
/// <returns>Returns 1, 2 or 3 if smoothing will work, 0 otherwise.</returns>
private int DoSmoothing(Otri badotri, Vertex torg, Vertex tdest, Vertex tapex,
ref double[] newloc)
{
int numpoints_p = 0;// keeps the number of points in a star of point p, q, r
int numpoints_q = 0;
int numpoints_r = 0;
//int i;
double[] possibilities = new double[6];//there can be more than one possibilities
int num_pos = 0; // number of possibilities
int flag1 = 0, flag2 = 0, flag3 = 0;
bool newLocFound = false;
//vertex v1, v2, v3; // for ccw test
//double p1[2], p2[2], p3[2];
//double temp[2];
//********************* TRY TO RELOCATE POINT "p" ***************
// get the surrounding points of p, so this gives us the triangles
numpoints_p = GetStarPoints(badotri, torg, tdest, tapex, 1, ref points_p);
// check if the points in counterclockwise order
// p1[0] = points_p[0]; p1[1] = points_p[1];
// p2[0] = points_p[2]; p2[1] = points_p[3];
// p3[0] = points_p[4]; p3[1] = points_p[5];
// v1 = (vertex)p1; v2 = (vertex)p2; v3 = (vertex)p3;
// if(counterclockwise(m,b,v1,v2,v3) < 0){
// // reverse the order to ccw
// for(i = 0; i < numpoints_p/2; i++){
// temp[0] = points_p[2*i];
// temp[1] = points_p[2*i+1];
// points_p[2*i] = points_p[2*(numpoints_p-1)-2*i];
// points_p[2*i+1] = points_p[2*(numpoints_p-1)+1-2*i];
// points_p[2*(numpoints_p-1)-2*i] = temp[0];
// points_p[2*(numpoints_p-1)+1-2*i] = temp[1];
// }
// }
// m.counterclockcount--;
// INTERSECTION OF PETALS
// first check whether the star angles are appropriate for relocation
if (torg.type == VertexType.FreeVertex && numpoints_p != 0 && ValidPolygonAngles(numpoints_p, points_p))
{
//newLocFound = getPetalIntersection(m, b, numpoints_p, points_p, newloc);
//newLocFound = getPetalIntersectionBruteForce(m, b,numpoints_p, points_p, newloc,torg[0],torg[1]);
if (behavior.MaxAngle == 0.0)
{
newLocFound = GetWedgeIntersectionWithoutMaxAngle(numpoints_p, points_p, ref newloc);
}
else
{
newLocFound = GetWedgeIntersection(numpoints_p, points_p, ref newloc);
}
//printf("call petal intersection for p\n");
// make sure the relocated point is a free vertex
if (newLocFound)
{
possibilities[0] = newloc[0];// something found
possibilities[1] = newloc[1];
num_pos++;// increase the number of possibilities
flag1 = 1;
}
}
//********************* TRY TO RELOCATE POINT "q" ***************
// get the surrounding points of q, so this gives us the triangles
numpoints_q = GetStarPoints(badotri, torg, tdest, tapex, 2, ref points_q);
// // check if the points in counterclockwise order
// v1[0] = points_q[0]; v1[1] = points_q[1];
// v2[0] = points_q[2]; v2[1] = points_q[3];
// v3[0] = points_q[4]; v3[1] = points_q[5];
// if(counterclockwise(m,b,v1,v2,v3) < 0){
// // reverse the order to ccw
// for(i = 0; i < numpoints_q/2; i++){
// temp[0] = points_q[2*i];
// temp[1] = points_q[2*i+1];
// points_q[2*i] = points_q[2*(numpoints_q-1)-2*i];
// points_q[2*i+1] = points_q[2*(numpoints_q-1)+1-2*i];
// points_q[2*(numpoints_q-1)-2*i] = temp[0];
// points_q[2*(numpoints_q-1)+1-2*i] = temp[1];
// }
// }
// m.counterclockcount--;
// INTERSECTION OF PETALS
// first check whether the star angles are appropriate for relocation
if (tdest.type == VertexType.FreeVertex && numpoints_q != 0 && ValidPolygonAngles(numpoints_q, points_q))
{
//newLocFound = getPetalIntersection(m, b,numpoints_q, points_q, newloc);
//newLocFound = getPetalIntersectionBruteForce(m, b,numpoints_q, points_q, newloc,tapex[0],tapex[1]);
if (behavior.MaxAngle == 0.0)
{
newLocFound = GetWedgeIntersectionWithoutMaxAngle(numpoints_q, points_q, ref newloc);
}
else
{
newLocFound = GetWedgeIntersection(numpoints_q, points_q, ref newloc);
}
//printf("call petal intersection for q\n");
// make sure the relocated point is a free vertex
if (newLocFound)
{
possibilities[2] = newloc[0];// something found
possibilities[3] = newloc[1];
num_pos++;// increase the number of possibilities
flag2 = 2;
}
}
//********************* TRY TO RELOCATE POINT "q" ***************
// get the surrounding points of r, so this gives us the triangles
numpoints_r = GetStarPoints(badotri, torg, tdest, tapex, 3, ref points_r);
// check if the points in counterclockwise order
// v1[0] = points_r[0]; v1[1] = points_r[1];
// v2[0] = points_r[2]; v2[1] = points_r[3];
// v3[0] = points_r[4]; v3[1] = points_r[5];
// if(counterclockwise(m,b,v1,v2,v3) < 0){
// // reverse the order to ccw
// for(i = 0; i < numpoints_r/2; i++){
// temp[0] = points_r[2*i];
// temp[1] = points_r[2*i+1];
// points_r[2*i] = points_r[2*(numpoints_r-1)-2*i];
// points_r[2*i+1] = points_r[2*(numpoints_r-1)+1-2*i];
// points_r[2*(numpoints_r-1)-2*i] = temp[0];
// points_r[2*(numpoints_r-1)+1-2*i] = temp[1];
// }
// }
// m.counterclockcount--;
// INTERSECTION OF PETALS
// first check whether the star angles are appropriate for relocation
if (tapex.type == VertexType.FreeVertex && numpoints_r != 0 && ValidPolygonAngles(numpoints_r, points_r))
{
//newLocFound = getPetalIntersection(m, b,numpoints_r, points_r, newloc);
//newLocFound = getPetalIntersectionBruteForce(m, b,numpoints_r, points_r, newloc,tdest[0],tdest[1]);
if (behavior.MaxAngle == 0.0)
{
newLocFound = GetWedgeIntersectionWithoutMaxAngle(numpoints_r, points_r, ref newloc);
}
else
{
newLocFound = GetWedgeIntersection(numpoints_r, points_r, ref newloc);
}
//printf("call petal intersection for r\n");
// make sure the relocated point is a free vertex
if (newLocFound)
{
possibilities[4] = newloc[0];// something found
possibilities[5] = newloc[1];
num_pos++;// increase the number of possibilities
flag3 = 3;
}
}
//printf("numpossibilities %d\n",num_pos);
//////////// AFTER FINISH CHECKING EVERY POSSIBILITY, CHOOSE ANY OF THE AVAILABLE ONE //////////////////////
if (num_pos > 0)
{
if (flag1 > 0)
{ // suggest to relocate origin
newloc[0] = possibilities[0];
newloc[1] = possibilities[1];
return flag1;
}
else
{
if (flag2 > 0)
{ // suggest to relocate apex
newloc[0] = possibilities[2];
newloc[1] = possibilities[3];
return flag2;
}
else
{// suggest to relocate destination
if (flag3 > 0)
{
newloc[0] = possibilities[4];
newloc[1] = possibilities[5];
return flag3;
}
}
}
}
return 0;// could not find any good relocation
}
/// <summary>
/// Insert a vertex into a Delaunay triangulation, performing flips as necessary
/// to maintain the Delaunay property.
/// </summary>
/// <param name="newvertex">The point to be inserted.</param>
/// <param name="searchtri">The triangle to start the search.</param>
/// <param name="splitseg">Segment to split.</param>
/// <param name="segmentflaws">Check for creation of encroached subsegments.</param>
/// <param name="triflaws">Check for creation of bad quality triangles.</param>
/// <returns>If a duplicate vertex or violated segment does not prevent the
/// vertex from being inserted, the return value will be ENCROACHINGVERTEX if
/// the vertex encroaches upon a subsegment (and checking is enabled), or
/// SUCCESSFULVERTEX otherwise. In either case, 'searchtri' is set to a handle
/// whose origin is the newly inserted vertex.</returns>
/// <remarks>
/// The point 'newvertex' is located. If 'searchtri.triangle' is not NULL,
/// the search for the containing triangle begins from 'searchtri'. If
/// 'searchtri.triangle' is NULL, a full point location procedure is called.
/// If 'insertvertex' is found inside a triangle, the triangle is split into
/// three; if 'insertvertex' lies on an edge, the edge is split in two,
/// thereby splitting the two adjacent triangles into four. Edge flips are
/// used to restore the Delaunay property. If 'insertvertex' lies on an
/// existing vertex, no action is taken, and the value DUPLICATEVERTEX is
/// returned. On return, 'searchtri' is set to a handle whose origin is the
/// existing vertex.
///
/// InsertVertex() does not use flip() for reasons of speed; some
/// information can be reused from edge flip to edge flip, like the
/// locations of subsegments.
///
/// Param 'splitseg': Normally, the parameter 'splitseg' is set to NULL,
/// implying that no subsegment should be split. In this case, if 'insertvertex'
/// is found to lie on a segment, no action is taken, and the value VIOLATINGVERTEX
/// is returned. On return, 'searchtri' is set to a handle whose primary edge is the
/// violated subsegment.
/// If the calling routine wishes to split a subsegment by inserting a vertex in it,
/// the parameter 'splitseg' should be that subsegment. In this case, 'searchtri'
/// MUST be the triangle handle reached by pivoting from that subsegment; no point
/// location is done.
///
/// Param 'segmentflaws': Flags that indicate whether or not there should
/// be checks for the creation of encroached subsegments. If a newly inserted
/// vertex encroaches upon subsegments, these subsegments are added to the list
/// of subsegments to be split if 'segmentflaws' is set.
///
/// Param 'triflaws': Flags that indicate whether or not there should be
/// checks for the creation of bad quality triangles. If bad triangles are
/// created, these are added to the queue if 'triflaws' is set.
/// </remarks>
internal InsertVertexResult InsertVertex(Vertex newvertex, ref Otri searchtri,
ref Osub splitseg, bool segmentflaws, bool triflaws)
{
Otri horiz = default(Otri);
Otri top = default(Otri);
Otri botleft = default(Otri), botright = default(Otri);
Otri topleft = default(Otri), topright = default(Otri);
Otri newbotleft = default(Otri), newbotright = default(Otri);
Otri newtopright = default(Otri);
Otri botlcasing = default(Otri), botrcasing = default(Otri);
Otri toplcasing = default(Otri), toprcasing = default(Otri);
Otri testtri = default(Otri);
Osub botlsubseg = default(Osub), botrsubseg = default(Osub);
Osub toplsubseg = default(Osub), toprsubseg = default(Osub);
Osub brokensubseg = default(Osub);
Osub checksubseg = default(Osub);
Osub rightsubseg = default(Osub);
Osub newsubseg = default(Osub);
BadSubseg encroached;
//FlipStacker newflip;
Vertex first;
Vertex leftvertex, rightvertex, botvertex, topvertex, farvertex;
Vertex segmentorg, segmentdest;
int region;
double area;
InsertVertexResult success;
LocateResult intersect;
bool doflip;
bool mirrorflag;
bool enq;
if (splitseg.seg == null)
{
// Find the location of the vertex to be inserted. Check if a good
// starting triangle has already been provided by the caller.
if (searchtri.tri.id == DUMMY)
{
// Find a boundary triangle.
horiz.tri = dummytri;
horiz.orient = 0;
horiz.Sym();
// Search for a triangle containing 'newvertex'.
intersect = locator.Locate(newvertex, ref horiz);
}
else
{
// Start searching from the triangle provided by the caller.
searchtri.Copy(ref horiz);
intersect = locator.PreciseLocate(newvertex, ref horiz, true);
}
}
else
{
// The calling routine provides the subsegment in which
// the vertex is inserted.
searchtri.Copy(ref horiz);
intersect = LocateResult.OnEdge;
}
if (intersect == LocateResult.OnVertex)
{
// There's already a vertex there. Return in 'searchtri' a triangle
// whose origin is the existing vertex.
horiz.Copy(ref searchtri);
locator.Update(ref horiz);
return InsertVertexResult.Duplicate;
}
if ((intersect == LocateResult.OnEdge) || (intersect == LocateResult.Outside))
{
// The vertex falls on an edge or boundary.
if (checksegments && (splitseg.seg == null))
{
// Check whether the vertex falls on a subsegment.
horiz.Pivot(ref brokensubseg);
if (brokensubseg.seg.hash != DUMMY)
{
// The vertex falls on a subsegment, and hence will not be inserted.
if (segmentflaws)
{
enq = behavior.NoBisect != 2;
if (enq && (behavior.NoBisect == 1))
{
// This subsegment may be split only if it is an
// internal boundary.
horiz.Sym(ref testtri);
enq = testtri.tri.id != DUMMY;
}
if (enq)
{
// Add the subsegment to the list of encroached subsegments.
encroached = new BadSubseg();
encroached.subseg = brokensubseg;
encroached.org = brokensubseg.Org();
encroached.dest = brokensubseg.Dest();
qualityMesher.AddBadSubseg(encroached);
}
}
// Return a handle whose primary edge contains the vertex,
// which has not been inserted.
horiz.Copy(ref searchtri);
locator.Update(ref horiz);
return InsertVertexResult.Violating;
}
}
// Insert the vertex on an edge, dividing one triangle into two (if
// the edge lies on a boundary) or two triangles into four.
horiz.Lprev(ref botright);
botright.Sym(ref botrcasing);
horiz.Sym(ref topright);
// Is there a second triangle? (Or does this edge lie on a boundary?)
mirrorflag = topright.tri.id != DUMMY;
if (mirrorflag)
{
topright.Lnext();
topright.Sym(ref toprcasing);
MakeTriangle(ref newtopright);
}
else
{
// Splitting a boundary edge increases the number of boundary edges.
hullsize++;
}
MakeTriangle(ref newbotright);
// Set the vertices of changed and new triangles.
rightvertex = horiz.Org();
leftvertex = horiz.Dest();
botvertex = horiz.Apex();
newbotright.SetOrg(botvertex);
newbotright.SetDest(rightvertex);
newbotright.SetApex(newvertex);
horiz.SetOrg(newvertex);
// Set the region of a new triangle.
newbotright.tri.label = botright.tri.label;
if (behavior.VarArea)
{
// Set the area constraint of a new triangle.
newbotright.tri.area = botright.tri.area;
}
if (mirrorflag)
{
topvertex = topright.Dest();
newtopright.SetOrg(rightvertex);
newtopright.SetDest(topvertex);
newtopright.SetApex(newvertex);
topright.SetOrg(newvertex);
// Set the region of another new triangle.
newtopright.tri.label = topright.tri.label;
if (behavior.VarArea)
{
// Set the area constraint of another new triangle.
newtopright.tri.area = topright.tri.area;
}
}
// There may be subsegments that need to be bonded
// to the new triangle(s).
if (checksegments)
{
botright.Pivot(ref botrsubseg);
if (botrsubseg.seg.hash != DUMMY)
{
botright.SegDissolve(dummysub);
newbotright.SegBond(ref botrsubseg);
}
if (mirrorflag)
{
topright.Pivot(ref toprsubseg);
if (toprsubseg.seg.hash != DUMMY)
{
topright.SegDissolve(dummysub);
newtopright.SegBond(ref toprsubseg);
}
}
}
// Bond the new triangle(s) to the surrounding triangles.
newbotright.Bond(ref botrcasing);
newbotright.Lprev();
newbotright.Bond(ref botright);
newbotright.Lprev();
if (mirrorflag)
{
newtopright.Bond(ref toprcasing);
newtopright.Lnext();
newtopright.Bond(ref topright);
newtopright.Lnext();
newtopright.Bond(ref newbotright);
}
if (splitseg.seg != null)
{
// Split the subsegment into two.
splitseg.SetDest(newvertex);
segmentorg = splitseg.SegOrg();
segmentdest = splitseg.SegDest();
splitseg.Sym();
splitseg.Pivot(ref rightsubseg);
InsertSubseg(ref newbotright, splitseg.seg.boundary);
newbotright.Pivot(ref newsubseg);
newsubseg.SetSegOrg(segmentorg);
newsubseg.SetSegDest(segmentdest);
splitseg.Bond(ref newsubseg);
newsubseg.Sym();
newsubseg.Bond(ref rightsubseg);
splitseg.Sym();
// Transfer the subsegment's boundary marker to the vertex if required.
if (newvertex.label == 0)
{
newvertex.label = splitseg.seg.boundary;
}
}
if (checkquality)
{
flipstack.Clear();
flipstack.Push(default(Otri)); // Dummy flip (see UndoVertex)
flipstack.Push(horiz);
}
// Position 'horiz' on the first edge to check for
// the Delaunay property.
horiz.Lnext();
}
else
{
// Insert the vertex in a triangle, splitting it into three.
horiz.Lnext(ref botleft);
horiz.Lprev(ref botright);
botleft.Sym(ref botlcasing);
botright.Sym(ref botrcasing);
MakeTriangle(ref newbotleft);
MakeTriangle(ref newbotright);
// Set the vertices of changed and new triangles.
rightvertex = horiz.Org();
leftvertex = horiz.Dest();
botvertex = horiz.Apex();
newbotleft.SetOrg(leftvertex);
newbotleft.SetDest(botvertex);
newbotleft.SetApex(newvertex);
newbotright.SetOrg(botvertex);
newbotright.SetDest(rightvertex);
newbotright.SetApex(newvertex);
horiz.SetApex(newvertex);
// Set the region of the new triangles.
newbotleft.tri.label = horiz.tri.label;
newbotright.tri.label = horiz.tri.label;
if (behavior.VarArea)
{
// Set the area constraint of the new triangles.
area = horiz.tri.area;
newbotleft.tri.area = area;
newbotright.tri.area = area;
}
// There may be subsegments that need to be bonded
// to the new triangles.
if (checksegments)
{
botleft.Pivot(ref botlsubseg);
if (botlsubseg.seg.hash != DUMMY)
{
botleft.SegDissolve(dummysub);
newbotleft.SegBond(ref botlsubseg);
}
botright.Pivot(ref botrsubseg);
if (botrsubseg.seg.hash != DUMMY)
{
botright.SegDissolve(dummysub);
newbotright.SegBond(ref botrsubseg);
}
}
// Bond the new triangles to the surrounding triangles.
newbotleft.Bond(ref botlcasing);
newbotright.Bond(ref botrcasing);
newbotleft.Lnext();
newbotright.Lprev();
newbotleft.Bond(ref newbotright);
newbotleft.Lnext();
botleft.Bond(ref newbotleft);
newbotright.Lprev();
botright.Bond(ref newbotright);
if (checkquality)
{
flipstack.Clear();
flipstack.Push(horiz);
}
}
// The insertion is successful by default, unless an encroached
// subsegment is found.
success = InsertVertexResult.Successful;
if (newvertex.tri.tri != null)
{
// Store the coordinates of the triangle that contains newvertex.
newvertex.tri.SetOrg(rightvertex);
newvertex.tri.SetDest(leftvertex);
newvertex.tri.SetApex(botvertex);
}
// Circle around the newly inserted vertex, checking each edge opposite it
// for the Delaunay property. Non-Delaunay edges are flipped. 'horiz' is
// always the edge being checked. 'first' marks where to stop circling.
first = horiz.Org();
rightvertex = first;
leftvertex = horiz.Dest();
// Circle until finished.
while (true)
{
// By default, the edge will be flipped.
doflip = true;
if (checksegments)
{
// Check for a subsegment, which cannot be flipped.
horiz.Pivot(ref checksubseg);
if (checksubseg.seg.hash != DUMMY)
{
// The edge is a subsegment and cannot be flipped.
doflip = false;
if (segmentflaws)
{
// Does the new vertex encroach upon this subsegment?
if (qualityMesher.CheckSeg4Encroach(ref checksubseg) > 0)
{
success = InsertVertexResult.Encroaching;
}
}
}
}
if (doflip)
{
// Check if the edge is a boundary edge.
horiz.Sym(ref top);
if (top.tri.id == DUMMY)
{
// The edge is a boundary edge and cannot be flipped.
doflip = false;
}
else
{
// Find the vertex on the other side of the edge.
farvertex = top.Apex();
// In the incremental Delaunay triangulation algorithm, any of
// 'leftvertex', 'rightvertex', and 'farvertex' could be vertices
// of the triangular bounding box. These vertices must be
// treated as if they are infinitely distant, even though their
// "coordinates" are not.
if ((leftvertex == infvertex1) || (leftvertex == infvertex2) ||
(leftvertex == infvertex3))
{
// 'leftvertex' is infinitely distant. Check the convexity of
// the boundary of the triangulation. 'farvertex' might be
// infinite as well, but trust me, this same condition should
// be applied.
doflip = predicates.CounterClockwise(newvertex, rightvertex, farvertex) > 0.0;
}
else if ((rightvertex == infvertex1) ||
(rightvertex == infvertex2) ||
(rightvertex == infvertex3))
{
// 'rightvertex' is infinitely distant. Check the convexity of
// the boundary of the triangulation. 'farvertex' might be
// infinite as well, but trust me, this same condition should
// be applied.
doflip = predicates.CounterClockwise(farvertex, leftvertex, newvertex) > 0.0;
}
else if ((farvertex == infvertex1) ||
(farvertex == infvertex2) ||
(farvertex == infvertex3))
{
// 'farvertex' is infinitely distant and cannot be inside
// the circumcircle of the triangle 'horiz'.
doflip = false;
}
else
{
// Test whether the edge is locally Delaunay.
doflip = predicates.InCircle(leftvertex, newvertex, rightvertex, farvertex) > 0.0;
}
if (doflip)
{
// We made it! Flip the edge 'horiz' by rotating its containing
// quadrilateral (the two triangles adjacent to 'horiz').
// Identify the casing of the quadrilateral.
top.Lprev(ref topleft);
topleft.Sym(ref toplcasing);
top.Lnext(ref topright);
topright.Sym(ref toprcasing);
horiz.Lnext(ref botleft);
botleft.Sym(ref botlcasing);
horiz.Lprev(ref botright);
botright.Sym(ref botrcasing);
// Rotate the quadrilateral one-quarter turn counterclockwise.
topleft.Bond(ref botlcasing);
botleft.Bond(ref botrcasing);
botright.Bond(ref toprcasing);
topright.Bond(ref toplcasing);
if (checksegments)
{
// Check for subsegments and rebond them to the quadrilateral.
topleft.Pivot(ref toplsubseg);
botleft.Pivot(ref botlsubseg);
botright.Pivot(ref botrsubseg);
topright.Pivot(ref toprsubseg);
if (toplsubseg.seg.hash == DUMMY)
{
topright.SegDissolve(dummysub);
}
else
{
topright.SegBond(ref toplsubseg);
}
if (botlsubseg.seg.hash == DUMMY)
{
topleft.SegDissolve(dummysub);
}
else
{
topleft.SegBond(ref botlsubseg);
}
if (botrsubseg.seg.hash == DUMMY)
{
botleft.SegDissolve(dummysub);
}
else
{
botleft.SegBond(ref botrsubseg);
}
if (toprsubseg.seg.hash == DUMMY)
{
botright.SegDissolve(dummysub);
}
else
{
botright.SegBond(ref toprsubseg);
}
}
// New vertex assignments for the rotated quadrilateral.
horiz.SetOrg(farvertex);
horiz.SetDest(newvertex);
horiz.SetApex(rightvertex);
top.SetOrg(newvertex);
top.SetDest(farvertex);
top.SetApex(leftvertex);
// Assign region.
// TODO: check region ok (no Math.Min necessary)
region = Math.Min(top.tri.label, horiz.tri.label);
top.tri.label = region;
horiz.tri.label = region;
if (behavior.VarArea)
{
if ((top.tri.area <= 0.0) || (horiz.tri.area <= 0.0))
{
area = -1.0;
}
else
{
// Take the average of the two triangles' area constraints.
// This prevents small area constraints from migrating a
// long, long way from their original location due to flips.
area = 0.5 * (top.tri.area + horiz.tri.area);
}
top.tri.area = area;
horiz.tri.area = area;
}
if (checkquality)
{
flipstack.Push(horiz);
}
// On the next iterations, consider the two edges that were exposed (this
// is, are now visible to the newly inserted vertex) by the edge flip.
horiz.Lprev();
leftvertex = farvertex;
}
}
}
if (!doflip)
{
// The handle 'horiz' is accepted as locally Delaunay.
if (triflaws)
{
// Check the triangle 'horiz' for quality.
qualityMesher.TestTriangle(ref horiz);
}
// Look for the next edge around the newly inserted vertex.
horiz.Lnext();
horiz.Sym(ref testtri);
// Check for finishing a complete revolution about the new vertex, or
// falling outside of the triangulation. The latter will happen when
// a vertex is inserted at a boundary.
if ((leftvertex == first) || (testtri.tri.id == DUMMY))
{
// We're done. Return a triangle whose origin is the new vertex.
horiz.Lnext(ref searchtri);
Otri recenttri = default(Otri);
horiz.Lnext(ref recenttri);
locator.Update(ref recenttri);
return success;
}
// Finish finding the next edge around the newly inserted vertex.
testtri.Lnext(ref horiz);
rightvertex = leftvertex;
leftvertex = horiz.Dest();
}
}
}
SplayNode FrontLocate(SplayNode splayroot, Otri bottommost, Vertex searchvertex,
ref Otri searchtri, ref bool farright)
{
bool farrightflag;
bottommost.Copy(ref searchtri);
splayroot = Splay(splayroot, searchvertex, ref searchtri);
farrightflag = false;
while (!farrightflag && RightOfHyperbola(ref searchtri, searchvertex))
{
searchtri.Onext();
farrightflag = searchtri.Equals(bottommost);
}
farright = farrightflag;
return splayroot;
}
/// <summary>
/// Set Origin
/// </summary>
internal void SetOrg(Vertex v)
{
tri.vertices[plus1Mod3[orient]] = v;
}
/// <summary>
/// Generates a structured mesh.
/// </summary>
/// <param name="bounds">Bounds of the mesh.</param>
/// <param name="nx">Number of segments in x direction.</param>
/// <param name="ny">Number of segments in y direction.</param>
/// <returns>Mesh</returns>
public static IMesh StructuredMesh(Rectangle bounds, int nx, int ny)
{
var polygon = new Polygon((nx + 1) * (ny + 1));
double x, y, dx, dy, left, bottom;
dx = bounds.Width / nx;
dy = bounds.Height / ny;
left = bounds.Left;
bottom = bounds.Bottom;
int i, j, k, l, n = 0;
// Add vertices.
var points = new Vertex[(nx + 1) * (ny + 1)];
for (i = 0; i <= nx; i++)
{
x = left + i * dx;
for (j = 0; j <= ny; j++)
{
y = bottom + j * dy;
points[n++] = new Vertex(x, y);
}
}
polygon.Points.AddRange(points);
n = 0;
// Set vertex hash and id.
foreach (var v in points)
{
v.hash = v.id = n++;
}
// Add boundary segments.
var segments = polygon.Segments;
segments.Capacity = 2 * (nx + ny);
Vertex a, b;
for (j = 0; j < ny; j++)
{
// Left
a = points[j];
b = points[j + 1];
segments.Add(new Segment(a, b, 1));
a.Label = b.Label = 1;
// Right
a = points[nx * (ny + 1) + j];
b = points[nx * (ny + 1) + (j + 1)];
segments.Add(new Segment(a, b, 1));
a.Label = b.Label = 1;
}
for (i = 0; i < nx; i++)
{
// Bottom
a = points[(ny + 1) * i];
b = points[(ny + 1) * (i + 1)];
segments.Add(new Segment(a, b, 1));
a.Label = b.Label = 1;
// Top
a = points[ny + (ny + 1) * i];
b = points[ny + (ny + 1) * (i + 1)];
segments.Add(new Segment(a, b, 1));
a.Label = b.Label = 1;
}
// Add triangles.
var triangles = new InputTriangle[2 * nx * ny];
n = 0;
for (i = 0; i < nx; i++)
{
for (j = 0; j < ny; j++)
{
k = j + (ny + 1) * i;
l = j + (ny + 1) * (i + 1);
// Create 2 triangles in rectangle [k, l, l + 1, k + 1].
if ((i + j) % 2 == 0)
{
// Diagonal from bottom left to top right.
triangles[n++] = new InputTriangle(k, l, l + 1);
triangles[n++] = new InputTriangle(k, l + 1, k + 1);
}
else
{
// Diagonal from top left to bottom right.
triangles[n++] = new InputTriangle(k, l, k + 1);
triangles[n++] = new InputTriangle(l, l + 1, k + 1);
}
}
}
return Converter.ToMesh(polygon, triangles);
}
SplayNode CircleTopInsert(SplayNode splayroot, Otri newkey,
Vertex pa, Vertex pb, Vertex pc, double topy)
{
double ccwabc;
double xac, yac, xbc, ybc;
double aclen2, bclen2;
Point searchpoint = new Point(); // TODO: mesh.nextras
Otri dummytri = default(Otri);
ccwabc = predicates.CounterClockwise(pa, pb, pc);
xac = pa.x - pc.x;
yac = pa.y - pc.y;
xbc = pb.x - pc.x;
ybc = pb.y - pc.y;
aclen2 = xac * xac + yac * yac;
bclen2 = xbc * xbc + ybc * ybc;
searchpoint.x = pc.x - (yac * bclen2 - ybc * aclen2) / (2.0 * ccwabc);
searchpoint.y = topy;
return SplayInsert(Splay(splayroot, searchpoint, ref dummytri), newkey, searchpoint);
}
/// <summary>
/// Inserts a vertex at the circumcenter of a triangle. Deletes
/// the newly inserted vertex if it encroaches upon a segment.
/// </summary>
/// <param name="badtri"></param>
private void SplitTriangle(BadTriangle badtri)
{
Otri badotri = default(Otri);
Vertex borg, bdest, bapex;
Point newloc; // Location of the new vertex
double xi = 0, eta = 0;
InsertVertexResult success;
bool errorflag;
badotri = badtri.poortri;
borg = badotri.Org();
bdest = badotri.Dest();
bapex = badotri.Apex();
// Make sure that this triangle is still the same triangle it was
// when it was tested and determined to be of bad quality.
// Subsequent transformations may have made it a different triangle.
if (!Otri.IsDead(badotri.tri) && (borg == badtri.org) &&
(bdest == badtri.dest) && (bapex == badtri.apex))
{
errorflag = false;
// Create a new vertex at the triangle's circumcenter.
// Using the original (simpler) Steiner point location method
// for mesh refinement.
// TODO: NewLocation doesn't work for refinement. Why? Maybe
// reset VertexType?
if (behavior.fixedArea || behavior.VarArea)
{
newloc = predicates.FindCircumcenter(borg, bdest, bapex, ref xi, ref eta, behavior.offconstant);
}
else
{
newloc = newLocation.FindLocation(borg, bdest, bapex, ref xi, ref eta, true, badotri);
}
// Check whether the new vertex lies on a triangle vertex.
if (((newloc.x == borg.x) && (newloc.y == borg.y)) ||
((newloc.x == bdest.x) && (newloc.y == bdest.y)) ||
((newloc.x == bapex.x) && (newloc.y == bapex.y)))
{
if (Log.Verbose)
{
logger.Warning("New vertex falls on existing vertex.", "Quality.SplitTriangle()");
errorflag = true;
}
}
else
{
// The new vertex must be in the interior, and therefore is a
// free vertex with a marker of zero.
Vertex newvertex = new Vertex(newloc.x, newloc.y, 0
#if USE_ATTRIBS
, mesh.nextras
#endif
);
newvertex.type = VertexType.FreeVertex;
// Ensure that the handle 'badotri' does not represent the longest
// edge of the triangle. This ensures that the circumcenter must
// fall to the left of this edge, so point location will work.
// (If the angle org-apex-dest exceeds 90 degrees, then the
// circumcenter lies outside the org-dest edge, and eta is
// negative. Roundoff error might prevent eta from being
// negative when it should be, so I test eta against xi.)
if (eta < xi)
{
badotri.Lprev();
}
// Assign triangle for attributes interpolation.
newvertex.tri.tri = newvertex_tri;
// Insert the circumcenter, searching from the edge of the triangle,
// and maintain the Delaunay property of the triangulation.
Osub tmp = default(Osub);
success = mesh.InsertVertex(newvertex, ref badotri, ref tmp, true, true);
if (success == InsertVertexResult.Successful)
{
newvertex.hash = mesh.hash_vtx++;
newvertex.id = newvertex.hash;
#if USE_ATTRIBS
if (mesh.nextras > 0)
{
Interpolation.InterpolateAttributes(newvertex, newvertex.tri.tri, mesh.nextras);
}
#endif
mesh.vertices.Add(newvertex.hash, newvertex);
if (mesh.steinerleft > 0)
{
mesh.steinerleft--;
}
}
else if (success == InsertVertexResult.Encroaching)
{
// If the newly inserted vertex encroaches upon a subsegment,
// delete the new vertex.
mesh.UndoVertex();
}
else if (success == InsertVertexResult.Violating)
{
// Failed to insert the new vertex, but some subsegment was
// marked as being encroached.
}
else
{ // success == DUPLICATEVERTEX
// Couldn't insert the new vertex because a vertex is already there.
if (Log.Verbose)
{
logger.Warning("New vertex falls on existing vertex.", "Quality.SplitTriangle()");
errorflag = true;
}
}
}
if (errorflag)
{
logger.Error("The new vertex is at the circumcenter of triangle: This probably "
+ "means that I am trying to refine triangles to a smaller size than can be "
+ "accommodated by the finite precision of floating point arithmetic.",
"Quality.SplitTriangle()");
throw new Exception("The new vertex is at the circumcenter of triangle.");
}
}
}
double CircleTop(Vertex pa, Vertex pb, Vertex pc, double ccwabc)
{
double xac, yac, xbc, ybc, xab, yab;
double aclen2, bclen2, ablen2;
Statistic.CircleTopCount++;
xac = pa.x - pc.x;
yac = pa.y - pc.y;
xbc = pb.x - pc.x;
ybc = pb.y - pc.y;
xab = pa.x - pb.x;
yab = pa.y - pb.y;
aclen2 = xac * xac + yac * yac;
bclen2 = xbc * xbc + ybc * ybc;
ablen2 = xab * xab + yab * yab;
return pc.y + (xac * bclen2 - xbc * aclen2 + Math.Sqrt(aclen2 * bclen2 * ablen2)) / (2.0 * ccwabc);
}