//Find all triangles opposite of vertex p
//But we will find all edges opposite to p, and from these edges we can find the triangles
private static void AddTrianglesOppositePToStack(MyVector2 p, Stack <HalfEdge2> trianglesOppositeP, HalfEdgeData2 triangulationData)
{
//Find a vertex at position p and then rotate around it, triangle-by-triangle, to find all opposite edges
HalfEdgeVertex2 rotateAroundThis = null;
foreach (HalfEdgeVertex2 v in triangulationData.vertices)
{
if (v.position.Equals(p))
{
rotateAroundThis = v;
}
}
//Which triangle is this vertex a part of, so we know when we have rotated all the way around
HalfEdgeFace2 tStart = rotateAroundThis.edge.face;
HalfEdgeFace2 tCurrent = null;
int safety = 0;
while (tCurrent != tStart)
{
safety += 1;
if (safety > 10000)
{
Debug.Log("Stuck in endless loop when finding opposite edges in Delaunay Sloan");
break;
}
//The edge opposite to p
HalfEdge2 edgeOppositeRotateVertex = rotateAroundThis.edge.nextEdge.oppositeEdge;
//Try to add the edge to the list iof triangles we are interested in
//Null might happen if we are at the border
//A stack might include duplicates so we have to check for that as well
if (edgeOppositeRotateVertex != null && !trianglesOppositeP.Contains(edgeOppositeRotateVertex))
{
trianglesOppositeP.Push(edgeOppositeRotateVertex);
}
//Rotate left - this assumes we can always rotate left so no holes are allowed
//and neither can we investigate one of the vertices thats a part of the supertriangle
//which we dont need to worry about because p is never a part of the supertriangle
rotateAroundThis = rotateAroundThis.edge.oppositeEdge.v;
//In which triangle are we now?
tCurrent = rotateAroundThis.edge.face;
}
}
public HalfEdge2(HalfEdgeVertex2 v)
{
this.v = v;
}
//
// Triangle to half-edge
//
public static HalfEdgeData2 Triangle2ToHalfEdge2(HashSet <Triangle2> triangles, HalfEdgeData2 data)
{
//Make sure the triangles have the same orientation, which is clockwise
triangles = HelpMethods.OrientTrianglesClockwise(triangles);
//Fill the data structure
foreach (Triangle2 t in triangles)
{
HalfEdgeVertex2 v1 = new HalfEdgeVertex2(t.p1);
HalfEdgeVertex2 v2 = new HalfEdgeVertex2(t.p2);
HalfEdgeVertex2 v3 = new HalfEdgeVertex2(t.p3);
//The vertices the edge points to
HalfEdge2 he1 = new HalfEdge2(v1);
HalfEdge2 he2 = new HalfEdge2(v2);
HalfEdge2 he3 = new HalfEdge2(v3);
he1.nextEdge = he2;
he2.nextEdge = he3;
he3.nextEdge = he1;
he1.prevEdge = he3;
he2.prevEdge = he1;
he3.prevEdge = he2;
//The vertex needs to know of an edge going from it
v1.edge = he2;
v2.edge = he3;
v3.edge = he1;
//The face the half-edge is connected to
HalfEdgeFace2 face = new HalfEdgeFace2(he1);
//Each edge needs to know of the face connected to this edge
he1.face = face;
he2.face = face;
he3.face = face;
//Add everything to the lists
data.edges.Add(he1);
data.edges.Add(he2);
data.edges.Add(he3);
data.faces.Add(face);
data.vertices.Add(v1);
data.vertices.Add(v2);
data.vertices.Add(v3);
}
//Step 4. Find the half-edges going in the opposite direction of each edge we have
//Is there a faster way to do this because this is the bottleneck?
foreach (HalfEdge2 e in data.edges)
{
HalfEdgeVertex2 goingToVertex = e.v;
HalfEdgeVertex2 goingFromVertex = e.prevEdge.v;
foreach (HalfEdge2 eOther in data.edges)
{
//Dont compare with itself
if (e == eOther)
{
continue;
}
//Is this edge going between the vertices in the opposite direction
if (goingFromVertex.position.Equals(eOther.v.position) && goingToVertex.position.Equals(eOther.prevEdge.v.position))
{
e.oppositeEdge = eOther;
break;
}
}
}
return(data);
}
//Create a new triangle face when splitting triangle face
private static void CreateNewFace(HalfEdge2 e_old, MyVector2 splitPosition, HalfEdgeData2 data, HashSet <HalfEdge2> newEdges)
{
//This triangle has the following positons
MyVector2 p_split = splitPosition;
MyVector2 p_next = e_old.prevEdge.v.position;
MyVector2 p_prev = e_old.v.position;
//Create the new stuff
HalfEdgeVertex2 v_split = new HalfEdgeVertex2(p_split);
HalfEdgeVertex2 v_next = new HalfEdgeVertex2(p_next);
HalfEdgeVertex2 v_prev = new HalfEdgeVertex2(p_prev);
//This is the edge that has the same position as the old edge
HalfEdge2 e_1 = new HalfEdge2(v_prev);
HalfEdge2 e_2 = new HalfEdge2(v_split);
HalfEdge2 e_3 = new HalfEdge2(v_next);
//The new face
HalfEdgeFace2 f = new HalfEdgeFace2(e_1);
//Create the connections
//The new edge e has the same opposite as the old edge
e_1.oppositeEdge = e_old.oppositeEdge;
//But the opposite edge needs a new reference to this edge if its not a border
if (e_1.oppositeEdge != null)
{
e_old.oppositeEdge.oppositeEdge = e_1;
}
//The other new edges will find the opposite in a loop when we have created all new edges
newEdges.Add(e_2);
newEdges.Add(e_3);
//Create the connections between the edges
e_1.nextEdge = e_2;
e_1.prevEdge = e_3;
e_2.nextEdge = e_3;
e_2.prevEdge = e_1;
e_3.nextEdge = e_1;
e_3.prevEdge = e_2;
//Each edge needs to connect to a face
e_1.face = f;
e_2.face = f;
e_3.face = f;
//The vertices need an edge that starts at that point
v_split.edge = e_3;
v_next.edge = e_1;
v_prev.edge = e_2;
//Add them to the lists
data.faces.Add(f);
data.edges.Add(e_1);
data.edges.Add(e_2);
data.edges.Add(e_3);
data.vertices.Add(v_split);
data.vertices.Add(v_next);
data.vertices.Add(v_prev);
}
//
// Flip triangle edge
//
//So the edge shared by two triangles is going between the two other vertices originally not part of the edge
public static void FlipTriangleEdge(HalfEdge2 e)
{
//The data we need
//This edge's triangle edges
HalfEdge2 e_1 = e;
HalfEdge2 e_2 = e_1.nextEdge;
HalfEdge2 e_3 = e_1.prevEdge;
//The opposite edge's triangle edges
HalfEdge2 e_4 = e_1.oppositeEdge;
HalfEdge2 e_5 = e_4.nextEdge;
HalfEdge2 e_6 = e_4.prevEdge;
//The 4 vertex positions
MyVector2 aPos = e_1.v.position;
MyVector2 bPos = e_2.v.position;
MyVector2 cPos = e_3.v.position;
MyVector2 dPos = e_5.v.position;
//The 6 old vertices, we can use
HalfEdgeVertex2 a_old = e_1.v;
HalfEdgeVertex2 b_old = e_1.nextEdge.v;
HalfEdgeVertex2 c_old = e_1.prevEdge.v;
HalfEdgeVertex2 a_opposite_old = e_4.prevEdge.v;
HalfEdgeVertex2 c_opposite_old = e_4.v;
HalfEdgeVertex2 d_old = e_4.nextEdge.v;
//Flip
//Vertices
//Triangle 1: b-c-d
HalfEdgeVertex2 b = b_old;
HalfEdgeVertex2 c = c_old;
HalfEdgeVertex2 d = d_old;
//Triangle 1: b-d-a
HalfEdgeVertex2 b_opposite = a_opposite_old;
b_opposite.position = bPos;
HalfEdgeVertex2 d_opposite = c_opposite_old;
d_opposite.position = dPos;
HalfEdgeVertex2 a = a_old;
//Change half-edge - half-edge connections
e_1.nextEdge = e_3;
e_1.prevEdge = e_5;
e_2.nextEdge = e_4;
e_2.prevEdge = e_6;
e_3.nextEdge = e_5;
e_3.prevEdge = e_1;
e_4.nextEdge = e_6;
e_4.prevEdge = e_2;
e_5.nextEdge = e_1;
e_5.prevEdge = e_3;
e_6.nextEdge = e_2;
e_6.prevEdge = e_4;
//Half-edge - vertex connection
e_1.v = b;
e_2.v = b_opposite;
e_3.v = c;
e_4.v = d_opposite;
e_5.v = d;
e_6.v = a;
//Half-edge - face connection
HalfEdgeFace2 f1 = e_1.face;
HalfEdgeFace2 f2 = e_4.face;
e_1.face = f1;
e_3.face = f1;
e_5.face = f1;
e_2.face = f2;
e_4.face = f2;
e_6.face = f2;
//Face - half-edge connection
f1.edge = e_3;
f2.edge = e_4;
//Vertices connection, which should have a reference to a half-edge going away from the vertex
//Triangle 1: b-c-d
b.edge = e_3;
c.edge = e_5;
d.edge = e_1;
//Triangle 1: b-d-a
b_opposite.edge = e_4;
d_opposite.edge = e_6;
a.edge = e_2;
//Opposite-edges are not changing!
//And neither are we adding, removing data so we dont need to update the lists with all data
}
