float SearchWidth(Vertex c, Triangle t, HalfEdge e, float d)
{
Vertex u = e.Src, v = e.Dest;
if (c.Position.dot2(v.Position, u.Position) <= 0
|| c.Position.dot2(u.Position, v.Position) <= 0)
{
return d;
}
float d2 = MathUtility.MinDistance2Segment(c.Position, e.Src.Position, e.Dest.Position);
if (d2 > d)
{
return d;
}
if (e.Constrained)
{
return d2;
}
Triangle t2 = e.Pair.Face;
if (t2 == null)
{
Debug.LogError("Invalid t2");
return d;
}
HalfEdge e2 = t2.GetOpposite(e.Src);
HalfEdge e3 = t2.GetOpposite(e.Dest);
d = SearchWidth(c, t2, e2, d);
return SearchWidth(c, t2, e3, d);
}
/// <summary>
/// 将点插入到三角形中.
/// </summary>
void InsertToTriangle(Vertex v, Triangle old)
{
Triangle ab = geomManager.CreateTriangle();
Triangle bc = geomManager.CreateTriangle();
Triangle ca = geomManager.CreateTriangle();
// 分别构造连接v和old的三个顶点的边, 将old一分为三.
HalfEdge av = geomManager.CreateEdge(old.A, v);
HalfEdge bv = geomManager.CreateEdge(old.B, v);
HalfEdge cv = geomManager.CreateEdge(old.C, v);
HalfEdge AB = old.AB, BC = old.BC, CA = old.CA;
// 更新Face.
AB.Face = bv.Face = av.Pair.Face = ab;
BC.Face = cv.Face = bv.Pair.Face = bc;
CA.Face = av.Face = cv.Pair.Face = ca;
// 释放旧三角形.
geomManager.ReleaseTriangle(old);
// 连接边.
ab.Edge = AB.CycleLink(bv, av.Pair);
bc.Edge = BC.CycleLink(cv, bv.Pair);
ca.Edge = CA.CycleLink(av, cv.Pair);
// 映射到格子地图上.
geomManager.RasterizeTriangle(ab);
geomManager.RasterizeTriangle(bc);
geomManager.RasterizeTriangle(ca);
Utility.Verify(av.Face == ca);
Utility.Verify(av.Pair.Face == ab);
Utility.Verify(bv.Face == ab);
Utility.Verify(bv.Pair.Face == bc);
Utility.Verify(cv.Face == bc);
Utility.Verify(cv.Pair.Face == ca);
// 维护delaunay特性.
FlipTriangles(ab.Edge);
FlipTriangles(bc.Edge);
FlipTriangles(ca.Edge);
}
/// <summary>
/// 将点插入到old的边上.
/// </summary>
void InsertOnEdge(Vertex v, Triangle old, HalfEdge hitEdge)
{
// 连接v和v所在的边正对的顶点, 将old一分为二.
Triangle split1 = geomManager.CreateTriangle();
Triangle split2 = geomManager.CreateTriangle();
Vertex opositeVertex = hitEdge.Next.Dest;
HalfEdge ov = geomManager.CreateEdge(opositeVertex, v);
HalfEdge v1 = geomManager.CreateEdge(v, hitEdge.Dest);
HalfEdge v2 = geomManager.CreateEdge(v, hitEdge.Pair.Dest);
HalfEdge sp1Edge0 = hitEdge.Next;
HalfEdge sp2Edge0 = hitEdge.Next.Next;
HalfEdge sp2Edge1 = v2.Pair;
HalfEdge sp2Edge2 = ov.Pair;
// 更新Face.
sp1Edge0.Face = ov.Face = v1.Face = split1;
sp2Edge0.Face = sp2Edge1.Face = sp2Edge2.Face = split2;
// 释放旧三角形.
geomManager.ReleaseTriangle(old);
// 连接边.
split1.Edge = sp1Edge0.CycleLink(ov, v1);
split2.Edge = sp2Edge0.CycleLink(sp2Edge1, sp2Edge2);
// 将新三角形映射到格子地图上.
geomManager.RasterizeTriangle(split1);
geomManager.RasterizeTriangle(split2);
Utility.Verify(ov.Face == split1);
Utility.Verify(ov.Pair.Face == split2);
Triangle other = hitEdge.Pair.Face;
Triangle oposite1 = null;
Triangle oposite2 = null;
// 分割另一侧的三角形.
if (other != null)
{
Vertex p = hitEdge.Pair.Next.Dest;
HalfEdge vp = geomManager.CreateEdge(v, p);
oposite1 = geomManager.CreateTriangle();
oposite2 = geomManager.CreateTriangle();
HalfEdge hpn = hitEdge.Pair.Next;
HalfEdge op1Edge0 = hpn.Next;
HalfEdge op1Edge1 = v1.Pair;
HalfEdge op1Edge2 = vp;
hpn.Face = vp.Pair.Face = v2.Face = oposite2;
op1Edge0.Face = op1Edge1.Face = op1Edge2.Face = oposite1;
geomManager.ReleaseTriangle(other);
oposite2.Edge = hpn.CycleLink(vp.Pair, v2);
oposite1.Edge = op1Edge0.CycleLink(op1Edge1, op1Edge2);
geomManager.RasterizeTriangle(oposite1);
geomManager.RasterizeTriangle(oposite2);
Utility.Verify(vp.Face == oposite1);
Utility.Verify(vp.Pair.Face == oposite2);
}
Utility.Verify(v1.Face == split1);
Utility.Verify(v1.Pair.Face == oposite1);
Utility.Verify(v2.Face == oposite2);
Utility.Verify(v2.Pair.Face == split2);
// 维护delaunay特性.
FlipTriangles(split1.Edge);
FlipTriangles(split2.Edge);
if (other != null)
{
FlipTriangles(oposite1.Edge);
FlipTriangles(oposite2.Edge);
}
}
public bool SharesEdgeWith(Triangle triangle)
{
var sharedVertices = Vertices.Where(o => triangle.Vertices.Contains(o)).Count();
return(sharedVertices == 2);
}
/// <summary>
/// 查找与triangle的外接矩形相交的格子.
/// </summary>
TiledMapRegion FindTriangleBoundingRectOverlappedTiles(Triangle triangle)
{
float xMin = Mathf.Min(triangle.A.Position.x, triangle.B.Position.x, triangle.C.Position.x);
float xMax = Mathf.Max(triangle.A.Position.x, triangle.B.Position.x, triangle.C.Position.x);
float zMin = Mathf.Min(triangle.A.Position.z, triangle.B.Position.z, triangle.C.Position.z);
float zMax = Mathf.Max(triangle.A.Position.z, triangle.B.Position.z, triangle.C.Position.z);
return tiledMap.GetTiles(xMin, xMax, zMin, zMax);
}
/// <summary>
/// 将triangle的映射从TiledMap上去掉.
/// </summary>
public void UnrasterizeTriangle(Triangle triangle)
{
TiledMapRegion tmr = FindTriangleBoundingRectOverlappedTiles(triangle);
for (; tmr.MoveNext(); )
{
Tile tile = tiledMap[tmr.Current.First, tmr.Current.Second];
if (tile.Face == triangle)
{
tile.Face = null;
}
}
}
/// <summary>
/// 将triangle映射到TiledMap上.
/// </summary>
public void RasterizeTriangle(Triangle triangle)
{
Vector3[] list = new Vector3[] { triangle.A.Position, triangle.B.Position, triangle.C.Position };
TiledMapRegion tmr = FindTriangleBoundingRectOverlappedTiles(triangle);
for (; tmr.MoveNext(); )
{
Tuple2<int, int> current = tmr.Current;
Tile tile = tiledMap[current.First, current.Second];
Vector3 center = tiledMap.GetTileCenter(current.First, current.Second);
if (MathUtility.PolygonContains(list, center))
{
tile.Face = triangle;
}
}
}
/// <summary>
/// 释放triangle.
/// </summary>
public void ReleaseTriangle(Triangle triangle)
{
UnrasterizeTriangle(triangle);
foreach (HalfEdge edge in triangle.BoundingEdges)
{
if (edge.Face == triangle)
{
edge.Face = null;
edge.Next = null;
}
if (edge.Face == null && edge.Pair.Face == null)
{
ReleaseEdge(edge);
}
}
}
