// Assumes that the vertices are located in the same plane
// https://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf
// Return null if triangulation does not succeed
// can potential also delete edges (if edges of length 0 is found)
public List <Face> Triangulate(bool step = false, StringWriter debug = null)
{
#if HMDebug
if (debug != null)
{
debug.WriteLine("Triangulate face with debug");
}
#endif
Debug.Assert(!IsDestroyed());
List <Face> res = new List <Face>();
res.Add(this);
var face = this;
bool isVerticesLinear = IsVerticesLinear();
#if HMDebug
if (debug != null)
{
debug.WriteLine("isVerticesLinear " + isVerticesLinear);
}
#endif
if (isVerticesLinear)
{
return(TriangulateFaceOnLine());
}
var halfedges = Circulate();
var normal = GetNormal();
int iterations = halfedges.Count * 2;
while (halfedges.Count > 3 && iterations > 0)
{
iterations--;
Halfedge zeroEdge = null;
Halfedge degenerateEdge = null;
Halfedge sharpCorner = null;
double minimumAngle = 999;
// find ear to clip
for (int i = 0; i < halfedges.Count; i++)
{
var he1 = halfedges[i];
var he2 = he1.next;
var dir1 = he1.GetDirection();
var dir2 = he2.GetDirection();
Vector3D crossDir = Vector3D.Cross(dir1, dir2);
var angle = Vector3D.Angle(dir1, dir2);
if (dir1.sqrMagnitude < face.hmesh.zeroMagnitudeTresholdSqr)
{
zeroEdge = he1;
break;
}
bool isParallel = Vector3D.IsParallelDist(dir1, dir2, hmesh.zeroMagnitudeTresholdSqr);
bool isSameDir = Vector3D.Dot(dir1, dir2) > 0;
bool isNormalSameDir = Vector3D.Dot(crossDir, normal) > 0;
if (isParallel && isSameDir == false)
{
degenerateEdge = he1;
break;
}
bool intersection = false;
if (isNormalSameDir && !isParallel)
{
for (int j = i + 2; j < i + halfedges.Count; j++)
{
var heJ = halfedges[j % halfedges.Count];
if (PointInTriangle(heJ.prev.vert.positionD, he1.prev.vert.positionD, he1.vert.positionD, he2.vert.positionD) ||
PointInTriangle(heJ.vert.positionD, he1.prev.vert.positionD, he1.vert.positionD, he2.vert.positionD))
{
intersection = true;
break; // break intersection test
}
}
// clip ear
if (intersection == false)
{
if (angle < minimumAngle)
{
minimumAngle = angle;
sharpCorner = he1;
}
}
}
}
if (zeroEdge != null)
{
#if HMDebug
if (debug != null)
{
debug.WriteLine("zeroEdge " + zeroEdge);
}
#endif
zeroEdge.Collapse();
if (face.IsDestroyed())
{
Debug.LogError("Fix");
return(new List <Face>()); // Fix
}
halfedges = face.Circulate();
}
else if (degenerateEdge != null)
{
// the main idea, is to cut away the degenerate edge (and collapse the degenerate face)
//
//
// Example (4 vertices)
// ||
// ||
// |\
// | \
// ----
#if HMDebug
if (debug != null)
{
debug.WriteLine("degenerateEdge " + degenerateEdge);
}
#endif
var he1 = degenerateEdge;
var he2 = he1.next;
// degenerate edges detected
Halfedge next = he2.next;
double thisDist = he1.GetDirection().magnitude;
double nextDist = he2.GetDirection().magnitude;
Vertex nextVert = he2.vert;
Vertex prevVert = he1.prev.vert;
if (Math.Abs(nextDist - thisDist) <= face.hmesh.zeroMagnitudeTreshold)
{
// cut from nextVert to prevVert
}
else if (nextDist > thisDist)
{
nextVert = he2.Split();
nextVert.positionD = prevVert.positionD;
}
else if (thisDist > nextDist)
{
prevVert = he1.Split();
prevVert.positionD = nextVert.positionD;
}
var cutFace = face.Cut(prevVert, nextVert);
var sharedEdge = nextVert.GetSharedEdge(prevVert);
sharedEdge.Collapse();
if (!cutFace.IsDestroyed())
{
#if HMDebug
Debug.LogWarning("Cut face survived \n" + cutFace.ExportLocalNeighbourhoodToObj());
#endif
return(new List <Face>()); // Fix
}
halfedges = face.Circulate();
}
else if (sharpCorner != null)
{
#if HMDebug
if (debug != null)
{
debug.WriteLine("sharpCorner ");
}
#endif
var he1 = sharpCorner;
var he2 = he1.next;
var newFace = face.Cut(he1.prev.vert, he2.vert);
newFace.label = label;
res.Add(newFace);
if (newFace.Circulate().Count > 3)
{
face = newFace;
}
halfedges = face.Circulate();
}
if (step)
{
return(res);
}
}
for (int i = res.Count - 1; i >= 0; i--)
{
if (res[i] == null || res[i].IsDestroyed())
{
res.RemoveAt(i);
}
}
return(res);
}