/// <summary>
/// Calculates the midpoint of the specifiec edge.
/// </summary>
/// <returns>The point.</returns>
/// <param name="edge">Edge.</param>
public static Point3d MidPoint(MeshEdge edge)
{
MeshHalfEdge halfEdge = edge.HalfEdge;
Point3d a = halfEdge.Vertex;
Point3d b = halfEdge.Twin.Vertex;
return((a + b) / 2);
}
/// <summary>
/// Computes the cotangent of the angle opposite to a half-edge.
/// </summary>
/// <returns>The cotangent value.</returns>
/// <param name="hE">The half-edge</param>
public static double Cotan(MeshHalfEdge hE)
{
if (hE.OnBoundary)
{
return(0.0);
}
var u = Vector(hE.Prev);
var v = -Vector(hE.Next);
return(u.Dot(v) / u.Cross(v).Length);
}
/// <summary>
/// Compute the centroid of the specified face.
/// </summary>
/// <returns>The centroid.</returns>
/// <param name="face">Face.</param>
public static Point3d Centroid(MeshFace face)
{
MeshHalfEdge hE = face.HalfEdge;
Point3d a = hE.Vertex;
Point3d b = hE.Next.Vertex;
Point3d c = hE.Prev.Vertex;
if (face.IsBoundaryLoop())
{
return((a + b) / 2);
}
return((a + b + c) / 3);
}
/// <summary>
/// Computes the signed angle (in radians) between the faces adjacent to the specified half-edge.
/// </summary>
/// <returns>The angle (in radians) between faces.</returns>
/// <param name="hE">H e.</param>
public static double DihedralAngle(MeshHalfEdge hE)
{
if (hE.OnBoundary || hE.Twin.OnBoundary)
{
return(0.0);
}
var n1 = FaceNormal(hE.Face);
var n2 = FaceNormal(hE.Twin.Face);
var w = Vector(hE).Unit();
var cosTheta = n1.Dot(n2);
var sinTheta = n1.Cross(n2).Dot(w);
return(Math.Atan2(sinTheta, cosTheta));
}
/// <summary>
/// Compute the circumcenter the specified face.
/// </summary>
/// <returns>The circumcenter.</returns>
/// <param name="face">Face.</param>
public static Point3d Circumcenter(MeshFace face)
{
MeshHalfEdge hE = face.HalfEdge;
Point3d a = hE.Vertex;
Point3d b = hE.Next.Vertex;
Point3d c = hE.Prev.Vertex;
if (face.IsBoundaryLoop())
{
return((a + b) / 2);
}
Vector3d ac = c - a;
Vector3d ab = b - a;
Vector3d w = ab.Cross(ac);
Vector3d u = w.Cross(ab) * ac.LengthSquared;
Vector3d v = ac.Cross(w) * ab.LengthSquared;
Point3d x = (Point3d)(u + v) / (2 * w.LengthSquared);
return(x + a);
}
/// <summary> /// Calculate the vector of a specified half-edge. /// </summary> /// <returns>The half-edge vector.</returns> /// <param name="halfEdge">Half edge.</param> public static Vector3d Vector(MeshHalfEdge halfEdge) => halfEdge.Vertex - halfEdge.Next.Vertex;
// Takes a List containing another List per face with the vertex indexes belonging to that face
private bool CreateFaces(IEnumerable <List <int> > faceIndexes)
{
var edgeCount = new Dictionary <string, int>();
var existingHalfEdges = new Dictionary <string, MeshHalfEdge>();
var hasTwinHalfEdge = new Dictionary <MeshHalfEdge, bool>();
// Create the faces, edges and half-edges, non-boundary loops and link references when possible;
foreach (var indexes in faceIndexes)
{
var f = new MeshFace();
this.Faces.Add(f);
var tempHEdges = new List <MeshHalfEdge>(indexes.Count);
// Create empty half-edges
for (var i = 0; i < indexes.Count; i++)
{
var h = new MeshHalfEdge();
tempHEdges.Add(h);
}
// Fill out each half edge
for (var i = 0; i < indexes.Count; i++)
{
// Edge goes from v0 to v1
var v0 = indexes[i];
var v1 = indexes[(i + 1) % indexes.Count];
var h = tempHEdges[i];
// Set previous and next
h.Next = tempHEdges[(i + 1) % indexes.Count];
h.Prev = tempHEdges[(i + indexes.Count - 1) % indexes.Count];
h.OnBoundary = false;
hasTwinHalfEdge.Add(h, false);
// Set half-edge & vertex mutually
h.Vertex = this.Vertices[v0];
this.Vertices[v0].HalfEdge = h;
// Set half-edge face & vice versa
h.Face = f;
f.HalfEdge = h;
// Reverse v0 and v1 if v0 > v1
if (v0 > v1)
{
var temp = v0;
v0 = v1;
v1 = temp;
}
var key = v0 + " " + v1;
if (existingHalfEdges.ContainsKey(key))
{
// If this half-edge key already exists, it is the twin of this current half-edge
var twin = existingHalfEdges[key];
h.Twin = twin;
twin.Twin = h;
h.Edge = twin.Edge;
hasTwinHalfEdge[h] = true;
hasTwinHalfEdge[twin] = true;
edgeCount[key]++;
}
else
{
// Create an edge and set its half-edge
var e = new MeshEdge();
this.Edges.Add(e);
h.Edge = e;
e.HalfEdge = h;
// Record the newly created half-edge
existingHalfEdges.Add(key, h);
edgeCount.Add(key, 1);
}
}
this.HalfEdges.AddRange(tempHEdges);
}
// Create boundary edges
for (var i = 0; i < this.HalfEdges.Count; i++)
{
var h = this.HalfEdges[i];
if (!hasTwinHalfEdge[h])
{
var f = new MeshFace();
this.Boundaries.Add(f);
var boundaryCycle = new List <MeshHalfEdge>();
var halfEdge = h;
do
{
var boundaryHalfEdge = new MeshHalfEdge();
this.HalfEdges.Add(boundaryHalfEdge);
boundaryCycle.Add(boundaryHalfEdge);
var nextHalfEdge = halfEdge.Next;
while (hasTwinHalfEdge[nextHalfEdge])
{
nextHalfEdge = nextHalfEdge.Twin.Next;
}
boundaryHalfEdge.Vertex = nextHalfEdge.Vertex;
boundaryHalfEdge.Edge = halfEdge.Edge;
boundaryHalfEdge.OnBoundary = true;
boundaryHalfEdge.Face = f;
f.HalfEdge = boundaryHalfEdge;
boundaryHalfEdge.Twin = halfEdge;
halfEdge.Twin = boundaryHalfEdge;
halfEdge = nextHalfEdge;
} while (halfEdge != h);
var n = boundaryCycle.Count;
for (var j = 0; j < n; j++)
{
boundaryCycle[j].Next = boundaryCycle[(j + n - 1) % n];
boundaryCycle[j].Prev = boundaryCycle[(j + 1) % n];
hasTwinHalfEdge[boundaryCycle[j]] = true;
hasTwinHalfEdge[boundaryCycle[j].Twin] = true;
}
}
if (h.OnBoundary)
{
continue;
}
var corner = new MeshCorner {
HalfEdge = h
};
h.Corner = corner;
this.Corners.Add(corner);
}
// Check mesh for common errors
if (this.HasIsolatedFaces() || this.HasIsolatedVertices() || this.HasNonManifoldEdges())
{
return(false);
}
// Index elements
this.IndexElements();
return(true);
}