private void ProcessEdges(FaceIndexTriplet[] faceIndexTriplets, Vector3[] vertices)
{
var vertexTriangleMap = new Dictionary <int, HashSet <FaceIndexTriplet> >();
foreach (var triplet in faceIndexTriplets)
{
for (int i = 0; i < 3; i++)
{
var vertex = triplet[i];
if (!vertexTriangleMap.ContainsKey(vertex))
{
vertexTriangleMap.Add(vertex, new HashSet <FaceIndexTriplet>());
}
vertexTriangleMap[vertex].Add(triplet);
}
}
//Contains all edges, linked to the triangles that connect to them.
var edgeTriangleMap = new Dictionary <EdgeIndices, HashSet <FaceIndexTriplet> >();
//Make a list of all edge index pairs, there are 3 per triangle
foreach (var triplet in faceIndexTriplets)
{
for (int i = 0; i < 3; i++)
{
var i1 = triplet[i];
var i2 = triplet[(i + 1) % 3];
var edge = new EdgeIndices(i1, i2);
if (!edgeTriangleMap.ContainsKey(edge))
{
edgeTriangleMap.Add(edge, new HashSet <FaceIndexTriplet>());
}
edgeTriangleMap[edge].UnionWith(vertexTriangleMap[i1]);
edgeTriangleMap[edge].UnionWith(vertexTriangleMap[i2]);
}
}
foreach (var edge in edgeTriangleMap)
{
_edgeGaussArea.Add(edge.Key, ProcessEdge(edge.Key, edge.Value.ToArray(), vertices));
}
//If an edge only has 1 triangle connected to it, it's a mesh edge, and should not have any gaussian area.
}
private float ProcessEdge(EdgeIndices edge, FaceIndexTriplet[] connectedTriangles, Vector3[] vertices)
{
var v1 = vertices[edge.I1];
var v2 = vertices[edge.I2];
var dv = (v2 - v1).normalized;
var n1 = _pivotNormals[edge.I1];
var n2 = _pivotNormals[edge.I2];
var ne = (n1 + n2).normalized;
var side1 = Vector3.Cross(ne, dv).normalized;
var side2 = -side1;
//For v1 on side 1:
//get the triangle edges on side 1 (dot(n1, v1-t1) should be more than 0)
//where v1 is the vertex and t1 the side of the triangle pointing away from the vertex
//then check if said triangles are actually connected to v1 (might be faster to do it the other way around, idk)
//Side 1
var nS1V1 = CalculateSidedPivot(edge.I1, connectedTriangles, side1, ne, dv, vertices);
var nS1V2 = CalculateSidedPivot(edge.I2, connectedTriangles, side1, ne, dv, vertices);
//Side 2
var nS2V1 = CalculateSidedPivot(edge.I1, connectedTriangles, side2, ne, dv, vertices);
var nS2V2 = CalculateSidedPivot(edge.I2, connectedTriangles, side2, ne, dv, vertices);
var polygon = new UnitSpherePolygon(CircularlySortNormals(new List <Vector3>
{
nS1V1,
nS1V2,
nS2V1,
nS2V2
}));
return(polygon.GetArea());
}