public static Vector4 GetInternalAnglesQuadUnitSphere(Vector3 a, Vector3 b, Vector3 c, Vector3 d)
{
var angles = new UnitSpherePolygon(new List <Vector3>
{
a, b, c, d
}).GetInternalAngles();
return(new Vector4(angles[0], angles[1], angles[2], angles[3]));
}
private float ProcessVertex(int vertexIndex, FaceIndexTriplet[] connectedTriangles, Vector3[] vertices)
{
if (connectedTriangles.Length < 1)
{
return(0.0f);
}
var normalInfo = CreatePivotNormalForVertex(vertexIndex, connectedTriangles, vertices, true);
var pivotNormal = normalInfo.Pivot;
var triangleNormals = normalInfo.TriangleNormals;
_pivotNormals.Add(vertexIndex, pivotNormal);
//We have our pivot normal now, so it's time to project the other vertices around this normal
//as they only occupy the half of the unit sphere where dot(n, p) > 0
//This allows us to project them down onto the plane and order them
var projectedNormals = new List <Vector3>(triangleNormals.Count);
foreach (var triangleNormal in triangleNormals)
{
projectedNormals.Add(Vector3.ProjectOnPlane(triangleNormal, pivotNormal));
}
//Now we have a plane with the normal vectors projected onto it, now we can use their angular difference
//from an arbitrary vector within the set, to order them
var angularOrigin = projectedNormals[0];
var angleNormalPairs = new SortedDictionary <float, Vector3>();
for (var i = 0; i < projectedNormals.Count; i++)
{
var projectedNormal = projectedNormals[i];
var angle = Vector3.SignedAngle(angularOrigin, projectedNormal, pivotNormal);
if (!angleNormalPairs.ContainsKey(angle))
{
angleNormalPairs.Add(angle, triangleNormals[i]);
}
}
var sortedNormals = new List <Vector3>(projectedNormals.Count);
foreach (var angleNormalPair in angleNormalPairs)
{
sortedNormals.Add(angleNormalPair.Value);
}
var polygon = new UnitSpherePolygon(sortedNormals);
//_vertexNormalPolygons.Add(vertexIndex, polygon);
var area = polygon.GetArea();
return(area);
}
private float ProcessFace(Vector3 n0, Vector3 n1, Vector3 n2)
{
var sortedVertices = CircularlySortNormals(new List <Vector3> {
n0, n1, n2
});
UnitSpherePolygon poly = new UnitSpherePolygon(sortedVertices);
return(poly.GetArea());
}
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());
}
