private static bool IsReallyACone(IEnumerable <PolygonalFace> facesAll, out double[] axis, out double coneAngle)
{
var faces = ListFunctions.FacesWithDistinctNormals(facesAll.ToList());
var n = faces.Count;
if (faces.Count <= 1)
{
axis = null;
coneAngle = double.NaN;
return(false);
}
if (faces.Count == 2)
{
axis = faces[0].Normal.crossProduct(faces[1].Normal).normalize();
coneAngle = 0.0;
return(false);
}
// a simpler approach: if the cross product of the normals are all parallel, it's a cylinder,
// otherwise, cone.
/*var r = new Random();
* var rndList = new List<int>();
* var crossProd = new List<double[]>();
* var c = 0;
* while (c < 20)
* {
* var ne = r.Next(facesAll.Count);
* if (!rndList.Contains(ne)) rndList.Add(ne);
* c++;
* }
* for (var i = 0; i < rndList.Count-1; i++)
* {
* for (var j = i + 1; j < rndList.Count; j++)
* {
* crossProd.Add(facesAll[i].Normal.crossProduct(facesAll[j].Normal).normalize());
* }
* }
* axis = crossProd[0];
* coneAngle = 0.0;
* for (var i = 0; i < crossProd.Count - 1; i++)
* {
* for (var j = i + 1; j < crossProd.Count; j++)
* {
* if (Math.Abs(crossProd[i].dotProduct(crossProd[j]) - 1) < 0.00000008) return true;
* }
* }
* return false;*/
// find the plane that the normals live on in the Gauss sphere. If it is not
// centered at 0 then you have a cone.
// since the vectors that are the difference of two normals (v = n1 - n2) would
// be in the plane, let's first figure out the average plane of this normal
var inPlaneVectors = new double[n][];
inPlaneVectors[0] = faces[0].Normal.subtract(faces[n - 1].Normal);
for (int i = 1; i < n; i++)
{
inPlaneVectors[i] = faces[i].Normal.subtract(faces[i - 1].Normal);
}
var normalsOfGaussPlane = new List <double[]>();
var tempCross = inPlaneVectors[0].crossProduct(inPlaneVectors[n - 1]).normalize();
if (!tempCross.Any(double.IsNaN))
{
normalsOfGaussPlane.Add(tempCross);
}
for (int i = 1; i < n; i++)
{
tempCross = inPlaneVectors[i].crossProduct(inPlaneVectors[i - 1]).normalize();
if (!tempCross.Any(double.IsNaN))
{
if (tempCross.dotProduct(normalsOfGaussPlane[0]) >= 0)
{
normalsOfGaussPlane.Add(tempCross);
}
else
{
normalsOfGaussPlane.Add(tempCross.multiply(-1));
}
}
}
var normalOfGaussPlane = new double[3];
normalOfGaussPlane = normalsOfGaussPlane.Aggregate(normalOfGaussPlane, (current, c) => current.add(c));
normalOfGaussPlane = normalOfGaussPlane.divide(normalsOfGaussPlane.Count);
var distance = faces.Sum(face => face.Normal.dotProduct(normalOfGaussPlane));
if (distance < 0)
{
axis = normalOfGaussPlane.multiply(-1);
distance = -distance / n;
}
else
{
distance /= n;
axis = normalOfGaussPlane;
}
coneAngle = Math.Asin(distance);
return(Math.Abs(distance) >= ClassificationConstants.MinConeGaussPlaneOffset);
}
private static bool IsReallyAFlat(IEnumerable <PolygonalFace> faces)
{
return(ListFunctions.FacesWithDistinctNormals(faces.ToList()).Count == 1);
}
