public static Surface ExtractSurface(Autodesk.Revit.DB.ConicalFace face, IEnumerable <PolyCurve> edgeLoops)
{
// Note: Internal representation of the cone
// S(u, v) = Origin + v*[sin(HalfAngle)*(cos(u)*Radius[0] + sin(u)*Radius[1]) + cos(HalfAngle)*Axis]
edgeLoops = edgeLoops.ToList();
// Get some data from the face
var axis = face.Axis.ToVector();
var x = face.get_Radius(0).ToVector();
var y = face.get_Radius(1).ToVector();
var tipPt = face.Origin.ToPoint();
var ang = face.HalfAngle;
// We use the max length in order to help find the lowest possible base point for the cone
var maxLength = edgeLoops.Max(pc => pc.Length);
// We don't know the "base" point of the cone, so we build it here
// by projecting a point on the edge loops onto the axis
var pt = edgeLoops.First().StartPoint;
var dir = pt.Subtract(tipPt.AsVector());
var projLength = dir.AsVector().Dot(axis);
var height = projLength + 2 * maxLength;
var o = tipPt.Add(axis.Normalized().Scale(height));
// there's not an easy way to create a conical surface in protogeometry outside of this
// note this coordinate system has the z axis reversed because we're building the cone
// from it's flat bottom surface
var baseCS = CoordinateSystem.ByOriginVectors(o, x, y.Reverse());
// Construct the radius
var rad = Math.Cos(ang) * height;
var cone = Cone.ByCoordinateSystemHeightRadius(baseCS, height, rad);
// PB: this is iffy code - we need to extract the surface that's not touching the origin
//return cone.Faces.Select(f => f.SurfaceGeometry()).First(s => s.DistanceTo(o) > 1e-5);
// the flat face of the cone is currently the second face in the Faces enumeration
return(cone.Faces[1].SurfaceGeometry());
}