/// <summary>
/// Returns the planar deviation of this face
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="face"></param>
/// <param name="getPosition"></param>
/// <returns></returns>
public static double GetPlanarity <V, E, F>(this IHeFace <V, E, F> face)
where V : IHeVertex <V, E, F>, IVertex3d
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
return(GetPlanarity(face, IVertex3dStatic <V> .GetPosition));
}
/// <summary>
/// Returns the circumcenter of the face.
/// Assumes face is triangular.
/// http://mathworld.wolfram.com/Incenter.html
/// </summary>
/// <returns></returns>
public static Vec3d GetIncenter <V, E, F>(this IHeFace <V, E, F> face)
where V : IHeVertex <V, E, F>, IVertex3d
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
return(GetIncenter(face, IVertex3dStatic <V> .GetPosition));
}
/// <summary>
/// Returns the average position of vertices in the face.
/// </summary>
/// <returns></returns>
public static Vec3d GetBarycenter <V, E, F>(this IHeFace <V, E, F> face)
where V : IHeVertex <V, E, F>, IVertex3d
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
return(face.Vertices.Mean(IVertex3dStatic <V> .GetPosition));
}
/// <summary>
/// Returns the average position of vertices in the face.
/// </summary>
/// <returns></returns>
public static Vec3d GetBarycenter <V, E, F>(this IHeFace <V, E, F> face, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
return(face.Vertices.Mean(getPosition));
}
/// <summary>
/// Returns the circumcircle of a triangular face.
/// Assumes the face is triangular.
/// http://mathworld.wolfram.com/Incenter.html
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="face"></param>
/// <param name="getPosition"></param>
/// <returns></returns>
public static Circle GetCircumcircle <V, E, F>(this IHeFace <V, E, F> face, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
var he = face.First;
Point3d p0 = getPosition(he.PreviousInFace.Start);
Point3d p1 = getPosition(he.PreviousInFace.Start);
Point3d p2 = getPosition(he.NextInFace.Start);
return(new Circle(p0, p1, p2));
}
/// <summary>
/// Returns the circumcenter of the face.
/// Assumes face is triangular.
/// http://mathworld.wolfram.com/Incenter.html
/// </summary>
/// <returns></returns>
public static Vec3d GetIncenter <V, E, F>(this IHeFace <V, E, F> face, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
var he = face.First;
return(GeometryUtil.GetIncenter(
getPosition(he.PreviousInFace.Start),
getPosition(he.Start),
getPosition(he.NextInFace.Start)
));
}
/// <summary>
/// Returns the unitized sum of halfedge normals in the face.
/// </summary>
/// <returns></returns>
public static Vec3d GetNormal <V, E, F>(this IHeFace <V, E, F> face, Func <E, Vec3d> getNormal)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
if (face.IsDegree(3))
{
return(getNormal(face.First).Direction);
}
else
{
return(face.Halfedges.Sum(getNormal).Direction);
}
}
/// <summary>
/// Returns the unitized sum of halfedge normals in the face.
/// </summary>
/// <returns></returns>
public static Vec3d GetNormal <V, E, F>(this IHeFace <V, E, F> face, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
if (face.IsDegree3)
{
return(face.First.GetNormal(getPosition).Direction);
}
else
{
return(face.Halfedges.Sum(he => he.GetNormal(getPosition)).Direction);
}
}
/// <summary>
/// Returns the planar deviation of this face
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="face"></param>
/// <param name="getPosition"></param>
/// <returns></returns>
public static double GetPlanarity <V, E, F>(this IHeFace <V, E, F> face, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
var he0 = face.First;
var he1 = he0;
var p0 = getPosition(he1.Start);
he1 = he1.NextInFace;
var p1 = getPosition(he1.Start);
he1 = he1.NextInFace;
var p2 = getPosition(he1.Start);
he1 = he1.NextInFace;
// tri case
if (ReferenceEquals(he1, he0))
{
return(0.0);
}
var p3 = getPosition(he1.Start);
he1 = he1.NextInFace;
// quad case
if (ReferenceEquals(he1, he0))
{
return(GeometryUtil.GetQuadPlanarity(p0, p1, p2, p3));
}
// general case
double sum = 0.0;
int count = 0;
foreach (var he in he1.CirculateFace)
{
sum += GeometryUtil.GetQuadPlanarity(p0, p1, p2, p3);
p0 = p1; p1 = p2; p2 = p3;
p3 = getPosition(he.Start);
}
return(sum / count);
}
/// <summary>
///
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="face"></param>
/// <param name="getPosition"></param>
/// <returns></returns>
public static Polyline ToPolyline <V, E, F>(this IHeFace <V, E, F> face, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
Polyline result = new Polyline();
foreach (var v in face.Vertices)
{
var p = getPosition(v);
result.Add(p.X, p.Y, p.Z);
}
result.Add(result.First);
return(result);
}
/// <summary>
/// Returns the planar deviation of this face
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <typeparam name="F"></typeparam>
/// <param name="face"></param>
/// <param name="getPosition"></param>
/// <returns></returns>
public static double GetPlanarity <V, E, F>(this IHeFace <V, E, F> face, Func <V, Vec3d> getPosition)
where V : IHeVertex <V, E, F>
where E : IHalfedge <V, E, F>
where F : IHeFace <V, E, F>
{
var he0 = face.First;
var he1 = he0;
var p0 = getPosition(he1.Start);
he1 = he1.NextInFace;
var p1 = getPosition(he1.Start);
he1 = he1.NextInFace;
var p2 = getPosition(he1.Start);
he1 = he1.NextInFace;
// tri case
if (ReferenceEquals(he1, he0))
{
return(0.0);
}
// quad case
if (ReferenceEquals(he1.NextInFace, he0))
{
return(GeometryUtil.LineLineShortestVector(p0, p2, p1, getPosition(he1.Start)).Length);
}
// general case
var he2 = he1;
double max = 0.0;
do
{
var p3 = getPosition(he2.Start);
max = Math.Max(GeometryUtil.LineLineShortestVector(p0, p2, p1, p3).Length, max);
he2 = he2.NextInFace;
p0 = p1; p1 = p2; p2 = p3;
} while (!ReferenceEquals(he2, he1));
return(max);
}
