/// <summary>
/// Returns the area of the given halfedge as per V in https://www.cs.cmu.edu/~kmcrane/Projects/Other/TriangleAreasCheatSheet.pdf
/// Assumes the halfedge is in a triangular face.
/// </summary>
public static double GetArea <V, E, F>(this HeStructure <V, E, F> .Halfedge hedge, Func <V, Vector3d> getPosition)
where V : HeStructure <V, E, F> .Vertex
where E : HeStructure <V, E, F> .Halfedge
where F : HeStructure <V, E, F> .Face
{
var p0 = getPosition(hedge.Start);
var p1 = getPosition(hedge.Next.Start);
var p2 = getPosition(hedge.Previous.Start);
return(p0.SquareDistanceTo(p1) * Vector3d.Cotangent(p0 - p2, p1 - p2) * 0.25);
}
/// <summary>
/// Calculates the cotangent of the angle opposite this halfedge.
/// Assumes the halfedge is in a triangular face.
/// </summary>
public static double GetCotangent <V, E, F>(this HeStructure <V, E, F> .Halfedge hedge, Func <V, Vector3d> getPosition)
where V : HeStructure <V, E, F> .Vertex
where E : HeStructure <V, E, F> .Halfedge
where F : HeStructure <V, E, F> .Face
{
Vector3d p = getPosition(hedge.Previous.Start);
return(Vector3d.Cotangent(
getPosition(hedge.Start) - p,
getPosition(hedge.End) - p
));
}
/// <summary>
/// Returns the area of the given halfedge as per D in https://www.cs.cmu.edu/~kmcrane/Projects/Other/TriangleAreasCheatSheet.pdf
/// Assumes adjacent faces are triangular.
/// </summary>
public static double GetEdgeArea <V, E, F>(this HeStructure <V, E, F> .Halfedge hedge, Func <V, Vector3d> getPosition)
where V : HeStructure <V, E, F> .Vertex
where E : HeStructure <V, E, F> .Halfedge
where F : HeStructure <V, E, F> .Face
{
var twin = hedge.Twin;
var p0 = getPosition(hedge.Start);
var p1 = getPosition(twin.Start);
var w = 0.0;
if (hedge.Face != null)
{
var p2 = getPosition(hedge.Previous.Start);
w += Vector3d.Cotangent(p0 - p2, p1 - p2);
}
if (twin.Face != null)
{
var p3 = getPosition(twin.Previous.Start);
w += Vector3d.Cotangent(p0 - p3, p1 - p3);
}
return(p0.SquareDistanceTo(p1) * w * 0.25);
}