/// <summary>
/// Verifica se la faccia è convessa. Un poligono semplice è strettamente convesso se ogni
/// angolo interno è strettamente inferiore a 180 gradi.
/// </summary>
/// <returns>True se la faccia è convessa, false altrimenti.</returns>
public bool IsConvex()
{
DCELHalfEdge he = this.Edge;
DCELHalfEdge prev = he.Previous();
DCELVertex first = he.Origin;
do
{
Vector3D v1 = new Vector3D(
prev.Origin.Coordinates.X - he.Origin.Coordinates.X,
prev.Origin.Coordinates.Y - he.Origin.Coordinates.Y,
prev.Origin.Coordinates.Z - he.Origin.Coordinates.Z);
Vector3D v2 = new Vector3D(
he.Next.Origin.Coordinates.X - he.Origin.Coordinates.X,
he.Next.Origin.Coordinates.Y - he.Origin.Coordinates.Y,
he.Next.Origin.Coordinates.Z - he.Origin.Coordinates.Z);
double dotProduct = (v1.X * v2.X + v1.Y * v2.Y + v1.Z * v2.Z);
double norm1 = Math.Sqrt(Math.Pow(v1.X, 2) + Math.Pow(v1.Y, 2) + Math.Pow(v1.Z, 2));
double norm2 = Math.Sqrt(Math.Pow(v2.X, 2) + Math.Pow(v2.Y, 2) + Math.Pow(v2.Z, 2));
double angle = (Math.Acos(dotProduct / (norm1 * norm2)) * 180) / Math.PI;
if (angle > 180)
{
return(false);
}
prev = he;
he = he.Next;
}while (he.Origin != first);
//returns true if every internal angle is less than or equal to 180 degrees
return(true);
}
/// <summary>
/// Restituisce tutti gli HalfEdge che partono da questo vertice.
/// </summary>
/// <returns>DCELHalfEdge collection.</returns>
public IEnumerable <DCELHalfEdge> LeavingEdges()
{
if (this.Leaving == null)
{
yield break;
}
DCELHalfEdge he = this.Leaving;
do
{
yield return(he);
he = he.Previous().Twin;
}while (he != this.Leaving);
}
