/// <summary>
/// Calculate the area enclosed by this curve, were the start and end points to be
/// joined by a straight line segment.
/// A plane may optionally be specified, otherwise by default the projected area on
/// the XY plane will be used.
/// </summary>
/// <param name="centroid">Output. The centroid of the enclosed area, in local coordinates
/// on the specified plane.</param>
/// <param name="onPlane">The plane to use to calculate the area.
/// If not specified, the XY plane will be used.</param>
/// <returns>The signed area enclosed by this curve on the specified plane,
/// as a double.</returns>
public override double CalculateEnclosedArea(out Vector centroid, Plane onPlane = null)
{
double result = 0;
centroid = Vector.Zero;
for (int i = 0; i < SubCurves.Count; i++)
{
Curve subCrv = SubCurves[i];
Vector start = subCrv.StartPoint;
Vector end = subCrv.EndPoint;
if (onPlane != null)
{
start = onPlane.GlobalToLocal(start);
end = onPlane.GlobalToLocal(end);
}
double areaUnder = MathsHelper.AreaUnder(start.X, start.Y, end.X, end.Y, ref centroid);
result += areaUnder;
Vector subCentroid;
double subArea = subCrv.CalculateEnclosedArea(out subCentroid, onPlane);
result += subArea;
centroid += subCentroid * subArea;
}
centroid /= result;
return(result);
}
public override double CalculateEnclosedIxx(Plane onPlane = null)
{
if (Circle != null)
{
if (Closed)
{
Vector localO = onPlane.GlobalToLocal(Circle.Origin);
double Io = (Math.PI / 4) * Circle.Radius.Power(4);
Vector v;
double area = CalculateEnclosedArea(out v, onPlane);
double yCentre = localO.Y;
return(Io + area * yCentre.Squared());
}
else
{
Vector origin = Circle.Origin;
double radius = Circle.Radius;
Vector centroid;
double area = CalculateEnclosedArea(out centroid, onPlane).Abs();
Plane oSys = new Plane(onPlane, origin);
Vector localS = oSys.GlobalToLocal(StartPoint);
Vector localE = oSys.GlobalToLocal(EndPoint);
Vector localM = oSys.GlobalToLocal(Vertices[1].Position);
Vector localC = oSys.GlobalToLocal(centroid);
Angle toS = localS.Angle;
Angle toE = localE.Angle;
Angle toM = localM.Angle;
double IxxS = SectorIxx(toS, radius);
double IxxE = SectorIxx(toE, radius);
double IxxTri = Math.Abs((localS.Y.Squared() + localS.Y * localE.Y + localE.Y.Squared()) * (localS.X * localE.Y - localE.X * localS.Y) / 12);
double result;
if (toM > Math.Min(toS, toE) && toM < Math.Max(toS, toE))
{
result = Math.Max(IxxS, IxxE) - Math.Min(IxxS, IxxE);
}
else
{
result = (Math.PI / 4) * radius.Power(4) - Math.Max(IxxS, IxxE) + Math.Min(IxxS, IxxE);
}
if (RadianMeasure.IsReflex)
{
result += IxxTri;
}
else
{
result -= IxxTri;
}
// Adjust for centroid offset:
double yC = onPlane.GlobalToLocal(centroid).Y;
result += area * (yC.Squared() - localC.Y.Squared());
return(result);
}
}
return(0);
}