# How to draw an orbit from Orbital Elements using Transform3DGroup

I am trying to draw an orbit using the Transform3DGroup class in the C# .NET framework. I have orbital elements a, e, i, RAAN, ArgPer, trueAnom. The algorithm that spits these out for me also gives me x y z coordinates in ECI. For some reason, when I try to use Transform3DGroup to do my rotations in order to basically draw out where the satellite is supposed to go in ECI (using the orbit elements I gave above) my result is not matching up with the ECI coordinates that the original algorithm is spitting out.

That original algorithm is my truth data. But I don't want to use those coordinates, I want to draw the orbit myself with the Keplarian elements using Transform3DGroup.

Here is my code:

public Point3D calculatePosition(double trueAnomaly)
{
double angle = trueAnomaly;
double a = semiMajorAxis;
double e = eccentricity;
double b = (a * (1 - e * e)) / (1 + e * Math.Cos(angle));
double SA = Math.Sin(angle);
double X = b * CA;//(CA * CR + SA * CI * SR);
double Y = b * SA; //(CA * SR + SA * CI);
double Z = 0; //b * SA * SI;
Point3D p = new Point3D(X, Y, Z);//new Point3D(Math.Cos(angle) * b,
Math.Sin(angle) * b, 0);
return p;
}
public void orient2OrbitalElements(double _time)
{

    orbitNorm = new Vector3D(0, 0, 1);
positionPoint = calculatePosition(trueAnomaly);//Position of Orbiter
Transform3DGroup tg = new Transform3DGroup();
tg.Children.Add(new TranslateTransform3D(positionVec));//Translates to Orbit Position (relative to Parent)
tg.Children.Add(new RotateTransform3D(new AxisAngleRotation3D(new Vector3D(1, 0, 0), inclinationDeg)));//Rotates Orbit to the set Inclination
tg.Children.Add(new RotateTransform3D(new AxisAngleRotation3D(new Vector3D(0, 0, 1), RAAN)));//Rotates Orbiter's model RAAN
orbitNorm = tgNoTranslation(tg).Transform(orbitNorm);
tg.Children.Add(new RotateTransform3D(new AxisAngleRotation3D(orbitNorm, argOfPerigee)));//Rotates Orbiter's model to the Arg of Perigee
Transform = tg;
if (HasEphem)
{
Console.WriteLine(ObjectName + ": " + Transform.Value.OffsetX + ", " + Transform.Value.OffsetY + ", " + Transform.Value.OffsetZ);
Console.WriteLine(ObjectName + ": " + cartesElems.xPos[ephemIndex] + ", " + cartesElems.yPos[ephemIndex] + ", " + cartesElems.zPos[ephemIndex]);
}
}
public Transform3DGroup tgNoTranslation(Transform3DGroup tgWithTranslations)
{
Transform3DGroup tempTg = tgWithTranslations.Clone();
tempTg.Children.RemoveAt(0);
return tempTg;
}


Basically I calculate an x,y position on the orbital plane w.r.t the Earth position using the basic eccentricity, semi-major axis, true anomaly formula as you'll see. Then I put the resulting coordinates into my Transform3DGroup as a TranslateTransform3D. This is the first object I put in.

Then I perform the rotations: --- a rotation is added for the inclination, rotating the position Vec about the unit x axis (1,0,0) --- a rotation for the RAAN, about the unit z-axis(0,0,1) --- then I create the orbit normal from that and perform a argPer rotation about that new axis

My understanding of how Transform3DGroup works is that it will apply the first one, then the second, and so on. Which means that the positionVec (which is just x, y coordinates in the reference frame of the 2d orbital plane) gets performed, then the rotations will all be performed as a rotation matrix on was is left after what was done before it.

Am I performing the argPer rotation incorrectly? RAAN or inc? Perhaps there is a more exact way to calculate my position in my orbital plane or a particular order of operations I must adhere to?

The more I think about it, the more I keep arriving at the thought that everything seems to be very simple if I use the Transform3DGroup and that I should be doing it right at this point, yet the ECI results don't line up.

But lo and behold, the Transform.Value.OffsetX/Y/Z does want to come close to agreeing with the truth data. Perhaps Transform.Value.Offset is not the X,Y,Z as I am thinking of it?