// ** Begin
public void Draw3D(RenderContext renderContext, float opacity, Vector3d centerPoint)
{
Matrix3d orbitalPlaneOrientation = Matrix3d.MultiplyMatrix(Matrix3d.RotationZ(Coordinates.DegreesToRadians(elements.w)),
Matrix3d.MultiplyMatrix(Matrix3d.RotationX(Coordinates.DegreesToRadians(elements.i)),
Matrix3d.RotationZ(Coordinates.DegreesToRadians(elements.omega))));
// Extra transformation required because the ellipse shader uses the xy-plane, but WWT uses the
// xz-plane as the reference.
orbitalPlaneOrientation = Matrix3d.MultiplyMatrix(orbitalPlaneOrientation, orbitalToWwt);
Matrix3d worldMatrix = Matrix3d.MultiplyMatrix(Matrix3d.MultiplyMatrix(orbitalPlaneOrientation, Matrix3d.Translation(centerPoint)), renderContext.World);
double M = elements.n * (SpaceTimeController.JNow - elements.T);
double F = 1;
if (M < 0)
{
F = -1;
}
M = Math.Abs(M) / 360.0;
M = (M - (int)(M)) * 360.0 * F;
Color color = Color.FromArgbColor((int)(opacity * 255.0f), orbitColor);
// Newton-Raphson iteration to solve Kepler's equation.
// This is faster than calling CAAKepler.Calculate(), and 5 steps
// is more than adequate for draw the orbit paths of small satellites
// (which are ultimately rendered using single-precision floating point.)
M = Coordinates.DegreesToRadians(M);
double E = M;
for (int i = 0; i < 5; i++)
{
E += (M - E + elements.e * Math.Sin(E)) / (1 - elements.e * Math.Cos(E));
}
EllipseRenderer.DrawEllipse(renderContext, elements.a / scale, elements.e, E, color, worldMatrix);
}