To give some context to this problem, I'm attempting to convert an orbit into a Cubic Bezier Spline, by first plotting four points around the Orbits Ellipse and then computing the Control points of the Bezier curve to get a curvature that matches the ellipse as best as possible. The orbits can only ever be elliptical in my case.
To do so however, I need to start by finding the XYZ coordinates of four points around the ellipse, the obvious candidates are the very end points of the Semi-Major and Semi-Minor axes. I already have all of the Orbital Elements for the given orbit:
- Eccentricity (E)
- Semi-Major Axis (A)
- Inclination (I)
- Longitude of Ascending Node (L)
- Argument of Periapsis (W)
- Mean Anomaly at Epoch (M)
Given these parameters, how can I find the extremities of the minor & major axis as a world-space vector (XYZ)? I hope I've explained this well, my first time posting here!
Bonus points for also figuring out the Tangent Vectors at each of the four points to plot the ellipse.