Need help rendering Orbits, with Orbital Elements

Question

Hi there!

Currently I'm working a space-related project, which includes the solar system. I have run into a bit of halt. I want to show the orbits of the major bodies in our solar system, but I do not need to simulate velocity or gravity or anything like that. I just want the path rendered out in the scene (im using Kerbal space programs "static" body orbits as inspiration).

I do have some ellipse rendering code here, but i really need some help or tips how to use orbital elements to show the orbits. Instead of x,y,z,angle, i want to use the 6 keplarian elements.

Any help is appreciated! :)

 public class OrbitHandler : MonoBehaviour {
 
     public Vector3 radius = new Vector3(1f, 1f, 1f);
     public float rotationAngle = 45;
     public int resolution = 500;
 
     private Vector3[] positions;
     private LineRenderer lr;
 
 
     void OnValidate()
     {
         UpdateEllipse();
     }
 
     public void UpdateEllipse()
     {
         if (lr == null)
             lr = GetComponent<LineRenderer>();
 
         lr.positionCount = resolution + 3;
 
         AddPointToLineRenderer(0f, 0);
         for (int i = 1; i <= resolution + 1; i++)
         {
             AddPointToLineRenderer((float)i / (float)(resolution) * 2.0f * Mathf.PI, i);
         }
         AddPointToLineRenderer(0f, resolution + 2);
     }
 
     void AddPointToLineRenderer(float angle, int index)
     {
         Quaternion pointQuaternion = Quaternion.AngleAxis(rotationAngle, Vector3.forward);
         Vector3 pointPosition;
 
         pointPosition = new Vector3(radius.x * Mathf.Cos(angle), radius.z * Mathf.Sin(angle), radius.y * Mathf.Sin(angle));
         pointPosition = pointQuaternion * pointPosition;
 
         lr.SetPosition(index, pointPosition);
     }
 }

Answer 1

Hi there i have been able to get a code going but i cant figure out the correct true anomaly, which seems to be the main problem. If anyone can help i would be very thankful! Attaching my code

  public void UpdateEllipse()
     {
         lr.positionCount = resolution + 2;
 
         lr.SetPosition(0,AddPointToLineRenderer( 0));
         for (int i = 1; i <= resolution + 1; i++)
         {
             lr.SetPosition(i, AddPointToLineRenderer(i*Mathf.Deg2Rad));
         }
     }
 
     Vector3 AddPointToLineRenderer(float index)
     {
         // pointQuaternion = Quaternion.AngleAxis(rotationAngle, Vector3.forward);
         Vector3 pointPosition;
 
         pointPosition = KeplerToCarthesian(index * Mathf.Rad2Deg, semiMajorAxis,eccentrity,argumentofP,longOfAccNode, inclination);
 
         return pointPosition;        
     }
 
     /// <summary>
     /// Convert keplarian elements into vector3, needs (Mean Anomaly, Semi Majoris Axis, Eccentricity, Argument of Periapsis, Longitude of Ascending node, Inclination) 
     /// </summary>
     /// <returns></returns>
     Vector3 KeplerToCarthesian(double meanAnomaly , float a, float e, float w, float lan, float inc)
     {
         //Fix so inlication calculates properly
         inc *= Mathf.Deg2Rad;
 
         //Gets E and True Anomaly
         double E = GetEccentricAnomaly(meanAnomaly, e);
         double T = GetTrueAnomaly(e, E);
 
         double r = a * (1 - e * Math.Cos(E));
 
         double X = r * (Math.Cos(lan) * Math.Cos(w + T) - Math.Sin(lan) * Math.Sin(w + T) * Math.Cos(inc));
         double Y = r * (Math.Sin(lan) * Math.Cos(w + T) + Math.Cos(lan) * Math.Sin(w + T) * Math.Cos(inc));
         double Z = r * (Math.Sin(inc) * Math.Sin(w + T));
 
         return new Vector3((float)X *10, (float) Z*10, (float) Y*10);
     }
 
     private double GetTrueAnomaly(float e, double E)
     {
         int dp = 6;
         double S = Math.Sin(E);
 
         double C = Math.Cos(E);
 
         double fak = Math.Sqrt(1.0 - e * e);
 
         double phi = Math.Atan2(fak * S, C - e) / Mathf.Deg2Rad;
 
         return Math.Round(phi * Math.Pow(10, dp)) / Math.Pow(10, dp);
     }
 
     private double GetEccentricAnomaly(double meanAnomaly, float e)
     {
         //Solve kepler equation to get Ecentric anomaly
         int tolerance = 6;
         int maxIter = 30, i = 0;
         double delta = Math.Pow(10, -tolerance);
         double E, F;
 
         meanAnomaly /= 360.0f;
 
         meanAnomaly = 2.0 * Math.PI * (meanAnomaly - Math.Floor(meanAnomaly));
 
         if (e < 0.8)
             E = meanAnomaly;
         else
             E = Math.PI;
 
         F = E - e * Math.Sin(meanAnomaly) - meanAnomaly;
 
         while ((Math.Abs(F) > delta) && (i < maxIter))
         {
 
             E = E - F / (1.0 - e * Math.Cos(E));
             F = E - e * Math.Sin(E) - meanAnomaly;
             i++;
         }
 
         E /= (Math.PI / 180.0);
 
         return Math.Round(E * Math.Pow(10, tolerance)) / Math.Pow(10, tolerance);
     }
 }

Need help rendering Orbits, with Orbital Elements

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