Why does this work?

Unity Engine
1

I have written a script to calculate the points of an ellipse and then draw them using a LineRenderer. I add some corrections to the calculated points: First, I want the GameObject to be in on of the foci of the ellipse, so the points get offset by that amount. Second, the GameObject.Transform.rotation is added to the points so I can use the GameObject rotation in the Editor to rotate the Ellipse. Third, the GameObject.Transform.position is added to all calculated points so I can move the ellipse around by moving the GameObject the script is attached to. I fiddled around with the correct order yesterday until it worked. Then I cleaned the script a bit and created a static function for calculating the ellipse points so that other scripts can use that functionality, too. After that the rotation behaved weird - rotating around strange axis, not moving in the local cardinal directions when I use the Editor arrows to move it etc. - until I cut the uppermentioned “First” and “Third” from the calculation. Now it works and I don’t have any clue, why. Please enlighten me.

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

[ExecuteInEditMode]
[RequireComponent (typeof(LineRenderer))]

public class Ellipse1 : MonoBehaviour
{
    public Vector2 axes = new Vector2(1f, 1f);
    public float width = 1f;
    public int resolution = 500;

    private Transform self_transform;
    private Vector3[] positions;
    private LineRenderer self_lineRenderer;

    void Update() {
        if(self_transform == null) {
            self_transform = GetComponent<Transform>();
        }
        if(self_transform.hasChanged) {
            CalcEllipse();
        }
    }

    public void CalcEllipse() {
        if(self_lineRenderer == null) {
            self_lineRenderer = GetComponent<LineRenderer>();
        }

        print(self_transform.rotation.eulerAngles);

        Vector3[] returnlist = returnEllipsePath(self_transform.position, self_transform.rotation.eulerAngles, axes, 500);
        self_lineRenderer.SetPositions(returnlist);
    }

    public static Vector3[] returnEllipsePath(Vector3 focus_pos, Vector3 rotation, Vector2 axes, int resolution, bool overlap) {
        Vector3[] returnlist = new Vector3[resolution+2];
        float f;
        Vector3 focus_offset;

        if(axes.x > axes.y) {
            f = Mathf.Sqrt(Mathf.Pow(axes.x, 2) - Mathf.Pow(axes.y, 2));
            focus_offset = new Vector3(f, 0, 0);
        } else if(axes.x < axes.y) {
            f = Mathf.Sqrt(Mathf.Pow(axes.y, 2) - Mathf.Pow(axes.x, 2));
            focus_offset = new Vector3(0, f, 0);
        } else {
            focus_offset = new Vector3(0,0,0);
        }
       
        float angle;

        for (int i = 0; i <= resolution + 1; i++)  {
            angle = (float)i / (float)(resolution) * 2.0f * Mathf.PI;
            // --- OLD CALCULATION:
            //Quaternion.Euler(rotation) * (new Vector3(axes.x * Mathf.Cos(angle), axes.y * Mathf.Sin(angle), 0.0f) + focus_offset) + focus_pos;

            // --- NEW CALCULATION:
            Vector3 pointPosition = Quaternion.Euler(rotation) * new Vector3(axes.x * Mathf.Cos(angle), axes.y * Mathf.Sin(angle), 0.0f);
           
            returnlist[i] = pointPosition;
        }

        return returnlist;
    }

    public static Vector3[] returnEllipsePath(Vector3 focus_pos, Vector3 rotation, Vector2 axes, int resolution) {
        return returnEllipsePath(focus_pos, rotation, axes, resolution, true);
    }
}
2

EDIT: Sorry, to clarify: Dis- or Enabling the focus_offset in the calculation has the normal effect of offsetting the ellipse. Its just the focus_position which is apparently not needed to be added. I seems to me the GameObject uses local coordinates since I moved it to a static function when before it used world coordinates (before and without the focus_position addition it would just remain at (0,0,0) as I would expect)

3

Depends on if you check the “Use World Space” box on the LineRenderer component, I think is your question?