/// <summary>
/// Calculates the intersection points of a line against this ellipse.
/// </summary>
/// <param name="lineP1">Origin point of the line.</param>
/// <param name="lineP2">End point of the line.</param>
/// <param name="inSegment">Choose only those intersection points in the segment P1-P2.</param>
/// <returns></returns>
public List <Vector2> Intersect(Vector3 lineP1, Vector3 lineP2, bool inSegment)
{
// Source:
//http://csharphelper.com/blog/2017/08/calculate-where-a-line-segment-and-an-ellipse-intersect-in-c/
float xVector2 = Mathf.Pow((lineP2.x - lineP1.x), 2);
float yVector2 = Mathf.Pow((lineP2.y - lineP1.y), 2);
float horizontalValue = (xVector2 / HorizontalRadius) / HorizontalRadius;
float verticalValue = (yVector2 / VerticalRadius) / VerticalRadius;
float A = horizontalValue + verticalValue;
float B = 2 * lineP1.x * horizontalValue + 2 * lineP1.y * verticalValue;
float C = lineP1.x * horizontalValue + lineP1.y * verticalValue - 1;
float[] t = Hedra.QuadraticFormula(A, B, C);
List <Vector2> intersectionPoints = new List <Vector2>();
for (int i = 0; i < t.Length; i++)
{
if (!inSegment || ((t[i] >= 0f) && (t[i] <= 1f)))
{
Vector2 point = new Vector2();
point.x = lineP1.x + (lineP2.x - lineP1.x) * t[i] + Center.x;
point.y = lineP1.y + (lineP2.y - lineP1.y) * t[i] + Center.y;
intersectionPoints.Add(point);
}
}
return(intersectionPoints);
}