2DLightPathSimulator/LensSimulatorCore/Shapes/Ellipse.cs

using LensSimulatorCore.MathsLib;
using LensSimulatorCore.Shapes;

namespace LensSimulatorCore.Shapes;

public class Ellipse
{
    public Ellipse(double angle, double semiMajorAxis, double semiMinorAxis, Point position)
    {
        _radianAngle = angle;//* (180 / Math.PI);
        _semiMajorAxis = semiMajorAxis;
        _semiMinorAxis = semiMinorAxis;
        _position = position;
    }

    private readonly double _semiMajorAxis;
    private readonly double _semiMinorAxis;
    private readonly Point _position;
    private readonly double _radianAngle = 0;

    public List<Point> GetIntersectionPoints(Line line)
    {
        var cosTheta = Math.Cos(_radianAngle);
        var sinTheta = Math.Sin(_radianAngle);

        var majorSquared = _semiMajorAxis * _semiMajorAxis;
        var minorSquared = _semiMinorAxis * _semiMinorAxis;

        var LCM = CoreMaths.CalculateLCM(majorSquared, minorSquared);

        var intersectionMinusXpos = line.C - _position.X;

        var intersectionMinusXposCosTheta = (intersectionMinusXpos * cosTheta);
        var intersectionMinusXposSinTheta = (intersectionMinusXpos * sinTheta);
        var ySinTheta = _position.Y * sinTheta;
        var yCosTheta = _position.Y * cosTheta;
        var slopeCosTheta = line.B * cosTheta;
        var slopeSinTheta = line.B * sinTheta;

        var a1 = minorSquared * Math.Pow(slopeCosTheta - sinTheta, 2);
        var b1 = minorSquared * (slopeCosTheta - sinTheta) * (intersectionMinusXposCosTheta + ySinTheta) * 2;
        var c1 = minorSquared * Math.Pow(intersectionMinusXposCosTheta + ySinTheta, 2);

        var a2 = majorSquared * Math.Pow(slopeSinTheta + cosTheta, 2);
        var b2 = majorSquared * (slopeSinTheta + cosTheta) * (intersectionMinusXposSinTheta - yCosTheta) * 2;
        var c2 = majorSquared * Math.Pow(intersectionMinusXposSinTheta - yCosTheta, 2);

        var a = a1 + a2;
        var b = b1 + b2;
        var c = c1 + c2 - LCM;

        var y = CoreMaths.SolveQuadratic(a, b, c);

        return y.Select(y => new Point(line.B * y!.Value + line.C, y.Value)).ToList();
    }
}