2DLightPathSimulator/LensSimulatorCore/Shapes/Ellipse.cs

using System.Drawing;
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 = 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 slopeCosThetaMinusSinTheta = slopeCosTheta - sinTheta;
        var intersectionMinusXposCosThetaPlusYSinTheta = intersectionMinusXposCosTheta + ySinTheta;

        var slopeCosThetaMinusSinThetaPow2 = Math.Pow(slopeCosThetaMinusSinTheta, 2);
        var ser = intersectionMinusXposCosThetaPlusYSinTheta * (slopeCosThetaMinusSinTheta) * 2;
        var intersectionMinusXposCosThetaPow2 = Math.Pow(intersectionMinusXposCosThetaPlusYSinTheta, 2);

        var a1 = minorSquared * slopeCosThetaMinusSinThetaPow2;
        var b1 = minorSquared * ser;
        var c1 = minorSquared * intersectionMinusXposCosThetaPow2;

        var slopeSinThetaPlusCosTheta = slopeSinTheta + cosTheta;
        var intersectionMinusXposSinThetaMinusYCosTheta = intersectionMinusXposSinTheta - yCosTheta;

        var slopeSinThetaMinusCosThetaPow2 = Math.Pow(slopeSinThetaPlusCosTheta, 2);
        var se = intersectionMinusXposSinThetaMinusYCosTheta * (slopeSinThetaPlusCosTheta) * 2;
        var intersectionMinusXposSinThetaMinusYCosThetaPow2 = Math.Pow(intersectionMinusXposSinThetaMinusYCosTheta, 2);

        var a2 = majorSquared * slopeSinThetaMinusCosThetaPow2;
        var b2 = majorSquared * se;
        var c2 = majorSquared * intersectionMinusXposSinThetaMinusYCosThetaPow2;

        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 + line.C, y)).ToList();
    }
}