import 'dart:math';

import 'dart:ui';
import 'package:flutter/material.dart';
import 'package:flutter/scheduler.dart';

void main() {
  runApp(const MyHomePage());
}

class MyHomePage extends StatefulWidget {
  const MyHomePage({super.key});

  @override
  State<MyHomePage> createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> with SingleTickerProviderStateMixin<MyHomePage> {
  late Ticker _ticker;
  double _t = 0.0;
  
  @override
  void initState() {
    super.initState();
    _ticker = createTicker((Duration elapsed) { setState(() { _t = elapsed.inMilliseconds.toDouble(); }); });
    _ticker.start();
  }

  @override
  void dispose() {
    _ticker.dispose();
    super.dispose();
  }
  
  @override
  Widget build(BuildContext context) {
    const double zoom = 0.2;
    const Offset offset = Offset(2.0, 2.0);
    const double timeScale = 0.001;
    return ColoredBox(
      color: Colors.black,
      child: Stack(
        textDirection: TextDirection.ltr,
        fit: StackFit.expand,
        children: <Widget>[
          CustomPaint(painter: Painter(t: _t * timeScale, period: 1.0, semiMajorAxis: 0.5, thetaZero: 0, eccentricity: 0.0, omega: 1.0, color: Colors.orange, zoom: zoom, offset: offset)),
          CustomPaint(painter: Painter(t: _t * timeScale, period: 2.0, semiMajorAxis: 1.0, thetaZero: -pi / 2.0, eccentricity: 0.1, omega: 1.0, color: Colors.green, zoom: zoom, offset: offset)),
          CustomPaint(painter: Painter(t: _t * timeScale, period: 3.0, semiMajorAxis: 1.5, thetaZero: -pi, eccentricity: 0.2, omega: 1.0, color: Colors.teal, zoom: zoom, offset: offset)),
          CustomPaint(painter: Painter(t: _t * timeScale, period: 20.0, semiMajorAxis: 2.0, thetaZero: -pi/5.0, eccentricity: 0.95, omega: pi / 4.0, color: Colors.yellow, zoom: zoom, offset: offset)),
          CustomPaint(painter: Painter(t: _t * timeScale, period: 4.0, semiMajorAxis: 1.0, thetaZero: 3*pi/4, eccentricity: 0.99, omega: -3*pi/4, color: Colors.red, zoom: zoom, offset: offset)),
        ],
      ),
    );
  }
}

class Painter extends CustomPainter {
  Painter({
    required this.t,
    required this.period,
    required this.semiMajorAxis,
    required this.thetaZero,
    required this.eccentricity,
    required this.omega,
    required this.color,
    required this.zoom,
    required this.offset,
  }) : assert(eccentricity >= 0.0), assert(eccentricity < 1.0);

  final double t;
  final double period;
  final double semiMajorAxis;
  final double thetaZero;
  final double eccentricity;
  final double omega;
  final Color color;
  final Offset offset;
  final double zoom;

  static const Offset unit = Offset(1.0, 1.0);
  
  @override
  void paint(Canvas canvas, Size size) {
    final double scale = size.shortestSide * zoom;

    // EVERYTHING BELOW IS FLIPPED BECAUSE WE'RE USING THE WRONG FOCAL POINT
    
    double semiMinorAxis = semiMajorAxis * sqrt(1 - eccentricity*eccentricity);
    double length = semiMajorAxis * (1 - eccentricity*eccentricity); // length of the semi latus rectum

    double time = (t % period) / period; // 0..1
    double theta = (2*pi*(((atan(time*50-25)+1.53081764)/3.06163528)*(eccentricity*0.25)+(1-eccentricity*0.25)*time) + omega);
    // theta = omega is the apoapsis (furthest point)
    // theta = omega + pi is the periapsis (nearest point)

    double r = length / (1 + eccentricity * cos(theta - omega));
    
    // current position of body
    Offset p = Offset(r * cos(theta), r * sin(theta));

    // axis aligned bounding box of ellipse
    double c = eccentricity * semiMajorAxis; // distance from focal point to center of ellipse, along major axis
    double sinOmega = sin(omega);
    double cosOmega = cos(omega);
    Offset cOffset = Offset(c * cosOmega, c * sinOmega);

    Rect oval = Rect.fromCenter(center: Offset(-c, 0.0) * scale, width: semiMajorAxis * 2.0 * scale, height: semiMinorAxis * 2.0 * scale);

//    double halfWidth = sqrt(semiMajorAxis * semiMajorAxis * cosOmega * cosOmega + semiMinorAxis * semiMinorAxis * sinOmega * sinOmega);
//    double halfHeight = sqrt(semiMajorAxis * semiMajorAxis * sinOmega * sinOmega + semiMinorAxis * semiMinorAxis * cosOmega * cosOmega);
//    Rect boundingBox = Rect.fromCenter(center: (offset + cOffset) * scale, width: (halfWidth * 2.0) * scale, height: (halfHeight * 2.0) * scale);
//    canvas.drawRect(boundingBox, Paint()..color = Color(0x08FFFFFF));
    
    canvas.drawPoints(
      PointMode.points,
      <Offset>[
        offset * scale,
        (p + offset + cOffset * 2.0) * scale,
      ],
      Paint()
        ..color = color
        ..strokeWidth = 10.0
        ..strokeCap = StrokeCap.round,
    );
    
    canvas.save();
    canvas.translate(offset.dx * scale, offset.dy * scale);
    canvas.rotate(omega + pi);
    canvas.drawOval(oval, Paint()..style= PaintingStyle.stroke..color = color);
    canvas.restore();
  }

  @override
  bool shouldRepaint(Painter oldDelegate) => oldDelegate.t != t;
}