using System;
using System.Linq;
using System.Collections.Generic;

namespace Test
{
public static class MathHelper
    {
        public static double ToRadians(double degrees)
        {
            return degrees * Math.PI / 180.0;
        }

        public static double ToDegrees(double radians)
        {
            return radians / Math.PI * 180.0;
        }
    }

    public class Planet
    {
        public string Name { get; set; }
        public double Inclination { get; set; }
        public double LongitudeOfAscent { get; set; }
        public double Distance { get; set; }
        public double MaxElevation { get; set; }
        double solarAngle { get; set; } // angle in radians for 1/2 of sun at this orbit, for +/- calculation

        public Planet(string name, double inclination, double longitude, double distance)
        {
            this.Name = name;
            this.Inclination = MathHelper.ToRadians(inclination);
            this.LongitudeOfAscent = MathHelper.ToRadians(longitude);
            this.Distance = distance;
            MaxElevation = Math.Tan(this.Inclination) * this.Distance;
            solarAngle = Math.Atan(0.6955/Distance); // 1/2 angular size of the sun at orbital distance
        }

        public static List<Planet> Planets;

        static Planet()
        {
            Planets = new List<Planet>();
            Planets.Add(new Planet("Mercury", 6.34, 48.331, 57.9));
            Planets.Add(new Planet("Venus", 2.19, 76.678, 108.20));
            Planets.Add(new Planet("Earth", 1.57, 348.73936, 149.60));
            Planets.Add(new Planet("Mars", 1.67, 49.562, 227.9));
            Planets.Add(new Planet("Jupiter", 0.32, 100.492, 778.3));
            Planets.Add(new Planet("Saturn", 0.93, 113.642811, 1427));
            Planets.Add(new Planet("Uranus", 1.02, 73.989, 2871));
            Planets.Add(new Planet("Neptune", 0.72, 131.79431, 4497.10));
        }

        /// <summary>
        /// For a given longitude on the invariable plane, calculate and return
        /// the minimum and maximum latitude where the planet's center could be
        /// seen with the sun in the background.
        /// </summary>
        /// <param name="longitude"></param>
        /// <returns></returns>
        public Range GetRange(double longitude)
        {
            double longitudeRadians = MathHelper.ToRadians(longitude);

            // ok, first we get the viewing longitude as relative to the angle of the ascending node
            double viewingLongitude = longitudeRadians - LongitudeOfAscent;

            // ok, angle above plane is inclination of plane * sin of viewing angle
            double planetAngle = Inclination * Math.Sin(viewingLongitude);

            return new Range() { Min = planetAngle - solarAngle, Max = planetAngle + solarAngle };
        }
    }

    public class Range
    {
        public double Min { get; set; }
        public double Max { get; set; }
    }

    public class ShowOrbits
    {
        public static void Main()
        {
            // for 360 degrees, show what other planets are visible from earth
            var others = Planet.Planets.Where(x => x.Name != "Earth");
            var earth = Planet.Planets.Where(x => x.Name == "Earth").Single();
            for (double angle = 0; angle < 360; angle += 1.0)
            {
                var er = earth.GetRange(angle);
                List<string> planets = new List<string>();
                foreach (var planet in others)
                {
                    var range = planet.GetRange(angle);
                    if (range.Min <= er.Max && range.Max >= er.Min)
                    {
                        planets.Add(planet.Name);
                    }
                }
                Console.WriteLine("{0:000} degrees: {1:##0.00} to {2:##0.00} can see {3}", 
                    angle, MathHelper.ToDegrees(er.Min), MathHelper.ToDegrees(er.Max), string.Join(", ", planets.ToArray()));
                    

                // at Earth's Longitude of Ascending node, show all planets
                if (angle == 349 || angle == 107)
                {
                    foreach (var p in Planet.Planets)
                    {
                        var r = p.GetRange(angle);
                        Console.WriteLine("{0:10}: {1:##0.00} to {2:##0.00}", p.Name, MathHelper.ToDegrees(r.Min), MathHelper.ToDegrees(r.Max));
                    }
                }
            }
        }
    }
}