using System;
using Ringtoets.Piping.Data;
using Ringtoets.Piping.IO.Properties;

namespace Ringtoets.Piping.IO.Calculation
{
    /// <summary>
    /// This class contains general mathematical routines for 2D lines.
    /// </summary>
    public static class Math2D
    {
        /// <summary>
        /// Constant which is used to precision errors in <see cref="double"/> comparisons.
        /// </summary>
        private const double epsilonForComparisons = 1e-8;

        /// <summary>
        /// Determines the intersection point of a line which passes through the <paramref name="line1Point1"/> and 
        /// the <paramref name="line1Point2"/>; and a line which passes through the <paramref name="line2Point1"/>
        /// and the <paramref name="line2Point2"/>.
        /// </summary>
        /// <param name="line1Point1">A <see cref="Point2D"/> which the first line passes through.</param>
        /// <param name="line1Point2">Another <see cref="Point2D"/> which the first line passes through.</param>
        /// <param name="line2Point1">A <see cref="Point2D"/> which the second line passes through.</param>
        /// <param name="line2Point2">Another <see cref="Point2D"/> which the second line passes through.</param>
        /// <returns>An <see cref="Point2D"/> with coordinates at the point where the lines intersect. Or <c>null</c> when no
        /// intersection point exists (lines are parallel).</returns>
        /// <remarks>
        /// <para>Taken from: https://www.topcoder.com/community/data-science/data-science-tutorials/geometry-concepts-line-intersection-and-its-applications/ </para>
        /// <para>Based on https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection </para>
        /// </remarks>
        /// <exception cref="ArgumentException">Thrown when <paramref name="line1Point1"/> equals <paramref name="line1Point2"/> or 
        /// <paramref name="line2Point1"/> equals <paramref name="line2Point2"/>, which makes it impossible to determine
        /// a line through the points.</exception>
        public static Point2D LineIntersectionWithLine(Point2D line1Point1, Point2D line1Point2, Point2D line2Point1, Point2D line2Point2)
        {
            if (line1Point1.Equals(line1Point2) || line2Point1.Equals(line2Point2))
            {
                throw new ArgumentException(Resources.Math2D_LineIntersectionWithLine_Line_points_are_equal);
            }

            var aLine = line1Point2.Y - line1Point1.Y;
            var bLine = line1Point1.X - line1Point2.X;
            var cLine = aLine*line1Point1.X + bLine*line1Point1.Y;

            var aOtherLine = line2Point2.Y - line2Point1.Y;
            var bOtherLine = line2Point1.X - line2Point2.X;
            var cOtherLine = aOtherLine*line2Point1.X + bOtherLine*line2Point1.Y;

            var determinant = aLine*bOtherLine - aOtherLine*bLine;
            if (Math.Abs(determinant) < epsilonForComparisons)
            {
                return null;
            }

            return new Point2D
            {
                X = (bOtherLine*cLine - bLine*cOtherLine)/determinant,
                Y = (aLine*cOtherLine - aOtherLine*cLine)/determinant
            };
        }
    }
}