Tests if two line segments intersect or not.
using System;
namespace ComputationalGeometry.Shapes
{
public static class MathUtility
{
/// <summary>
/// Tests if two line segments intersect or not.
/// The orientation of each line to other line's endpoints is used to determine
/// the intersection.
/// </summary>
/// <param name="line1">Line 1.</param>
/// <param name="line2">Line 2.</param>
/// <returns>True if the lines intersect each other.</returns>
public static bool DoLinesIntersect(Line2D line1, Line2D line2)
{
return CrossProduct(line1.InitialPoint, line1.TerminalPoint, line2.InitialPoint) !=
CrossProduct(line1.InitialPoint, line1.TerminalPoint, line2.TerminalPoint) ||
CrossProduct(line2.InitialPoint, line2.TerminalPoint, line1.InitialPoint) !=
CrossProduct(line2.InitialPoint, line2.TerminalPoint, line1.TerminalPoint);
}
/// <summary>
/// Finds the cross product of the 2 vectors created by the 3 vertices.
/// Vector 1 = v1 -> v2, Vector 2 = v2 -> v3
/// The vectors make a "right turn" if the sign of the cross product is negative.
/// The vectors make a "left turn" if the sign of the cross product is positive.
/// The vectors are colinear (on the same line) if the cross product is zero.
/// </summary>
/// <param name="p1">First point.</param>
/// <param name="p2">Second point.</param>
/// <param name="p3">Third point.</param>
/// <returns>Cross product of the two vectors.</returns>
public static double CrossProduct(Point2D p1, Point2D p2, Point2D p3)
{
return (p2.X - p1.X) * (p3.Y - p1.Y) - (p3.X - p1.X) * (p2.Y - p1.Y);
}
}
}