/// <summary>
/// 点と直線の距離
/// </summary>
/// <param name="l">直線</param>
/// <param name="p">点</param>
/// <returns></returns>
public static double distance_lp(Line3D l, Point3D p)
{
return(dist(p - project_lp(l, p)));
}
/// <summary>
/// 点が線分上にあるか
/// </summary>
/// <param name="l">線分</param>
/// <param name="p">点</param>
/// <returns></returns>
public static bool is_in_segment(Line3D l, Point3D p)
{
return(Math.Abs(dist(l.a - p) + dist(l.b - p) - dist(l.a - l.b)) < Eps);
}
/// <summary>
/// 点の射影(点から直線に引いた垂線と線分の交点)
/// </summary>
/// <param name="l">直線</param>
/// <param name="p">点</param>
/// <returns></returns>
public static Point3D project_lp(Line3D l, Point3D p)
{
Point3D point = l.a, vec = l.b - l.a;
return(point + dot(p - point, vec) / norm(vec) * vec);
}