/// <summary>
/// Point on the perpendicular to the line
/// </summary>
public Point3d PerpendicularTo(Line3d l)
{
Vector3d r1 = this.Point.ToVector;
Vector3d r2 = l.Point.ToVector;
Vector3d s1 = this.Direction;
Vector3d s2 = l.Direction;
if (s1.Cross(s2).Norm > GeometRi3D.Tolerance)
{
Point3d p = l.PerpendicularTo(new Line3d(this.Point, this.Direction));
if (p.BelongsTo(this))
{
r1 = r2 + (r2 - r1) * s1.Cross(s1.Cross(s2)) / (s1 * s2.Cross(s1.Cross(s2))) * s2;
return(r1.ToPoint);
}
else
{
return(this.Point.ProjectionTo(l));
}
}
else
{
throw new Exception("Lines are parallel");
}
}
/// <summary>
/// Shortest distance to a line
/// </summary>
public double DistanceTo(Line3d l)
{
Vector3d r1 = this.Point.ToVector;
Vector3d r2 = l.Point.ToVector;
Vector3d s1 = this.Direction;
Vector3d s2 = l.Direction;
if (s1.Cross(s2).Norm > GeometRi3D.Tolerance)
{
// Crossing lines
Point3d p = l.PerpendicularTo(new Line3d(this.Point, this.Direction));
if (p.BelongsTo(this))
{
return(Abs((r2 - r1) * s1.Cross(s2)) / s1.Cross(s2).Norm);
}
else
{
return(this.Point.DistanceTo(l));
}
}
else
{
// Parallel lines
return((r2 - r1).Cross(s1).Norm / s1.Norm);
}
}
/// <summary>
/// Returns shortest distance from segment to the line
/// </summary>
public double DistanceTo(Line3d l)
{
if (l.PerpendicularTo(this.ToLine).BelongsTo(this))
{
return(l.DistanceTo(this.ToLine));
}
else
{
return(Min(this.P1.DistanceTo(l), this.P2.DistanceTo(l)));
}
}
/// <summary>
/// Get intersection of line with other line.
/// Returns 'null' (no intersection) or object of type 'Point3d' or 'Line3d'.
/// </summary>
public object IntersectionWith(Line3d l)
{
if (l.IsParallelTo(this) && l.Point.BelongsTo(this))
{
return(this.Copy());
}
Point3d p = l.PerpendicularTo(this);
if (p.BelongsTo(l))
{
return(p);
}
else
{
return(null);
}
}
/// <summary>
/// Get intersection of segment with line.
/// Returns 'null' (no intersection) or object of type 'Point3d' or 'Segment3d'.
/// </summary>
public object IntersectionWith(Line3d l)
{
if (this.BelongsTo(l))
{
return(this.Copy());
}
Point3d p = l.PerpendicularTo(this.ToLine);
if (p.BelongsTo(this) && p.BelongsTo(l))
{
return(p);
}
else
{
return(null);
}
}
/// <summary>
/// Get intersection of segment with other segment.
/// Returns 'null' (no intersection) or object of type 'Point3d' or 'Segment3d'.
/// </summary>
public object IntersectionWith(Segment3d s)
{
if (this == s)
{
return(this.Copy());
}
Line3d l1 = this.ToLine;
Line3d l2 = s.ToLine;
if (this.BelongsTo(l2) || s.BelongsTo(l1))
{
// Segments are collinear
// Relative tolerance check ================================
double tol = GeometRi3D.Tolerance;
if (!GeometRi3D.UseAbsoluteTolerance)
{
tol = GeometRi3D.Tolerance * Max(this.Length, s.Length);
}
//==========================================================
// Create local CS with X-axis along segment 's'
Vector3d v2 = s.ToVector.OrthogonalVector;
Coord3d cs = new Coord3d(s.P1, s.ToVector, v2);
double x1 = 0.0;
double x2 = s.Length;
double t3 = this.P1.ConvertTo(cs).X;
double t4 = this.P2.ConvertTo(cs).X;
double x3 = Min(t3, t4);
double x4 = Max(t3, t4);
// Segments do not overlap
if (GeometRi3D.Smaller(x4, x1, tol) || GeometRi3D.Greater(x3, x2, tol))
{
return(null);
}
// One common point
if (GeometRi3D.AlmostEqual(Max(x3, x4), x1, tol))
{
return(new Point3d(x1, 0, 0, cs));
}
if (GeometRi3D.AlmostEqual(Min(x3, x4), x2, tol))
{
return(new Point3d(x2, 0, 0, cs));
}
// Overlaping segments
x1 = Max(x1, x3);
x2 = Min(x2, x4);
return(new Segment3d(new Point3d(x1, 0, 0, cs), new Point3d(x2, 0, 0, cs)));
}
else
{
Point3d p = l1.PerpendicularTo(l2);
if (p.BelongsTo(this) && p.BelongsTo(s))
{
return(p);
}
else
{
return(null);
}
}
}