/// <summary>
/// Finds the shortest distance between two line segments.
/// </summary>
/// <param name="lineSegment"></param>
/// <param name="otherLineSegment"></param>
/// <param name="shortestDistanceSegment">Outputs a line segment for the shortest found distance.
/// PointA is on the first input line segment, PointB is on the second input line segment. </param>
/// <returns></returns>
public static double ShortestSquaredDistanceToOtherLineSegment(this LineSegment2D lineSegment, LineSegment2D otherLineSegment, out LineSegment2D shortestDistanceSegment)
{
Point2D?intersectionPoint;
if (lineSegment.IntersectsOtherLineSegment(otherLineSegment, out intersectionPoint))
{
shortestDistanceSegment = new LineSegment2D(intersectionPoint.Value, intersectionPoint.Value);
return(0);
}
Point2D pointA, pointB;
double shortestSquaredDistance;
// Check first end point on first segment to second line segment.
pointA = lineSegment.PointA;
shortestSquaredDistance = otherLineSegment.ShortestSquaredDistanceToPoint(lineSegment.PointA, out pointB);
Point2D pointCandidate;
double distanceCandidate;
// Check second end point on first segment to second line segment.
distanceCandidate = otherLineSegment.ShortestSquaredDistanceToPoint(lineSegment.PointB, out pointCandidate);
if (distanceCandidate < shortestSquaredDistance)
{
shortestSquaredDistance = distanceCandidate;
pointA = lineSegment.PointB;
pointB = pointCandidate;
}
// Check first end point on second line segment to first line segment.
distanceCandidate = lineSegment.ShortestSquaredDistanceToPoint(otherLineSegment.PointA, out pointCandidate);
if (distanceCandidate < shortestSquaredDistance)
{
shortestSquaredDistance = distanceCandidate;
pointA = pointCandidate;
pointB = otherLineSegment.PointA;
}
// Check second end point on second line segment to first line segment.
distanceCandidate = lineSegment.ShortestSquaredDistanceToPoint(otherLineSegment.PointB, out pointCandidate);
if (distanceCandidate < shortestSquaredDistance)
{
shortestSquaredDistance = distanceCandidate;
pointA = pointCandidate;
pointB = otherLineSegment.PointB;
}
shortestDistanceSegment = new LineSegment2D(pointA, pointB);
return(shortestSquaredDistance);
}
public static double ShortestSquaredDistanceToPoint(this LineSegment2D lineSegment, Point2D point, out Point2D pointOnSegment)
{
var lineSegmentSquaredLength = lineSegment.SquaredLength();
var pA = lineSegment.PointA;
var pB = lineSegment.PointB;
if (lineSegmentSquaredLength == 0)
{
pointOnSegment = pA;
return((point - pA).SquaredLength());
}
var t = ((point.X - pA.X) * (pB.X - pA.X) + (point.Y - pA.Y) * (pB.Y - pA.Y)) / lineSegmentSquaredLength;
t = Math.Max(0, Math.Min(1, t));
pointOnSegment = new Point2D(pA.X + t * (pB.X - pA.X), pA.Y + t * (pB.Y - pA.Y));
return((pointOnSegment - point).SquaredLength());
}
public static double ShortestSquaredDistanceToOtherLineSegment(this LineSegment2D lineSegment, LineSegment2D otherLineSegment)
{
LineSegment2D shortestDistanceSegment;
return(ShortestSquaredDistanceToOtherLineSegment(lineSegment, otherLineSegment, out shortestDistanceSegment));
}
public static double ShortestDistanceToOtherLineSegment(this LineSegment2D lineSegment, LineSegment2D otherLineSegment)
{
return(Math.Sqrt(ShortestSquaredDistanceToOtherLineSegment(lineSegment, otherLineSegment)));
}
public static double ShortestSquaredDistanceToPoint(this LineSegment2D lineSegment, Point2D point)
{
Point2D pointOnSegment;
return(ShortestSquaredDistanceToPoint(lineSegment, point, out pointOnSegment));
}
public static bool IntersectsOtherLineSegment(this LineSegment2D lineSegment, LineSegment2D otherLineSegment, out Point2D?intersectionPoint)
{
var line0 = new Line2D(lineSegment);
var line1 = new Line2D(otherLineSegment);
if (line0.IntersectsOtherLine(line1, out intersectionPoint))
{
var lineSegmentSquaredLength = lineSegment.SquaredLength();
if ((intersectionPoint.Value - line0.PointA).SquaredLength() > lineSegmentSquaredLength ||
(intersectionPoint.Value - line0.PointB).SquaredLength() > lineSegmentSquaredLength)
{
intersectionPoint = null;
return(false);
}
var lineSegmentSquaredLength1 = otherLineSegment.SquaredLength();
if ((intersectionPoint.Value - line1.PointA).SquaredLength() > lineSegmentSquaredLength1 ||
(intersectionPoint.Value - line1.PointB).SquaredLength() > lineSegmentSquaredLength1)
{
intersectionPoint = null;
return(false);
}
return(true);
}
return(false);
}
public static bool IntersectsOtherLineSegment(this LineSegment2D lineSegment, LineSegment2D otherLineSegment)
{
Point2D?intersectionPoint;
return(IntersectsOtherLineSegment(lineSegment, otherLineSegment, out intersectionPoint));
}
public Line2D(LineSegment2D lineSegment)
{
PointA = lineSegment.PointA;
PointB = lineSegment.PointB;
}
public static double ShortestSquaredDistanceToOtherPolygon(this Polygon2D polygon, Polygon2D otherPolygon, out LineSegment2D shortestDistanceSegment)
{
var shortestSquaredDistance = double.MaxValue;
shortestDistanceSegment = new LineSegment2D();
LineSegment2D candidateSegment;
double candidateSquaredDistance;
foreach (var lineSegment0 in polygon.GetLineSegments())
{
foreach (var lineSegment1 in otherPolygon.GetLineSegments())
{
candidateSquaredDistance = lineSegment0.ShortestSquaredDistanceToOtherLineSegment(lineSegment1, out candidateSegment);
if (candidateSquaredDistance < shortestSquaredDistance)
{
shortestSquaredDistance = candidateSquaredDistance;
shortestDistanceSegment = candidateSegment;
}
}
}
return(shortestSquaredDistance);
}
public static double ShortestDistanceToOtherPolygon(this Polygon2D polygon, Polygon2D otherPolygon, out LineSegment2D shortestDistanceSegment)
{
return(Math.Sqrt(ShortestSquaredDistanceToOtherPolygon(polygon, otherPolygon, out shortestDistanceSegment)));
}
