/// <summary>
/// Finds the endpoint of the segments P and Q which
/// is closest to the other segment.
/// This is a reasonable surrogate for the true
/// intersection points in ill-conditioned cases
/// (e.g. where two segments are nearly coincident,
/// or where the endpoint of one segment lies almost on the other segment).
/// </summary>
/// <remarks>
/// This replaces the older CentralEndpoint heuristic,
/// which chose the wrong endpoint in some cases
/// where the segments had very distinct slopes
/// and one endpoint lay almost on the other segment.
/// </remarks>
/// <param name="p1">an endpoint of segment P</param>
/// <param name="p2">an endpoint of segment P</param>
/// <param name="q1">an endpoint of segment Q</param>
/// <param name="q2">an endpoint of segment Q</param>
/// <returns>the nearest endpoint to the other segment</returns>
private static Coordinate NearestEndpoint(Coordinate p1, Coordinate p2,
Coordinate q1, Coordinate q2)
{
var nearestPt = p1;
double minDist = DistanceComputer.PointToSegment(p1, q1, q2);
double dist = DistanceComputer.PointToSegment(p2, q1, q2);
if (dist < minDist)
{
minDist = dist;
nearestPt = p2;
}
dist = DistanceComputer.PointToSegment(q1, p1, p2);
if (dist < minDist)
{
minDist = dist;
nearestPt = q1;
}
dist = DistanceComputer.PointToSegment(q2, p1, p2);
if (dist < minDist)
{
minDist = dist;
nearestPt = q2;
}
return(nearestPt);
}
/// <summary>
/// Computes the distance from a point to a sequence of line segments.
/// </summary>
/// <param name="p">A point</param>
/// <param name="line">A sequence of contiguous line segments defined by their vertices</param>
/// <returns>The minimum distance between the point and the line segments</returns>
public static double PointToSegmentString(Coordinate p, Coordinate[] line)
{
if (line.Length == 0)
{
throw new ArgumentException(
"Line array must contain at least one vertex");
}
// this handles the case of length = 1
double minDistance = p.Distance(line[0]);
for (int i = 0; i < line.Length - 1; i++)
{
double dist = DistanceComputer.PointToSegment(p, line[i], line[i + 1]);
if (dist < minDistance)
{
minDistance = dist;
}
}
return(minDistance);
}
/// <summary>
/// Computes the distance from a point to a sequence of line segments.
/// </summary>
/// <param name="p">A point</param>
/// <param name="line">A sequence of contiguous line segments defined by their vertices</param>
/// <returns>The minimum distance between the point and the line segments</returns>
public static double PointToSegmentString(Coordinate p, ICoordinateSequence line)
{
if (line.Count == 0)
{
throw new ArgumentException(
"Line array must contain at least one vertex");
}
// this handles the case of length = 1
var lastStart = line.GetCoordinate(0);
double minDistance = p.Distance(lastStart);
for (int i = 1; i < line.Count - 1; i++)
{
var currentEnd = line.GetCoordinate(i);
double dist = DistanceComputer.PointToSegment(p, lastStart, currentEnd);
if (dist < minDistance)
{
minDistance = dist;
}
lastStart = currentEnd;
}
return(minDistance);
}
public static double DistanceLineLine(Coordinate A, Coordinate B, Coordinate C, Coordinate D)
{
return(DistanceComputer.SegmentToSegment(A, B, C, D));
}
public static double DistancePointLine(Coordinate p, Coordinate[] line)
{
return(DistanceComputer.PointToSegmentString(p, line));
}
public static double DistancePointLinePerpendicular(Coordinate p, Coordinate A, Coordinate B)
{
return(DistanceComputer.PointToLinePerpendicular(p, A, B));
}
public static double DistancePointLine(Coordinate p, Coordinate A, Coordinate B)
{
return(DistanceComputer.PointToSegment(p, A, B));
}
/// <summary>
/// Computes the distance from a line segment AB to a line segment CD
/// <para/>
/// Note: NON-ROBUST!
/// </summary>
/// <param name="A">The first point of the first line</param>
/// <param name="B">The second point of the first line (must be different to A)</param>
/// <param name="C">The first point of the second line</param>
/// <param name="D">The second point of the second line (must be different to C)</param>
/// <returns>The distance from a line segment AB to a line segment CD</returns>
public static double SegmentToSegment(Coordinate A, Coordinate B,
Coordinate C, Coordinate D)
{
// check for zero-length segments
if (A.Equals(B))
{
return(DistanceComputer.PointToSegment(A, C, D));
}
if (C.Equals(D))
{
return(DistanceComputer.PointToSegment(D, A, B));
}
// AB and CD are line segments
/*
* from comp.graphics.algo
*
* Solving the above for r and s yields
*
* (Ay-Cy)(Dx-Cx)-(Ax-Cx)(Dy-Cy)
* r = ----------------------------- (eqn 1)
* (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
*
* (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
* s = ----------------------------- (eqn 2)
* (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
*
* Let P be the position vector of the
* intersection point, then
* P=A+r(B-A) or
* Px=Ax+r(Bx-Ax)
* Py=Ay+r(By-Ay)
* By examining the values of r & s, you can also determine some other limiting
* conditions:
* If 0<=r<=1 & 0<=s<=1, intersection exists
* r<0 or r>1 or s<0 or s>1 line segments do not intersect
* If the denominator in eqn 1 is zero, AB & CD are parallel
* If the numerator in eqn 1 is also zero, AB & CD are collinear.
*/
bool noIntersection = false;
if (!Envelope.Intersects(A, B, C, D))
{
noIntersection = true;
}
else
{
double denom = (B.X - A.X) * (D.Y - C.Y) - (B.Y - A.Y) * (D.X - C.X);
if (denom == 0)
{
noIntersection = true;
}
else
{
double r_num = (A.Y - C.Y) * (D.X - C.X) - (A.X - C.X) * (D.Y - C.Y);
double s_num = (A.Y - C.Y) * (B.X - A.X) - (A.X - C.X) * (B.Y - A.Y);
double s = s_num / denom;
double r = r_num / denom;
if ((r < 0) || (r > 1) || (s < 0) || (s > 1))
{
noIntersection = true;
}
}
}
if (noIntersection)
{
return(MathUtil.Min(
DistanceComputer.PointToSegment(A, C, D),
DistanceComputer.PointToSegment(B, C, D),
DistanceComputer.PointToSegment(C, A, B),
DistanceComputer.PointToSegment(D, A, B)));
}
// segments intersect
return(0.0);
}
