/// <summary>
/// Finds the vertical border of the <see cref="ClippingBounds"/> towards which the Voronoi
/// region containing the specified horizontal border coordinates is open.</summary>
/// <param name="p">
/// The first <see cref="PointD"/> to examine.</param>
/// <param name="q">
/// The second <see cref="PointD"/> to examine.</param>
/// <returns>
/// The <see cref="RectD.Left"/> or <see cref="RectD.Right"/> border of the <see
/// cref="ClippingBounds"/>, depending on the specified <paramref name="p"/> and <paramref
/// name="q"/>.</returns>
/// <remarks>
/// The specified <paramref name="p"/> and <paramref name="q"/> must lie on opposite
/// horizontal borders of the <see cref="ClippingBounds"/>, and their Voronoi region must
/// open to one of the vertical borders, including both adjacent corners.</remarks>
private double FindVerticalBorder(PointD p, PointD q)
{
// line from top to bottom of clipping bounds
LineD line = (p.Y < q.Y) ? new LineD(p, q) : new LineD(q, p);
Debug.Assert(line.Start.Y == ClippingBounds.Top);
Debug.Assert(line.End.Y == ClippingBounds.Bottom);
// check for vertex on either side of line
// (LineLocation assumes y-coordinates increase upward!)
foreach (PointD vertex in VoronoiVertices)
{
switch (line.Locate(vertex))
{
case LineLocation.Left: return(ClippingBounds.Right);
case LineLocation.Right: return(ClippingBounds.Left);
}
}
Debug.Fail("Cannot identify open side of Voronoi region.");
return(ClippingBounds.Left);
}
/// <summary>
/// Splits the specified line segments on the specified intersection points.</summary>
/// <param name="lines">
/// An <see cref="Array"/> containing the <see cref="LineD"/> instances to split.</param>
/// <param name="crossings">
/// An <see cref="Array"/> of <see cref="MultiLinePoint"/> instances containing all points
/// of intersection between the <paramref name="lines"/>.</param>
/// <returns>
/// An <see cref="Array"/> containing the <see cref="LineD"/> instances resulting from
/// splitting all <paramref name="lines"/> on the matching <paramref name="crossings"/>.
/// </returns>
/// <exception cref="ArgumentNullException">
/// <paramref name="lines"/> or <paramref name="crossings"/> is a null reference.
/// </exception>
/// <exception cref="IndexOutOfRangeException">
/// <paramref name="crossings"/> contains one or more <see cref="MultiLinePoint.Lines"/>
/// indices that are equal to or greater than the number of <paramref name="lines"/>.
/// </exception>
/// <remarks><para>
/// <b>Split</b> returns a collection of line segments that are guaranteed not to intersect,
/// except at their <see cref="LineD.Start"/> or <see cref="LineD.End"/> points. The
/// specified <paramref name="crossings"/> are usually the result of <see cref="Find"/> or
/// <see cref="FindSimple"/> for the specified <paramref name="lines"/>.
/// </para><para>
/// <b>Split</b> sets the <see cref="LineD.Start"/> or <see cref="LineD.End"/> point of any
/// line segment that participates in a <see cref="LineLocation.Start"/> or <see
/// cref="LineLocation.End"/> intersection to the <see cref="MultiLinePoint.Shared"/>
/// coordinates of that intersection, so as to preserve coordinate identities that were
/// established by a positive comparison epsilon.</para></remarks>
public static LineD[] Split(LineD[] lines, MultiLinePoint[] crossings)
{
if (lines == null)
{
ThrowHelper.ThrowArgumentNullException("lines");
}
if (crossings == null)
{
ThrowHelper.ThrowArgumentNullException("crossings");
}
// list of split segments, or null to use original line
int count = lines.Length;
List <PointD>[] segmentPoints = new List <PointD> [count];
// process all epsilon-matched intersection points
foreach (MultiLinePoint crossing in crossings)
{
for (int k = 0; k < crossing.Lines.Length; k++)
{
int i = crossing.Lines[k];
List <PointD> points = segmentPoints[i];
// initialize split segment list with start & end points
if (points == null)
{
points = new List <PointD>(4);
points.Add(lines[i].Start);
points.Add(lines[i].End);
segmentPoints[i] = points;
}
switch (crossing.Locations[k])
{
case LineLocation.Start:
// replace start point with epsilon-matched intersection
points[0] = crossing.Shared;
break;
case LineLocation.End:
// replace end point with epsilon-matched intersection
points[1] = crossing.Shared;
break;
case LineLocation.Between:
// add intersection point that defines new split segment
points.Add(crossing.Shared);
++count;
break;
}
}
}
/*
* Comparison function to sort split segment point list.
*
* We cannot use lexicographic or other single-coordinate comparisons because
* epsilon matching might cause coordinate aberrations in the wrong direction.
* So we compare the squared distances of both points from the start point.
*/
PointD start = PointD.Empty;
Comparison <PointD> comparison = (a, b) => {
double ax = a.X - start.X, ay = a.Y - start.Y;
double bx = b.X - start.X, by = b.Y - start.Y;
double d = (ax * ax + ay * ay) - (bx * bx + by * by);
if (d < 0)
{
return(-1);
}
if (d > 0)
{
return(+1);
}
return(0);
};
LineD[] segments = new LineD[count];
int index = 0;
for (int i = 0; i < lines.Length; i++)
{
List <PointD> points = segmentPoints[i];
if (points == null)
{
// no intersections, store original line
segments[index++] = lines[i];
}
else
{
Debug.Assert(points.Count > 2);
// sort points by distance from start point
start = points[0];
points.Sort(comparison);
// convert sorted points to split line segments
for (int j = 0; j < points.Count - 1; j++)
{
segments[index++] = new LineD(points[j], points[j + 1]);
}
}
}
Debug.Assert(index == count);
return(segments);
}
