////////////////////////////////////////////////////////////////////////////////////////////////////
/// <summary>
/// Clip this voronoi cell with a passed in bounding box.
/// </summary>
/// <remarks>
/// <para>
/// I'm trying to handle all the exceptional cases. There is one incredibly exceptional
/// case which I'm ignoring. That is the case where there are two vertices at infinity which are
/// at such nearly opposite directions without being completely collinear that we can't push
/// their points at infinity out far enough to encompass the rest of the box within the range of
/// a double. If this is important to you, then see the comments below, but it's hard to imagine
/// it ever arising.
/// </para>
/// <para>
/// Editorial comment - The annoying thing about all of this is that, like in so much of
/// computational geometry, the rarer and less significant the exceptional cases are, the more
/// difficult they are to handle. It's both a blessing and a curse - it means that the normal
/// cases are generally faster, but it also makes it difficult to get excited about slogging
/// through the tedious details of situations that will probably never arise in practice. Still,
/// in order to keep our noses clean, we press on regardless.
/// </para>
/// Darrellp, 2/26/2011.
/// </remarks>
/// <param name="ptUL"> The upper left point of the box. </param>
/// <param name="ptLR"> The lower right point of the box. </param>
/// <returns> An enumerable of real points representing the voronoi cell clipped to the box. </returns>
////////////////////////////////////////////////////////////////////////////////////////////////////
public IEnumerable <Vector> BoxVertices(Vector ptUL, Vector ptLR)
{
// If no edges, then it's just the entire box
if (!Edges.Any())
{
foreach (var pt in BoxPoints(ptUL, ptLR))
{
yield return(pt);
}
yield break;
}
var ptsBox = BoxPoints(ptUL, ptLR);
var fFound = FCheckEasy(out var ptsToBeClipped);
if (!fFound)
{
fFound = FCheckParallelLines(ptsBox, out ptsToBeClipped);
}
if (!fFound)
{
fFound = FCheckDoublyInfinite(ptsBox, out ptsToBeClipped);
}
if (!fFound)
{
ptsToBeClipped = RealVertices(CalcRayLength(ptsBox));
}
foreach (var pt in ConvexPolyIntersection.FindIntersection(ptsToBeClipped, ptsBox))
{
yield return(pt);
}
}
////////////////////////////////////////////////////////////////////////////////////////////////////
/// <summary> Lloyd relaxation. </summary>
/// <remarks>
/// This routine performs a single Lloyd relaxation on a fortune winged edge structure. That
/// means the points for the voronoi diagram are moved to the centroid of their cell and the
/// voronoi algorithm is run again. In order to do this we have to be able to clip the infinite
/// polygons or else their centroid is undefined so a clipping polygon is passed in to clip to.
/// Also, as usual, we need a ray length to know how far to extend any infinite rays. This
/// should be a large enough value that all rays extend to the side of the clipping polygon.
/// Currently, my clipping algorithm only works for convex polygons so the clipping polygon
/// passed in must be convex and the points must be in counterclockwise order. This works fine
/// for clipping to rectangles or voronoi cells which are the two cases I'm currently interested
/// in.
/// Darrellp, 2/24/2011.
/// </remarks>
/// <param name="we"> WingedEdge structure we'll relax. </param>
/// <param name="rayLength"> Length of the rays we extend. </param>
/// <param name="polyClip"> The polygon to clip to. </param>
/// <param name="strength">
/// Strength of relaxation. The default is 1 for "standard"
/// relaxation. 0 has no effect. Negative values can make it more
/// "spikey".
/// </param>
/// <returns> The relaxed Winged Edge structure. </returns>
////////////////////////////////////////////////////////////////////////////////////////////////////
public static WE LloydRelax(WE we, double rayLength, IEnumerable <Vector> polyClip, double strength = 1)
{
// Locals
var ptsRelaxed = new List <Vector>();
// For each polygon in the Winged edge
foreach (var poly in we.LstPolygons)
{
// Skip the polygon at infinity
if (poly.FAtInfinity)
{
continue;
}
// Get the polygon vertices in CCW order
var ptsPoly = poly.RealVertices(rayLength);
// Clip them to our clipping polygon
// ReSharper disable PossibleMultipleEnumeration
var ptsCentroid =
ConvexPolyIntersection.FindIntersection(polyClip, ptsPoly);
// If this polygon is outside our bounding box, just skip it
if (!ptsCentroid.Any())
{
continue;
}
// Locals for the centroid calculations
var cpts = 0;
var ptCentroid = new Vector();
// For each point in the clipped polygon
foreach (var pt in ptsCentroid)
{
// Add it in to the centroid accumulator
ptCentroid += pt;
cpts++;
}
// ReSharper restore PossibleMultipleEnumeration
// Determine the centroid
var ctrd = new Vector(ptCentroid.X / cpts, ptCentroid.Y / cpts);
// If strength is the default -1, just take our centroid
// ReSharper disable once CompareOfFloatsByEqualityOperator
if (strength == 1)
{
// Calculate the new centroid and add it to our list of points
ptsRelaxed.Add(new Vector(ptCentroid.X / cpts, ptCentroid.Y / cpts));
}
else
{
// Move the original voronoi point nearer or further from the centroid
ptsRelaxed.Add(poly.VoronoiPoint + (poly.VoronoiPoint - ctrd) * -strength);
}
}
// Return the voronoi diagram on all the centroids
return(ComputeVoronoi(ptsRelaxed));
}