private Atomizer.AtomicRegion PolygonDefinesRegion(UndirectedPlanarGraph.PlanarGraph graph)
{
List <Segment> sides = new List <Segment>();
//
// All connections between adjacent connections MUST be segments.
//
for (int p = 0; p < points.Count; p++)
{
Segment segment = new Segment(points[p], points[(p + 1) % points.Count]);
sides.Add(segment);
if (graph.GetEdge(points[p], points[(p + 1) % points.Count]).edgeType != UndirectedPlanarGraph.EdgeType.REAL_SEGMENT)
{
return(null);
}
}
//
// All iterative connections cannot be arcs.
//
for (int p1 = 0; p1 < points.Count - 1; p1++)
{
// We want to check for a direct cycle, therefore, p2 starts at p1 not p1 + 1
for (int p2 = p1; p2 < points.Count; p2++)
{
UndirectedPlanarGraph.PlanarGraphEdge edge = graph.GetEdge(points[p1], points[(p2 + 1) % points.Count]);
if (edge != null)
{
if (edge.edgeType == UndirectedPlanarGraph.EdgeType.REAL_ARC)
{
return(null);
}
}
}
}
//
// Make the Polygon
//
Polygon poly = Polygon.MakePolygon(sides);
if (poly == null)
{
throw new ArgumentException("Real segments should define a polygon; they did not.");
}
return(new ShapeAtomicRegion(poly));
}
//
// Collect all arcs attributed to this this cycle;
//
private List <MinorArc> CollectStrictArcs(List <Circle> circles, UndirectedPlanarGraph.PlanarGraph graph)
{
List <MinorArc> minors = new List <MinorArc>();
for (int p = 0; p < points.Count; p++)
{
UndirectedPlanarGraph.PlanarGraphEdge edge = graph.GetEdge(points[p], points[(p + 1) % points.Count]);
if (edge.edgeType == UndirectedPlanarGraph.EdgeType.REAL_ARC)
{
// Find the applicable circle.
Circle theCircle = null;
foreach (Circle circle in circles)
{
if (circle.HasArc(points[p], points[(p + 1) % points.Count]))
{
theCircle = circle;
break;
}
}
minors.Add(new MinorArc(theCircle, points[p], points[(p + 1) % points.Count]));
}
}
return(minors);
}
//
// Based on the two points, extract the circle which results in the connection (if the connection exists).
//
private List <AtomicRegion> HandleConnection(UndirectedPlanarGraph.PlanarGraph graph, List <Circle> circles, Point pt1, Point pt2)
{
List <AtomicRegion> atoms = new List <AtomicRegion>();
UndirectedPlanarGraph.PlanarGraphEdge edge = graph.GetEdge(pt1, pt2);
if (edge == null)
{
return(atoms);
}
//
// Find the one circle that applies to this set of points.
//
Circle theCircle = null;
foreach (Circle circle in circles)
{
if (circle.PointLiesOn(pt1) && circle.PointLiesOn(pt2))
{
theCircle = circle;
}
}
switch (edge.edgeType)
{
case UndirectedPlanarGraph.EdgeType.REAL_ARC:
case UndirectedPlanarGraph.EdgeType.REAL_DUAL:
atoms.AddRange(CreateSectors(theCircle, pt1, pt2));
// atoms.AddRange(CreateSemiCircleRegions());
break;
}
return(atoms);
}
private List <Atomizer.AtomicRegion> SectorOrTruncationDefinesRegion(List <Circle> circles, UndirectedPlanarGraph.PlanarGraph graph)
{
//
// Do there exist any real-dual edges or extended segments? If so, this is not a sector.
//
for (int p = 0; p < points.Count; p++)
{
UndirectedPlanarGraph.PlanarGraphEdge edge = graph.GetEdge(points[p], points[(p + 1) % points.Count]);
if (edge.edgeType == UndirectedPlanarGraph.EdgeType.EXTENDED_SEGMENT)
{
return(null);
}
else if (edge.edgeType == UndirectedPlanarGraph.EdgeType.REAL_DUAL)
{
return(null);
}
}
//
// Collect all segments; split into two collinear lists.
//
List <Segment> segments = CollectSegments(graph);
List <List <Segment> > collinearSegmentSet = SplitSegmentsIntoCollinearSequences(segments);
// A sector requires one (semicircl) or two sets of segments ('normal' arc).
if (collinearSegmentSet.Count > 2)
{
return(null);
}
//
// Collect all arcs.
//
List <MinorArc> arcs = CollectStrictArcs(circles, graph);
List <List <MinorArc> > collinearArcSet = SplitArcsIntoCollinearSequences(arcs);
// A sector requires one set of arcs (no more, no less).
if (collinearArcSet.Count != 1)
{
return(null);
}
// Semicircle has one set of sides
if (collinearSegmentSet.Count == 1)
{
return(ConvertToTruncationOrSemicircle(collinearSegmentSet[0], collinearArcSet[0]));
}
// Pacman shape created with a circle results in Sector
return(ConvertToGeneralSector(collinearSegmentSet[0], collinearSegmentSet[1], collinearArcSet[0]));
}
//
// Collect all segments attributed to this this cycle
//
private List <Segment> CollectSegments(UndirectedPlanarGraph.PlanarGraph graph)
{
List <Segment> segments = new List <Segment>();
for (int p = 0; p < points.Count; p++)
{
UndirectedPlanarGraph.PlanarGraphEdge edge = graph.GetEdge(points[p], points[(p + 1) % points.Count]);
if (edge.edgeType == UndirectedPlanarGraph.EdgeType.REAL_SEGMENT)
{
segments.Add(new Segment(points[p], points[(p + 1) % points.Count]));
}
}
return(segments);
}
private List <Atomizer.AtomicRegion> MixedArcChordedRegion(List <Circle> thatCircles, UndirectedPlanarGraph.PlanarGraph graph)
{
List <AtomicRegion> regions = new List <AtomicRegion>();
// Every segment may be have a set of circles. (on each side) surrounding it.
// Keep parallel lists of: (1) segments, (2) (real) arcs, (3) left outer circles, and (4) right outer circles
Segment[] regionsSegments = new Segment[points.Count];
Arc[] arcSegments = new Arc[points.Count];
Circle[] leftOuterCircles = new Circle[points.Count];
Circle[] rightOuterCircles = new Circle[points.Count];
//
// Populate the parallel arrays.
//
int currCounter = 0;
for (int p = 0; p < points.Count;)
{
UndirectedPlanarGraph.PlanarGraphEdge edge = graph.GetEdge(points[p], points[(p + 1) % points.Count]);
Segment currSegment = new Segment(points[p], points[(p + 1) % points.Count]);
//
// If a known segment, seek a sequence of collinear segments.
//
if (edge.edgeType == UndirectedPlanarGraph.EdgeType.REAL_SEGMENT)
{
Segment actualSeg = currSegment;
bool collinearExists = false;
int prevPtIndex;
for (prevPtIndex = p + 1; prevPtIndex < points.Count; prevPtIndex++)
{
// Make another segment with the next point.
Segment nextSeg = new Segment(points[p], points[(prevPtIndex + 1) % points.Count]);
// CTA: This criteria seems invalid in some cases....; may not have collinearity
// We hit the end of the line of collinear segments.
if (!currSegment.IsCollinearWith(nextSeg))
{
break;
}
collinearExists = true;
actualSeg = nextSeg;
}
// If there exists an arc over the actual segment, we have an embedded circle to consider.
regionsSegments[currCounter] = actualSeg;
if (collinearExists)
{
UndirectedPlanarGraph.PlanarGraphEdge collEdge = graph.GetEdge(actualSeg.Point1, actualSeg.Point2);
if (collEdge != null)
{
if (collEdge.edgeType == UndirectedPlanarGraph.EdgeType.REAL_ARC)
{
// Find all applicable circles
List <Circle> circles = GetAllApplicableCircles(thatCircles, actualSeg.Point1, actualSeg.Point2);
// Get the exact outer circles for this segment (and create any embedded regions).
regions.AddRange(ConvertToCircleCircle(actualSeg, circles, out leftOuterCircles[currCounter], out rightOuterCircles[currCounter]));
}
}
}
currCounter++;
p = prevPtIndex;
}
else if (edge.edgeType == UndirectedPlanarGraph.EdgeType.REAL_DUAL)
{
regionsSegments[currCounter] = new Segment(points[p], points[(p + 1) % points.Count]);
// Get the exact chord and set of circles
Segment chord = regionsSegments[currCounter];
// Find all applicable circles
List <Circle> circles = GetAllApplicableCircles(thatCircles, points[p], points[(p + 1) % points.Count]);
// Get the exact outer circles for this segment (and create any embedded regions).
regions.AddRange(ConvertToCircleCircle(chord, circles, out leftOuterCircles[currCounter], out rightOuterCircles[currCounter]));
currCounter++;
p++;
}
else if (edge.edgeType == UndirectedPlanarGraph.EdgeType.REAL_ARC)
{
//
// Find the unique circle that contains these two points.
// (if more than one circle has these points, we would have had more intersections and it would be a direct chorded region)
//
List <Circle> circles = GetAllApplicableCircles(thatCircles, points[p], points[(p + 1) % points.Count]);
if (circles.Count != 1)
{
throw new Exception("Need ONLY 1 circle for REAL_ARC atom id; found (" + circles.Count + ")");
}
arcSegments[currCounter++] = new MinorArc(circles[0], points[p], points[(p + 1) % points.Count]);
p++;
}
}
//
// Check to see if this is a region in which some connections are segments and some are arcs.
// This means there were no REAL_DUAL edges.
//
List <AtomicRegion> generalRegions = GeneralAtomicRegion(regionsSegments, arcSegments);
if (generalRegions.Any())
{
return(generalRegions);
}
// Copy the segments into a list (ensuring no nulls)
List <Segment> actSegments = new List <Segment>();
foreach (Segment side in regionsSegments)
{
if (side != null)
{
actSegments.Add(side);
}
}
// Construct a polygon out of the straight-up segments
// This might be a polygon that defines a pathological region.
Polygon poly = Polygon.MakePolygon(actSegments);
// Determine which outermost circles apply inside of this polygon.
Circle[] circlesCutInsidePoly = new Circle[actSegments.Count];
for (int p = 0; p < actSegments.Count; p++)
{
if (leftOuterCircles[p] != null && rightOuterCircles[p] == null)
{
circlesCutInsidePoly[p] = CheckCircleCutInsidePolygon(poly, leftOuterCircles[p], actSegments[p].Point1, actSegments[p].Point2);
}
else if (leftOuterCircles[p] == null && rightOuterCircles[p] != null)
{
circlesCutInsidePoly[p] = CheckCircleCutInsidePolygon(poly, rightOuterCircles[p], actSegments[p].Point1, actSegments[p].Point2);
}
else if (leftOuterCircles[p] != null && rightOuterCircles[p] != null)
{
circlesCutInsidePoly[p] = CheckCircleCutInsidePolygon(poly, leftOuterCircles[p], actSegments[p].Point1, actSegments[p].Point2);
if (circlesCutInsidePoly[p] == null)
{
circlesCutInsidePoly[p] = rightOuterCircles[p];
}
}
else
{
circlesCutInsidePoly[p] = null;
}
}
bool isStrictPoly = true;
for (int p = 0; p < actSegments.Count; p++)
{
if (circlesCutInsidePoly[p] != null || arcSegments[p] != null)
{
isStrictPoly = false;
break;
}
}
// This is just a normal shape region: polygon.
if (isStrictPoly)
{
regions.Add(new ShapeAtomicRegion(poly));
}
// A circle cuts into the polygon.
else
{
//
// Now that all interior arcs have been identified, construct the atomic (probably pathological) region
//
AtomicRegion pathological = new AtomicRegion();
for (int p = 0; p < actSegments.Count; p++)
{
//
// A circle cutting inside the polygon
//
if (circlesCutInsidePoly[p] != null)
{
Arc theArc = null;
if (circlesCutInsidePoly[p].DefinesDiameter(regionsSegments[p]))
{
Point midpt = circlesCutInsidePoly[p].Midpoint(regionsSegments[p].Point1, regionsSegments[p].Point2);
if (!poly.IsInPolygon(midpt))
{
midpt = circlesCutInsidePoly[p].OppositePoint(midpt);
}
theArc = new Semicircle(circlesCutInsidePoly[p], regionsSegments[p].Point1, regionsSegments[p].Point2, midpt, regionsSegments[p]);
}
else
{
theArc = new MinorArc(circlesCutInsidePoly[p], regionsSegments[p].Point1, regionsSegments[p].Point2);
}
pathological.AddConnection(regionsSegments[p].Point1, regionsSegments[p].Point2, ConnectionType.ARC, theArc);
}
//
else
{
// We have a direct arc
if (arcSegments[p] != null)
{
pathological.AddConnection(regionsSegments[p].Point1, regionsSegments[p].Point2,
ConnectionType.ARC, arcSegments[p]);
}
// Use the segment
else
{
pathological.AddConnection(regionsSegments[p].Point1, regionsSegments[p].Point2,
ConnectionType.SEGMENT, regionsSegments[p]);
}
}
}
regions.Add(pathological);
}
return(regions);
}