// // 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]); }
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); }
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; }
// // 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; }
// // 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; }