public static List<AtomicRegion> AcquireAtomicRegionsFromGraph(List<Point> points, List<Segment> segments,
List<Arc> arcs, List<Circle> circles, Dictionary<Circle, int> circGranularity)
{
//
// Construct the Planar graph for atomic region identification.
//
GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph graph = new GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph();
// Add the points as nodes in the graph.
foreach (Point pt in points)
{
graph.AddNode(pt);
}
//
// Edges are based on all the collinear relationships.
//
foreach (Segment segment in segments)
{
for (int p = 0; p < segment.collinear.Count - 1; p++)
{
graph.AddUndirectedEdge(segment.collinear[p], segment.collinear[p + 1],
new Segment(segment.collinear[p], segment.collinear[p + 1]).Length,
GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_SEGMENT);
}
}
foreach (Arc arc in arcs)
{
List<Point> applicWithMidpoints = GetArcPoints(arc, circGranularity);
// Add the points to the graph
foreach (Point pt in applicWithMidpoints)
{
graph.AddNode(pt);
}
for (int p = 0; p < applicWithMidpoints.Count - 1; p++)
{
graph.AddUndirectedEdge(applicWithMidpoints[p], applicWithMidpoints[p + 1],
new Segment(applicWithMidpoints[p], applicWithMidpoints[p + 1]).Length,
GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_ARC);
}
}
//
// Convert the planar graph to atomic regions.
//
GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph copy = new GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph(graph);
FacetCalculator atomFinder = new FacetCalculator(copy);
List<Primitive> primitives = atomFinder.GetPrimitives();
return PrimitiveToRegionConverter.Convert(graph, primitives, circles);
}
public List<Area_Based_Analyses.Atomizer.AtomicRegion> Atomize(List<Point> figurePoints)
{
List<Segment> constructedChords = new List<Segment>();
List<Segment> constructedRadii = new List<Segment>();
List<Point> imagPoints = new List<Point>();
List<Point> interPts = GetIntersectingPoints();
//
// Construct the radii
//
switch (interPts.Count)
{
// If there are no points of interest, the circle is the atomic region.
case 0:
return Utilities.MakeList<AtomicRegion>(new ShapeAtomicRegion(this));
// If only 1 intersection point, create the diameter.
case 1:
Point opp = Utilities.AcquirePoint(figurePoints, this.OppositePoint(interPts[0]));
constructedRadii.Add(new Segment(center, interPts[0]));
constructedRadii.Add(new Segment(center, opp));
imagPoints.Add(opp);
interPts.Add(opp);
break;
default:
foreach (Point interPt in interPts)
{
constructedRadii.Add(new Segment(center, interPt));
}
break;
}
//
// Construct the chords
//
List<Segment> chords = new List<Segment>();
for (int p1 = 0; p1 < interPts.Count - 1; p1++)
{
for (int p2 = p1 + 1; p2 < interPts.Count; p2++)
{
Segment chord = new Segment(interPts[p1], interPts[p2]);
if (!DefinesDiameter(chord)) constructedChords.Add(chord);
}
}
//
// Do any of the created segments result in imaginary intersection points.
//
foreach (Segment chord in constructedChords)
{
foreach (Segment radius in constructedRadii)
{
Point inter = Utilities.AcquireRestrictedPoint(figurePoints, chord.FindIntersection(radius), chord, radius);
if (inter != null)
{
chord.AddCollinearPoint(inter);
radius.AddCollinearPoint(inter);
// if (!Utilities.HasStructurally<Point>(figurePoints, inter)) imagPoints.Add(inter);
Utilities.AddUnique<Point>(imagPoints, inter);
}
}
}
for (int c1 = 0; c1 < constructedChords.Count - 1; c1++)
{
for (int c2 = c1 + 1; c2 < constructedChords.Count; c2++)
{
Point inter = constructedChords[c1].FindIntersection(constructedChords[c2]);
inter = Utilities.AcquireRestrictedPoint(figurePoints, inter, constructedChords[c1], constructedChords[c2]);
if (inter != null)
{
constructedChords[c1].AddCollinearPoint(inter);
constructedChords[c2].AddCollinearPoint(inter);
//if (!Utilities.HasStructurally<Point>(figurePoints, inter)) imagPoints.Add(inter);
Utilities.AddUnique<Point>(imagPoints, inter);
}
}
}
//
// Add all imaginary points to the list of figure points.
//
Utilities.AddUniqueList<Point>(figurePoints, imagPoints);
//
// Construct the Planar graph for atomic region identification.
//
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph graph = new Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph();
//
// Add all imaginary points, intersection points, and center.
//
foreach (Point pt in imagPoints)
{
graph.AddNode(pt);
}
foreach (Point pt in interPts)
{
graph.AddNode(pt);
}
graph.AddNode(this.center);
//
// Add all chords and radii as edges.
//
foreach (Segment chord in constructedChords)
{
for (int p = 0; p < chord.collinear.Count - 1; p++)
{
graph.AddUndirectedEdge(chord.collinear[p], chord.collinear[p + 1],
new Segment(chord.collinear[p], chord.collinear[p + 1]).Length,
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_SEGMENT);
}
}
foreach (Segment radius in constructedRadii)
{
for (int p = 0; p < radius.collinear.Count - 1; p++)
{
graph.AddUndirectedEdge(radius.collinear[p], radius.collinear[p + 1],
new Segment(radius.collinear[p], radius.collinear[p + 1]).Length,
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_SEGMENT);
}
}
//
// Add all arcs
//
List<Point> arcPts = this.ConstructAllMidpoints(interPts);
for (int p = 0; p < arcPts.Count; p++)
{
graph.AddNode(arcPts[p]);
graph.AddNode(arcPts[(p + 1) % arcPts.Count]);
graph.AddUndirectedEdge(arcPts[p], arcPts[(p + 1) % arcPts.Count],
new Segment(arcPts[p], arcPts[(p + 1) % interPts.Count]).Length,
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_ARC);
}
//
// Convert the planar graph to atomic regions.
//
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph copy = new Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph(graph);
FacetCalculator atomFinder = new FacetCalculator(copy);
List<Primitive> primitives = atomFinder.GetPrimitives();
List<AtomicRegion> atoms = PrimitiveToRegionConverter.Convert(graph, primitives, Utilities.MakeList<Circle>(this));
//
// A filament may result in the creation of a major AND minor arc; both are not required.
// Figure out which one to omit.
// Multiple semi-circles may arise as well; omit if they can be broken into constituent elements.
//
List <AtomicRegion> trueAtoms = new List<AtomicRegion>();
for (int a1 = 0; a1 < atoms.Count; a1++)
{
bool trueAtom = true;
for (int a2 = 0; a2 < atoms.Count; a2++)
{
if (a1 != a2)
{
if (atoms[a1].Contains(atoms[a2]))
{
trueAtom = false;
break;
}
}
}
if (trueAtom) trueAtoms.Add(atoms[a1]);
}
atoms = trueAtoms;
return trueAtoms;
}
public List<Area_Based_Analyses.Atomizer.AtomicRegion> Atomize(List<Point> figurePoints)
{
//
// Clear collinearities in preparation for determining intersection points.
//
List<Segment> extendedSegments = new List<Segment>();
foreach (Segment side in orderedSides)
{
side.ClearCollinear();
}
//
// Determine if any side intersects a non-adjacent side.
// If so, track all the intersection points.
//
List<Point> imagPts = new List<Point>();
for (int s1 = 0; s1 < orderedSides.Count - 1; s1++)
{
// +2 excludes this side and the adjacent side
for (int s2 = s1 + 2; s2 < orderedSides.Count; s2++)
{
// Avoid intersecting the first with the last.
if (s1 != 0 || s2 != orderedSides.Count - 1)
{
Point intersection = orderedSides[s1].FindIntersection(orderedSides[s2]);
intersection = Utilities.AcquirePoint(figurePoints, intersection);
if (intersection != null)
{
// The point of interest must be on the perimeter of the polygon.
if (this.PointLiesOn(intersection) || this.PointLiesInside(intersection))
{
orderedSides[s1].AddCollinearPoint(intersection);
orderedSides[s2].AddCollinearPoint(intersection);
// The intersection point may be a vertex; avoid redundant additions.
if (!Utilities.HasStructurally<Point>(imagPts, intersection))
{
imagPts.Add(intersection);
}
}
}
}
}
}
//
// Add the imaginary points to the list of figure points;
// this is needed for consistency among all regions / polygons.
//
Utilities.AddUniqueList<Point>(figurePoints, imagPts);
//
// Construct the Planar graph for atomic region identification.
//
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph graph = new Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph();
// Add all imaginary points and intersection points
foreach (Point pt in this.points)
{
graph.AddNode(pt);
}
foreach (Point pt in imagPts)
{
graph.AddNode(pt);
}
//
// Cycle through collinearities adding to the graph.
// Ensure that a connection is interior to this polygon.
//
foreach (Segment side in orderedSides)
{
for (int p = 0; p < side.collinear.Count - 1; p++)
{
//
// Find the midpoint of this segment and determine if it is interior to the polygon.
// If it is, then this is a legitimate connection.
//
Segment thisSegment = new Segment(side.collinear[p], side.collinear[p + 1]);
Point midpoint = thisSegment.Midpoint();
if (this.PointLiesInOrOn(midpoint))
{
graph.AddUndirectedEdge(side.collinear[p], side.collinear[p + 1], thisSegment.Length,
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_SEGMENT);
}
}
}
//
// Convert the planar graph to atomic regions.
//
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph copy = new Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph(graph);
FacetCalculator atomFinder = new FacetCalculator(copy);
List<Primitive> primitives = atomFinder.GetPrimitives();
List<AtomicRegion> atoms = PrimitiveToRegionConverter.Convert(graph, primitives, new List<Circle>()); // No circles here.
// State ownership
foreach (AtomicRegion atom in atoms)
{
atom.AddOwner(this);
this.AddAtomicRegion(atom);
}
return atoms;
}
//
// Using a single atomic region as a set of bounds:
// (1) Find all interesting regions (contained and intersecting)
// (2) Recursively compose all contained regions.
// (3) Combine all into the original boundary region.
//
private static List<AtomicRegion> ComposeSingleRegion(List<Point> figurePoints, AtomicRegion outerBounds, List<AtomicRegion> allRegions,
List<AtomicRegion> knownAtomicRegions, List<AtomicRegion> knownNonAtomicRegions,
List<List<AtomicRegion>> setsForNonAtomicRegions, Dictionary<Circle, int> circGranularity)
{
//
// Base cases: we have already processed this atom as a sub-atom in a previous iteration.
//
if (knownAtomicRegions.Contains(outerBounds)) return Utilities.MakeList<AtomicRegion>(outerBounds);
// We've processed this atom already.
int index = knownNonAtomicRegions.IndexOf(outerBounds);
if (index != -1) return setsForNonAtomicRegions[index];
//
// Acquire the current set of regions under consideration.
//
List<AtomicRegion> currentAtoms = new List<AtomicRegion>(allRegions);
AddRange(currentAtoms, knownAtomicRegions);
//
// Collect all interesting regions for this region: those that intersect with it and those that are contained inside.
//
List<AtomicRegion> intersectingSet = null;
List<AtomicRegion> containedSet = null;
GetInterestingRegions(currentAtoms, outerBounds, out intersectingSet, out containedSet);
// If we have have no interactions, this is a truly atomic region.
if (!intersectingSet.Any() && !containedSet.Any()) return Utilities.MakeList<AtomicRegion>(outerBounds);
//
// Recur on all containing regions.
//
List<AtomicRegion> newContainedAtoms = new List<AtomicRegion>();
foreach (AtomicRegion containedAtom in containedSet)
{
if (knownAtomicRegions.Contains(containedAtom)) AddAtom(newContainedAtoms, containedAtom);
else if (knownNonAtomicRegions.Contains(containedAtom))
{
AddRange(newContainedAtoms, setsForNonAtomicRegions[knownNonAtomicRegions.IndexOf(containedAtom)]);
}
else
{
// Get all regions using containedAtom as the boundary region.
List<AtomicRegion> newContainedBoundedAtoms = ComposeSingleRegion(figurePoints, containedAtom, currentAtoms,
knownAtomicRegions, knownNonAtomicRegions, setsForNonAtomicRegions, circGranularity);
AddRange(newContainedAtoms, newContainedBoundedAtoms);
//
// This is a true atomic region that cannot be split.
//
if (newContainedBoundedAtoms.Count == 1) AddAtom(knownAtomicRegions, containedAtom);
//
// The boundary atom is replaced by all of the newAtoms
else
{
// Save all of the contained atomic regions for this atom.
if (AddAtom(knownNonAtomicRegions, containedAtom))
{
setsForNonAtomicRegions.Add(newContainedBoundedAtoms);
}
// Indicate all found regions are truly atomic
AddRange(knownAtomicRegions, newContainedBoundedAtoms);
}
}
}
//
// Now that all contained regions are atomized, combine ALL intersections and atomic regions.
//
// Collect all segments and arcs (with explicit endpoints).
// Extend only if they do not touch the sides of the boundaries.
//
// inside of the boundaries; determine all intersection points.
//
// (1) All intersecting regions.
// (a) For all vertices inside the boundaries, extend to the closest atom.
// (b) For all sides that pass through determine any intersections.
// (2) All contained atoms
// (a) For each side of a region, extend to the closest region.
// (b) If a single circle or concentric circles, extend a diameter from the closest point inside the region, through the center.
// (c) If several non-intersecting circles, extend diameters through the centers of each pair.
//
List<Point> points = new List<Point>();
List<Segment> segments = new List<Segment>();
List<Arc> arcs = new List<Arc>();
//
// Add the outer boundaries.
//
points.AddRange(outerBounds.GetVertices());
foreach (Connection boundaryConn in outerBounds.connections)
{
if (boundaryConn.type == ConnectionType.ARC)
{
arcs.Add(boundaryConn.segmentOrArc as Arc);
}
if (boundaryConn.type == ConnectionType.SEGMENT)
{
segments.Add(boundaryConn.segmentOrArc as Segment);
}
}
//
// Regions that intersect the boundaries; selectively take connections.
//
foreach (AtomicRegion intersecting in intersectingSet)
{
List<AtomicRegion.IntersectionAgg> intersections = outerBounds.GetIntersections(figurePoints, intersecting);
// Determine which intersections are interior to the boundaries.
foreach (AtomicRegion.IntersectionAgg agg in intersections)
{
if (agg.overlap) { /* No-op */ }
else
{
if (agg.intersection1 != null)
{
if (outerBounds.PointLiesOnOrInside(agg.intersection1))
{
if (!outerBounds.NotInteriorTo(agg.thatConn))
{
if (agg.thatConn.type == ConnectionType.ARC) GeometryTutorLib.Utilities.AddUnique<Arc>(arcs, agg.thatConn.segmentOrArc as Arc);
if (agg.thatConn.type == ConnectionType.SEGMENT)
GeometryTutorLib.Utilities.AddUnique<Segment>(segments, agg.thatConn.segmentOrArc as Segment);
}
GeometryTutorLib.Utilities.AddUnique<Point>(points, agg.intersection1);
}
}
if (agg.intersection2 != null)
{
if (outerBounds.PointLiesOnOrInside(agg.intersection2))
{
GeometryTutorLib.Utilities.AddUnique<Point>(points, agg.intersection2);
}
}
}
}
}
//
// Deal with contained regions.
//
// TO BE COMPLETED: Deal with isolated circles.
foreach (AtomicRegion contained in newContainedAtoms)
{
List<Point> verts = contained.GetVertices();
GeometryTutorLib.Utilities.AddUniqueList<Point>(points, verts);
foreach (Connection conn in contained.connections)
{
if (conn.type == ConnectionType.ARC) Utilities.AddUnique<Arc>(arcs, conn.segmentOrArc as Arc);
if (conn.type == ConnectionType.SEGMENT)
{
Utilities.AddUnique<Segment>(segments, conn.segmentOrArc as Segment);
}
}
}
//
// Find all intersections...among segments and arcs.
//
foreach (Segment segment in segments)
{
segment.ClearCollinear();
}
foreach (Arc arc in arcs)
{
arc.ClearCollinear();
}
HandleSegmentSegmentIntersections(figurePoints, points, segments, outerBounds);
HandleSegmentArcIntersections(figurePoints, points, segments, arcs, outerBounds);
HandleArcArcIntersections(figurePoints, points, arcs, outerBounds);
// Returns the list of maximal segments.
segments = HandleCollinearSubSegments(segments);
// HandleCollinearSubArcs(arcs);
//
// Construct the Planar graph for atomic region identification.
//
GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph graph = new GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph();
// Add the points as nodes in the graph.
foreach (Point pt in points)
{
graph.AddNode(pt);
}
//
// Edges are based on all the collinear relationships.
// To ensure we are taking ONLY the closest extended intersections, choose ONLY the 1 point around the actual endpoints of the arc or segment.
//
foreach (Segment segment in segments)
{
for (int p = 0; p < segment.collinear.Count - 1; p++)
{
if (outerBounds.PointLiesInOrOn(segment.collinear[p]) && outerBounds.PointLiesInOrOn(segment.collinear[p + 1]))
{
graph.AddUndirectedEdge(segment.collinear[p], segment.collinear[p + 1],
new Segment(segment.collinear[p], segment.collinear[p + 1]).Length,
GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_SEGMENT);
}
}
}
foreach (Arc arc in arcs)
{
List<Point> applicWithMidpoints = GetArcPoints(arc, circGranularity);
// Add the points to the graph; preprocess to see if all points are inside the region.
bool[] inOrOn = new bool[applicWithMidpoints.Count];
for (int p = 0; p < applicWithMidpoints.Count; p++)
{
if (outerBounds.PointLiesInOrOn(applicWithMidpoints[p]))
{
graph.AddNode(applicWithMidpoints[p]);
inOrOn[p] = true;
}
}
for (int p = 0; p < applicWithMidpoints.Count - 1; p++)
{
if (inOrOn[p] && inOrOn[p + 1])
{
graph.AddUndirectedEdge(applicWithMidpoints[p], applicWithMidpoints[p + 1],
new Segment(applicWithMidpoints[p], applicWithMidpoints[p + 1]).Length,
GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_ARC);
}
}
}
//
// Collect the circles from the arcs.
//
List<Circle> circles = new List<Circle>();
foreach (Arc arc in arcs)
{
GeometryTutorLib.Utilities.AddStructurallyUnique<Circle>(circles, arc.theCircle);
}
//
// Convert the planar graph to atomic regions.
//
GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph copy = new GeometryTutorLib.Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph(graph);
FacetCalculator atomFinder = new FacetCalculator(copy);
List<Primitive> primitives = atomFinder.GetPrimitives();
List<AtomicRegion> boundedAtoms = PrimitiveToRegionConverter.Convert(graph, primitives, circles);
////
//// Realign this set of atoms with the current set of working atoms; this guarantees we are looking at the same atom objects.
////
//List<AtomicRegion> finalBoundedAtoms = new List<AtomicRegion>();
//foreach (AtomicRegion boundedAtom in boundedAtoms)
//{
// int tempIndex = currentAtoms.IndexOf(boundedAtom);
// if (tempIndex == -1) finalBoundedAtoms.Add(boundedAtom);
// else finalBoundedAtoms.Add(currentAtoms[tempIndex]);
//}
//
// Determine ownership of the atomic regions.
//
foreach (AtomicRegion boundedAtom in boundedAtoms)
{
boundedAtom.AddOwners(outerBounds.owners);
// Indicate that the given boundary shape owns all of the new regions within.
ShapeAtomicRegion shapeAtom = outerBounds as ShapeAtomicRegion;
if (shapeAtom != null)
{
shapeAtom.shape.AddAtomicRegion(boundedAtom);
}
}
return boundedAtoms;
}
//
// Compose this atomic region with a segment
// This operation will return a list of atomic regions iff the segment passes through the atomic region; this
// creates two new atomic regions since the segment divides the atom.
//
//public static List<AtomicRegion> Compose(AtomicRegion thisAtom, Segment that, Figure owner)
//{
// List<AtomicRegion> newAtoms = new List<AtomicRegion>();
// List<AtomicRegion.IntersectionAgg> intersections = thisAtom.GetIntersections(that);
// // If there is only 1 intersection then we may have a 'corner' inside of the atomic region.
// if (intersections.Count == 1) return newAtoms;
// if (intersections.Count > 2) throw new ArgumentException("More than 3 intersections due to a segment during atomic region composition");
// // If there are two intersection points, this atomic region is split into 2 regions.
// if (intersections.Count != 2)
// {
// throw new ArgumentException("Expected 2 intersections due to a segment during atomic region composition; have " + intersections.Count);
// }
// //
// // Split the region into 2 new atomic regions.
// //
// // (0) Order the connections of this atomic region.
// // (1) Make a copy of the list of connections
// // (2) Replace 2 intersected connections with (up to) 4 new connections.
// // (3) Add this segment connection
// //
// thisAtom.OrderConnections();
// AtomicRegion newAtom1 = new AtomicRegion();
// AtomicRegion newAtom2 = new AtomicRegion();
// bool[] marked = new bool[intersections.Count];
// bool atom1 = true;
// foreach (Connection conn in thisAtom.connections)
// {
// bool found = false;
// for (int i = 0; i < intersections.Count; i++)
// {
// if (!marked[i])
// {
// marked[i] = true;
// if (conn.Equals(intersections[i].Key))
// {
// found = true;
// //
// // How does this new segment intersect this connection?
// //
// // Endpoint
// if (conn.HasPoint(intersections[i].Value))
// {
// // No-op
// }
// // Split this connection in the middle
// else
// {
// Connection newConn1 = new Connection(conn.endpoint1, intersections[i].Value, conn.type, conn.segmentOwner);
// Connection newConn2 = new Connection(conn.endpoint2, intersections[i].Value, conn.type, conn.segmentOwner);
// //
// // Which atomic region owns which new connection.
// //
// if (newAtom1.HasPoint(conn.endpoint1))
// {
// newAtom1.AddConnection(newConn1);
// newAtom2.AddConnection(newConn2);
// }
// else if (newAtom2.HasPoint(conn.endpoint1))
// {
// newAtom2.AddConnection(newConn1);
// newAtom1.AddConnection(newConn2);
// }
// // Neither atomic region has the point (possibly the first connection encountered).
// else
// {
// // Arbitrary assignment
// newAtom1.AddConnection(newConn1);
// newAtom2.AddConnection(newConn2);
// }
// }
// // Shift to the second (new) atomic region.
// atom1 = false;
// }
// }
// }
// // This is not a splittable connection so just add it to the list.
// if (!found)
// {
// if (atom1) newAtom1.AddConnection(conn);
// else newAtom2.AddConnection(conn);
// }
// }
// //
// // Add this new segment as a connection to both atomic regions.
// //
// newAtom1.AddConnection(intersections[0].Value, intersections[1].Value, ConnectionType.SEGMENT, owner);
// newAtom2.AddConnection(intersections[0].Value, intersections[1].Value, ConnectionType.SEGMENT, owner);
// // Order the connections in the new regions we created.
// newAtom1.OrderConnections();
// newAtom2.OrderConnections();
// newAtoms.Add(newAtom1);
// newAtoms.Add(newAtom2);
// return newAtoms;
//}
public static void Overlap(List<Point> figurePoints, AtomicRegion thisAtom, AtomicRegion thatAtom, out List<AtomicRegion> toAdd, out List<AtomicRegion> toRemove)
{
//
// Acquire all arcs and segments.
//
List<Arc> graphArcs = new List<Arc>();
List<Segment> graphSegments = new List<Segment>();
foreach (Connection thisConn in thisAtom.connections)
{
if (thisConn.type == ConnectionType.SEGMENT) graphSegments.Add(thisConn.segmentOrArc as Segment);
else graphArcs.Add(thisConn.segmentOrArc as Arc);
}
foreach (Connection thatConn in thatAtom.connections)
{
if (thatConn.type == ConnectionType.SEGMENT) graphSegments.Add(thatConn.segmentOrArc as Segment);
else graphArcs.Add(thatConn.segmentOrArc as Arc);
}
//
// Clear collinearities of all segments / arcs.
//
List<Circle> circles = new List<Circle>(); // get the list of applicable circles to these atoms.
foreach (Segment seg in graphSegments) seg.ClearCollinear();
foreach (Arc arc in graphArcs)
{
Utilities.AddStructurallyUnique<Circle>(circles, arc.theCircle);
arc.ClearCollinear();
}
//
// All points of interest for these atoms.
//
List<Point> allPoints = new List<Point>();
allPoints.AddRange(thisAtom.GetVertices());
allPoints.AddRange(thatAtom.GetVertices());
//
// Determine 'collinearities' for the intersections.
//
List<AtomicRegion.IntersectionAgg> intersections = thisAtom.GetIntersections(figurePoints, thatAtom);
List<Point> intersectionPts = new List<Point>();
foreach (AtomicRegion.IntersectionAgg agg in intersections)
{
if (agg.intersection1 != null)
{
if (!Utilities.HasStructurally<Point>(allPoints, agg.intersection1)) intersectionPts.Add(agg.intersection1);
agg.thisConn.segmentOrArc.AddCollinearPoint(agg.intersection1);
agg.thatConn.segmentOrArc.AddCollinearPoint(agg.intersection1);
}
if (agg.intersection2 != null)
{
if (!Utilities.HasStructurally<Point>(allPoints, agg.intersection2)) intersectionPts.Add(agg.intersection2);
intersectionPts.Add(agg.intersection2);
agg.thisConn.segmentOrArc.AddCollinearPoint(agg.intersection2);
agg.thatConn.segmentOrArc.AddCollinearPoint(agg.intersection2);
}
}
// Add any unlabeled intersection points.
allPoints.AddRange(intersectionPts);
//
// Construct the Planar graph for atomic region identification.
//
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph graph = new Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph();
// Add the points as nodes in the graph.
foreach (Point pt in allPoints)
{
graph.AddNode(pt);
}
//
// Edges are based on all the collinear relationships.
//
foreach (Segment segment in graphSegments)
{
for (int p = 0; p < segment.collinear.Count - 1; p++)
{
graph.AddUndirectedEdge(segment.collinear[p], segment.collinear[p+1],
new Segment(segment.collinear[p], segment.collinear[p + 1]).Length,
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_SEGMENT);
}
}
foreach (Arc arc in graphArcs)
{
for (int p = 0; p < arc.collinear.Count - 1; p++)
{
graph.AddUndirectedEdge(arc.collinear[p], arc.collinear[p + 1],
new Segment(arc.collinear[p], arc.collinear[p + 1]).Length,
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_ARC);
}
}
//
// Convert the planar graph to atomic regions.
//
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph copy = new Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph(graph);
FacetCalculator atomFinder = new FacetCalculator(copy);
List<Primitive> primitives = atomFinder.GetPrimitives();
List<AtomicRegion> atoms = PrimitiveToRegionConverter.Convert(graph, primitives, circles);
//
// Determine ownership of the atomic regions.
//
foreach (AtomicRegion atom in atoms)
{
if (thisAtom.Contains(atom))
{
atom.AddOwners(thisAtom.owners);
}
if (thatAtom.Contains(atom))
{
atom.AddOwners(thatAtom.owners);
}
}
toAdd = atoms;
toRemove = new List<AtomicRegion>();
toRemove.Add(thisAtom);
toRemove.Add(thatAtom);
}
//
// Compose this atomic region with a segment
// This operation will return a list of atomic regions iff the segment passes through the atomic region; this
// creates two new atomic regions since the segment divides the atom.
//
//public static List<AtomicRegion> Compose(AtomicRegion thisAtom, Segment that, Figure owner)
//{
// List<AtomicRegion> newAtoms = new List<AtomicRegion>();
// List<AtomicRegion.IntersectionAgg> intersections = thisAtom.GetIntersections(that);
// // If there is only 1 intersection then we may have a 'corner' inside of the atomic region.
// if (intersections.Count == 1) return newAtoms;
// if (intersections.Count > 2) throw new ArgumentException("More than 3 intersections due to a segment during atomic region composition");
// // If there are two intersection points, this atomic region is split into 2 regions.
// if (intersections.Count != 2)
// {
// throw new ArgumentException("Expected 2 intersections due to a segment during atomic region composition; have " + intersections.Count);
// }
// //
// // Split the region into 2 new atomic regions.
// //
// // (0) Order the connections of this atomic region.
// // (1) Make a copy of the list of connections
// // (2) Replace 2 intersected connections with (up to) 4 new connections.
// // (3) Add this segment connection
// //
// thisAtom.OrderConnections();
// AtomicRegion newAtom1 = new AtomicRegion();
// AtomicRegion newAtom2 = new AtomicRegion();
// bool[] marked = new bool[intersections.Count];
// bool atom1 = true;
// foreach (Connection conn in thisAtom.connections)
// {
// bool found = false;
// for (int i = 0; i < intersections.Count; i++)
// {
// if (!marked[i])
// {
// marked[i] = true;
// if (conn.Equals(intersections[i].Key))
// {
// found = true;
// //
// // How does this new segment intersect this connection?
// //
// // Endpoint
// if (conn.HasPoint(intersections[i].Value))
// {
// // No-op
// }
// // Split this connection in the middle
// else
// {
// Connection newConn1 = new Connection(conn.endpoint1, intersections[i].Value, conn.type, conn.segmentOwner);
// Connection newConn2 = new Connection(conn.endpoint2, intersections[i].Value, conn.type, conn.segmentOwner);
// //
// // Which atomic region owns which new connection.
// //
// if (newAtom1.HasPoint(conn.endpoint1))
// {
// newAtom1.AddConnection(newConn1);
// newAtom2.AddConnection(newConn2);
// }
// else if (newAtom2.HasPoint(conn.endpoint1))
// {
// newAtom2.AddConnection(newConn1);
// newAtom1.AddConnection(newConn2);
// }
// // Neither atomic region has the point (possibly the first connection encountered).
// else
// {
// // Arbitrary assignment
// newAtom1.AddConnection(newConn1);
// newAtom2.AddConnection(newConn2);
// }
// }
// // Shift to the second (new) atomic region.
// atom1 = false;
// }
// }
// }
// // This is not a splittable connection so just add it to the list.
// if (!found)
// {
// if (atom1) newAtom1.AddConnection(conn);
// else newAtom2.AddConnection(conn);
// }
// }
// //
// // Add this new segment as a connection to both atomic regions.
// //
// newAtom1.AddConnection(intersections[0].Value, intersections[1].Value, ConnectionType.SEGMENT, owner);
// newAtom2.AddConnection(intersections[0].Value, intersections[1].Value, ConnectionType.SEGMENT, owner);
// // Order the connections in the new regions we created.
// newAtom1.OrderConnections();
// newAtom2.OrderConnections();
// newAtoms.Add(newAtom1);
// newAtoms.Add(newAtom2);
// return newAtoms;
//}
public static void Overlap(List <Point> figurePoints, AtomicRegion thisAtom, AtomicRegion thatAtom, out List <AtomicRegion> toAdd, out List <AtomicRegion> toRemove)
{
//
// Acquire all arcs and segments.
//
List <Arc> graphArcs = new List <Arc>();
List <Segment> graphSegments = new List <Segment>();
foreach (Connection thisConn in thisAtom.connections)
{
if (thisConn.type == ConnectionType.SEGMENT)
{
graphSegments.Add(thisConn.segmentOrArc as Segment);
}
else
{
graphArcs.Add(thisConn.segmentOrArc as Arc);
}
}
foreach (Connection thatConn in thatAtom.connections)
{
if (thatConn.type == ConnectionType.SEGMENT)
{
graphSegments.Add(thatConn.segmentOrArc as Segment);
}
else
{
graphArcs.Add(thatConn.segmentOrArc as Arc);
}
}
//
// Clear collinearities of all segments / arcs.
//
List <Circle> circles = new List <Circle>(); // get the list of applicable circles to these atoms.
foreach (Segment seg in graphSegments)
{
seg.ClearCollinear();
}
foreach (Arc arc in graphArcs)
{
Utilities.AddStructurallyUnique <Circle>(circles, arc.theCircle);
arc.ClearCollinear();
}
//
// All points of interest for these atoms.
//
List <Point> allPoints = new List <Point>();
allPoints.AddRange(thisAtom.GetVertices());
allPoints.AddRange(thatAtom.GetVertices());
//
// Determine 'collinearities' for the intersections.
//
List <AtomicRegion.IntersectionAgg> intersections = thisAtom.GetIntersections(figurePoints, thatAtom);
List <Point> intersectionPts = new List <Point>();
foreach (AtomicRegion.IntersectionAgg agg in intersections)
{
if (agg.intersection1 != null)
{
if (!Utilities.HasStructurally <Point>(allPoints, agg.intersection1))
{
intersectionPts.Add(agg.intersection1);
}
agg.thisConn.segmentOrArc.AddCollinearPoint(agg.intersection1);
agg.thatConn.segmentOrArc.AddCollinearPoint(agg.intersection1);
}
if (agg.intersection2 != null)
{
if (!Utilities.HasStructurally <Point>(allPoints, agg.intersection2))
{
intersectionPts.Add(agg.intersection2);
}
intersectionPts.Add(agg.intersection2);
agg.thisConn.segmentOrArc.AddCollinearPoint(agg.intersection2);
agg.thatConn.segmentOrArc.AddCollinearPoint(agg.intersection2);
}
}
// Add any unlabeled intersection points.
allPoints.AddRange(intersectionPts);
//
// Construct the Planar graph for atomic region identification.
//
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph graph = new Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph();
// Add the points as nodes in the graph.
foreach (Point pt in allPoints)
{
graph.AddNode(pt);
}
//
// Edges are based on all the collinear relationships.
//
foreach (Segment segment in graphSegments)
{
for (int p = 0; p < segment.collinear.Count - 1; p++)
{
graph.AddUndirectedEdge(segment.collinear[p], segment.collinear[p + 1],
new Segment(segment.collinear[p], segment.collinear[p + 1]).Length,
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_SEGMENT);
}
}
foreach (Arc arc in graphArcs)
{
for (int p = 0; p < arc.collinear.Count - 1; p++)
{
graph.AddUndirectedEdge(arc.collinear[p], arc.collinear[p + 1],
new Segment(arc.collinear[p], arc.collinear[p + 1]).Length,
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.EdgeType.REAL_ARC);
}
}
//
// Convert the planar graph to atomic regions.
//
Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph copy = new Area_Based_Analyses.Atomizer.UndirectedPlanarGraph.PlanarGraph(graph);
FacetCalculator atomFinder = new FacetCalculator(copy);
List <Primitive> primitives = atomFinder.GetPrimitives();
List <AtomicRegion> atoms = PrimitiveToRegionConverter.Convert(graph, primitives, circles);
//
// Determine ownership of the atomic regions.
//
foreach (AtomicRegion atom in atoms)
{
if (thisAtom.Contains(atom))
{
atom.AddOwners(thisAtom.owners);
}
if (thatAtom.Contains(atom))
{
atom.AddOwners(thatAtom.owners);
}
}
toAdd = atoms;
toRemove = new List <AtomicRegion>();
toRemove.Add(thisAtom);
toRemove.Add(thatAtom);
}
