// Construct the region between a circle and circle:
// __
// ( (
// ( (
// ( (
// ( (
// ( (
// --
private Atomizer.AtomicRegion ConstructBasicCircleCircleRegion(Segment chord, Circle smaller, Circle larger)
{
AtomicRegion region = new AtomicRegion();
Arc arc1 = null;
if (smaller.DefinesDiameter(chord))
{
Point midpt = smaller.Midpoint(chord.Point1, chord.Point2, larger.Midpoint(chord.Point1, chord.Point2));
arc1 = new Semicircle(smaller, chord.Point1, chord.Point2, midpt, chord);
}
else
{
arc1 = new MinorArc(smaller, chord.Point1, chord.Point2);
}
MinorArc arc2 = new MinorArc(larger, chord.Point1, chord.Point2);
region.AddConnection(chord.Point1, chord.Point2, ConnectionType.ARC, arc1);
region.AddConnection(chord.Point1, chord.Point2, ConnectionType.ARC, arc2);
return(region);
}
private List <Atomizer.AtomicRegion> ConvertToTruncation(Segment chord, MinorArc arc)
{
AtomicRegion atom = new AtomicRegion();
atom.AddConnection(new Connection(chord.Point1, chord.Point2, ConnectionType.SEGMENT, chord));
atom.AddConnection(new Connection(chord.Point1, chord.Point2, ConnectionType.ARC, arc));
return(Utilities.MakeList <AtomicRegion>(atom));
}
// Construct the region between a chord and the circle arc:
// (|
// ( |
// ( |
// ( |
// (|
//
private List <AtomicRegion> ConstructBasicLineCircleRegion(Segment chord, Circle circle)
{
//
// Standard
//
if (!circle.DefinesDiameter(chord))
{
AtomicRegion region = new AtomicRegion();
Arc theArc = new MinorArc(circle, chord.Point1, chord.Point2);
region.AddConnection(chord.Point1, chord.Point2, ConnectionType.ARC, theArc);
region.AddConnection(chord.Point1, chord.Point2, ConnectionType.SEGMENT, chord);
return(Utilities.MakeList <AtomicRegion>(region));
}
//
// Semi-circles
//
Point midpt = circle.Midpoint(chord.Point1, chord.Point2);
Arc semi1 = new Semicircle(circle, chord.Point1, chord.Point2, midpt, chord);
ShapeAtomicRegion region1 = new ShapeAtomicRegion(new Sector(semi1));
Point opp = circle.OppositePoint(midpt);
Arc semi2 = new Semicircle(circle, chord.Point1, chord.Point2, opp, chord);
ShapeAtomicRegion region2 = new ShapeAtomicRegion(new Sector(semi2));
List <AtomicRegion> regions = new List <AtomicRegion>();
regions.Add(region1);
regions.Add(region2);
return(regions);
}
//
// Determine if this is a true polygon situation or if it is a sequence of segments and arcs.
//
private List <AtomicRegion> GeneralAtomicRegion(Segment[] segments, Arc[] arcs)
{
List <AtomicRegion> regions = new List <AtomicRegion>();
//
// Determine if the parts are all segments.
// Concurrently determine the proper starting point in the sequence to construct the atomic region.
//
bool hasArc = false;
bool hasSegment = false;
int startIndex = 0;
for (int i = 0; i < segments.Length && i < arcs.Length; i++)
{
// Both an arc and a segment.
if (segments[i] != null && arcs[i] != null)
{
return(regions);
}
// Determine if we have an arc and/or a segment.
if (segments[i] != null)
{
hasSegment = true;
}
if (arcs[i] != null)
{
hasArc = true;
}
// A solid starting point is an arc right after a null.
if (arcs[i] == null && arcs[(i + 1) % arcs.Length] != null)
{
// Assign only once to the startIndex
if (startIndex == 0)
{
startIndex = (i + 1) % arcs.Length;
}
}
}
// If only segments, we have a polygon.
if (hasSegment && !hasArc)
{
return(regions);
}
//
// If the set ONLY consists of arcs, ensure we have a good starting point.
//
if (hasArc && !hasSegment)
{
// Seek the first index where a change among arcs occurs.
for (int i = 0; i < arcs.Length; i++)
{
// A solid starting point is an arc right after a null.
if (!arcs[i].theCircle.StructurallyEquals(arcs[(i + 1) % arcs.Length].theCircle))
{
startIndex = (i + 1) % arcs.Length;
break;
}
}
}
AtomicRegion theRegion = new AtomicRegion();
for (int i = 0; i < segments.Length && i < arcs.Length; i++)
{
int currIndex = (i + startIndex) % arcs.Length;
if (segments[currIndex] == null && arcs[currIndex] == null) /* No-Op */ } {
if (segments[currIndex] != null)
{
theRegion.AddConnection(new Connection(segments[currIndex].Point1,
segments[currIndex].Point2, ConnectionType.SEGMENT, segments[currIndex]));
}
else if (arcs[currIndex] != null)
{
//
// Compose the arcs (from a single circle) together.
//
List <MinorArc> sequentialArcs = new List <MinorArc>();
sequentialArcs.Add(arcs[currIndex] as MinorArc);
int seqIndex;
for (seqIndex = (currIndex + 1) % arcs.Length; ; seqIndex = (seqIndex + 1) % arcs.Length, i++)
{
if (arcs[seqIndex] == null)
{
break;
}
if (arcs[currIndex].theCircle.StructurallyEquals(arcs[seqIndex].theCircle))
{
sequentialArcs.Add(arcs[seqIndex] as MinorArc);
}
else
{
break;
}
}
Arc composed;
if (sequentialArcs.Count > 1)
{
composed = this.ComposeArcsIntoArc(sequentialArcs);
}
else
{
composed = arcs[currIndex];
}
//
// Add the connection.
//
theRegion.AddConnection(new Connection(composed.endpoint1, composed.endpoint2, ConnectionType.ARC, composed));
}
}
return(Utilities.MakeList <AtomicRegion>(theRegion));
}
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);
}
//
// The order of the points in the filament were established by the algorithm
// Recursively seek smaller and smaller circular regions.
//
// Returns the set of atomic regions characterized by the largest circle (containing all the other atoms).
private Agg MakeRegions(UndirectedPlanarGraph.PlanarGraph graph, List<Circle> circles, int beginIndex, int endIndex)
{
if (memoized[beginIndex, endIndex] != null) return memoized[beginIndex, endIndex];
//
// Find the circle for these given points.
//
Circle outerCircle = null;
foreach (Circle circle in circles)
{
if (circle.PointLiesOn(points[beginIndex]) && circle.PointLiesOn(points[endIndex])) outerCircle = circle;
}
//
// Base Case: Gap between the given indices is 1.
//
if (endIndex - beginIndex == 1)
{
return new Agg(beginIndex, endIndex, -1, outerCircle, HandleConnection(graph, circles, points[beginIndex], points[endIndex]));
}
//
// Look at all combinations of indices from beginIndex to endIndex; start with larger gaps between indices -> small gaps
//
Agg maxLeftCoveredAgg = null;
Agg maxRightCoveredAgg = null;
int maxCoveredNodes = 0;
for (int gap = endIndex - beginIndex - 1; gap > 0; gap--)
{
for (int index = beginIndex; index < endIndex; index++)
{
Agg left = MakeRegions(graph, circles, index, index + gap);
Agg right = MakeRegions(graph, circles, index + gap, endIndex);
// Check for new maxmimum coverage.
if (left.coveredPoints + right.coveredPoints > maxCoveredNodes)
{
maxLeftCoveredAgg = left;
maxRightCoveredAgg = right;
}
// Found complete coverage
if (left.coveredPoints + right.coveredPoints == endIndex - beginIndex + 1)
{
maxCoveredNodes = endIndex - beginIndex + 1;
break;
}
}
}
//
// We have the two maximal circles: create the new regions.
//
// The atoms from the left / right.
List<AtomicRegion> atoms = new List<AtomicRegion>();
atoms.AddRange(maxLeftCoveredAgg.atoms);
atoms.AddRange(maxRightCoveredAgg.atoms);
// New regions are based on this outer circle minus the left / right outer circles.
AtomicRegion newAtomTop = new AtomicRegion();
AtomicRegion newAtomBottom = new AtomicRegion();
// The outer circle.
newAtomTop.AddConnection(points[beginIndex], points[endIndex], ConnectionType.ARC, outerCircle);
newAtomBottom.AddConnection(points[beginIndex], points[endIndex], ConnectionType.ARC, outerCircle);
// The left / right maximal circles.
newAtomTop.AddConnection(points[maxLeftCoveredAgg.beginPointIndex], points[maxLeftCoveredAgg.endPointIndex], ConnectionType.ARC, maxLeftCoveredAgg.outerCircle);
newAtomBottom.AddConnection(points[maxLeftCoveredAgg.beginPointIndex], points[maxLeftCoveredAgg.endPointIndex], ConnectionType.ARC, maxLeftCoveredAgg.outerCircle);
newAtomTop.AddConnection(points[maxRightCoveredAgg.beginPointIndex], points[maxRightCoveredAgg.endPointIndex], ConnectionType.ARC, maxRightCoveredAgg.outerCircle);
newAtomBottom.AddConnection(points[maxRightCoveredAgg.beginPointIndex], points[maxRightCoveredAgg.endPointIndex], ConnectionType.ARC, maxRightCoveredAgg.outerCircle);
atoms.Add(newAtomTop);
atoms.Add(newAtomBottom);
//
// Make / return the new aggregator
//
return new Agg(beginIndex, endIndex, maxCoveredNodes, outerCircle, atoms);
}
//
// The order of the points in the filament were established by the algorithm
// Recursively seek smaller and smaller circular regions.
//
// Returns the set of atomic regions characterized by the largest circle (containing all the other atoms).
private Agg MakeRegions(UndirectedPlanarGraph.PlanarGraph graph, List <Circle> circles, int beginIndex, int endIndex)
{
if (memoized[beginIndex, endIndex] != null)
{
return(memoized[beginIndex, endIndex]);
}
//
// Find the circle for these given points.
//
Circle outerCircle = null;
foreach (Circle circle in circles)
{
if (circle.PointLiesOn(points[beginIndex]) && circle.PointLiesOn(points[endIndex]))
{
outerCircle = circle;
}
}
//
// Base Case: Gap between the given indices is 1.
//
if (endIndex - beginIndex == 1)
{
return(new Agg(beginIndex, endIndex, -1, outerCircle, HandleConnection(graph, circles, points[beginIndex], points[endIndex])));
}
//
// Look at all combinations of indices from beginIndex to endIndex; start with larger gaps between indices -> small gaps
//
Agg maxLeftCoveredAgg = null;
Agg maxRightCoveredAgg = null;
int maxCoveredNodes = 0;
for (int gap = endIndex - beginIndex - 1; gap > 0; gap--)
{
for (int index = beginIndex; index < endIndex; index++)
{
Agg left = MakeRegions(graph, circles, index, index + gap);
Agg right = MakeRegions(graph, circles, index + gap, endIndex);
// Check for new maxmimum coverage.
if (left.coveredPoints + right.coveredPoints > maxCoveredNodes)
{
maxLeftCoveredAgg = left;
maxRightCoveredAgg = right;
}
// Found complete coverage
if (left.coveredPoints + right.coveredPoints == endIndex - beginIndex + 1)
{
maxCoveredNodes = endIndex - beginIndex + 1;
break;
}
}
}
//
// We have the two maximal circles: create the new regions.
//
// The atoms from the left / right.
List <AtomicRegion> atoms = new List <AtomicRegion>();
atoms.AddRange(maxLeftCoveredAgg.atoms);
atoms.AddRange(maxRightCoveredAgg.atoms);
// New regions are based on this outer circle minus the left / right outer circles.
AtomicRegion newAtomTop = new AtomicRegion();
AtomicRegion newAtomBottom = new AtomicRegion();
// The outer circle.
newAtomTop.AddConnection(points[beginIndex], points[endIndex], ConnectionType.ARC, outerCircle);
newAtomBottom.AddConnection(points[beginIndex], points[endIndex], ConnectionType.ARC, outerCircle);
// The left / right maximal circles.
newAtomTop.AddConnection(points[maxLeftCoveredAgg.beginPointIndex], points[maxLeftCoveredAgg.endPointIndex], ConnectionType.ARC, maxLeftCoveredAgg.outerCircle);
newAtomBottom.AddConnection(points[maxLeftCoveredAgg.beginPointIndex], points[maxLeftCoveredAgg.endPointIndex], ConnectionType.ARC, maxLeftCoveredAgg.outerCircle);
newAtomTop.AddConnection(points[maxRightCoveredAgg.beginPointIndex], points[maxRightCoveredAgg.endPointIndex], ConnectionType.ARC, maxRightCoveredAgg.outerCircle);
newAtomBottom.AddConnection(points[maxRightCoveredAgg.beginPointIndex], points[maxRightCoveredAgg.endPointIndex], ConnectionType.ARC, maxRightCoveredAgg.outerCircle);
atoms.Add(newAtomTop);
atoms.Add(newAtomBottom);
//
// Make / return the new aggregator
//
return(new Agg(beginIndex, endIndex, maxCoveredNodes, outerCircle, atoms));
}
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;
}
//
// Determine if this is a true polygon situation or if it is a sequence of segments and arcs.
//
private List<AtomicRegion> GeneralAtomicRegion(Segment[] segments, Arc[] arcs)
{
List<AtomicRegion> regions = new List<AtomicRegion>();
//
// Determine if the parts are all segments.
// Concurrently determine the proper starting point in the sequence to construct the atomic region.
//
bool hasArc = false;
bool hasSegment = false;
int startIndex = 0;
for (int i = 0; i < segments.Length && i < arcs.Length; i++)
{
// Both an arc and a segment.
if (segments[i] != null && arcs[i] != null) return regions;
// Determine if we have an arc and/or a segment.
if (segments[i] != null) hasSegment = true;
if (arcs[i] != null) hasArc = true;
// A solid starting point is an arc right after a null.
if (arcs[i] == null && arcs[(i + 1) % arcs.Length] != null)
{
// Assign only once to the startIndex
if (startIndex == 0) startIndex = (i + 1) % arcs.Length;
}
}
// If only segments, we have a polygon.
if (hasSegment && !hasArc) return regions;
//
// If the set ONLY consists of arcs, ensure we have a good starting point.
//
if (hasArc && !hasSegment)
{
// Seek the first index where a change among arcs occurs.
for (int i = 0; i < arcs.Length; i++)
{
// A solid starting point is an arc right after a null.
if (!arcs[i].theCircle.StructurallyEquals(arcs[(i + 1) % arcs.Length].theCircle))
{
startIndex = (i + 1) % arcs.Length;
break;
}
}
}
AtomicRegion theRegion = new AtomicRegion();
for (int i = 0; i < segments.Length && i < arcs.Length; i++)
{
int currIndex = (i + startIndex) % arcs.Length;
if (segments[currIndex] == null && arcs[currIndex] == null) { /* No-Op */ }
if (segments[currIndex] != null)
{
theRegion.AddConnection(new Connection(segments[currIndex].Point1,
segments[currIndex].Point2, ConnectionType.SEGMENT, segments[currIndex]));
}
else if (arcs[currIndex] != null)
{
//
// Compose the arcs (from a single circle) together.
//
List<MinorArc> sequentialArcs = new List<MinorArc>();
sequentialArcs.Add(arcs[currIndex] as MinorArc);
int seqIndex;
for (seqIndex = (currIndex + 1) % arcs.Length; ; seqIndex = (seqIndex + 1) % arcs.Length, i++)
{
if (arcs[seqIndex] == null) break;
if (arcs[currIndex].theCircle.StructurallyEquals(arcs[seqIndex].theCircle))
{
sequentialArcs.Add(arcs[seqIndex] as MinorArc);
}
else break;
}
Arc composed;
if (sequentialArcs.Count > 1) composed = this.ComposeArcsIntoArc(sequentialArcs);
else composed = arcs[currIndex];
//
// Add the connection.
//
theRegion.AddConnection(new Connection(composed.endpoint1, composed.endpoint2, ConnectionType.ARC, composed));
}
}
return Utilities.MakeList<AtomicRegion>(theRegion);
}
private List<Atomizer.AtomicRegion> ConvertToTruncation(Segment chord, MinorArc arc)
{
AtomicRegion atom = new AtomicRegion();
atom.AddConnection(new Connection(chord.Point1, chord.Point2, ConnectionType.SEGMENT, chord));
atom.AddConnection(new Connection(chord.Point1, chord.Point2, ConnectionType.ARC, arc));
return Utilities.MakeList<AtomicRegion>(atom);
}
// Construct the region between a chord and the circle arc:
// (|
// ( |
// ( |
// ( |
// (|
//
private List<AtomicRegion> ConstructBasicLineCircleRegion(Segment chord, Circle circle)
{
//
// Standard
//
if (!circle.DefinesDiameter(chord))
{
AtomicRegion region = new AtomicRegion();
Arc theArc = new MinorArc(circle, chord.Point1, chord.Point2);
region.AddConnection(chord.Point1, chord.Point2, ConnectionType.ARC, theArc);
region.AddConnection(chord.Point1, chord.Point2, ConnectionType.SEGMENT, chord);
return Utilities.MakeList<AtomicRegion>(region);
}
//
// Semi-circles
//
Point midpt = circle.Midpoint(chord.Point1, chord.Point2);
Arc semi1 = new Semicircle(circle, chord.Point1, chord.Point2, midpt, chord);
ShapeAtomicRegion region1 = new ShapeAtomicRegion(new Sector(semi1));
Point opp = circle.OppositePoint(midpt);
Arc semi2 = new Semicircle(circle, chord.Point1, chord.Point2, opp, chord);
ShapeAtomicRegion region2 = new ShapeAtomicRegion(new Sector(semi2));
List<AtomicRegion> regions = new List<AtomicRegion>();
regions.Add(region1);
regions.Add(region2);
return regions;
}
// Construct the region between a circle and circle:
// __
// ( (
// ( (
// ( (
// ( (
// ( (
// --
private Atomizer.AtomicRegion ConstructBasicCircleCircleRegion(Segment chord, Circle smaller, Circle larger)
{
AtomicRegion region = new AtomicRegion();
Arc arc1 = null;
if (smaller.DefinesDiameter(chord))
{
Point midpt = smaller.Midpoint(chord.Point1, chord.Point2, larger.Midpoint(chord.Point1, chord.Point2));
arc1 = new Semicircle(smaller, chord.Point1, chord.Point2, midpt, chord);
}
else
{
arc1 = new MinorArc(smaller, chord.Point1, chord.Point2);
}
MinorArc arc2 = new MinorArc(larger, chord.Point1, chord.Point2);
region.AddConnection(chord.Point1, chord.Point2, ConnectionType.ARC, arc1);
region.AddConnection(chord.Point1, chord.Point2, ConnectionType.ARC, arc2);
return region;
}