public static Circle ConstructCircle(Point p1, Point p2, Point p3)
{
//
// Find the center of the circle.
//
Segment chord1 = new Segment(p1, p2);
Segment chord2 = new Segment(p2, p3);
Segment perpBis1 = chord1.GetPerpendicular(chord1.Midpoint());
Segment perpBis2 = chord2.GetPerpendicular(chord2.Midpoint());
Point center = perpBis1.FindIntersection(perpBis2);
//
// Radius is the distance between the circle and any of the original points.
//
return new Circle(center, Point.calcDistance(center, p1));
}
public static Circle ConstructCircle(Point p1, Point p2, Point p3)
{
//
// Find the center of the circle.
//
Segment chord1 = new Segment(p1, p2);
Segment chord2 = new Segment(p2, p3);
Segment perpBis1 = chord1.GetPerpendicular(chord1.Midpoint());
Segment perpBis2 = chord2.GetPerpendicular(chord2.Midpoint());
Point center = perpBis1.FindIntersection(perpBis2);
//
// Radius is the distance between the circle and any of the original points.
//
return(new Circle(center, Point.calcDistance(center, p1)));
}
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);
}
// return the midpoint between these two on the circle.
public Point Midpoint(Point a, Point b)
{
if (!this.PointLiesOn(a)) return null;
if (!this.PointLiesOn(b)) return null;
// Make the chord.
Segment chord = new Segment(a, b);
Point pt1 = null;
Point pt2 = null;
// Is this a diameter? If so, quickly return a point perpendicular to the diameter
if (DefinesDiameter(chord))
{
Segment perp = chord.GetPerpendicular(center);
this.FindIntersection(perp, out pt1, out pt2);
// Arbitrarily choose one of the points.
return pt1 != null ? pt1 : pt2;
}
// Make radius through the midpoint of the chord.
Segment radius = new Segment(center, chord.Midpoint());
this.FindIntersection(radius, out pt1, out pt2);
if (pt2 == null) return pt1;
Point theMidpoint = Arc.StrictlyBetweenMinor(pt1, new MinorArc(this, a, b)) ? pt1 : pt2;
double angle1 = new Angle(a, center, theMidpoint).measure;
double angle2 = new Angle(b, center, theMidpoint).measure;
if (!Utilities.CompareValues(angle1, angle2))
{
throw new ArgumentException("Midpoint is incorrect; angles do not equate: " + angle1 + " " + angle2);
}
return theMidpoint;
}
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;
}