/// <summary>
/// Removes any points in the polygon which are collinear with its nearest neighbors.
/// </summary>
/// <param name="polygon">The polygon to search for collinear points</param>
private Polygon RemoveCollinearPoints(Polygon polygon)
{
if (polygon.Count <= 3)
{
return(polygon);
}
Polygon result = new Polygon();
for (int i = 0; i < polygon.Count; i++)
{
Microsoft.Xna.Framework.Vector2 prev = polygon.At(i - 1);
Microsoft.Xna.Framework.Vector2 current = polygon[i];
Microsoft.Xna.Framework.Vector2 next = polygon.At(i + 1);
// Skip adding this point to the result if it is collinear with its neighbors.
if (LineAlgorithms.AreCollinear(prev, current, next))
{
continue;
}
result.Add(current);
}
return(result);
}
List <Event> sortedEvents = new List <Event>(); // sorted list of event pointers
public EventQueue(Polygon polygon)
{
nextIndex = 0;
eventCount = 2 * polygon.Count; // 2 vertex events for each edge
events.AddRange(Enumerable.Range(0, eventCount).Select(i => new Event()));
sortedEvents.AddRange(events);
// Initialize event queue with edge segment endpoints
for (int i = 0; i < polygon.Count; i++)
{
// Initialize data for edge i
// The original C code had either an issue or an undocumented assumption here:
// they used polygon[i + 1] which could result in an out of memory error, unless
// the next point was automatically returned.
sortedEvents[2 * i].Edge = i;
sortedEvents[2 * i + 1].Edge = i;
sortedEvents[2 * i].Vertex = polygon.At(i);
sortedEvents[2 * i + 1].Vertex = polygon.At(i + 1);
// determine type
if (XYOrder(polygon.At(i), polygon.At(i + 1)) <= 0)
{
sortedEvents[2 * i].EventType = EventType.Left;
sortedEvents[2 * i + 1].EventType = EventType.Right;
}
else
{
sortedEvents[2 * i].EventType = EventType.Right;
sortedEvents[2 * i + 1].EventType = EventType.Left;
}
}
// Sort Eq[] by increasing x and y
sortedEvents.Sort(EventComparison);
}
public SweepLineSegment Add(Event E)
{
SweepLineSegment segToAdd = new SweepLineSegment {
Edge = E.Edge
};
// if it is being added, then it must be a LEFT edge event
// but need to determine which endpoint is the left one
Microsoft.Xna.Framework.Vector2 v1 = polygon.At(segToAdd.Edge);
Microsoft.Xna.Framework.Vector2 v2 = polygon.At(segToAdd.Edge + 1);
// determine which is leftmost
if (XYOrder(v1, v2) < 0)
{
segToAdd.LeftVertex = v1;
segToAdd.RightVertex = v2;
}
else
{
segToAdd.LeftVertex = v2;
segToAdd.RightVertex = v1;
}
segToAdd.Above = null;
segToAdd.Below = null;
// add a node to the balanced binary tree
BinaryTreeNode <SweepLineSegment> nd = tree.Add(segToAdd);
BinaryTreeNode <SweepLineSegment> nx = nd.Next();
BinaryTreeNode <SweepLineSegment> np = nd.Previous();
if (nx != null)
{
segToAdd.Above = nx.Value;
segToAdd.Above.Below = segToAdd;
}
if (np != null)
{
segToAdd.Below = np.Value;
segToAdd.Below.Above = segToAdd;
}
return(segToAdd);
}
/// <summary>
/// Copies a range of vertices from a polygon with wrap-around on the indices.
/// </summary>
/// <param name="polygon"></param>
/// <param name="start"></param>
/// <param name="end"></param>
/// <returns></returns>
public static Polygon CopyRange(this Polygon polygon, int start, int end)
{
Polygon p = new Polygon();
while (end < start)
{
end += polygon.Count;
}
for (; start <= end; ++start)
{
p.Add(polygon.At(start));
}
return(p);
}
/// <summary>
/// Decomposes a concave polygon into a set of convex polygons.
/// </summary>
/// <param name="polygon"></param>
/// <returns></returns>
public IReadOnlyList <Polygon> BuildConvexDecomposition(Polygon polygon)
{
//We force it to CCW as it is a precondition in this algorithm.
polygon = ForceCounterClockWise(polygon);
List <Polygon> list = new List <Polygon>();
// YOGESH : Convex Partition can not happen if there are less than 3, ie 2,1 vertices
if (polygon.Count < 3)
{
return(list);
}
double d = 0.0;
double lowerDist, upperDist;
Microsoft.Xna.Framework.Vector2 p;
Microsoft.Xna.Framework.Vector2 lowerInt = new Microsoft.Xna.Framework.Vector2();
Microsoft.Xna.Framework.Vector2 upperInt = new Microsoft.Xna.Framework.Vector2(); // intersection points
int lowerIndex = 0, upperIndex = 0;
Polygon lowerPoly, upperPoly;
// Go thru all Verices until we find a reflex vertex i.
// Extend the edges incident at i until they hit an edge
// Find BEST vertex within the range, that the partitioning chord
// A polygon can be broken into convex regions by eliminating all reflex vertices
// Eliminating two reflex vertices with one diagonal is better than eliminating just one
// A reflex vertex can only be removed if the diagonal connecting to it is within the range given by extending its neighbouring edges;
// otherwise, its angle is only reduced
for (int i = 0; i < polygon.Count; i++)
{
Microsoft.Xna.Framework.Vector2 prev = polygon.At(i - 1);
Microsoft.Xna.Framework.Vector2 on = polygon.At(i);
Microsoft.Xna.Framework.Vector2 next = polygon.At(i + 1);
if (IsReflex(prev, on, next))
{
lowerDist = double.MaxValue;
upperDist = double.MaxValue;
for (int j = 0; j < polygon.Count; j++)
{
// YOGESH: if any of j line's endpoints matches with reflex i, skip
if ((i == j) ||
(i == NormalizeIndex(j - 1, polygon.Count)) ||
(i == NormalizeIndex(j + 1, polygon.Count)))
{
continue; // no self and prev and next, for testing
}
// testing incoming edge:
// if line coming into i vertex (i-1 to i) has j vertex of the test-line on left
// AND have j-i on right, then they will be intersecting
Microsoft.Xna.Framework.Vector2 iPrev = polygon.At(i - 1);
Microsoft.Xna.Framework.Vector2 iSelf = polygon.At(i);
Microsoft.Xna.Framework.Vector2 jSelf = polygon.At(j);
Microsoft.Xna.Framework.Vector2 jPrev = polygon.At(j - 1);
bool leftOK = Left(iPrev, iSelf, jSelf);
bool rightOK = Right(iPrev, iSelf, jPrev);
bool leftOnOK = LineAlgorithms.AreCollinear(iPrev, iSelf, jSelf); // YOGESH: cached into variables for better debugging
bool rightOnOK = LineAlgorithms.AreCollinear(iPrev, iSelf, jPrev); // YOGESH: cached into variables for better debugging
if (leftOnOK || rightOnOK) // YOGESH: Checked "ON" condition as well, collinearity
{
// lines are colinear, they can not be overlapping as polygon is simple
// find closest point which is not internal to incoming line i , i -1
d = Microsoft.Xna.Framework.Vector2.DistanceSquared(iSelf, jSelf);
// this lower* is the point got from incoming edge into the i vertex,
// lowerInt incoming edge intersection point
// lowerIndex incoming edge intersection edge
if (d < lowerDist)
{
// keep only the closest intersection
lowerDist = d;
lowerInt = jSelf;
lowerIndex = j - 1;
}
d = Microsoft.Xna.Framework.Vector2.DistanceSquared(iSelf, jPrev);
// this lower* is the point got from incoming edge into the i vertex,
// lowerInt incoming edge intersection point
// lowerIndex incoming edge intersection edge
if (d < lowerDist)
{
// keep only the closest intersection
lowerDist = d;
lowerInt = jPrev;
lowerIndex = j;
}
}
else if (leftOK && rightOK) // YOGESH: Intersection in-between. Bayazit had ON condition in built here, which I have taken care above.
{
// find the point of intersection
var intersection = LineAlgorithms.LineSegmentIntersection(
polygon.At(i - 1), polygon.At(i), polygon.At(j), polygon.At(j - 1))
?.IntersectionPoint;
if (intersection != null)
{
p = intersection.Value;
// make sure it's inside the poly,
if (Right(polygon.At(i + 1), polygon.At(i), p))
{
d = Microsoft.Xna.Framework.Vector2.DistanceSquared(polygon.At(i), p);
// this lower* is the point got from incoming edge into the i vertex,
// lowerInt incoming edge intersection point
// lowerIndex incoming edge intersection edge
if (d < lowerDist)
{
// keep only the closest intersection
lowerDist = d;
lowerInt = p;
lowerIndex = j;
}
}
}
}
// testing outgoing edge:
// if line outgoing from i vertex (i to i+1) has j vertex of the test-line on right
// AND has j+1 on left, they they will be intersecting
Microsoft.Xna.Framework.Vector2 iNext = polygon.At(i + 1);
Microsoft.Xna.Framework.Vector2 jNext = polygon.At(j + 1);
bool leftOKn = Left(iNext, iSelf, jNext);
bool rightOKn = Right(iNext, iSelf, jSelf);
bool leftOnOKn = LineAlgorithms.AreCollinear(iNext, iSelf, jNext); // YOGESH: cached into variables for better debugging
bool rightOnOKn = LineAlgorithms.AreCollinear(iNext, iSelf, jSelf);
if (leftOnOKn || rightOnOKn) // YOGESH: Checked "ON" condition as well, collinearity
{
// lines are colinear, they can not be overlapping as polygon is simple
// find closest point which is not internal to incoming line i , i -1
d = Microsoft.Xna.Framework.Vector2.DistanceSquared(iSelf, jNext);
// this upper* is the point got from outgoing edge into the i vertex,
// upperInt outgoing edge intersection point
// upperIndex outgoing edge intersection edge
if (d < upperDist)
{
// keep only the closest intersection
upperDist = d;
upperInt = jNext;
upperIndex = j + 1;
}
d = Microsoft.Xna.Framework.Vector2.DistanceSquared(polygon.At(i), polygon.At(j));
// this upper* is the point got from outgoing edge into the i vertex,
// upperInt outgoing edge intersection point
// upperIndex outgoing edge intersection edge
if (d < upperDist)
{
// keep only the closest intersection
upperDist = d;
upperInt = jSelf;
upperIndex = j;
}
}
else if (leftOKn && rightOKn) // YOGESH: Intersection in-between. Bayazit had ON condition in built here, which I have taken care above.
{
var intersection = LineAlgorithms.LineSegmentIntersection(
polygon.At(i + 1), polygon.At(i), polygon.At(j), polygon.At(j + 1))
?.IntersectionPoint;
if (intersection != null)
{
p = intersection.Value;
if (Left(polygon.At(i - 1), polygon.At(i), p))
{
d = Microsoft.Xna.Framework.Vector2.DistanceSquared(polygon.At(i), p);
// this upper* is the point got from outgoing edge from the i vertex,
// upperInt outgoing edge intersection point
// upperIndex outgoing edge intersection edge
if (d < upperDist)
{
upperDist = d;
upperIndex = j;
upperInt = p;
}
}
}
}
}
// YOGESH: If no vertices in the range, lets not choose midpoint but closet point of that segment
//// if there are no vertices to connect to, choose a point in the middle
if (lowerIndex == (upperIndex + 1) % polygon.Count)
{
Microsoft.Xna.Framework.Vector2 sp = ((lowerInt + upperInt) / 2);
lowerPoly = polygon.CopyRange(i, upperIndex);
lowerPoly.Add(sp);
upperPoly = polygon.CopyRange(lowerIndex, i);
upperPoly.Add(sp);
}
else
{
//find vertex to connect to
double highestScore = 0, bestIndex = lowerIndex;
while (upperIndex < lowerIndex)
{
upperIndex += polygon.Count;
}
// go throuh all the vertices between the range of lower and upper
for (int j = lowerIndex; j <= upperIndex; ++j)
{
if (CanSee(polygon, i, j))
{
double score = 1 / (Microsoft.Xna.Framework.Vector2.DistanceSquared(polygon.At(i), polygon.At(j)) + 1);
// if another vertex is Reflex, choosing it has highest score
Microsoft.Xna.Framework.Vector2 prevj = polygon.At(j - 1);
Microsoft.Xna.Framework.Vector2 onj = polygon.At(j);
Microsoft.Xna.Framework.Vector2 nextj = polygon.At(j + 1);
if (IsReflex(prevj, onj, nextj))
{
if (RightOrOn(polygon.At(j - 1), polygon.At(j), polygon.At(i)) &&
LeftOrOn(polygon.At(j + 1), polygon.At(j), polygon.At(i)))
{
score += 3;
}
else
{
score += 2;
}
}
else
{
score += 1;
}
if (score > highestScore)
{
bestIndex = j;
highestScore = score;
}
}
}
// YOGESH : Pending: if there are 2 vertices as 'bestIndex', its better to disregard both and put midpoint (M case)
lowerPoly = polygon.CopyRange(i, (int)bestIndex);
upperPoly = polygon.CopyRange((int)bestIndex, i);
}
// solve smallest poly first (SAW in Bayazit's C++ code)
if (lowerPoly.Count < upperPoly.Count)
{
list.AddRange(BuildConvexDecomposition(lowerPoly));
list.AddRange(BuildConvexDecomposition(upperPoly));
}
else
{
list.AddRange(BuildConvexDecomposition(upperPoly));
list.AddRange(BuildConvexDecomposition(lowerPoly));
}
return(list);
}
}
// polygon is already convex
if (polygon.Count > MaxPolygonVertices)
{
lowerPoly = polygon.CopyRange(0, polygon.Count / 2);
upperPoly = polygon.CopyRange(polygon.Count / 2, 0);
list.AddRange(BuildConvexDecomposition(lowerPoly));
list.AddRange(BuildConvexDecomposition(upperPoly));
}
else
{
list.Add(polygon);
}
// The polygons are not guaranteed to be without collinear points. We remove
// them to be sure.
for (int i = 0; i < list.Count; i++)
{
list[i] = RemoveCollinearPoints(list[i]);
}
return(list);
}
/// <summary>
/// Returns true if vertex j can be seen from vertex i without any obstructions.
/// </summary>
/// <param name="polygon"></param>
/// <param name="i"></param>
/// <param name="j"></param>
/// <returns></returns>
private bool CanSee(Polygon polygon, int i, int j)
{
Microsoft.Xna.Framework.Vector2 prev = polygon.At(i - 1);
Microsoft.Xna.Framework.Vector2 on = polygon.At(i);
Microsoft.Xna.Framework.Vector2 next = polygon.At(i + 1);
if (IsReflex(prev, on, next))
{
if (LeftOrOn(polygon.At(i), polygon.At(i - 1), polygon.At(j)) &&
RightOrOn(polygon.At(i), polygon.At(i + 1), polygon.At(j)))
{
return(false);
}
}
else
{
if (RightOrOn(polygon.At(i), polygon.At(i + 1), polygon.At(j)) ||
LeftOrOn(polygon.At(i), polygon.At(i - 1), polygon.At(j)))
{
return(false);
}
}
Microsoft.Xna.Framework.Vector2 prevj = polygon.At(j - 1);
Microsoft.Xna.Framework.Vector2 onj = polygon.At(j);
Microsoft.Xna.Framework.Vector2 nextj = polygon.At(j + 1);
if (IsReflex(prevj, onj, nextj))
{
if (LeftOrOn(polygon.At(j), polygon.At(j - 1), polygon.At(i)) &&
RightOrOn(polygon.At(j), polygon.At(j + 1), polygon.At(i)))
{
return(false);
}
}
else
{
if (RightOrOn(polygon.At(j), polygon.At(j + 1), polygon.At(i)) ||
LeftOrOn(polygon.At(j), polygon.At(j - 1), polygon.At(i)))
{
return(false);
}
}
for (int k = 0; k < polygon.Count; ++k)
{
// YOGESH : changed from Line-Line intersection to Segment-Segment Intersection
Microsoft.Xna.Framework.Vector2 p1 = polygon.At(i);
Microsoft.Xna.Framework.Vector2 p2 = polygon.At(j);
Microsoft.Xna.Framework.Vector2 q1 = polygon.At(k);
Microsoft.Xna.Framework.Vector2 q2 = polygon.At(k + 1);
// ignore incident edges
if (p1.Equals(q1) || p1.Equals(q2) || p2.Equals(q1) || p2.Equals(q2))
{
continue;
}
var intersection = LineAlgorithms.LineSegmentIntersection(p1, p2, q1, q2);
if (intersection != null &&
intersection.WithinFirstSegment &&
intersection.WithinSecondSegment)
{
Microsoft.Xna.Framework.Vector2 intPoint = intersection.IntersectionPoint;
// intPoint is not any of the j line then false, else continue. Intersection has to be interior to qualify s 'false' from here
if ((!intPoint.Equals(polygon.At(k))) || (!intPoint.Equals(polygon.At(k + 1))))
{
return(false);
}
}
}
return(true);
}
