public TrapezoidalMap()
{
Map = new HashSet<Trapezoid>();
_margin = 50.0f;
_bCross = null;
_cross = null;
}
// Case 2: Trapezoid contains point p, q lies outside
// break trapezoid into 3 smaller trapezoids
public Trapezoid[] Case2(Trapezoid t, Edge e)
{
Point rp;
if (e.Q.X == t.RightPoint.X)
rp = e.Q;
else
rp = t.RightPoint;
Trapezoid[] trapezoids = new Trapezoid[3];
trapezoids[0] = new Trapezoid(t.LeftPoint, e.P, t.Top, t.Bottom);
trapezoids[1] = new Trapezoid(e.P, rp, t.Top, e);
trapezoids[2] = new Trapezoid(e.P, rp, e, t.Bottom);
trapezoids[0].UpdateLeft(t.UpperLeft, t.LowerLeft);
trapezoids[1].UpdateLeftRight(trapezoids[0], null, t.UpperRight, null);
trapezoids[2].UpdateLeftRight(null, trapezoids[0], null, t.LowerRight);
_bCross = t.Bottom;
_cross = t.Top;
e.Above = trapezoids[1];
e.Below = trapezoids[2];
return trapezoids;
}
public void Case1(Sink sink, Edge edge, Trapezoid[] tList)
{
YNode yNode = new YNode(edge, Sink.Isink(tList[1]), Sink.Isink(tList[2]));
XNode qNode = new XNode(edge.Q, yNode, Sink.Isink(tList[3]));
XNode pNode = new XNode(edge.P, Sink.Isink(tList[0]), qNode);
Replace(sink, pNode);
}
public Trapezoid(Point leftPoint, Point rightPoint, Edge top, Edge bottom)
{
LeftPoint = leftPoint;
RightPoint = rightPoint;
Top = top;
Bottom = bottom;
UpperLeft = null;
UpperRight = null;
LowerLeft = null;
LowerRight = null;
Inside = true;
Sink = null;
}
// Case 1: segment completely enclosed by trapezoid
// break trapezoid into 4 smaller trapezoids
public Trapezoid[] Case1(Trapezoid t, Edge e)
{
Trapezoid[] trapezoids = new Trapezoid[4];
trapezoids[0] = new Trapezoid(t.LeftPoint, e.P, t.Top, t.Bottom);
trapezoids[1] = new Trapezoid(e.P, e.Q, t.Top, e);
trapezoids[2] = new Trapezoid(e.P, e.Q, e, t.Bottom);
trapezoids[3] = new Trapezoid(e.Q, t.RightPoint, t.Top, t.Bottom);
trapezoids[0].UpdateLeft(t.UpperLeft, t.LowerLeft);
trapezoids[1].UpdateLeftRight(trapezoids[0], null, trapezoids[3], null);
trapezoids[2].UpdateLeftRight(null, trapezoids[0], null, trapezoids[3]);
trapezoids[3].UpdateRight(t.UpperRight, t.LowerRight);
return trapezoids;
}
// Case 3: Trapezoid is bisected
public Trapezoid[] Case3(Trapezoid t, Edge e)
{
Point lp;
if (e.P.X == t.LeftPoint.X)
lp = e.P;
else
lp = t.LeftPoint;
Point rp;
if (e.Q.X == t.RightPoint.X)
rp = e.Q;
else
rp = t.RightPoint;
Trapezoid[] trapezoids = new Trapezoid[2];
if (_cross == t.Top)
{
trapezoids[0] = t.UpperLeft;
trapezoids[0].UpdateRight(t.UpperRight, null);
trapezoids[0].RightPoint = rp;
}
else
{
trapezoids[0] = new Trapezoid(lp, rp, t.Top, e);
trapezoids[0].UpdateLeftRight(t.UpperLeft, e.Above, t.UpperRight, null);
}
if (_bCross == t.Bottom)
{
trapezoids[1] = t.LowerLeft;
trapezoids[1].UpdateRight(null, t.LowerRight);
trapezoids[1].RightPoint = rp;
}
else
{
trapezoids[1] = new Trapezoid(lp, rp, e, t.Bottom);
trapezoids[1].UpdateLeftRight(e.Below, t.LowerLeft, null, t.LowerRight);
}
_bCross = t.Bottom;
_cross = t.Top;
e.Above = trapezoids[0];
e.Below = trapezoids[1];
return trapezoids;
}
public List<Trapezoid> FollowEdge(Edge edge)
{
List<Trapezoid> trapezoids = new List<Trapezoid>();
trapezoids.Add(Locate(edge));
int j = 0;
while (edge.Q.X > trapezoids[j].RightPoint.X)
{
if (edge.IsAbove(trapezoids[j].RightPoint))
{
trapezoids.Add(trapezoids[j].UpperRight);
}
else
{
trapezoids.Add(trapezoids[j].LowerRight);
}
j += 1;
}
return trapezoids;
}
// Create an AABB around segments
public Trapezoid BoundingBox(List<Edge> edges)
{
Point max = edges[0].P + _margin;
Point min = edges[0].Q - _margin;
foreach (Edge e in edges)
{
if (e.P.X > max.X) max = new Point(e.P.X + _margin, max.Y);
if (e.P.Y > max.Y) max = new Point(max.X, e.P.Y + _margin);
if (e.Q.X > max.X) max = new Point(e.Q.X + _margin, max.Y);
if (e.Q.Y > max.Y) max = new Point(max.X, e.Q.Y + _margin);
if (e.P.X < min.X) min = new Point(e.P.X - _margin, min.Y);
if (e.P.Y < min.Y) min = new Point(min.X, e.P.Y - _margin);
if (e.Q.X < min.X) min = new Point(e.Q.X - _margin, min.Y);
if (e.Q.Y < min.Y) min = new Point(min.X, e.Q.Y - _margin);
}
Edge top = new Edge(new Point(min.X, max.Y), new Point(max.X, max.Y));
Edge bottom = new Edge(new Point(min.X, min.Y), new Point(max.X, min.Y));
Point left = bottom.P;
Point right = top.Q;
return new Trapezoid(left, right, top, bottom);
}
private Point LineIntersect(Edge edge, float x)
{
float y = edge.Slope * x + edge.B;
return new Point(x, y);
}
public void Clear()
{
_bCross = null;
_cross = null;
}
public void Case3(Sink sink, Edge edge, Trapezoid[] tList)
{
YNode yNode = new YNode(edge, Sink.Isink(tList[0]), Sink.Isink(tList[1]));
Replace(sink, yNode);
}
private Trapezoid Locate(Edge edge)
{
return(_head.Locate(edge).Trapezoid);
}
public void Case3(Sink sink, Edge edge, Trapezoid[] tList)
{
YNode yNode = new YNode(edge, Sink.Isink(tList[0]), Sink.Isink(tList[1]));
Replace(sink, yNode);
}
private Trapezoid Locate(Edge edge)
{
return _head.Locate(edge).Trapezoid;
}
public void Clear()
{
this._bCross = null;
this._cross = null;
}
public abstract Sink Locate(Edge s);
// Case 4: Trapezoid contains point q, p lies outside
// break trapezoid into 3 smaller trapezoids
public Trapezoid[] Case4(Trapezoid t, Edge e)
{
Point lp;
if (e.P.X == t.LeftPoint.X)
lp = e.P;
else
lp = t.LeftPoint;
Trapezoid[] trapezoids = new Trapezoid[3];
if (_cross == t.Top)
{
trapezoids[0] = t.UpperLeft;
trapezoids[0].RightPoint = e.Q;
}
else
{
trapezoids[0] = new Trapezoid(lp, e.Q, t.Top, e);
trapezoids[0].UpdateLeft(t.UpperLeft, e.Above);
}
if (_bCross == t.Bottom)
{
trapezoids[1] = t.LowerLeft;
trapezoids[1].RightPoint = e.Q;
}
else
{
trapezoids[1] = new Trapezoid(lp, e.Q, e, t.Bottom);
trapezoids[1].UpdateLeft(e.Below, t.LowerLeft);
}
trapezoids[2] = new Trapezoid(e.Q, t.RightPoint, t.Top, t.Bottom);
trapezoids[2].UpdateLeftRight(trapezoids[0], trapezoids[1], t.UpperRight, t.LowerRight);
return trapezoids;
}