public ConvexPolygon(Point[] points)
{
if (points.Length < 3)
{
throw new ArgumentException("Too few points (" + points.Length + "). There should be at least 3 points to make a polygon");
}
// Checking convexity
double sign_value = Vector.CrossProduct(
(Vector)points[0] - (Vector)points[points.Length - 1],
(Vector)points[1] - (Vector)points[points.Length - 1]);
double sign_value2 = Vector.CrossProduct(
(Vector)points[points.Length - 1] - (Vector)points[points.Length - 2],
(Vector)points[0] - (Vector)points[points.Length - 2]);
if (Math.Sign(sign_value) * Math.Sign(sign_value2) < 0)
throw new PolygonNotConvexException("Polygon isn't convex");
for (int i = 0; i < points.Length - 2; i++)
{
double sign_value_i = Vector.CrossProduct(
(Vector)points[i + 1] - (Vector)points[i],
(Vector)points[i + 2] - (Vector)points[i]);
if (Math.Sign(sign_value) * Math.Sign(sign_value_i) < 0)
throw new PolygonNotConvexException("Polygon isn't convex");
}
// Sorting points clockwise
if (sign_value > 0)
mVertex = points;
else
{
mVertex = new Point[points.Length];
for (int i = 0; i < points.Length; i++)
{
mVertex[i] = points[points.Length - 1 - i];
}
}
// Constructing sides
mSides = new Segment[mVertex.Length];
mSides[mVertex.Length - 1] = new Segment(mVertex[mVertex.Length - 1], mVertex[0]);
for (int i = 0; i < mVertex.Length - 1; i++)
mSides[i] = new Segment(mVertex[i], mVertex[i + 1]);
// Calculating bounding box
mXMin = mVertex[0].X; mXMax = mVertex[0].X;
mYMin = mVertex[0].Y; mYMax = mVertex[0].Y;
for (int i = 1; i < mVertex.Length; i++)
{
if (mXMin > mVertex[i].X) mXMin = mVertex[i].X;
if (mYMin > mVertex[i].Y) mYMin = mVertex[i].Y;
if (mXMax < mVertex[i].X) mXMax = mVertex[i].X;
if (mYMax < mVertex[i].Y) mYMax = mVertex[i].Y;
}
}
public static Point GetCrossing(Segment s1, Segment s2)
{
// Algorithmic equality
if (s1 == s2)
throw new SelfCrossingException("Trying to find selfcrossing");
// TODO: Add rough estimation here (i.e. rectangle estimation)
if (s1._Crossings.ContainsKey(s2))
return s1._Crossings[s2];
// TODO: Check integrity
// Parallelism and zero-length
Vector AB1 = new Vector(s1._B.X - s1._A.X, s1._B.Y - s1._A.Y);
Vector AB2 = new Vector(s2._B.X - s2._A.X, s2._B.Y - s2._A.Y);
double D = Vector.CrossProduct(AB2, AB1);
if (Math.Abs(D) == 0) return null;
if (s1._A == s2._A || s1._A == s2._B) return s1._A;
if (s1._B == s2._A || s1._B == s2._B) return s1._B;
// Calculating crossing between lines
double m = Vector.CrossProduct((Vector)s1._A, AB1);
double n = Vector.CrossProduct((Vector)s2._A, AB2);
double x = (m * AB2.X - n * AB1.X) / D;
double y = (m * AB2.Y - n * AB1.Y) / D;
// Checking if an endpoint of one segment is contained by other
if (s1._A.X == x && s1._A.Y == y) return s1._A;
if (s1._B.X == x && s1._B.Y == y) return s1._B;
if (s2._A.X == x && s2._A.Y == y) return s2._A;
if (s2._B.X == x && s2._B.Y == y) return s2._B;
// Checking if the crossing point is in both segments
Vector AC1 = new Vector(x - s1._A.X, y - s1._A.Y);
Vector BC1 = new Vector(x - s1._B.X, y - s1._B.Y);
if ((AB1 * AC1) * (-AB1 * BC1) < 0) return null;
Vector AC2 = new Vector(x - s2._A.X, y - s2._A.Y);
Vector BC2 = new Vector(x - s2._B.X, y - s2._B.Y);
if ((AB2 * AC2) * (-AB2 * BC2) < 0) return null;
// Adding the point to crossing dictionaries
Point crs = new Point(x, y);
s1._Crossings.Add(s2, crs);
s2._Crossings.Add(s1, crs);
return crs;
}
public int IndexOfSide(Segment side)
{
for (int i = 0; i < mSides.Length; i++)
if (mSides[i] == side) return i;
return -1;
}
public bool HasCrossing(Point crossing, out Segment mySide, out Segment other)
{
mySide = null; other = null;
for (int i = 0; i < mSides.Length; i++)
{
Segment res = mSides[i].HasCrossing(crossing);
if (res != null)
{
mySide = mSides[i];
other = res;
return true;
}
}
return false;
}
