/// <summary>
/// Checks if the vertices forms an simple polygon by checking for edge crossings.
/// </summary>
public bool IsSimple()
{
//The simplest polygon which can exist in the Euclidean plane has 3 sides.
if (Count < 3)
{
return(false);
}
for (int i = 0; i < Count; ++i)
{
FPVector2 a1 = this[i];
FPVector2 a2 = NextVertex(i);
for (int j = i + 1; j < Count; ++j)
{
FPVector2 b1 = this[j];
FPVector2 b2 = NextVertex(j);
FPVector2 temp;
if (LineTools.LineIntersect2(ref a1, ref a2, ref b1, ref b2, out temp))
{
return(false);
}
}
}
return(true);
}
private static bool CanSee(int i, int j, Vertices vertices)
{
if (Reflex(i, vertices))
{
if (LeftOn(At(i, vertices), At(i - 1, vertices), At(j, vertices)) && RightOn(At(i, vertices), At(i + 1, vertices), At(j, vertices)))
{
return(false);
}
}
else
{
if (RightOn(At(i, vertices), At(i + 1, vertices), At(j, vertices)) || LeftOn(At(i, vertices), At(i - 1, vertices), At(j, vertices)))
{
return(false);
}
}
if (Reflex(j, vertices))
{
if (LeftOn(At(j, vertices), At(j - 1, vertices), At(i, vertices)) && RightOn(At(j, vertices), At(j + 1, vertices), At(i, vertices)))
{
return(false);
}
}
else
{
if (RightOn(At(j, vertices), At(j + 1, vertices), At(i, vertices)) || LeftOn(At(j, vertices), At(j - 1, vertices), At(i, vertices)))
{
return(false);
}
}
for (int k = 0; k < vertices.Count; ++k)
{
if ((k + 1) % vertices.Count == i || k == i || (k + 1) % vertices.Count == j || k == j)
{
continue; // ignore incident edges
}
FPVector2 intersectionPoint;
if (LineTools.LineIntersect(At(i, vertices), At(j, vertices), At(k, vertices), At(k + 1, vertices), out intersectionPoint))
{
return(false);
}
}
return(true);
}
private static void SimplifySection(Vertices vertices, int i, int j, bool[] usePoint, FP distanceTolerance)
{
if ((i + 1) == j)
{
return;
}
FPVector2 a = vertices[i];
FPVector2 b = vertices[j];
FP maxDistance = -1.0;
int maxIndex = i;
for (int k = i + 1; k < j; k++)
{
FPVector2 point = vertices[k];
FP distance = LineTools.DistanceBetweenPointAndLineSegment(ref point, ref a, ref b);
if (distance > maxDistance)
{
maxDistance = distance;
maxIndex = k;
}
}
if (maxDistance <= distanceTolerance)
{
for (int k = i + 1; k < j; k++)
{
usePoint[k] = false;
}
}
else
{
SimplifySection(vertices, i, maxIndex, usePoint, distanceTolerance);
SimplifySection(vertices, maxIndex, j, usePoint, distanceTolerance);
}
}
private static List <Vertices> TriangulatePolygon(Vertices vertices)
{
List <Vertices> list = new List <Vertices>();
FPVector2 lowerInt = new FPVector2();
FPVector2 upperInt = new FPVector2(); // intersection points
int lowerIndex = 0, upperIndex = 0;
Vertices lowerPoly, upperPoly;
for (int i = 0; i < vertices.Count; ++i)
{
if (Reflex(i, vertices))
{
FP upperDist;
FP lowerDist = upperDist = FP.MaxValue;
for (int j = 0; j < vertices.Count; ++j)
{
// if line intersects with an edge
FP d;
FPVector2 p;
if (Left(At(i - 1, vertices), At(i, vertices), At(j, vertices)) && RightOn(At(i - 1, vertices), At(i, vertices), At(j - 1, vertices)))
{
// find the point of intersection
p = LineTools.LineIntersect(At(i - 1, vertices), At(i, vertices), At(j, vertices), At(j - 1, vertices));
if (Right(At(i + 1, vertices), At(i, vertices), p))
{
// make sure it's inside the poly
d = SquareDist(At(i, vertices), p);
if (d < lowerDist)
{
// keep only the closest intersection
lowerDist = d;
lowerInt = p;
lowerIndex = j;
}
}
}
if (Left(At(i + 1, vertices), At(i, vertices), At(j + 1, vertices)) && RightOn(At(i + 1, vertices), At(i, vertices), At(j, vertices)))
{
p = LineTools.LineIntersect(At(i + 1, vertices), At(i, vertices), At(j, vertices), At(j + 1, vertices));
if (Left(At(i - 1, vertices), At(i, vertices), p))
{
d = SquareDist(At(i, vertices), p);
if (d < upperDist)
{
upperDist = d;
upperIndex = j;
upperInt = p;
}
}
}
}
// if there are no vertices to connect to, choose a point in the middle
if (lowerIndex == (upperIndex + 1) % vertices.Count)
{
FPVector2 p = ((lowerInt + upperInt) / 2);
lowerPoly = Copy(i, upperIndex, vertices);
lowerPoly.Add(p);
upperPoly = Copy(lowerIndex, i, vertices);
upperPoly.Add(p);
}
else
{
FP highestScore = 0, bestIndex = lowerIndex;
while (upperIndex < lowerIndex)
{
upperIndex += vertices.Count;
}
for (int j = lowerIndex; j <= upperIndex; ++j)
{
if (CanSee(i, j, vertices))
{
FP score = 1 / (SquareDist(At(i, vertices), At(j, vertices)) + 1);
if (Reflex(j, vertices))
{
if (RightOn(At(j - 1, vertices), At(j, vertices), At(i, vertices)) && LeftOn(At(j + 1, vertices), At(j, vertices), At(i, vertices)))
{
score += 3;
}
else
{
score += 2;
}
}
else
{
score += 1;
}
if (score > highestScore)
{
bestIndex = j;
highestScore = score;
}
}
}
lowerPoly = Copy(i, (int)bestIndex, vertices);
upperPoly = Copy((int)bestIndex, i, vertices);
}
list.AddRange(TriangulatePolygon(lowerPoly));
list.AddRange(TriangulatePolygon(upperPoly));
return(list);
}
}
// polygon is already convex
if (vertices.Count > Settings.MaxPolygonVertices)
{
lowerPoly = Copy(0, vertices.Count / 2, vertices);
upperPoly = Copy(vertices.Count / 2, 0, vertices);
list.AddRange(TriangulatePolygon(lowerPoly));
list.AddRange(TriangulatePolygon(upperPoly));
}
else
{
list.Add(vertices);
}
return(list);
}
/// <summary>
/// Calculates all intersections between two polygons.
/// </summary>
/// <param name="polygon1">The first polygon.</param>
/// <param name="polygon2">The second polygon.</param>
/// <param name="slicedPoly1">Returns the first polygon with added intersection points.</param>
/// <param name="slicedPoly2">Returns the second polygon with added intersection points.</param>
private static void CalculateIntersections(Vertices polygon1, Vertices polygon2,
out Vertices slicedPoly1, out Vertices slicedPoly2)
{
slicedPoly1 = new Vertices(polygon1);
slicedPoly2 = new Vertices(polygon2);
// Iterate through polygon1's edges
for (int i = 0; i < polygon1.Count; i++)
{
// Get edge vertices
FPVector2 a = polygon1[i];
FPVector2 b = polygon1[polygon1.NextIndex(i)];
// Get intersections between this edge and polygon2
for (int j = 0; j < polygon2.Count; j++)
{
FPVector2 c = polygon2[j];
FPVector2 d = polygon2[polygon2.NextIndex(j)];
FPVector2 intersectionPoint;
// Check if the edges intersect
if (LineTools.LineIntersect(a, b, c, d, out intersectionPoint))
{
// calculate alpha values for sorting multiple intersections points on a edge
FP alpha;
// Insert intersection point into first polygon
alpha = GetAlpha(a, b, intersectionPoint);
if (alpha > 0f && alpha < 1f)
{
int index = slicedPoly1.IndexOf(a) + 1;
while (index < slicedPoly1.Count &&
GetAlpha(a, b, slicedPoly1[index]) <= alpha)
{
++index;
}
slicedPoly1.Insert(index, intersectionPoint);
}
// Insert intersection point into second polygon
alpha = GetAlpha(c, d, intersectionPoint);
if (alpha > 0f && alpha < 1f)
{
int index = slicedPoly2.IndexOf(c) + 1;
while (index < slicedPoly2.Count &&
GetAlpha(c, d, slicedPoly2[index]) <= alpha)
{
++index;
}
slicedPoly2.Insert(index, intersectionPoint);
}
}
}
}
// Check for very small edges
for (int i = 0; i < slicedPoly1.Count; ++i)
{
int iNext = slicedPoly1.NextIndex(i);
//If they are closer than the distance remove vertex
if ((slicedPoly1[iNext] - slicedPoly1[i]).LengthSquared() <= ClipperEpsilonSquared)
{
slicedPoly1.RemoveAt(i);
--i;
}
}
for (int i = 0; i < slicedPoly2.Count; ++i)
{
int iNext = slicedPoly2.NextIndex(i);
//If they are closer than the distance remove vertex
if ((slicedPoly2[iNext] - slicedPoly2[i]).LengthSquared() <= ClipperEpsilonSquared)
{
slicedPoly2.RemoveAt(i);
--i;
}
}
}