/// <summary>
/// Check and return polygon intersections
/// </summary>
/// <param name="polygon1"></param>
/// <param name="polygon2"></param>
/// <param name="intersections"></param>
/// <returns></returns>
private static bool VerticesIntersect(Vertices polygon1, Vertices polygon2,
out List <EdgeIntersectInfo> intersections)
{
intersections = new List <EdgeIntersectInfo>();
// Iterate through polygon1's edges
for (int i = 0; i < polygon1.Count; i++)
{
// Get edge vertices
Vector2 p1 = polygon1[i];
Vector2 p2 = polygon1[polygon1.NextIndex(i)];
// Get intersections between this edge and polygon2
for (int j = 0; j < polygon2.Count; j++)
{
Vector2 point;
Vector2 p3 = polygon2[j];
Vector2 p4 = polygon2[polygon2.NextIndex(j)];
// Check if the edges intersect
if (LineTools.LineIntersect(p1, p2, p3, p4, true, true, out point))
{
// Here, we round the returned intersection point to its nearest whole number.
// This prevents floating point anomolies where 99.9999-> is returned instead of 100.
point = new Vector2((float)Math.Round(point.X, 0), (float)Math.Round(point.Y, 0));
// Record the intersection
intersections.Add(new EdgeIntersectInfo(new Edge(p1, p2), new Edge(p3, p4), point));
}
}
}
// true if any intersections were found.
return(intersections.Count > 0);
}
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
}
Vector2 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 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
}
//if(QLineF(at(i), at(j)).intersect(QLineF(at(k), at(k + 1)), NULL) == QLineF::BoundedIntersection) {
if (LineTools.LineIntersect(At(i, vertices), At(j, vertices), At(k, vertices), At(k + 1, vertices)) !=
Vector2.Zero)
{
return(false);
}
}
return(true);
}
/// <summary>
/// Decompose the polygon into several smaller non-concave polygon.
/// If the polygon is already convex, it will return the original polygon, unless it is over Settings.MaxPolygonVertices.
/// Precondition: Counter Clockwise polygon
/// </summary>
/// <param name="vertices"></param>
/// <returns></returns>
public static List <Vertices> ConvexPartition(Vertices vertices)
{
//We force it to CCW as it is a precondition in this algorithm.
vertices.ForceCounterClockWise();
List <Vertices> list = new List <Vertices>();
float d, lowerDist, upperDist;
Vector2 p;
Vector2 lowerInt = new Vector2();
Vector2 upperInt = new Vector2(); // intersection points
int lowerIndex = 0, upperIndex = 0;
Vertices lowerPoly, upperPoly;
for (int i = 0; i < vertices.Count; ++i)
{
if (Reflex(i, vertices))
{
lowerDist = upperDist = float.MaxValue; // std::numeric_limits<qreal>::max();
for (int j = 0; j < vertices.Count; ++j)
{
// if line intersects with an edge
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)
{
Vector2 sp = ((lowerInt + upperInt) / 2);
lowerPoly = Copy(i, upperIndex, vertices);
lowerPoly.Add(sp);
upperPoly = Copy(lowerIndex, i, vertices);
upperPoly.Add(sp);
}
else
{
double highestScore = 0, bestIndex = lowerIndex;
while (upperIndex < lowerIndex)
{
upperIndex += vertices.Count;
}
for (int j = lowerIndex; j <= upperIndex; ++j)
{
if (CanSee(i, j, vertices))
{
double 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(ConvexPartition(lowerPoly));
list.AddRange(ConvexPartition(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(ConvexPartition(lowerPoly));
list.AddRange(ConvexPartition(upperPoly));
}
else
{
list.Add(vertices);
}
//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] = SimplifyTools.CollinearSimplify(list[i], 0);
}
//Remove empty vertice collections
for (int i = list.Count - 1; i >= 0; i--)
{
if (list[i].Count == 0)
{
list.RemoveAt(i);
}
}
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
Vector2 a = polygon1[i];
Vector2 b = polygon1[polygon1.NextIndex(i)];
// Get intersections between this edge and polygon2
for (int j = 0; j < polygon2.Count; j++)
{
Vector2 c = polygon2[j];
Vector2 d = polygon2[polygon2.NextIndex(j)];
Vector2 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
float 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]).sqrMagnitude <= 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]).sqrMagnitude <= ClipperEpsilonSquared)
{
slicedPoly2.RemoveAt(i);
--i;
}
}
}
private static List <Vertices> TriangulatePolygon(Vertices vertices)
{
List <Vertices> list = new List <Vertices>();
Vector2 lowerInt = new Vector2();
Vector2 upperInt = new Vector2(); // intersection points
int lowerIndex = 0, upperIndex = 0;
Vertices lowerPoly, upperPoly;
for (int i = 0; i < vertices.Count; ++i)
{
if (Reflex(i, vertices))
{
float upperDist;
float lowerDist = upperDist = float.MaxValue;
for (int j = 0; j < vertices.Count; ++j)
{
// if line intersects with an edge
float d;
Vector2 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)
{
Vector2 p = ((lowerInt + upperInt) / 2);
lowerPoly = Copy(i, upperIndex, vertices);
lowerPoly.Add(p);
upperPoly = Copy(lowerIndex, i, vertices);
upperPoly.Add(p);
}
else
{
double highestScore = 0, bestIndex = lowerIndex;
while (upperIndex < lowerIndex)
{
upperIndex += vertices.Count;
}
for (int j = lowerIndex; j <= upperIndex; ++j)
{
if (CanSee(i, j, vertices))
{
double 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>
/// Precondition: Counter Clockwise polygon
/// Decompose the polygon into several smaller non-concave polygon.
/// If the polygon is already convex, it will return the original polygon, unless it is over Settings.MaxPolygonVertices.
/// </summary>
/// <param name="vertices"></param>
/// <returns></returns>
public static List <Vertices> ConvexPartition(Vertices vertices)
{
List <Vertices> list = new List <Vertices>();
float d, dist1, dist2;
Vector2 ip;
Vector2 ip1 = new Vector2();
Vector2 ip2 = new Vector2(); // intersection points
int ind1 = 0, ind2 = 0;
Vertices poly1, poly2;
for (int i = 0; i < vertices.Count; ++i)
{
if (Reflex(i, vertices))
{
dist1 = dist2 = float.MaxValue; // std::numeric_limits<qreal>::max();
for (int j = 0; j < vertices.Count; ++j)
{
if (Left(At(i - 1, vertices), At(i, vertices), At(j, vertices)) &&
RightOn(At(i - 1, vertices), At(i, vertices), At(j - 1, vertices)))
{
// if ray (i-1)->(i) intersects with edge (j, j-1)
//QLineF(at(i - 1), at(i)).intersect(QLineF(at(j), at(j - 1)), ip);
ip = 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), ip))
{
// intersection point isn't caused by backwards ray
d = SquareDist(At(i, vertices), ip);
if (d < dist1)
{
// take the closest intersection so we know it isn't blocked by another edge
dist1 = d;
ind1 = j;
ip1 = ip;
}
}
}
if (Left(At(i + 1, vertices), At(i, vertices), At(j + 1, vertices)) &&
RightOn(At(i + 1, vertices), At(i, vertices), At(j, vertices)))
{
// if ray (i+1)->(i) intersects with edge (j+1, j)
//QLineF(at(i + 1), at(i)).intersect(QLineF(at(j), at(j + 1)), ip);
ip = 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), ip))
{
d = SquareDist(At(i, vertices), ip);
if (d < dist2)
{
dist2 = d;
ind2 = j;
ip2 = ip;
}
}
}
}
if (ind1 == (ind2 + 1) % vertices.Count)
{
// no vertices in range
Vector2 sp = ((ip1 + ip2) / 2);
poly1 = Copy(i, ind2, vertices);
poly1.Add(sp);
poly2 = Copy(ind1, i, vertices);
poly2.Add(sp);
}
else
{
double highestScore = 0, bestIndex = ind1;
while (ind2 < ind1)
{
ind2 += vertices.Count;
}
for (int j = ind1; j <= ind2; ++j)
{
if (CanSee(i, j, vertices))
{
double 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;
}
}
}
poly1 = Copy(i, (int)bestIndex, vertices);
poly2 = Copy((int)bestIndex, i, vertices);
}
list.AddRange(ConvexPartition(poly1));
list.AddRange(ConvexPartition(poly2));
return(list);
}
}
// polygon is already convex
if (vertices.Count > Settings.MaxPolygonVertices)
{
poly1 = Copy(0, vertices.Count / 2, vertices);
poly2 = Copy(vertices.Count / 2, 0, vertices);
list.AddRange(ConvexPartition(poly1));
list.AddRange(ConvexPartition(poly2));
}
else
{
list.Add(vertices);
}
//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] = SimplifyTools.CollinearSimplify(list[i], 0);
}
return(list);
}
