// A parent is a shape which fully contains another shape
public bool IsParentOf(CompositeShapeData otherShape)
{
if (otherShape.parents.Contains(this))
{
return(true);
}
if (parents.Contains(otherShape))
{
return(false);
}
// check if first point in otherShape is inside this shape. If not, parent test fails.
// if yes, then continue to line seg intersection test between the two shapes
// (this point test is important because without it, if all line seg intersection tests fail,
// we wouldn't know if otherShape is entirely inside or entirely outside of this shape)
bool pointInsideShape = false;
for (int i = 0; i < triangles.Length; i += 3)
{
if (Maths2D.PointInTriangle(polygon.points[triangles[i]], polygon.points[triangles[i + 1]], polygon.points[triangles[i + 2]], otherShape.points[0]))
{
pointInsideShape = true;
break;
}
}
if (!pointInsideShape)
{
return(false);
}
// Check for intersections between line segs of this shape and otherShape (any intersections will fail the parent test)
for (int i = 0; i < points.Length; i++)
{
LineSegment parentSeg = new LineSegment(points[i], points[(i + 1) % points.Length]);
for (int j = 0; j < otherShape.points.Length; j++)
{
LineSegment childSeg = new LineSegment(otherShape.points[j], otherShape.points[(j + 1) % otherShape.points.Length]);
if (Maths2D.LineSegmentsIntersect(parentSeg.a, parentSeg.b, childSeg.a, childSeg.b))
{
return(false);
}
}
}
return(true);
}
// Test if the shapes overlap partially (test will fail if one shape entirely contains other shape, i.e. one is parent of the other).
public bool OverlapsPartially(CompositeShapeData otherShape)
{
// Check for intersections between line segs of this shape and otherShape (any intersection will validate the overlap test)
for (int i = 0; i < points.Length; i++)
{
LineSegment segA = new LineSegment(points[i], points[(i + 1) % points.Length]);
for (int j = 0; j < otherShape.points.Length; j++)
{
LineSegment segB = new LineSegment(otherShape.points[j], otherShape.points[(j + 1) % otherShape.points.Length]);
if (Maths2D.LineSegmentsIntersect(segA.a, segA.b, segB.a, segB.b))
{
return(true);
}
}
}
return(false);
}
// Checks if any of the line segments making up this shape intersect
public bool IntersectsWithSelf()
{
for (int i = 0; i < points.Length; i++)
{
LineSegment segA = new LineSegment(points[i], points[(i + 1) % points.Length]);
for (int j = i + 2; j < points.Length; j++)
{
if ((j + 1) % points.Length == i)
{
continue;
}
LineSegment segB = new LineSegment(points[j], points[(j + 1) % points.Length]);
if (Maths2D.LineSegmentsIntersect(segA.a, segA.b, segB.a, segB.b))
{
return(true);
}
}
}
return(false);
}
// check if triangle contains any verts (note, only necessary to check reflex verts).
bool TriangleContainsVertex(Vertex v0, Vertex v1, Vertex v2)
{
LinkedListNode <Vertex> vertexNode = vertsInClippedPolygon.First;
for (int i = 0; i < vertsInClippedPolygon.Count; i++)
{
if (!vertexNode.Value.isConvex) // convex verts will never be inside triangle
{
Vertex vertexToCheck = vertexNode.Value;
if (vertexToCheck.index != v0.index && vertexToCheck.index != v1.index && vertexToCheck.index != v2.index) // dont check verts that make up triangle
{
if (Maths2D.PointInTriangle(v0.position, v1.position, v2.position, vertexToCheck.position))
{
return(true);
}
}
}
vertexNode = vertexNode.Next;
}
return(false);
}
// Creates a linked list of all vertices in the polygon, with the hole vertices joined to the hull at optimal points.
LinkedList <Vertex> GenerateVertexList(Polygon polygon)
{
LinkedList <Vertex> vertexList = new LinkedList <Vertex>();
LinkedListNode <Vertex> currentNode = null;
// Add all hull points to the linked list
for (int i = 0; i < polygon.numHullPoints; i++)
{
int prevPointIndex = (i - 1 + polygon.numHullPoints) % polygon.numHullPoints;
int nextPointIndex = (i + 1) % polygon.numHullPoints;
bool vertexIsConvex = IsConvex(polygon.points[prevPointIndex], polygon.points[i], polygon.points[nextPointIndex]);
Vertex currentHullVertex = new Vertex(polygon.points[i], i, vertexIsConvex);
if (currentNode == null)
{
currentNode = vertexList.AddFirst(currentHullVertex);
}
else
{
currentNode = vertexList.AddAfter(currentNode, currentHullVertex);
}
}
// Process holes:
List <HoleData> sortedHoleData = new List <HoleData>();
for (int holeIndex = 0; holeIndex < polygon.numHoles; holeIndex++)
{
// Find index of rightmost point in hole. This 'bridge' point is where the hole will be connected to the hull.
Vector2 holeBridgePoint = new Vector2(float.MinValue, 0);
int holeBridgeIndex = 0;
for (int i = 0; i < polygon.numPointsPerHole[holeIndex]; i++)
{
if (polygon.GetHolePoint(i, holeIndex).x > holeBridgePoint.x)
{
holeBridgePoint = polygon.GetHolePoint(i, holeIndex);
holeBridgeIndex = i;
}
}
sortedHoleData.Add(new HoleData(holeIndex, holeBridgeIndex, holeBridgePoint));
}
// Sort hole data so that holes furthest to the right are first
sortedHoleData.Sort((x, y) => (x.bridgePoint.x > y.bridgePoint.x) ? -1 : 1);
foreach (HoleData holeData in sortedHoleData)
{
// Find first edge which intersects with rightwards ray originating at the hole bridge point.
Vector2 rayIntersectPoint = new Vector2(float.MaxValue, holeData.bridgePoint.y);
List <LinkedListNode <Vertex> > hullNodesPotentiallyInBridgeTriangle = new List <LinkedListNode <Vertex> >();
LinkedListNode <Vertex> initialBridgeNodeOnHull = null;
currentNode = vertexList.First;
while (currentNode != null)
{
LinkedListNode <Vertex> nextNode = (currentNode.Next == null) ? vertexList.First : currentNode.Next;
Vector2 p0 = currentNode.Value.position;
Vector2 p1 = nextNode.Value.position;
// at least one point must be to right of holeData.bridgePoint for intersection with ray to be possible
if (p0.x > holeData.bridgePoint.x || p1.x > holeData.bridgePoint.x)
{
// one point is above, one point is below
if (p0.y > holeData.bridgePoint.y != p1.y > holeData.bridgePoint.y)
{
float rayIntersectX = p1.x; // only true if line p0,p1 is vertical
if (!Mathf.Approximately(p0.x, p1.x))
{
float intersectY = holeData.bridgePoint.y;
float gradient = (p0.y - p1.y) / (p0.x - p1.x);
float c = p1.y - gradient * p1.x;
rayIntersectX = (intersectY - c) / gradient;
}
// intersection must be to right of bridge point
if (rayIntersectX > holeData.bridgePoint.x)
{
LinkedListNode <Vertex> potentialNewBridgeNode = (p0.x > p1.x) ? currentNode : nextNode;
// if two intersections occur at same x position this means is duplicate edge
// duplicate edges occur where a hole has been joined to the outer polygon
bool isDuplicateEdge = Mathf.Approximately(rayIntersectX, rayIntersectPoint.x);
// connect to duplicate edge (the one that leads away from the other, already connected hole, and back to the original hull) if the
// current hole's bridge point is higher up than the bridge point of the other hole (so that the new bridge connection doesn't intersect).
bool connectToThisDuplicateEdge = holeData.bridgePoint.y > potentialNewBridgeNode.Previous.Value.position.y;
if (!isDuplicateEdge || connectToThisDuplicateEdge)
{
// if this is the closest ray intersection thus far, set bridge hull node to point in line having greater x pos (since def to right of hole).
if (rayIntersectX < rayIntersectPoint.x || isDuplicateEdge)
{
rayIntersectPoint.x = rayIntersectX;
initialBridgeNodeOnHull = potentialNewBridgeNode;
}
}
}
}
}
// Determine if current node might lie inside the triangle formed by holeBridgePoint, rayIntersection, and bridgeNodeOnHull
// We only need consider those which are reflex, since only these will be candidates for visibility from holeBridgePoint.
// A list of these nodes is kept so that in next step it is not necessary to iterate over all nodes again.
if (currentNode != initialBridgeNodeOnHull)
{
if (!currentNode.Value.isConvex && p0.x > holeData.bridgePoint.x)
{
hullNodesPotentiallyInBridgeTriangle.Add(currentNode);
}
}
currentNode = currentNode.Next;
}
// Check triangle formed by hullBridgePoint, rayIntersection, and bridgeNodeOnHull.
// If this triangle contains any points, those points compete to become new bridgeNodeOnHull
LinkedListNode <Vertex> validBridgeNodeOnHull = initialBridgeNodeOnHull;
foreach (LinkedListNode <Vertex> nodePotentiallyInTriangle in hullNodesPotentiallyInBridgeTriangle)
{
if (nodePotentiallyInTriangle.Value.index == initialBridgeNodeOnHull.Value.index)
{
continue;
}
// if there is a point inside triangle, this invalidates the current bridge node on hull.
if (Maths2D.PointInTriangle(holeData.bridgePoint, rayIntersectPoint, initialBridgeNodeOnHull.Value.position, nodePotentiallyInTriangle.Value.position))
{
// Duplicate points occur at hole and hull bridge points.
bool isDuplicatePoint = validBridgeNodeOnHull.Value.position == nodePotentiallyInTriangle.Value.position;
// if multiple nodes inside triangle, we want to choose the one with smallest angle from holeBridgeNode.
// if is a duplicate point, then use the one occurring later in the list
float currentDstFromHoleBridgeY = Mathf.Abs(holeData.bridgePoint.y - validBridgeNodeOnHull.Value.position.y);
float pointInTriDstFromHoleBridgeY = Mathf.Abs(holeData.bridgePoint.y - nodePotentiallyInTriangle.Value.position.y);
if (pointInTriDstFromHoleBridgeY < currentDstFromHoleBridgeY || isDuplicatePoint)
{
validBridgeNodeOnHull = nodePotentiallyInTriangle;
}
}
}
// Insert hole points (starting at holeBridgeNode) into vertex list at validBridgeNodeOnHull
currentNode = validBridgeNodeOnHull;
for (int i = holeData.bridgeIndex; i <= polygon.numPointsPerHole[holeData.holeIndex] + holeData.bridgeIndex; i++)
{
int previousIndex = currentNode.Value.index;
int currentIndex = polygon.IndexOfPointInHole(i % polygon.numPointsPerHole[holeData.holeIndex], holeData.holeIndex);
int nextIndex = polygon.IndexOfPointInHole((i + 1) % polygon.numPointsPerHole[holeData.holeIndex], holeData.holeIndex);
if (i == polygon.numPointsPerHole[holeData.holeIndex] + holeData.bridgeIndex) // have come back to starting point
{
nextIndex = validBridgeNodeOnHull.Value.index; // next point is back to the point on the hull
}
bool vertexIsConvex = IsConvex(polygon.points[previousIndex], polygon.points[currentIndex], polygon.points[nextIndex]);
Vertex holeVertex = new Vertex(polygon.points[currentIndex], currentIndex, vertexIsConvex);
currentNode = vertexList.AddAfter(currentNode, holeVertex);
}
// Add duplicate hull bridge vert now that we've come all the way around. Also set its concavity
Vector2 nextVertexPos = (currentNode.Next == null) ? vertexList.First.Value.position : currentNode.Next.Value.position;
bool isConvex = IsConvex(holeData.bridgePoint, validBridgeNodeOnHull.Value.position, nextVertexPos);
Vertex repeatStartHullVert = new Vertex(validBridgeNodeOnHull.Value.position, validBridgeNodeOnHull.Value.index, isConvex);
vertexList.AddAfter(currentNode, repeatStartHullVert);
//Set concavity of initial hull bridge vert, since it may have changed now that it leads to hole vert
LinkedListNode <Vertex> nodeBeforeStartBridgeNodeOnHull = (validBridgeNodeOnHull.Previous == null) ? vertexList.Last : validBridgeNodeOnHull.Previous;
LinkedListNode <Vertex> nodeAfterStartBridgeNodeOnHull = (validBridgeNodeOnHull.Next == null) ? vertexList.First : validBridgeNodeOnHull.Next;
validBridgeNodeOnHull.Value.isConvex = IsConvex(nodeBeforeStartBridgeNodeOnHull.Value.position, validBridgeNodeOnHull.Value.position, nodeAfterStartBridgeNodeOnHull.Value.position);
}
return(vertexList);
}
// v1 is considered a convex vertex if v0-v1-v2 are wound in a counter-clockwise order.
bool IsConvex(Vector2 v0, Vector2 v1, Vector2 v2)
{
return(Maths2D.SideOfLine(v0, v2, v1) == -1);
}