//Find reflect vertices (that also have a higher x pos than the hole)
private static List <MyVector2> FindReflectVertices(EarClippingPolygon hull, EarClippingPolygon hole)
{
List <MyVector2> reflectVertices = new List <MyVector2>();
List <MyVector2> verticesHull = hull.Vertices;
for (int i = 0; i < verticesHull.Count; i++)
{
MyVector2 p = verticesHull[i];
//We dont need to check this vertex if it's to the left of the point on the hull
//because that vertex can't be visible
if (p.x < hole.maxX_Vert.x)
{
continue;
}
MyVector2 p_prev = verticesHull[MathUtility.ClampListIndex(i - 1, verticesHull.Count)];
MyVector2 p_next = verticesHull[MathUtility.ClampListIndex(i + 1, verticesHull.Count)];
if (!_EarClipping.IsVertexConvex(p_prev, p, p_next))
{
reflectVertices.Add(p);
}
}
return(reflectVertices);
}
//Merge holes with hull so we get one big list of vertices we can triangulate
//We merge by creating "bridges" between the holes and the hull
public static List <MyVector2> MergeHolesWithHull(List <MyVector2> verticesHull, List <List <MyVector2> > allHoleVertices)
{
//Validate
if (allHoleVertices == null || allHoleVertices.Count == 0)
{
return(null);
}
//Change data structure
EarClippingPolygon hull = new EarClippingPolygon(new Polygon2(verticesHull));
List <EarClippingPolygon> holes = new List <EarClippingPolygon>();
int counter = 1;
foreach (List <MyVector2> hole in allHoleVertices)
{
//Validate data
if (hole == null || hole.Count <= 2)
{
Debug.Log("The hole doesn't have enough vertices");
continue;
}
EarClippingPolygon holePolygon = new EarClippingPolygon(new Polygon2(hole));
holes.Add(holePolygon);
holePolygon.id = counter;
counter++;
}
//Sort the holes by their max x-value coordinate, from highest to lowest
holes = holes.OrderByDescending(o => o.maxX_Vert.x).ToList();
//Merge the holes with the hull so we get a hull with seams that we can triangulate like a hull without holes
foreach (EarClippingPolygon hole in holes)
{
MergeHoleWithHull(hull, hole);
}
return(hull.Vertices);
}
//Merge a single hole with the hull
//Basic idea is to find a vertex in the hole that can also see a vertex in the hull
//Connect these vertices with two edges, and the hole is now a part of the hull with an invisible seam
//between the hole and the hull
private static void MergeHoleWithHull(EarClippingPolygon hull, EarClippingPolygon hole)
{
//Step 1. Find the vertex in the hole which has the maximum x-value
//Has already been done when we created the data structure
//Step 2. Form a line going from this vertex towards (in x-direction) to a position outside of the hull
MyVector2 lineStart = hole.maxX_Vert;
//Just add some value so we know we are outside
MyVector2 lineEnd = new MyVector2(hull.maxX_Vert.x + 0.01f, hole.maxX_Vert.y);
//Important to add lineStart first because we will need it later
Edge2 line_hole_to_outside = new Edge2(lineStart, lineEnd);
//Step 3. Find a vertex on the hull which is visible to the point on the hole with max x pos
//The first and second point on the hull is defined as edge 0, and so on...
int closestEdge = -1;
MyVector2 visibleVertex;
FindVisibleVertexOnHUll(hull, hole, line_hole_to_outside, out closestEdge, out visibleVertex);
//This means we couldn't find a closest edge
if (closestEdge == -1)
{
Debug.Log("Couldn't find a closest edge to hole");
return;
}
//Step 4. Modify the hull vertices so we get an edge from the hull to the hole, around the hole, and back to the hull
//First reconfigure the hole list to start at the vertex with the largest x pos
//[a, b, c, d, e] and c is the one with the largest x pos, we get:
//[a, b, c, d, e, a, b]
//[c, d, e, a, b]
//We also need two extra vertices, one from the hole and one from the hull
//If p is the visible vertex, we get:
//[c, d, e, a, b, c, p]
//Maybe more efficient if we turn the list into a queue?
//Add to back of list
for (int i = 0; i < hole.maxX_ListPos; i++)
{
hole.Vertices.Add(hole.Vertices[i]);
}
//Remove those we added to the back of the list
hole.Vertices.RemoveRange(0, hole.maxX_ListPos);
//Add the two extra vertices we need
hole.Vertices.Add(hole.Vertices[0]);
hole.Vertices.Add(visibleVertex);
//Merge the hole with the hull
List <MyVector2> verticesHull = hull.Vertices;
//Find where we should insert the hole
int visibleVertex_ListPos = hull.GetLastListPos(visibleVertex);
if (visibleVertex_ListPos == -1)
{
Debug.Log("Cant find corresponding pos in list");
return;
}
//Insert the hole after the visible vertex
verticesHull.InsertRange(visibleVertex_ListPos + 1, hole.Vertices);
//Debug.Log($"Number of vertices on the hull after adding a hole: {verticesHull.Count}");
}
//The hull may still intersect with the edge between the point on the hole and the "visible" point on the hull,
//so the point on the hull might not be visible, so we should try to find a better point
private static void FindActualVisibleVertexOnHull(EarClippingPolygon hull, EarClippingPolygon hole, MyVector2 intersectionVertex, ref MyVector2 visibleVertex)
{
//Form a triangle
Triangle2 t = new Triangle2(hole.maxX_Vert, intersectionVertex, visibleVertex);
//According to litterature, we check if a reflect vertex is within this triangle
//If so, one of them is a better visible vertex on the hull
List <MyVector2> reflectVertices = FindReflectVertices(hull, hole);
//Pick the reflect vertex with the smallest angle
//The angle is measure from the point on the hole towards:
//- intersection point on the hull
//- reflect vertex
float minAngle = Mathf.Infinity;
//If more than one reflect vertex have the same angle then pick the one closest to the point on the hole
float minDistSqr = Mathf.Infinity;
foreach (MyVector2 v in reflectVertices)
{
if (_Intersections.PointTriangle(t, v, includeBorder: true))
{
float angle = MathUtility.AngleBetween(intersectionVertex - hole.maxX_Vert, v - hole.maxX_Vert);
//Debug.DrawLine(v.ToVector3(1f), hole.maxX_Vert.ToVector3(1f), Color.blue, 2f);
//Debug.DrawLine(intersectionVertex.ToVector3(1f), hole.maxX_Vert.ToVector3(1f), Color.black, 2f);
//TestAlgorithmsHelpMethods.DebugDrawCircle(v.ToVector3(1f), 0.3f, Color.blue);
//Debug.Log(angle * Mathf.Rad2Deg);
if (angle < minAngle)
{
minAngle = angle;
visibleVertex = v;
//We also need to calculate this in case a future point has the same angle
minDistSqr = MyVector2.SqrDistance(v, hole.maxX_Vert);
//Debug.Log(minDistanceSqr);
//TestAlgorithmsHelpMethods.DebugDrawCircle(v.ToVector3(1f), 0.3f, Color.green);
}
//If the angle is the same, then pick the vertex which is the closest to the point on the hull
else if (Mathf.Abs(angle - minAngle) < MathUtility.EPSILON)
{
float distSqr = MyVector2.SqrDistance(v, hole.maxX_Vert);
//Debug.Log(minDistanceSqr);
if (distSqr < minDistSqr)
{
visibleVertex = v;
minDistSqr = distSqr;
//TestAlgorithmsHelpMethods.DebugDrawCircle(v.ToVector3(1f), 0.3f, Color.red);
//Debug.Log(distSqr);
}
}
}
}
//Will show how the holes are connected with the hull
//Debug.DrawLine(visibleVertex.ToVector3(1f), hole.maxX_Vert.ToVector3(1f), Color.red, 5f);
//TestAlgorithmsHelpMethods.DebugDrawCircle(visibleVertex.ToVector3(1f), 0.3f, Color.red);
//TestAlgorithmsHelpMethods.DebugDrawCircle(hole.maxX_Vert.ToVector3(1f), 0.3f, Color.red);
}
//Find a vertex on the hull that should be visible from the hole
private static void FindVisibleVertexOnHUll(EarClippingPolygon hull, EarClippingPolygon hole, Edge2 line_hole_to_outside, out int closestEdge, out MyVector2 visibleVertex)
{
//The first and second point on the hull is defined as edge 0, and so on...
closestEdge = -1;
//The vertex that should be visible to the hole (which is the max of the line that's intersecting with the line)
visibleVertex = new MyVector2(-1f, -1f);
//Do line-line intersection to find intersectionVertex which is the point of intersection that's the closest to the hole
MyVector2 intersectionVertex = new MyVector2(-1f, -1f);
float minDistanceSqr = Mathf.Infinity;
List <MyVector2> verticesHull = hull.Vertices;
for (int i = 0; i < verticesHull.Count; i++)
{
MyVector2 p1_hull = verticesHull[i];
MyVector2 p2_hull = verticesHull[MathUtility.ClampListIndex(i + 1, verticesHull.Count)];
//We dont need to check this line if it's to the left of the point on the hole
//If so they cant intersect
if (p1_hull.x < hole.maxX_Vert.x && p2_hull.x < hole.maxX_Vert.x)
{
continue;
}
Edge2 line_hull = new Edge2(p1_hull, p2_hull);
bool isIntersecting = _Intersections.LineLine(line_hole_to_outside, line_hull, includeEndPoints: true);
//Here we can maybe add a check if any of the vertices is on the line???
if (isIntersecting)
{
MyVector2 testIntersectionVertex = _Intersections.GetLineLineIntersectionPoint(line_hole_to_outside, line_hull);
//if (hole.id == 3) TestAlgorithmsHelpMethods.DebugDrawCircle(testIntersectionVertex.ToVector3(), 0.2f, Color.green);
float distanceSqr = MyVector2.SqrDistance(line_hole_to_outside.p1, testIntersectionVertex);
if (distanceSqr < minDistanceSqr)
{
closestEdge = i;
minDistanceSqr = distanceSqr;
intersectionVertex = testIntersectionVertex;
}
}
}
//This means we couldn't find a closest edge
if (closestEdge == -1)
{
Debug.Log("Couldn't find a closest edge to hole");
return;
}
//But we can't connect the hole with this intersection point, so we need to find a vertex which is visible from the hole
//The closest edge has two vertices. Pick the one with the highest x-value, which is the vertex
//that should be visible from the hole
MyVector2 p1 = hull.Vertices[closestEdge];
MyVector2 p2 = hull.Vertices[MathUtility.ClampListIndex(closestEdge + 1, hull.Vertices.Count)];
visibleVertex = p1;
//They are the same so pick the one that is the closest
if (Mathf.Abs(p1.x - p2.x) < MathUtility.EPSILON)
{
float hole_p1 = MyVector2.SqrDistance(hole.maxX_Vert, p1);
float hole_p2 = MyVector2.SqrDistance(hole.maxX_Vert, p2);
visibleVertex = hole_p1 < hole_p2 ? p1 : p2;
}
else if (p2.x > visibleVertex.x)
{
visibleVertex = p2;
}
if (hole.id == 3)
{
//TestAlgorithmsHelpMethods.DebugDrawCircle(intersectionVertex.ToVector3(), 0.4f, Color.black);
//TestAlgorithmsHelpMethods.DebugDrawCircle(visibleVertex.ToVector3(), 0.4f, Color.green);
}
//But the hull may still intersect with this edge between the point on the hole and the visible point on the hull,
//so the visible point on the hull might not be visible after all
//So we might have to find a new point which is visible
FindActualVisibleVertexOnHull(hull, hole, intersectionVertex, ref visibleVertex);
}