internal static List<PolygonalFace> Triangulate(MonotonePolygon monotonePolygon)
{
var triangles = new List<PolygonalFace>();
var scan = new List<Node>();
var leftChain = monotonePolygon.LeftChain;
var rightChain = monotonePolygon.RightChain;
var sortedNodes = monotonePolygon.SortedNodes;
var k = 0;
var j = 0;
//Add first two nodes to scan and adjust the counter
scan.Add(sortedNodes[0]);
scan.Add(sortedNodes[1]);
if (leftChain[j + 1] == sortedNodes[1])
{
j++;
}
else
{
k++;
}
//Begin to find triangles
for (var i = 2; i < sortedNodes.Count; i++)
{
var node = sortedNodes[i];
var boolstatus = false;
var isLeftChain = false;
if (rightChain[k + 1] == node && leftChain[j + 1] == node) //If both chains have reached the root node.
{
triangles.Add(new PolygonalFace(new[] { node.Point.References[0], scan[0].Point.References[0], scan[1].Point.References[0] }));
break;
}
else if (leftChain[j + 1] == node)
{
if (leftChain[j] == scan.Last() && leftChain[j-1] == scan[scan.Count-2]) //If all the nodes are on the left chain
{
boolstatus = false;
}
else
{
boolstatus = true;
}
j++;
isLeftChain = true;
}
else //rightChain[k+1] == node
{
if (rightChain[k] == scan.Last() && leftChain[k-1] == scan[scan.Count-1])
{
boolstatus = false;
}
else
{
boolstatus = true;
}
k++;
isLeftChain = false;
}
//If either condition above was true, do the following
if (boolstatus == true)
{
while (scan.Count > 1)
{
triangles.Add(new PolygonalFace(new[] { node.Point.References[0], scan[0].Point.References[0], scan[1].Point.References[0] }));
//Remove first item in scan list.
scan.RemoveAt(0);
}
//add node to end of scan list
scan.Add(node);
}
else
{
while (GetAngle(scan[scan.Count - 2], scan.Last(), node, isLeftChain) < Math.PI && scan.Count() > 1) //NOTE: Assume positive loop only (since the negative loops have been merged)
{
triangles.Add(new PolygonalFace(new[] { scan[scan.Count - 2].Point.References[0], scan.Last().Point.References[0], node.Point.References[0] }));
//Remove last node from scan list
scan.Remove(scan.Last());
}
//Regardless of whether the while loop is activated, add node to scan list
scan.Add(node);
}
}
return triangles;
}
/// <summary>
/// Triangulates a Polygon into faces.
/// </summary>
/// <param name="points2D">The 2D points represented in loops.</param>
/// <param name="isPositive">Indicates whether the corresponding loop is positive or not.</param>
/// <returns>List<Point[]>, which represents vertices of new faces.</returns>
/// <exception cref="System.NotImplementedException"></exception>
public static List<PolygonalFace> Run(List<Point[]> points2D, Boolean[] isPositive)
{
//Return variable triangles
var triangles = new List<PolygonalFace>();
#region Preprocessing
//Preprocessing
// 1) For each loop in points2D
// 2) Create nodes and lines from points, and retain whether a point
// was in a positive or negative loop.
// 3) Add nodes to an ordered loop (same as points2D except now Nodes)
// and a sorted loop (used for sweeping).
var i = 0;
var orderedLoops = new List<List<Node>>();
var sortedLoops = new List<List<Node>>();
var listPositive = isPositive.ToList<bool>();
foreach (var loop in points2D)
{
var orderedLoop = new List<Node>();
//Create first node
var nodeType = GetNodeType(loop.Last(), loop[0], loop[1], isPositive[i]);
var firstNode = new Node(loop[0], nodeType, i);
var previousNode = firstNode;
orderedLoop.Add(firstNode);
//Create other nodes
for (var j = 1; j < loop.Count() - 1; j++)
{
//Create New Node
nodeType = GetNodeType(loop[j - 1], loop[j], loop[j + 1], isPositive[i]);
var node = new Node(loop[j], nodeType, i);
//Add node to the ordered loop
orderedLoop.Add(node);
//Create New Line
var line = new Line(previousNode, node);
previousNode.StartLine = line;
node.EndLine = line;
previousNode = node;
}
//Create last node
nodeType = GetNodeType(loop[loop.Count() - 2], loop[loop.Count() - 1], loop[0], isPositive[i]);
var lastNode = new Node(loop[loop.Count() - 1], nodeType, i);
orderedLoop.Add(lastNode);
//Create both missing lines
var line1 = new Line(previousNode, lastNode);
previousNode.StartLine = line1;
lastNode.EndLine = line1;
var line2 = new Line(lastNode, firstNode);
lastNode.StartLine = line2;
firstNode.EndLine = line2;
//Sort nodes by descending Y, ascending X
var sortedLoop = orderedLoop.OrderByDescending(node => node.Y).ThenBy(node => node.X).ToList<Node>();
orderedLoops.Add(orderedLoop);
sortedLoops.Add(sortedLoop);
i++;
}
#endregion
// 1) For each positive loop
// 2) Remove it from orderedLoops.
// 3) Create a new group
// 4) Insert the first node from all the negative loops remaining into the group list in the correct sorted order.
// 5) Use the red-black tree to determine if the first node from a negative loop is inside the polygon.
// Refer to http://alienryderflex.com/polygon/ for how to determine if a point is inside a polygon.
// 6) If not inside, remove that nodes from the group list.
// 7) else remove the negative loop from orderedLoops and merge the negative loop with the group list.
// 8) Continue with Trapezoidation
List<List<Node>> completeListSortedLoops = new List<List<Node>>(sortedLoops);
while (orderedLoops.Any())
{
//Get information about positive loop, remove from loops, and create new group
i = listPositive.FindIndex(true);
var posOrderedLoop = new List<Node>(orderedLoops[i]);
var sortedGroup = new List<Node>(sortedLoops[i]);
listPositive.RemoveAt(i);
orderedLoops.RemoveAt(i);
sortedLoops.RemoveAt(i);
//Insert the first node from all the negative loops remaining into the group list in the correct sorted order.
for (var j = 0; j < orderedLoops.Count(); j++)
{
if (listPositive[j] == false)
{
InsertNodeInSortedList(sortedGroup, sortedLoops[j][0]);
}
}
//inititallize lineList and sortedNodes
var lineList = new List<Line>();
var nodes = new List<Node>();
#region Trapezoidize Polygons
var trapTree = new List<PartialTrapezoid>();
var completedTrapezoids = new List<Trapezoid>();
//Use the red-black tree to determine if the first node from a negative loop is inside the polygon.
//for each node in sortedNodes, update the lineList. Note that at this point each node only has two edges.
foreach (var node in sortedGroup)
{
Line leftLine = null;
Line rightLine = null;
//Check if negative loop is inside polygon
//note that listPositive changes order /size , while isPositive is static like loopID.
//Similarly points2D is static.
if (node == completeListSortedLoops[node.LoopID][0] && isPositive[node.LoopID] == false) //if first point in the sorted loop and loop is negative
{
if (LinesToLeft(node, lineList, out leftLine) % 2 != 0) //If remainder is not equal to 0, then it is odd.
{
if (LinesToRight(node, lineList, out rightLine) % 2 == 0) //If remainder is not equal to 0, then it is odd.
{
//NOTE: This node must be a reflex upward point by observation
//leftLine and rightLine are set in the two previous call and are now not null.
//Add remaining points from loop into sortedGroup.
MergeSortedListsOfNodes(sortedGroup, completeListSortedLoops[node.LoopID], node);
}
else //Number of lines is even. Remove from group and go to next node
{
sortedGroup.Remove(node);
continue;
}
}
else //Number of lines is even. Remove from group and go to next node
{
sortedGroup.Remove(node);
continue;
}
}
//Add to or remove from Red-Black Tree
if (lineList.Contains(node.StartLine))
{
lineList.Remove(node.StartLine);
}
else
{
lineList.Add(node.StartLine);
}
if (lineList.Contains(node.EndLine))
{
lineList.Remove(node.EndLine);
}
else
{
lineList.Add(node.EndLine);
}
switch (node.Type)
{
case NodeType.DownwardReflex:
{
FindLeftLine(node, lineList, out leftLine);
FindRightLine(node, lineList, out rightLine);
//Close two trapezoids
//Left trapezoid:
InsertTrapezoid(node, leftLine, node.StartLine, ref trapTree, ref completedTrapezoids);
//Right trapezoid:
InsertTrapezoid(node, node.EndLine, rightLine, ref trapTree, ref completedTrapezoids);
//Create one new partial trapezoid
var newPartialTrapezoid = new PartialTrapezoid(node, leftLine, rightLine);
trapTree.Add(newPartialTrapezoid);
}
break;
case NodeType.UpwardReflex:
{
if (leftLine == null) //If from the first negative point, leftLine and rightLine will already be set.
{
FindLeftLine(node, lineList, out leftLine);
FindRightLine(node, lineList, out rightLine);
}
//Close one trapezoid
InsertTrapezoid(node, leftLine, rightLine, ref trapTree, ref completedTrapezoids);
//Create two new partial trapezoids
//Left Trapezoid
var newPartialTrapezoid1 = new PartialTrapezoid(node, leftLine, node.EndLine);
trapTree.Add(newPartialTrapezoid1);
//Right Trapezoid
var newPartialTrapezoid2 = new PartialTrapezoid(node, node.StartLine, rightLine);
trapTree.Add(newPartialTrapezoid2);
}
break;
case NodeType.Peak:
{
//Create one new partial trapezoid
var newPartialTrapezoid = new PartialTrapezoid(node, node.StartLine, node.EndLine);
trapTree.Add(newPartialTrapezoid);
}
break;
case NodeType.Root:
{
//Close one trapezoid
InsertTrapezoid(node, node.EndLine, node.StartLine, ref trapTree, ref completedTrapezoids);
}
break;
case NodeType.Left:
{
//Create one trapezoid
FindLeftLine(node, lineList, out leftLine);
rightLine = node.StartLine;
InsertTrapezoid(node, leftLine, rightLine, ref trapTree, ref completedTrapezoids);
//Create one new partial trapezoid
var newPartialTrapezoid = new PartialTrapezoid(node, leftLine, node.EndLine);
trapTree.Add(newPartialTrapezoid);
}
break;
case NodeType.Right:
{
//Create one trapezoid
FindRightLine(node, lineList, out rightLine);
leftLine = node.EndLine;
InsertTrapezoid(node, leftLine, rightLine, ref trapTree, ref completedTrapezoids);
//Create one new partial trapezoid
var newPartialTrapezoid = new PartialTrapezoid(node, node.StartLine, rightLine);
trapTree.Add(newPartialTrapezoid);
}
break;
}
}
#endregion
#region Create Monotone Polygons
//for each trapezoid with a reflex edge, split in two.
//Insert new trapezoids in correct position in list.
for (var j = 0; j < completedTrapezoids.Count; j++)
{
var trapezoid = completedTrapezoids[j];
if (trapezoid.TopNode.Type == NodeType.DownwardReflex) //If upper node is reflex down (bottom node could be reflex up, reflex down, or other)
{
var newLine = new Line(trapezoid.TopNode, trapezoid.BottomNode);
completedTrapezoids.RemoveAt(j);
var leftTrapezoid = new Trapezoid(trapezoid.TopNode, trapezoid.BottomNode, trapezoid.LeftLine, newLine);
var rightTrapezoid = new Trapezoid(trapezoid.TopNode, trapezoid.BottomNode, newLine, trapezoid.RightLine);
completedTrapezoids.Insert(j, rightTrapezoid); //right trapezoid will end up right below left trapezoid
completedTrapezoids.Insert(j, leftTrapezoid); //left trapezoid will end up were the original trapezoid was located
j++; //Extra counter to skip extra trapezoid
}
else if (trapezoid.BottomNode.Type == NodeType.UpwardReflex) //If bottom node is reflex up (if TopNode.Type = 0, this if statement will be skipped).
{
var newLine = new Line(trapezoid.TopNode, trapezoid.BottomNode);
completedTrapezoids.RemoveAt(j);
var leftTrapezoid = new Trapezoid(trapezoid.TopNode, trapezoid.BottomNode, trapezoid.LeftLine, newLine);
var rightTrapezoid = new Trapezoid(trapezoid.TopNode, trapezoid.BottomNode, newLine, trapezoid.RightLine);
completedTrapezoids.Insert(j, rightTrapezoid); //right trapezoid will end up right below left trapezoid
completedTrapezoids.Insert(j, leftTrapezoid); //left trapezoid will end up were the original trapezoid was located
j++; //Extra counter to skip extra trapezoid
}
}
//Create Monotone Polygons from Trapezoids
var currentTrap = completedTrapezoids[0];
var monotoneTrapPolygon = new List<Trapezoid> { currentTrap };
var monotoneTrapPolygons = new List<List<Trapezoid>> { monotoneTrapPolygon };
//for each trapezoid except the first one, which was added in the intitialization above.
for (var j = 1; j < completedTrapezoids.Count; j++)
{
//Check if next trapezoid can attach to any existing monotone polygon
var boolstatus = false;
for (var k = 0; k < monotoneTrapPolygons.Count; k++)
{
currentTrap = monotoneTrapPolygons[k].Last();
if (currentTrap.BottomNode == completedTrapezoids[j].TopNode)
{
if (currentTrap.LeftLine == completedTrapezoids[j].LeftLine ||
currentTrap.RightLine == completedTrapezoids[j].RightLine)
{
monotoneTrapPolygons[k].Add(completedTrapezoids[j]);
boolstatus = true;
break;
}
}
}
// If they cannot be attached to any existing monotone polygon, create a new monotone polygon
if (boolstatus == false)
{
var trapezoidList = new List<Trapezoid> { completedTrapezoids[j] };
monotoneTrapPolygons.Add(trapezoidList);
}
}
//Convert the lists of trapezoids that form monotone polygons into the monotone polygon class\
//This class includes a sorted list of all the points in the monotone polygon and two monotone chains.
//Both of these lists are used during traingulation.
var monotonePolygons = new List<MonotonePolygon>();
foreach (var monotoneTrapPoly in monotoneTrapPolygons)
{
//Biuld the right left chains and the sorted list of all nodes
var monotoneRightChain = new List<Node>();
var monotoneLeftChain = new List<Node>();
var sortedMonotonePolyNodes = new List<Node>();
//Add upper node to both chains and sorted list
monotoneRightChain.Add(monotoneTrapPoly[0].TopNode);
monotoneLeftChain.Add(monotoneTrapPoly[0].TopNode);
sortedMonotonePolyNodes.Add(monotoneTrapPoly[0].TopNode);
//Add all the middle nodes to one chain (right or left)
for (var j = 1; j < monotoneTrapPoly.Count; j++)
{
//Add the topNode of each trapezoid (minus the initial trapezoid) to the sorted list.
sortedMonotonePolyNodes.Add(monotoneTrapPoly[j].TopNode);
//If trapezoid upper node is on the right line, add it to the right chain
if (monotoneTrapPoly[j].RightLine.FromNode == monotoneTrapPoly[j].TopNode ||
monotoneTrapPoly[j].RightLine.ToNode == monotoneTrapPoly[j].TopNode)
{
monotoneRightChain.Add(monotoneTrapPoly[j].TopNode);
}
//Else add it to the left chain
else
{
monotoneLeftChain.Add(monotoneTrapPoly[j].TopNode);
}
}
//Add bottom node of last trapezoid to both chains and sorted list
monotoneRightChain.Add(monotoneTrapPoly.Last().BottomNode);
monotoneLeftChain.Add(monotoneTrapPoly.Last().BottomNode);
sortedMonotonePolyNodes.Add(monotoneTrapPoly.Last().BottomNode);
//Create new monotone polygon based on these two chains and sorted list.
var monotonePolygon = new MonotonePolygon(monotoneLeftChain, monotoneRightChain, sortedMonotonePolyNodes);
monotonePolygons.Add(monotonePolygon);
}
#endregion
#region Triangulate Monotone Polygons
//Triangulates the monotone polygons
foreach (var monotonePolygon2 in monotonePolygons)
triangles.AddRange(Triangulate(monotonePolygon2));
#endregion
}
return triangles;
}
