//
// Orient triangles so they have the correct orientation
//
public static HashSet <Triangle2> OrientTrianglesClockwise(HashSet <Triangle2> triangles)
{
//Convert to list or we will no be able to update the orientation
List <Triangle2> trianglesList = new List <Triangle2>(triangles);
for (int i = 0; i < trianglesList.Count; i++)
{
Triangle2 t = trianglesList[i];
if (!_Geometry.IsTriangleOrientedClockwise(t.p1, t.p2, t.p3))
{
t.ChangeOrientation();
trianglesList[i] = t;
//Debug.Log("Changed orientation");
}
}
//Back to hashset
triangles = new HashSet <Triangle2>(trianglesList);
return(triangles);
}
//Used for debugging so we can see what's going on
//public static List<MyVector2> GenerateConvexHull(List<MyVector2> originalPoints, bool includeColinearPoints, AABB normalizingbox, float dMax)
public static List <MyVector2> GenerateConvexHull(List <MyVector2> originalPoints, bool includeColinearPoints)
{
List <MyVector2> pointsOnConvexHull = new List <MyVector2>();
//Step 1.
//Find the extreme points along each axis
//This is similar to AABB but we need both x and y coordinates at each extreme point
MyVector2 maxX = originalPoints[0];
MyVector2 minX = originalPoints[0];
MyVector2 maxY = originalPoints[0];
MyVector2 minY = originalPoints[0];
for (int i = 1; i < originalPoints.Count; i++)
{
MyVector2 p = originalPoints[i];
if (p.x > maxX.x)
{
maxX = p;
}
if (p.x < minX.x)
{
minX = p;
}
if (p.y > maxY.y)
{
maxY = p;
}
if (p.y < minY.y)
{
minY = p;
}
}
//Step 2.
//From the 4 extreme points, choose the pair that's furthest appart
//These two are the first two points on the hull
List <MyVector2> extremePoints = new List <MyVector2>()
{
maxX, minX, maxY, minY
};
//Just pick some points as start value
MyVector2 p1 = maxX;
MyVector2 p2 = minX;
//Can use sqr because we are not interested in the exact distance
float maxDistanceSqr = -Mathf.Infinity;
//Loop through all points and compare them
//TODO is comparing too many times: example maxX with maxY, and then maxY with maxX
//https://stackoverflow.com/questions/12249051/unique-combinations-of-list
for (int i = 0; i < extremePoints.Count; i++)
{
MyVector2 p1_test = extremePoints[i];
for (int j = 0; j < extremePoints.Count; j++)
{
//Dont compare the point with itself
if (i == j)
{
continue;
}
MyVector2 p2_test = extremePoints[j];
float distSqr = MyVector2.SqrDistance(p1_test, p2_test);
if (distSqr > maxDistanceSqr)
{
maxDistanceSqr = distSqr;
p1 = p1_test;
p2 = p2_test;
}
}
}
//Convert the list to hashset to easier remove points which are on the hull or are inside of the hull
HashSet <MyVector2> pointsToAdd = new HashSet <MyVector2>(originalPoints);
//Remove the first 2 points on the hull
pointsToAdd.Remove(p1);
pointsToAdd.Remove(p2);
//Step 3.
//Find the third point on the hull, by finding the point which is the furthest
//from the line between p1 and p2
MyVector2 p3 = FindPointFurthestFromEdge(p1, p2, pointsToAdd);
//Remove it from the points we want to add
pointsToAdd.Remove(p3);
//Step 4. Form the intitial triangle
//Make sure the hull is oriented counter-clockwise
Triangle2 tStart = new Triangle2(p1, p2, p3);
if (_Geometry.IsTriangleOrientedClockwise(tStart.p1, tStart.p2, tStart.p3))
{
tStart.ChangeOrientation();
}
//New p1-p3
p1 = tStart.p1;
p2 = tStart.p2;
p3 = tStart.p3;
//pointsOnConvexHull.Add(p1);
//pointsOnConvexHull.Add(p2);
//pointsOnConvexHull.Add(p3);
//Remove the points that we now know are within the hull triangle
RemovePointsWithinTriangle(tStart, pointsToAdd);
//Step 5.
//Associate the rest of the points to their closest edge
HashSet <MyVector2> edge_p1p2_points = new HashSet <MyVector2>();
HashSet <MyVector2> edge_p2p3_points = new HashSet <MyVector2>();
HashSet <MyVector2> edge_p3p1_points = new HashSet <MyVector2>();
foreach (MyVector2 p in pointsToAdd)
{
//p1 p2
LeftOnRight pointRelation1 = _Geometry.IsPoint_Left_On_Right_OfVector(p1, p2, p);
if (pointRelation1 == LeftOnRight.On || pointRelation1 == LeftOnRight.Right)
{
edge_p1p2_points.Add(p);
continue;
}
//p2 p3
LeftOnRight pointRelation2 = _Geometry.IsPoint_Left_On_Right_OfVector(p2, p3, p);
if (pointRelation2 == LeftOnRight.On || pointRelation2 == LeftOnRight.Right)
{
edge_p2p3_points.Add(p);
continue;
}
//p3 p1
//If the point hasnt been added yet, we know it belong to this edge
edge_p3p1_points.Add(p);
}
//Step 6
//For each edge, find the point furthest away and create a new triangle
//and repeat the above steps by finding which points are inside of the hull
//and which points are outside and belong to a new edge
//Will automatically ignore the last point on this sub-hull to avoid doubles
List <MyVector2> pointsOnHUll_p1p2 = CreateSubConvexHUll(p1, p2, edge_p1p2_points);
List <MyVector2> pointsOnHUll_p2p3 = CreateSubConvexHUll(p2, p3, edge_p2p3_points);
List <MyVector2> pointsOnHUll_p3p1 = CreateSubConvexHUll(p3, p1, edge_p3p1_points);
//Create the final hull by combing the points
pointsOnConvexHull.Clear();
pointsOnConvexHull.AddRange(pointsOnHUll_p1p2);
pointsOnConvexHull.AddRange(pointsOnHUll_p2p3);
pointsOnConvexHull.AddRange(pointsOnHUll_p3p1);
//Step 7. Add colinear points
//I think the easiest way to add colinear points is to add them when the algorithm is finished
if (includeColinearPoints)
{
pointsOnConvexHull = AddColinearPoints(pointsOnConvexHull, originalPoints);
}
//Debug.Log("Points on hull: " + pointsOnConvexHull.Count);
return(pointsOnConvexHull);
}
