//List<VoronoiCell2>
public static List <VoronoiCell2> UnNormalize(List <VoronoiCell2> data, AABB2 aabb, float dMax)
{
List <VoronoiCell2> unNormalizedData = new List <VoronoiCell2>();
foreach (VoronoiCell2 cell in data)
{
MyVector2 sitePosUnNormalized = HelpMethods.UnNormalize(cell.sitePos, aabb, dMax);
VoronoiCell2 cellUnNormalized = new VoronoiCell2(sitePosUnNormalized);
foreach (VoronoiEdge2 e in cell.edges)
{
MyVector2 p1UnNormalized = HelpMethods.UnNormalize(e.p1, aabb, dMax);
MyVector2 p2UnNormalized = HelpMethods.UnNormalize(e.p2, aabb, dMax);
VoronoiEdge2 eUnNormalized = new VoronoiEdge2(p1UnNormalized, p2UnNormalized, sitePosUnNormalized);
cellUnNormalized.edges.Add(eUnNormalized);
}
unNormalizedData.Add(cellUnNormalized);
}
return(unNormalizedData);
}
//
// Algorithms that test if we can form a convex hull
//
private static bool CanFormConvexHull(List <MyVector2> points)
{
//First test of we can form a convex hull
//If fewer points, then we cant create a convex hull
if (points.Count < 3)
{
Debug.Log("Too few points co calculate a convex hull");
return(false);
}
//Find the bounding box of the points
//If the spread is close to 0, then they are all at the same position, and we cant create a hull
AABB box = HelpMethods.GetAABB(points);
if (Mathf.Abs(box.maxX - box.minX) < MathUtility.EPSILON || Mathf.Abs(box.maxY - box.minY) < MathUtility.EPSILON)
{
Debug.Log("The points cant form a convex hull");
return(false);
}
return(true);
}
//For debugging
private static void DisplayPoints(HashSet <MyVector2> points, AABB2 normalizingbox, float dMax)
{
foreach (MyVector2 p in points)
{
MyVector2 pUnNormalize = HelpMethods.UnNormalize(p, normalizingbox, dMax);
Debug.DrawLine(pUnNormalize.ToVector3(), Vector3.zero, Color.blue, 3f);
}
}
//HalfEdgeData2
public static HalfEdgeData2 UnNormalize(HalfEdgeData2 data, AABB2 aabb, float dMax)
{
foreach (HalfEdgeVertex2 v in data.vertices)
{
MyVector2 vUnNormalized = HelpMethods.UnNormalize(v.position, aabb, dMax);
v.position = vUnNormalized;
}
return(data);
}
//HashSet<Triangle2>
public static HashSet <Triangle2> UnNormalize(HashSet <Triangle2> normalized, AABB2 aabb, float dMax)
{
HashSet <Triangle2> unNormalized = new HashSet <Triangle2>();
foreach (Triangle2 t in normalized)
{
MyVector2 p1 = HelpMethods.UnNormalize(t.p1, aabb, dMax);
MyVector2 p2 = HelpMethods.UnNormalize(t.p2, aabb, dMax);
MyVector2 p3 = HelpMethods.UnNormalize(t.p3, aabb, dMax);
Triangle2 tUnNormalized = new Triangle2(p1, p2, p3);
unNormalized.Add(tUnNormalized);
}
return(unNormalized);
}
//Calculate the angle between the vectors if we are going from p1-p2-p3
//Return +180 if "small" or -180 if "large"
//public static float CalculateAngleBetweenVectors(MyVector2 p1, MyVector2 p2, MyVector2 p3)
//{
// MyVector2 from = p1 - p2;
// MyVector2 to = p3 - p2;
// float angle = Vector2.SignedAngle(from, to);
// return angle;
//}
//Create a supertriangle that contains all other points
//According to the book "Geometric tools for computer graphics" a reasonably sized triangle
//is one that contains a circle that contains the axis-aligned bounding rectangle of the points
//Is currently not used anywhere because our points are normalized to the range 0-1
//and then we can make a supertriangle by just setting its size to 100
public static Triangle2 GenerateSupertriangle(HashSet <MyVector2> points)
{
//Step 1. Create a AABB around the points
AABB aabb = HelpMethods.GetAABB(new List <MyVector2>(points));
MyVector2 TL = new MyVector2(aabb.minX, aabb.maxY);
MyVector2 TR = new MyVector2(aabb.maxX, aabb.maxY);
MyVector2 BR = new MyVector2(aabb.maxX, aabb.minY);
//Step2. Find the inscribed circle - the smallest circle that surrounds the AABB
MyVector2 circleCenter = (TL + BR) * 0.5f;
float circleRadius = MyVector2.Magnitude(circleCenter - TR);
//Step 3. Create the smallest triangle that surrounds the circle
//All edges of this triangle have the same length
float halfSideLenghth = circleRadius / Mathf.Tan(30f * Mathf.Deg2Rad);
//The center position of the bottom-edge
MyVector2 t_B = new MyVector2(circleCenter.x, circleCenter.y - circleRadius);
MyVector2 t_BL = new MyVector2(t_B.x - halfSideLenghth, t_B.y);
MyVector2 t_BR = new MyVector2(t_B.x + halfSideLenghth, t_B.y);
//The height from the bottom edge to the top vertex
float triangleHeight = halfSideLenghth * Mathf.Tan(60f * Mathf.Deg2Rad);
MyVector2 t_T = new MyVector2(circleCenter.x, t_B.y + triangleHeight);
//The final triangle
Triangle2 superTriangle = new Triangle2(t_BR, t_BL, t_T);
return(superTriangle);
}
//
// Triangle to half-edge
//
public static HalfEdgeData2 Triangle2ToHalfEdge2(HashSet <Triangle2> triangles, HalfEdgeData2 data)
{
//Make sure the triangles have the same orientation, which is clockwise
triangles = HelpMethods.OrientTrianglesClockwise(triangles);
//Fill the data structure
foreach (Triangle2 t in triangles)
{
HalfEdgeVertex2 v1 = new HalfEdgeVertex2(t.p1);
HalfEdgeVertex2 v2 = new HalfEdgeVertex2(t.p2);
HalfEdgeVertex2 v3 = new HalfEdgeVertex2(t.p3);
//The vertices the edge points to
HalfEdge2 he1 = new HalfEdge2(v1);
HalfEdge2 he2 = new HalfEdge2(v2);
HalfEdge2 he3 = new HalfEdge2(v3);
he1.nextEdge = he2;
he2.nextEdge = he3;
he3.nextEdge = he1;
he1.prevEdge = he3;
he2.prevEdge = he1;
he3.prevEdge = he2;
//The vertex needs to know of an edge going from it
v1.edge = he2;
v2.edge = he3;
v3.edge = he1;
//The face the half-edge is connected to
HalfEdgeFace2 face = new HalfEdgeFace2(he1);
//Each edge needs to know of the face connected to this edge
he1.face = face;
he2.face = face;
he3.face = face;
//Add everything to the lists
data.edges.Add(he1);
data.edges.Add(he2);
data.edges.Add(he3);
data.faces.Add(face);
data.vertices.Add(v1);
data.vertices.Add(v2);
data.vertices.Add(v3);
}
//Step 4. Find the half-edges going in the opposite direction of each edge we have
//Is there a faster way to do this because this is the bottleneck?
foreach (HalfEdge2 e in data.edges)
{
HalfEdgeVertex2 goingToVertex = e.v;
HalfEdgeVertex2 goingFromVertex = e.prevEdge.v;
foreach (HalfEdge2 eOther in data.edges)
{
//Dont compare with itself
if (e == eOther)
{
continue;
}
//Is this edge going between the vertices in the opposite direction
if (goingFromVertex.position.Equals(eOther.v.position) && goingToVertex.position.Equals(eOther.prevEdge.v.position))
{
e.oppositeEdge = eOther;
break;
}
}
}
return(data);
}
