//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);
}
//
// Are two Axis-aligned-bounding-box (boxes are here rectangles) intersecting?
//
//2d
public static bool AABB_AABB(AABB2 r1, AABB2 r2)
{
//If the min of one box in one dimension is greater than the max of another box then the boxes are not intersecting
//They have to intersect in 2 dimensions. We have to test if box 1 is to the left or box 2 and vice versa
bool isIntersecting = true;
//X axis
///r1_minX - the smallest x-coordinate of all corners belonging to rectangle 1
if (r1.min.x > r2.max.x)
{
isIntersecting = false;
}
else if (r2.min.x > r1.max.x)
{
isIntersecting = false;
}
//Y axis
else if (r1.min.y > r2.max.y)
{
isIntersecting = false;
}
else if (r2.min.y > r1.max.y)
{
isIntersecting = false;
}
return(isIntersecting);
}
//
// 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
AABB2 box = new AABB2(points);
if (Mathf.Abs(box.max.x - box.min.x) < MathUtility.EPSILON || Mathf.Abs(box.max.y - box.min.y) < MathUtility.EPSILON)
{
Debug.Log("The points cant form a convex hull");
return(false);
}
return(true);
}
//
// Are two Axis-aligned-bounding-box (boxes are here rectangles) intersecting?
//
//r1_minX - the smallest x-coordinate of all corners belonging to rectangle 1
public static bool AABB_AABB_2D(AABB2 r1, AABB2 r2)
{
//If the min of one box in one dimension is greater than the max of another box then the boxes are not intersecting
//They have to intersect in 2 dimensions. We have to test if box 1 is to the left or box 2 and vice versa
bool isIntersecting = true;
//X axis
if (r1.minX > r2.maxX)
{
isIntersecting = false;
}
else if (r2.minX > r1.maxX)
{
isIntersecting = false;
}
//Y axis
else if (r1.minY > r2.maxY)
{
isIntersecting = false;
}
else if (r2.minY > r1.maxY)
{
isIntersecting = false;
}
return(isIntersecting);
}
//
// Algorithms that test if we can form a convex hull
//
private static bool CanFormConvexHull_2d(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
AABB2 rectangle = new AABB2(points);
if (!rectangle.IsRectangleARectangle())
{
Debug.Log("The points cant form a convex hull");
return(false);
}
return(true);
}
//Normalize stuff
//MyVector2
public static MyVector2 Normalize(MyVector2 point, AABB2 boundingBox, float dMax)
{
float x = (point.x - boundingBox.minX) / dMax;
float y = (point.y - boundingBox.minY) / dMax;
MyVector2 pNormalized = new MyVector2(x, y);
return(pNormalized);
}
//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);
}
}
//UnNormalize different stuff
//MyVector2
public static MyVector2 UnNormalize(MyVector2 point, AABB2 boundingBox, float dMax)
{
float x = (point.x * dMax) + boundingBox.minX;
float y = (point.y * dMax) + boundingBox.minY;
MyVector2 pUnNormalized = new MyVector2(x, y);
return(pUnNormalized);
}
//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<MyVector2>
public static HashSet <MyVector2> Normalize(HashSet <MyVector2> points, AABB2 boundingBox, float dMax)
{
HashSet <MyVector2> normalizedPoints = new HashSet <MyVector2>();
foreach (MyVector2 p in points)
{
normalizedPoints.Add(Normalize(p, boundingBox, dMax));
}
return(normalizedPoints);
}
//List<MyVector2>
public static List <MyVector2> UnNormalize(List <MyVector2> normalized, AABB2 aabb, float dMax)
{
List <MyVector2> unNormalized = new List <MyVector2>();
foreach (MyVector2 p in normalized)
{
MyVector2 pUnNormalized = UnNormalize(p, aabb, dMax);
unNormalized.Add(pUnNormalized);
}
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
AABB2 aabb = new AABB2(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);
}
//
// Are two triangles intersecting in 2d space
//
public static bool TriangleTriangle2D(Triangle2 t1, Triangle2 t2, bool do_AABB_test)
{
bool isIntersecting = false;
//Step 0. AABB intersection which may speed up the algorithm if the triangles are far apart
if (do_AABB_test)
{
//Rectangle that covers t1
AABB2 r1 = new AABB2(t1.MinX(), t1.MaxX(), t1.MinY(), t1.MaxY());
//Rectangle that covers t2
AABB2 r2 = new AABB2(t2.MinX(), t2.MaxX(), t2.MinY(), t2.MaxY());
if (!AABB_AABB_2D(r1, r2))
{
return(false);
}
}
//Step 1. Line-line instersection
//Line 1 of t1 against all lines of t2
if (
LineLine(t1.p1, t1.p2, t2.p1, t2.p2, true) ||
LineLine(t1.p1, t1.p2, t2.p2, t2.p3, true) ||
LineLine(t1.p1, t1.p2, t2.p3, t2.p1, true)
)
{
isIntersecting = true;
}
//Line 2 of t1 against all lines of t2
else if (
LineLine(t1.p2, t1.p3, t2.p1, t2.p2, true) ||
LineLine(t1.p2, t1.p3, t2.p2, t2.p3, true) ||
LineLine(t1.p2, t1.p3, t2.p3, t2.p1, true)
)
{
isIntersecting = true;
}
//Line 3 of t1 against all lines of t2
else if (
LineLine(t1.p3, t1.p1, t2.p1, t2.p2, true) ||
LineLine(t1.p3, t1.p1, t2.p2, t2.p3, true) ||
LineLine(t1.p3, t1.p1, t2.p3, t2.p1, true)
)
{
isIntersecting = true;
}
//Now we can return if we are intersecting so we dont need to spend time testing something else
if (isIntersecting)
{
return(isIntersecting);
}
//Step 2. Point-in-triangle intersection
//We only need to test one corner from each triangle
//If this point is not in the triangle, then the other points can't be in the triangle, because if this point is outside
//and another point is inside, then the line between them would have been covered by step 1: line-line intersections test
if (PointTriangle(t2, t1.p1, true) || PointTriangle(t1, t2.p1, true))
{
isIntersecting = true;
}
return(isIntersecting);
}
//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);
}
//
// Normalize points to the range (0 -> 1)
//
//From "A fast algorithm for constructing Delaunay triangulations in the plane" by Sloan
//boundingBox is the rectangle that covers all original points before normalization
public static float CalculateDMax(AABB2 boundingBox)
{
float dMax = Mathf.Max(boundingBox.maxX - boundingBox.minX, boundingBox.maxY - boundingBox.minY);
return(dMax);
}
//From "A fast algorithm for constructing Delaunay triangulations in the plane" by Sloan
//boundingBox is the rectangle that covers all original points before normalization
public float CalculateDMax(AABB2 boundingBox)
{
float dMax = Mathf.Max(boundingBox.max.x - boundingBox.min.x, boundingBox.max.y - boundingBox.min.y);
return(dMax);
}
public Normalizer2(List <MyVector2> points)
{
this.boundingBox = new AABB2(points);
this.dMax = CalculateDMax(this.boundingBox);
}
