//
// 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);
}
//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);
}