//
// Does a point p lie to the left, to the right, or on a vector going from a to b
//
//https://gamedev.stackexchange.com/questions/71328/how-can-i-add-and-subtract-convex-polygons
public static float GetPointInRelationToVectorValue(MyVector2 a, MyVector2 b, MyVector2 p)
{
float x1 = a.x - p.x;
float x2 = a.y - p.y;
float y1 = b.x - p.x;
float y2 = b.y - p.y;
float determinant = MathUtility.Det2(x1, x2, y1, y2);
return(determinant);
}
//Alternative 2 in 2d space [radians]
public static float AngleFromToCCW(MyVector2 from, MyVector2 to)
{
//The determinant is similar to the dot product
//The dot product is always 0 no matter in which direction the perpendicular vector is pointing
//But the determinant is -1 or 1 depending on which way the perpendicular vector is pointing (up or down)
//AngleBetween goes from 0 to 180 so we can now determine if we need to compensate to get 360 degrees
if (MathUtility.Det2(from, to) > 0f)
{
return(AngleBetween(from, to));
}
else
{
return((Mathf.PI * 2f) - AngleBetween(from, to));
}
}
//
// Calculate the center of circle in 2d space given three coordinates - Simple version
//
//From the book "Geometric Tools for Computer Graphics"
public static MyVector2 CalculateCircleCenter(MyVector2 a, MyVector2 b, MyVector2 c)
{
//Make sure the triangle a-b-c is counterclockwise
if (!IsTriangleOrientedClockwise(a, b, c))
{
//Swap two vertices to change orientation
(a, b) = (b, a);
//Debug.Log("Swapped vertices");
}
//The area of the triangle
float X_1 = b.x - a.x;
float X_2 = c.x - a.x;
float Y_1 = b.y - a.y;
float Y_2 = c.y - a.y;
float A = 0.5f * MathUtility.Det2(X_1, Y_1, X_2, Y_2);
//Debug.Log(A);
//The center coordinates:
//float L_10 = MyVector2.Magnitude(b - a);
//float L_20 = MyVector2.Magnitude(c - a);
//float L_10_square = L_10 * L_10;
//float L_20_square = L_20 * L_20;
float L_10_square = MyVector2.SqrMagnitude(b - a);
float L_20_square = MyVector2.SqrMagnitude(c - a);
float one_divided_by_4_A = 1f / (4f * A);
float x = a.x + one_divided_by_4_A * ((Y_2 * L_10_square) - (Y_1 * L_20_square));
float y = a.y + one_divided_by_4_A * ((X_1 * L_20_square) - (X_2 * L_10_square));
MyVector2 center = new MyVector2(x, y);
return(center);
}
//In 2d space [radians]
//If you want to calculate the angle from vector a to b both originating from c, from is a-c and to is b-c
public static float AngleFromToCCW(MyVector2 from, MyVector2 to, bool shouldNormalize = false)
{
from = MyVector2.Normalize(from);
to = MyVector2.Normalize(to);
float angleRad = AngleBetween(from, to, shouldNormalize = false);
//The determinant is similar to the dot product
//The dot product is always 0 no matter in which direction the perpendicular vector is pointing
//But the determinant is -1 or 1 depending on which way the perpendicular vector is pointing (up or down)
//AngleBetween goes from 0 to 180 so we can now determine if we need to compensate to get 360 degrees
if (MathUtility.Det2(from, to) > 0f)
{
return(angleRad);
}
else
{
return((Mathf.PI * 2f) - angleRad);
}
}