private List <Vector2> Roots(Segment s)
{
// Get the derivatives of this segment
List <Vector2> Ders = Derivatives(s);
// Calculate the co-efficients
Vector2 a = Ders[0] - (2f * Ders[1]) + Ders[2];
Vector2 b = 2f * (Ders[1] - Ders[0]);
Vector2 c = Ders[0];
// Get the initail boundary
Vector2 Lower = s.P1;
Vector2 Upper = s.P4;
// Re-arrange the boundary so points are in the right spot
if (Lower.x > Upper.x)
{
float temp = Lower.x;
Lower.x = Upper.x;
Upper.x = temp;
}
if (Lower.y > Upper.y)
{
float temp = Lower.y;
Lower.y = Upper.y;
Upper.y = temp;
}
// Calculate the square root of the quadratic formula for both axes
float XSqe = (b.x * b.x) - (4f * a.x * c.x);
float YSqe = (b.y * b.y) - (4f * a.y * c.y);
// Assure the square root is positive
if (!MathF.Signbit(XSqe))
{
// Calculate the plus quadratic formula
float Time = (-b.x + MathF.Sqrt(XSqe)) / (2f * a.x);
// Is this time valid?
if (Valid(Time))
{
// Calculate the point using the time
float Val = Bezier(s.P1.x, s.P2.x, s.P3.x, s.P4.x, Time);
// Is point less than the current lowest?
if (Val < Lower.x)
{
Lower.x = Val;
}
}
// Calculate the minus quadratic formula
Time = (-b.x - MathF.Sqrt(XSqe)) / (2f * a.x);
// Is this time valid
if (Valid(Time))
{
// Calculate the point using the time
float Val = Bezier(s.P1.x, s.P2.x, s.P3.x, s.P4.x, Time);
// Is point greater than the current highest?
if (Val > Upper.x)
{
Upper.x = Val;
}
}
}
// Assure the square root is positive
if (!MathF.Signbit(YSqe))
{
// Calculate the plus quadratic formula
float Time = (-b.y + MathF.Sqrt(YSqe)) / (2f * a.y);
// Is this time valid?
if (Valid(Time))
{
// Calculate the point using the time
float Val = Bezier(s.P1.y, s.P2.y, s.P3.y, s.P4.y, Time);
// Is point less than the current lowest?
if (Val < Lower.y)
{
Lower.y = Val;
}
}
// Calculate the minus quadratic formula
Time = (-b.y - MathF.Sqrt(YSqe)) / (2f * a.y);
// Is this time valid
if (Valid(Time))
{
// Calculate the point using the time
float Val = Bezier(s.P1.y, s.P2.y, s.P3.y, s.P4.y, Time);
// Is point greater than the current highest?
if (Val > Upper.y)
{
Upper.y = Val;
}
}
}
// Create the list
List <Vector2> Roo = new List <Vector2>(2);
// Add the roots to the list
Roo.Add(Lower);
Roo.Add(Upper);
// Return the roots
return(Roo);
}
// ----- FUNCTIONS ----- \\
public float Magnitude()
{
return(MathF.Sqrt(Squared()));
}
