/*
* Return the count of the number of horizontal sections of the
* specified cubic Bezier curve. Put the parameters for the
* horizontal sections into the specified <code>ret</code> array.
* <p>
* If we examine the parametric equation in t, we have:
* Py(t) = C0(1-t)^3 + 3CP0 t(1-t)^2 + 3CP1 t^2(1-t) + C1 t^3
* = C0 - 3C0t + 3C0t^2 - C0t^3 +
* 3CP0t - 6CP0t^2 + 3CP0t^3 +
* 3CP1t^2 - 3CP1t^3 +
* C1t^3
* Py(t) = (C1 - 3CP1 + 3CP0 - C0) t^3 +
* (3C0 - 6CP0 + 3CP1) t^2 +
* (3CP0 - 3C0) t +
* (C0)
* If we take the derivative, we get:
* Py(t) = Dt^3 + At^2 + Bt + C
* dPy(t) = 3Dt^2 + 2At + B = 0
* 0 = 3*(C1 - 3*CP1 + 3*CP0 - C0)t^2
* + 2*(3*CP1 - 6*CP0 + 3*C0)t
* + (3*CP0 - 3*C0)
* 0 = 3*(C1 - 3*CP1 + 3*CP0 - C0)t^2
* + 3*2*(CP1 - 2*CP0 + C0)t
* + 3*(CP0 - C0)
* 0 = (C1 - CP1 - CP1 - CP1 + CP0 + CP0 + CP0 - C0)t^2
* + 2*(CP1 - CP0 - CP0 + C0)t
* + (CP0 - C0)
* 0 = (C1 - CP1 + CP0 - CP1 + CP0 - CP1 + CP0 - C0)t^2
* + 2*(CP1 - CP0 - CP0 + C0)t
* + (CP0 - C0)
* 0 = ((C1 - CP1) - (CP1 - CP0) - (CP1 - CP0) + (CP0 - C0))t^2
* + 2*((CP1 - CP0) - (CP0 - C0))t
* + (CP0 - C0)
* that this method will return 0 if the equation is a line,
* which is either always horizontal or never horizontal.
* Completely horizontal curves need to be eliminated by other
* means outside of this method.
*/
public static int GetHorizontalParams(double c0, double cp0,
double cp1, double c1,
double[] ret)
{
if (c0 <= cp0 && cp0 <= cp1 && cp1 <= c1)
{
return(0);
}
c1 -= cp1;
cp1 -= cp0;
cp0 -= c0;
ret[0] = cp0;
ret[1] = (cp1 - cp0) * 2;
ret[2] = (c1 - cp1 - cp1 + cp0);
int numroots = QuadCurve.SolveQuadratic(ret, ret);
int j = 0;
for (int i = 0; i < numroots; i++)
{
double t = ret[i];
// No splits at t==0 and t==1
if (t > 0 && t < 1)
{
if (j < i)
{
ret[j] = t;
}
j++;
}
}
return(j);
}
public override double NextVertical(double t0, double t1)
{
double[] eqn = { _xcoeff1, 2 * _xcoeff2, 3 * _xcoeff3 };
int numroots = QuadCurve.SolveQuadratic(eqn, eqn);
for (int i = 0; i < numroots; i++)
{
if (eqn[i] > t0 && eqn[i] < t1)
{
t1 = eqn[i];
}
}
return(t1);
}
public override void Enlarge(Rectangle r)
{
r.Add((int)(_x0 + .5),
(int)(_y0 + .5));
double[] eqn = { _xcoeff1, 2 * _xcoeff2, 3 * _xcoeff3 };
int numroots = QuadCurve.SolveQuadratic(eqn, eqn);
for (int i = 0; i < numroots; i++)
{
double t = eqn[i];
if (t > 0 && t < 1)
{
r.Add((int)(XforT(t) + .5), (int)(YforT(t) + .5));
}
}
r.Add((int)(_x1 + .5), (int)(_y1 + .5));
}