public float SolveYAtX_original(float x)
{
// see BezierMath for explanation of what and why this does.
if (x < 0f || x > 1f)
{
throw new ArgumentOutOfRangeException(nameof(x));
}
var fx = new Polynomial3(_fx.A, _fx.B, _fx.C, _fx.D - x); // Newton-Raphson finds 0-point of function (t where f(t)=0), but we want t where f(t) = x, so subtract x from D of the polynomial to be able to look for 0-point.
var fxDerivative = fx.GetDerivative();
// use Newton-Raphson to find a T that yields an fx(t) closer to 0 than allowed tolerance.
var s = x; // initial guess = what t would be if the spline was perfectly linear.
for (var i = 0; i < 100; i++) // lets not try more than 100 times :)
{
var resultX = fx.Solve(s);
if (resultX >= 0 && resultX < _tolerance || resultX < 0 && resultX > -_tolerance)
{
break;
}
s -= resultX / fxDerivative.Calc(s);
}
return(_fy.Solve(s));
}
public BezierCurveSolver(BezierCurve bezierCurve, float tolerance = 0.002f)
{
_tolerance = tolerance;
_fx = bezierCurve.GetFx();
_fdx = _fx.GetDerivative();
_fy = bezierCurve.GetFy();
}