static element ComputeMaxError(vector[] d, int first, int last, cubicbezier bezCurve, element[] u, out int splitPoint)
{
var sp = (last - first + 1) / 2;
element maxDist2 = 0;
for (var i = first + 1; i < last; i++)
{
var dist2 = (bezCurve.Interpolate(u[i - first]) - d[i]).LengthSquare;
if (maxDist2 <= dist2)
{
maxDist2 = dist2;
sp = i;
}
}
splitPoint = sp;
return(maxDist2);
}
/// <summary>
/// Use Newton-Raphson iteration to find better root.
/// </summary>
/// <param name="Q">Current fitted curve</param>
/// <param name="P">Digitized point</param>
/// <param name="u">Parameter value for <see cref="P"/></param>
/// <returns>パラメータ</returns>
static element NewtonRaphsonRootFind(cubicbezier Q, vector P, element u)
{
/* Compute Q(u) */
var Q_u = Q.Interpolate(u);
/* Generate control vertices for Q' */
var Q1 = new vector[3]; /* Q' and Q'' */
for (int i = 0; i <= 2; i++)
{
Q1[i] = (Q[i + 1] - Q[i]) * 3;
}
/* Generate control vertices for Q'' */
var Q2 = new vector[2];
for (int i = 0; i <= 1; i++)
{
Q2[i] = (Q1[i + 1] - Q1[i]) * 2;
}
/* Compute Q'(u) and Q''(u) */
var Q1_u = Interpolate2(u, Q1[0], Q1[1], Q1[2]);
var Q2_u = Interpolate1(u, Q2[0], Q2[1]);
/* Compute f(u)/f'(u) */
var Q_u_P = Q_u - P;
var numerator = Q_u_P.Dot(Q1_u);
var denominator = Q1_u.LengthSquare + Q_u_P.Dot(Q2_u);
if (denominator == 0)
{
return(u);
}
/* u = u - f(u)/f'(u) */
return(u - numerator / denominator);
}