/// <summary>
/// 指定された頂点列の指定範囲にベジェ曲線をフィットさせる
/// </summary>
/// <param name="d">フィット元頂点列</param>
/// <param name="first"><see cref="d"/>内の範囲開始インデックス</param>
/// <param name="last"><see cref="d"/>内の範囲終了インデックス</param>
/// <param name="tHat1">指定範囲開始点の長さ１の順方向ベクトル</param>
/// <param name="tHat2">指定範囲終了点の長さ１の逆方向ベクトル</param>
/// <param name="error">フィット時許容誤差の二乗</param>
/// <param name="result">ここにベジェ曲線列が追加される</param>
static void FitCubic(vector[] d, int first, int last, vector tHat1, vector tHat2, element error, List <cubicbezier> result)
{
cubicbezier bezCurve; /*Control points of fitted Bezier curve*/
var nPts = last - first + 1; /* Number of points in subset */
/* Use heuristic if region only has two points in it */
if (nPts == 2)
{
bezCurve = new cubicbezier();
bezCurve.P0 = d[first];
bezCurve.P3 = d[last];
var dist = (d[last] - d[first]).Length / 3;
bezCurve.P1 = bezCurve.P0 + tHat1.Relength(dist);
bezCurve.P2 = bezCurve.P3 + tHat2.Relength(dist);
result.Add(bezCurve);
return;
}
/* Parameterize points, and attempt to fit curve */
var u = ChordLengthParameterize(d, first, last);
bezCurve = GenerateBezier(d, first, last, u, tHat1, tHat2);
/* Find max deviation of points to fitted curve */
int splitPoint; /* Point to split point set at */
var maxError = ComputeMaxError(d, first, last, bezCurve, u, out splitPoint);
if (maxError < error)
{
result.Add(bezCurve);
return;
}
/* If error not too large, try some reparameterization */
/* and iteration */
var iterationError = error * error; /*Error below which you try iterating */
if (maxError < iterationError)
{
var maxIterations = 4; /* Max times to try iterating */
for (var i = 0; i < maxIterations; i++)
{
var uPrime = Reparameterize(d, first, last, u, bezCurve);
bezCurve = GenerateBezier(d, first, last, uPrime, tHat1, tHat2);
maxError = ComputeMaxError(d, first, last, bezCurve, uPrime, out splitPoint);
if (maxError < error)
{
result.Add(bezCurve);
return;
}
u = uPrime;
}
}
/* Fitting failed -- split at max error point and fit recursively */
var tHatCenter = ((d[splitPoint - 1] - d[splitPoint + 1]) * (element)0.5).Normalize();
FitCubic(d, first, splitPoint, tHat1, tHatCenter, error, result);
tHatCenter = -tHatCenter;
FitCubic(d, splitPoint, last, tHatCenter, tHat2, error, result);
}
