/// <summary>
/// Attempts to find a slightly better parameterization for u on the given curve.
/// </summary>
protected void Reparameterize(int first, int last, CubicBezier curve)
{
#if OPTIMIZED_REPARAMETERIZE
using var _ = ReparameterizeMarker.Auto();
unsafe
{
using (_pts.ViewAsNativeArray(out var pts))
using (_u.ViewAsNativeArray(out var u))
OptimizedHelpers.Reparameterize(first, last, curve, (VECTOR *)pts.GetUnsafePtr(), (FLOAT *)u.GetUnsafePtr());
}
#else
using var _ = ReparameterizeMarker.Auto();
List <VECTOR> pts = _pts;
List <FLOAT> u = _u;
int nPts = last - first;
for (int i = 1; i < nPts; i++)
{
VECTOR p = pts[first + i];
FLOAT t = u[i];
FLOAT ti = 1 - t;
// Control vertices for Q'
VECTOR qp0 = (curve.p1 - curve.p0) * 3;
VECTOR qp1 = (curve.p2 - curve.p1) * 3;
VECTOR qp2 = (curve.p3 - curve.p2) * 3;
// Control vertices for Q''
VECTOR qpp0 = (qp1 - qp0) * 2;
VECTOR qpp1 = (qp2 - qp1) * 2;
// Evaluate Q(t), Q'(t), and Q''(t)
VECTOR p0 = curve.Sample(t);
VECTOR p1 = ((ti * ti) * qp0) + ((2 * ti * t) * qp1) + ((t * t) * qp2);
VECTOR p2 = (ti * qpp0) + (t * qpp1);
// these are the actual fitting calculations using http://en.wikipedia.org/wiki/Newton%27s_method
// We can't just use .X and .Y because Unity uses lower-case "x" and "y".
FLOAT num = ((VectorHelper.GetX(p0) - VectorHelper.GetX(p)) * VectorHelper.GetX(p1)) + ((VectorHelper.GetY(p0) - VectorHelper.GetY(p)) * VectorHelper.GetY(p1));
FLOAT den = (VectorHelper.GetX(p1) * VectorHelper.GetX(p1)) + (VectorHelper.GetY(p1) * VectorHelper.GetY(p1)) + ((VectorHelper.GetX(p0) - VectorHelper.GetX(p)) * VectorHelper.GetX(p2)) + ((VectorHelper.GetY(p0) - VectorHelper.GetY(p)) * VectorHelper.GetY(p2));
FLOAT newU = t - num / den;
if (Math.Abs(den) > EPSILON && newU >= 0 && newU <= 1)
{
u[i] = newU;
}
}
#endif
}
/// <summary>
/// Computes the maximum squared distance from a point to the curve using the current parameterization.
/// </summary>
protected FLOAT FindMaxSquaredError(int first, int last, CubicBezier curve, out int split)
{
#if OPTIMIZED_FINDMAXSQUAREDERROR
using var _ = FindMaxSquaredErrorMarker.Auto();
unsafe
{
using (_pts.ViewAsNativeArray(out var pts))
using (_u.ViewAsNativeArray(out var u))
{
OptimizedHelpers.FindMaxSquaredError(first, last, curve, out split, (VECTOR *)pts.GetUnsafePtr(), (FLOAT *)u.GetUnsafePtr(), out var max);
return(max);
}
}
#else
using var _ = FindMaxSquaredErrorMarker.Auto();
List <VECTOR> pts = _pts;
List <FLOAT> u = _u;
int s = (last - first + 1) / 2;
int nPts = last - first + 1;
FLOAT max = 0;
for (int i = 1; i < nPts; i++)
{
VECTOR v0 = pts[first + i];
VECTOR v1 = curve.Sample(u[i]);
FLOAT d = VectorHelper.DistanceSquared(v0, v1);
if (d > max)
{
max = d;
s = i;
}
}
// split at point of maximum error
split = s + first;
if (split <= first)
{
split = first + 1;
}
if (split >= last)
{
split = last - 1;
}
return(max);
#endif
}
/// <summary>
/// Updates the internal arc length array for a curve. Expects the list to contain enough elements.
/// </summary>
private void UpdateArcLengths(int iCurve)
{
CubicBezier curve = _curves[iCurve];
int nSamples = _samplesPerCurve;
List <FLOAT> arclen = _arclen;
FLOAT clen = iCurve > 0 ? arclen[iCurve * nSamples - 1] : 0;
VECTOR pp = curve.p0;
Debug.Assert(arclen.Count >= ((iCurve + 1) * nSamples));
for (int iPoint = 0; iPoint < nSamples; iPoint++)
{
int idx = (iCurve * nSamples) + iPoint;
FLOAT t = (iPoint + 1) / (FLOAT)nSamples;
VECTOR np = curve.Sample(t);
FLOAT d = VectorHelper.Distance(np, pp);
clen += d;
arclen[idx] = clen;
pp = np;
}
}