| private GetY ( System.Windows.Vector v ) : System.Double | ||
| v | System.Windows.Vector | |
| return | System.Double | |
/// <summary>
/// Attempts to find a slightly better parameterization for u on the given curve.
/// </summary>
protected void Reparameterize(int first, int last, CubicBezier curve)
{
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;
}
}
}
private static void RdpRecursive(List <VECTOR> pts, FLOAT error, int first, int last, List <int> keepIndex)
{
int nPts = last - first + 1;
if (nPts < 3)
{
return;
}
VECTOR a = pts[first];
VECTOR b = pts[last];
FLOAT abDist = VectorHelper.Distance(a, b);
FLOAT aCrossB = VectorHelper.GetX(a) * VectorHelper.GetY(b) - VectorHelper.GetX(b) * VectorHelper.GetY(a);
FLOAT maxDist = error;
int split = 0;
for (int i = first + 1; i < last - 1; i++)
{
VECTOR p = pts[i];
FLOAT pDist = PerpendicularDistance(a, b, abDist, aCrossB, p);
if (pDist > maxDist)
{
maxDist = pDist;
split = i;
}
}
if (split != 0)
{
keepIndex.Add(split);
RdpRecursive(pts, error, first, split, keepIndex);
RdpRecursive(pts, error, split, last, keepIndex);
}
}
public override int GetHashCode()
{
JenkinsHash hash = new JenkinsHash();
hash.Mixin(VectorHelper.GetX(p0).GetHashCode());
hash.Mixin(VectorHelper.GetY(p0).GetHashCode());
hash.Mixin(VectorHelper.GetX(p1).GetHashCode());
hash.Mixin(VectorHelper.GetY(p1).GetHashCode());
hash.Mixin(VectorHelper.GetX(p2).GetHashCode());
hash.Mixin(VectorHelper.GetY(p2).GetHashCode());
hash.Mixin(VectorHelper.GetX(p3).GetHashCode());
hash.Mixin(VectorHelper.GetY(p3).GetHashCode());
return(hash.GetValue());
}
[MethodImpl(MethodImplOptions.AggressiveInlining)] // originally this method wasn't be inlined
#endif
private static FLOAT PerpendicularDistance(VECTOR a, VECTOR b, FLOAT abDist, FLOAT aCrossB, VECTOR p)
{
// a profile with the test data showed that originally this was eating up ~44% of the runtime. So, this went through
// several iterations of optimization and staring at the disassembly. I tried different methods of using cross
// products, doing the computation with larger vector types, etc... this is the best I could do in ~45 minutes
// running on 3 hours of sleep, which is all scalar math, but RyuJIT puts it into XMM registers and does
// ADDSS/SUBSS/MULSS/DIVSS because that's what it likes to do whenever it sees a vector in a function.
FLOAT area = Math.Abs(aCrossB +
VectorHelper.GetX(b) * VectorHelper.GetY(p) + VectorHelper.GetX(p) * VectorHelper.GetY(a) -
VectorHelper.GetX(p) * VectorHelper.GetY(b) - VectorHelper.GetX(a) * VectorHelper.GetY(p));
FLOAT height = area / abDist;
return(height);
}
public override string ToString()
{
StringBuilder sb = new StringBuilder();
sb.Append("CubicBezier: (<");
sb.Append(VectorHelper.GetX(p0).ToString("#.###", CultureInfo.InvariantCulture));
sb.Append(", ");
sb.Append(VectorHelper.GetY(p0).ToString("#.###", CultureInfo.InvariantCulture));
sb.Append("> <");
sb.Append(VectorHelper.GetX(p1).ToString("#.###", CultureInfo.InvariantCulture));
sb.Append(", ");
sb.Append(VectorHelper.GetY(p1).ToString("#.###", CultureInfo.InvariantCulture));
sb.Append("> <");
sb.Append(VectorHelper.GetX(p2).ToString("#.###", CultureInfo.InvariantCulture));
sb.Append(", ");
sb.Append(VectorHelper.GetY(p2).ToString("#.###", CultureInfo.InvariantCulture));
sb.Append("> <");
sb.Append(VectorHelper.GetX(p3).ToString("#.###", CultureInfo.InvariantCulture));
sb.Append(", ");
sb.Append(VectorHelper.GetY(p3).ToString("#.###", CultureInfo.InvariantCulture));
sb.Append(">)");
return(sb.ToString());
}
