private void CalculateSamples()
{
var workingSegment = new CubicBezierSegment();
workingSegment.StartPoint = _segment.StartPoint;
workingSegment.StartControlPoint = _segment.StartControlPoint;
workingSegment.EndControlPoint = _segment.EndControlPoint;
workingSegment.EndPoint = _segment.EndPoint;
_length = 0.0f;
// First, break the working segment down into a discrete number of segments. We only care about the approximate
// length of these segments, not the curve segments themselves.
CubicBezierSegment leftSegment = new CubicBezierSegment(), rightSegment = new CubicBezierSegment();
for (int i = 0; i < NumberOfSamples; ++i)
{
// Subdivide another part off the curve. We take 1/64 of the curve on the first loop, and keep the
// remaining 63/64 of the curve. On the next loop, we want 1/63 of the curve and so on, to keep the
// segment size consistent.
double splitT = 1 / (double)(NumberOfSamples - i);
workingSegment.Subdivide(leftSegment, rightSegment, splitT);
float nodeLength = leftSegment.CalculateLength();
_length += nodeLength;
SegmentSample sample = new SegmentSample();
sample.Length = nodeLength;
sample.StartTime = 0.0f;
sample.EndTime = 1.0f;
_samples.Add(sample);
// Copy the right curve segment into the working curve segment.
workingSegment.StartPoint = rightSegment.StartPoint;
workingSegment.StartControlPoint = rightSegment.StartControlPoint;
workingSegment.EndControlPoint = rightSegment.EndControlPoint;
workingSegment.EndPoint = rightSegment.EndPoint;
}
// Knowing what the length of the curve segments are, and a total approximate length, we can calculate the
// the start/end times of each segment. These will be the values we use for our runtime lookup.
float runningLength = _samples[0].Length;
for (int i = 1; i < _samples.Count; ++i)
{
float t = (float)runningLength / _length;
SegmentSample sample = _samples[i];
sample.StartTime = t;
_samples[i] = sample;
SegmentSample oldSample = _samples[i - 1];
oldSample.EndTime = t;
_samples[i - 1] = oldSample;
runningLength += sample.Length;
}
}
/// <summary>
/// Calculates the length of a CubicBezierSegment. Note that because this uses a numerical method to get the length,
/// it won't be completely accurate.
/// </summary>
/// <returns>The length of the bezier segment.</returns>
/// <param name="segment">The segment to calculate the length of.</param>
public static float CalculateLength(this CubicBezierSegment segment)
{
// Subdividing the segment into 4 pieces, then getting an approximate length on those 4 pieces, gives
// a fairly accurate length (< 1% error), and is very quick.
CubicBezierSegment l = new CubicBezierSegment(), r = new CubicBezierSegment(),
ll = new CubicBezierSegment(), lr = new CubicBezierSegment(), rl = new CubicBezierSegment(),
rr = new CubicBezierSegment();
segment.Subdivide(l, r, 0.5);
l.Subdivide(ll, lr, 0.5);
r.Subdivide(rl, rr, 0.5);
return(ll.CalculateApproximateLength() + lr.CalculateApproximateLength() + rl.CalculateApproximateLength() +
rr.CalculateApproximateLength());
}
