private static bool SubdividePoints(float[] points, BezierCalculation bezierFunction, float t0, Vector2 p0, float t1, Vector2 p1, out float midT, out Vector2 midPoint, float errorSquared)
{
midT = (t1 + t0) / 2;
float midX = (p1.X + p0.X) / 2;
float midY = (p1.Y + p0.Y) / 2;
midPoint = bezierFunction(midT, points);
float xError = midPoint.X - midX;
float yError = midPoint.Y - midY;
float midErrorSquared = (xError * xError) + (yError * yError);
return(midErrorSquared > errorSquared);
}
static void AddBezier(float[] points, BezierCalculation bezierFunction, List <Vector2> segmentPoints,
List <float> lengths, float errorSquared, bool doubleCheckDivision)
{
points[7] = points[5];
points[6] = points[4];
points[5] = points[3];
points[4] = points[2];
points[3] = points[1];
points[2] = points[0];
points[1] = 0;
points[0] = 0;
var tToPoint = new List <KeyValuePair <float, Vector2> >
{
new KeyValuePair <float, Vector2>(0, bezierFunction(0, points)),
new KeyValuePair <float, Vector2>(1, bezierFunction(1, points))
};
for (int i = 0; i < tToPoint.Count - 1; i++)
{
bool needsSubdivision;
do
{
needsSubdivision = SubdividePoints(points, bezierFunction, tToPoint[i].Key, tToPoint[i].Value,
tToPoint[i + 1].Key,
tToPoint[i + 1].Value, out var midT, out var midPoint, errorSquared);
if (!needsSubdivision && doubleCheckDivision)
{
needsSubdivision = SubdividePoints(points, bezierFunction, tToPoint[i].Key, tToPoint[i].Value,
midT,
midPoint, out _, out _, errorSquared);
if (needsSubdivision)
{
// Found an inflection point. No need to double-check.
doubleCheckDivision = false;
}
}
if (needsSubdivision)
{
tToPoint.Insert(i + 1, new KeyValuePair <float, Vector2>(midT, midPoint));
}
} while (needsSubdivision);
}
// Now that each division can use linear interpolation with less than the allowed error
foreach (var iter in tToPoint)
{
AddLine(segmentPoints, lengths, new[] { iter.Value.X, iter.Value.Y });
}
}
static void AddBezier(float[] points, BezierCalculation bezierFunction, List <Vector2> segmentPoints,
List <float> lengths, float errorSquared, bool doubleCheckDivision)
{
points[7] = points[5];
points[6] = points[4];
points[5] = points[3];
points[4] = points[2];
points[3] = points[1];
points[2] = points[0];
points[1] = 0;
points[0] = 0;
var tToPoint = new List <KeyValuePair <float, Vector2> >
{
new(0, bezierFunction(0, points)),
new(1, bezierFunction(1, points))
};
