public Tuple <PrimitiveBezier, PrimitiveBezier> Split(double t)
{
// Splitting the curve using de Casteljau's algorithm: https://pomax.github.io/bezierinfo/#decasteljau
if (t < 0.0 || t > 1.0)
{
throw new ArgumentOutOfRangeException(nameof(t), "Curves can only be split on the interval [0.0, 1.0].");
}
var midPoint = ComputeParameterizedPoint(t);
var midControlPoint = Point.ScaledAlongPath(P2, P3, t);
// compute the first curve part
var newP2 = Point.ScaledAlongPath(P1, P2, t);
var newP3 = Point.ScaledAlongPath(newP2, midControlPoint, t);
var newP4 = midPoint;
var curve1 = new PrimitiveBezier(P1, newP2, newP3, newP4);
// compute the second curve part
var newP1 = midPoint;
newP3 = Point.ScaledAlongPath(P3, P4, t);
newP2 = Point.ScaledAlongPath(midControlPoint, newP3, t);
var curve2 = new PrimitiveBezier(newP1, newP2, newP3, P4);
return(Tuple.Create(curve1, curve2));
}
/// <summary>
/// Approximate the given Bezier curve as lines and arcs.
/// </summary>
internal static IPrimitive[] AsSimplePrimitives(PrimitiveBezier bezier)
{
var simplePrimitives = new List <IPrimitive>();
var intervals = new Queue <Tuple <double, double, int> >();
intervals.Enqueue(Tuple.Create(0.0, 1.0, 0));
while (intervals.Count > 0)
{
var interval = intervals.Dequeue();
var intervalStart = interval.Item1;
var intervalEnd = interval.Item2;
var currentSplitCount = interval.Item3;
var intervalSpread = intervalEnd - intervalStart;
var intervalMid = intervalStart + (intervalSpread * 0.5);
var pStart = bezier.ComputeParameterizedPoint(intervalStart);
var pMid = bezier.ComputeParameterizedPoint(intervalMid);
var pEnd = bezier.ComputeParameterizedPoint(intervalEnd);
var intervalLine = new PrimitiveLine(pStart, pEnd);
var candidatePrimitive = intervalLine.IsPointOnPrimitive(pMid, MathHelper.BezierEpsilon)
? (IPrimitive)intervalLine
: PrimitiveEllipse.ThreePointArc(pStart, pMid, pEnd, idealNormal: Vector.ZAxis);
candidatePrimitive = candidatePrimitive ?? intervalLine; // ensure it has a value
var intervalFirstQuarter = intervalStart + (intervalSpread * 0.25);
var intervalThirdQuarter = intervalStart + (intervalSpread * 0.75);
var pFirstQuarter = bezier.ComputeParameterizedPoint(intervalFirstQuarter);
var pThirdQuarter = bezier.ComputeParameterizedPoint(intervalThirdQuarter);
if (currentSplitCount >= MaximumPrimitiveSplitCount ||
(candidatePrimitive.IsPointOnPrimitive(pFirstQuarter, MathHelper.BezierEpsilon) &&
candidatePrimitive.IsPointOnPrimitive(pThirdQuarter, MathHelper.BezierEpsilon)))
{
simplePrimitives.Add(candidatePrimitive);
}
else
{
intervals.Enqueue(Tuple.Create(intervalStart, intervalMid, currentSplitCount + 1));
intervals.Enqueue(Tuple.Create(intervalMid, intervalEnd, currentSplitCount + 1));
}
}
return(simplePrimitives.ToArray());
}