/// <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());
}
/// <summary>
/// Creates a circle that passes through the three specified points. Null if the points are co-linear
/// </summary>
/// <param name="a">The first point.</param>
/// <param name="b">The second point.</param>
/// <param name="c">The third point.</param>
/// <param name="idealNormal">The ideal normal to normalize to if specified.</param>
/// <returns>The resultant circle or null.</returns>
public static PrimitiveEllipse ThreePointCircle(Point a, Point b, Point c, Optional <Vector> idealNormal = default(Optional <Vector>))
{
var v1 = a - b;
var v2 = c - b;
var normal = v1.Cross(v2);
if (normal.IsZeroVector)
{
return(null);
}
normal = normal.Normalize();
var m1 = v1.Cross(normal);
var m2 = v2.Cross(normal);
var b1a = (a + b) / 2.0;
var b2a = (c + b) / 2.0;
var b1 = new PrimitiveLine(b1a, b1a + m1);
var b2 = new PrimitiveLine(b2a, b2a + m2);
var center = b1.IntersectionPoint(b2, false);
if (center == null)
{
return(null);
}
if (idealNormal.HasValue && idealNormal.Value == normal * -1.0)
{
normal = idealNormal.Value;
}
return(new PrimitiveEllipse(center.GetValueOrDefault(), (a - center.GetValueOrDefault()).Length, normal));
}
