/// <summary>
/// Implements "A new algorithm for Boolean operations on general polygons"
/// available here: http://liama.ia.ac.cn/wiki/_media/user:dong:dong_cg_05.pdf
/// Merges two polygons, a subject and a clip with the specified operation. Polygons may not be
/// self-intersecting.
///
/// Warning: May yield incorrect results or even crash if polygons contain collinear points.
/// </summary>
/// <param name="subject">The subject polygon.</param>
/// <param name="clip">The clip polygon, which is added,
/// substracted or intersected with the subject</param>
/// <param name="clipType">The operation to be performed. Either
/// Union, Difference or Intersection.</param>
/// <param name="error">The error generated (if any)</param>
/// <returns>A list of closed polygons, which make up the result of the clipping operation.
/// Outer contours are ordered counter clockwise, holes are ordered clockwise.</returns>
private static List<Polygon> Execute(Polygon subject, Polygon clip,
PolyClipType clipType, out PolyClipError error)
{
//Debug.Assert(subject.IsSimple() && clip.IsSimple(), "Non simple input!", "Input polygons must be simple (cannot intersect themselves).");
// Copy polygons
Polygon slicedSubject;
Polygon slicedClip;
// Calculate the intersection and touch points between
// subject and clip and add them to both
CalculateIntersections(subject, clip, out slicedSubject, out slicedClip);
// Translate polygons into upper right quadrant
// as the algorithm depends on it
Vector2D lbSubject = subject.GetCollisionBox().LowerBound;
Vector2D lbClip = clip.GetCollisionBox().LowerBound;
Vector2D translate;
Vector2D.Min(ref lbSubject, ref lbClip, out translate);
translate = Vector2D.One - translate;
if (translate != Vector2D.Zero)
{
slicedSubject.Translate(ref translate);
slicedClip.Translate(ref translate);
}
// Enforce counterclockwise contours
slicedSubject.ForceCounterClockWise();
slicedClip.ForceCounterClockWise();
List<Edge> subjectSimplices;
List<double> subjectCoeff;
List<Edge> clipSimplices;
List<double> clipCoeff;
// Build simplical chains from the polygons and calculate the
// the corresponding coefficients
CalculateSimplicalChain(slicedSubject, out subjectCoeff, out subjectSimplices);
CalculateSimplicalChain(slicedClip, out clipCoeff, out clipSimplices);
List<Edge> resultSimplices;
// Determine the characteristics function for all non-original edges
// in subject and clip simplical chain and combine the edges contributing
// to the result, depending on the clipType
CalculateResultChain(subjectCoeff, subjectSimplices, clipCoeff, clipSimplices, clipType,
out resultSimplices);
List<Polygon> result;
// Convert result chain back to polygon(s)
error = BuildPolygonsFromChain(resultSimplices, out result);
// Reverse the polygon translation from the beginning
// and remove collinear points from output
translate *= -1f;
for (int i = 0; i < result.Count; ++i)
{
result[i].Translate(ref translate);
SimplifyTools.CollinearSimplify(result[i].Vertices);
}
return result;
}