xref: /trunk/main/basegfx/source/polygon/b2dpolygontools.cxx (revision 09dbbe93)

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 *
 * Licensed to the Apache Software Foundation (ASF) under one
 * or more contributor license agreements.  See the NOTICE file
 * distributed with this work for additional information
 * regarding copyright ownership.  The ASF licenses this file
 * to you under the Apache License, Version 2.0 (the
 * "License"); you may not use this file except in compliance
 * with the License.  You may obtain a copy of the License at
 *
 *   http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing,
 * software distributed under the License is distributed on an
 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
 * KIND, either express or implied.  See the License for the
 * specific language governing permissions and limitations
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// MARKER(update_precomp.py): autogen include statement, do not remove
#include "precompiled_basegfx.hxx"
#include <basegfx/numeric/ftools.hxx>
#include <basegfx/polygon/b2dpolygontools.hxx>
#include <osl/diagnose.h>
#include <rtl/math.hxx>
#include <basegfx/polygon/b2dpolygon.hxx>
#include <basegfx/polygon/b2dpolypolygon.hxx>
#include <basegfx/range/b2drange.hxx>
#include <basegfx/curve/b2dcubicbezier.hxx>
#include <basegfx/polygon/b2dpolypolygoncutter.hxx>
#include <basegfx/point/b3dpoint.hxx>
#include <basegfx/matrix/b3dhommatrix.hxx>
#include <basegfx/matrix/b2dhommatrix.hxx>
#include <basegfx/curve/b2dbeziertools.hxx>
#include <basegfx/matrix/b2dhommatrixtools.hxx>
#include <osl/mutex.hxx>

#include <numeric>
#include <limits>

// #i37443#
#define ANGLE_BOUND_START_VALUE		(2.25)
#define ANGLE_BOUND_MINIMUM_VALUE	(0.1)
#define COUNT_SUBDIVIDE_DEFAULT		(4L)
#ifdef DBG_UTIL
static double fAngleBoundStartValue = ANGLE_BOUND_START_VALUE;
#endif
#define STEPSPERQUARTER     (3)

//////////////////////////////////////////////////////////////////////////////

namespace basegfx
{
	namespace tools
	{
		void openWithGeometryChange(B2DPolygon& rCandidate)
		{
			if(rCandidate.isClosed())
			{
				if(rCandidate.count())
				{
					rCandidate.append(rCandidate.getB2DPoint(0));

					if(rCandidate.areControlPointsUsed() && rCandidate.isPrevControlPointUsed(0))
					{
						rCandidate.setPrevControlPoint(rCandidate.count() - 1, rCandidate.getPrevControlPoint(0));
						rCandidate.resetPrevControlPoint(0);
					}
				}

				rCandidate.setClosed(false);
			}
		}

		void closeWithGeometryChange(B2DPolygon& rCandidate)
		{
			if(!rCandidate.isClosed())
			{
				while(rCandidate.count() > 1 && rCandidate.getB2DPoint(0) == rCandidate.getB2DPoint(rCandidate.count() - 1))
				{
					if(rCandidate.areControlPointsUsed() && rCandidate.isPrevControlPointUsed(rCandidate.count() - 1))
					{
						rCandidate.setPrevControlPoint(0, rCandidate.getPrevControlPoint(rCandidate.count() - 1));
					}

					rCandidate.remove(rCandidate.count() - 1);
				}

				rCandidate.setClosed(true);
			}
		}

		void checkClosed(B2DPolygon& rCandidate)
		{
			// #i80172# Removed unnecessary assertion
			// OSL_ENSURE(!rCandidate.isClosed(), "checkClosed: already closed (!)");

			if(rCandidate.count() > 1 && rCandidate.getB2DPoint(0) == rCandidate.getB2DPoint(rCandidate.count() - 1))
			{
				closeWithGeometryChange(rCandidate);
			}
		}

		// Get successor and predecessor indices. Returning the same index means there
		// is none. Same for successor.
		sal_uInt32 getIndexOfPredecessor(sal_uInt32 nIndex, const B2DPolygon& rCandidate)
		{
			OSL_ENSURE(nIndex < rCandidate.count(), "getIndexOfPredecessor: Access to polygon out of range (!)");

			if(nIndex)
			{
				return nIndex - 1L;
			}
			else if(rCandidate.count())
			{
				return rCandidate.count() - 1L;
			}
			else
			{
				return nIndex;
			}
		}

		sal_uInt32 getIndexOfSuccessor(sal_uInt32 nIndex, const B2DPolygon& rCandidate)
		{
			OSL_ENSURE(nIndex < rCandidate.count(), "getIndexOfPredecessor: Access to polygon out of range (!)");

			if(nIndex + 1L < rCandidate.count())
			{
				return nIndex + 1L;
			}
			else if(nIndex + 1L == rCandidate.count())
			{
				return 0L;
			}
			else
			{
				return nIndex;
			}
		}

		B2VectorOrientation getOrientation(const B2DPolygon& rCandidate)
		{
			B2VectorOrientation eRetval(ORIENTATION_NEUTRAL);

			if(rCandidate.count() > 2L || rCandidate.areControlPointsUsed())
			{
				const double fSignedArea(getSignedArea(rCandidate));

				if(fTools::equalZero(fSignedArea))
				{
					// ORIENTATION_NEUTRAL, already set
				}
				if(fSignedArea > 0.0)
				{
					eRetval = ORIENTATION_POSITIVE;
				}
				else if(fSignedArea < 0.0)
				{
					eRetval = ORIENTATION_NEGATIVE;
				}
			}

			return eRetval;
		}

		B2VectorContinuity getContinuityInPoint(const B2DPolygon& rCandidate, sal_uInt32 nIndex)
		{
			return rCandidate.getContinuityInPoint(nIndex);
		}

		B2DPolygon adaptiveSubdivideByDistance(const B2DPolygon& rCandidate, double fDistanceBound)
		{
			if(rCandidate.areControlPointsUsed())
			{
				const sal_uInt32 nPointCount(rCandidate.count());
				B2DPolygon aRetval;

				if(nPointCount)
				{
					// prepare edge-oriented loop
					const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
					B2DCubicBezier aBezier;
					aBezier.setStartPoint(rCandidate.getB2DPoint(0));

					// perf: try to avoid too many realloctions by guessing the result's pointcount
					aRetval.reserve(nPointCount*4);

					// add start point (always)
					aRetval.append(aBezier.getStartPoint());

					for(sal_uInt32 a(0L); a < nEdgeCount; a++)
					{
						// get next and control points
						const sal_uInt32 nNextIndex((a + 1) % nPointCount);
						aBezier.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
						aBezier.setControlPointA(rCandidate.getNextControlPoint(a));
						aBezier.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
						aBezier.testAndSolveTrivialBezier();

						if(aBezier.isBezier())
						{
							// add curved edge and generate DistanceBound
							double fBound(0.0);

							if(0.0 == fDistanceBound)
							{
								// If not set, use B2DCubicBezier functionality to guess a rough value
								const double fRoughLength((aBezier.getEdgeLength() + aBezier.getControlPolygonLength()) / 2.0);

								// take 1/100th of the rough curve length
								fBound = fRoughLength * 0.01;
							}
							else
							{
								// use given bound value
								fBound = fDistanceBound;
							}

							// make sure bound value is not too small. The base units are 1/100th mm, thus
							// just make sure it's not smaller then 1/100th of that
							if(fBound < 0.01)
							{
								fBound = 0.01;
							}

							// call adaptive subdivide which adds edges to aRetval accordingly
							aBezier.adaptiveSubdivideByDistance(aRetval, fBound);
						}
						else
						{
							// add non-curved edge
							aRetval.append(aBezier.getEndPoint());
						}

						// prepare next step
						aBezier.setStartPoint(aBezier.getEndPoint());
					}

					if(rCandidate.isClosed())
					{
						// set closed flag and correct last point (which is added double now).
						closeWithGeometryChange(aRetval);
					}
				}

				return aRetval;
			}
			else
			{
				return rCandidate;
			}
		}

		B2DPolygon adaptiveSubdivideByAngle(const B2DPolygon& rCandidate, double fAngleBound)
		{
			if(rCandidate.areControlPointsUsed())
			{
				const sal_uInt32 nPointCount(rCandidate.count());
				B2DPolygon aRetval;

				if(nPointCount)
				{
					// prepare edge-oriented loop
					const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
					B2DCubicBezier aBezier;
					aBezier.setStartPoint(rCandidate.getB2DPoint(0));

					// perf: try to avoid too many realloctions by guessing the result's pointcount
					aRetval.reserve(nPointCount*4);

					// add start point (always)
					aRetval.append(aBezier.getStartPoint());

					// #i37443# prepare convenient AngleBound if none was given
					if(0.0 == fAngleBound)
					{
#ifdef DBG_UTIL
						fAngleBound = fAngleBoundStartValue;
#else
						fAngleBound = ANGLE_BOUND_START_VALUE;
#endif
					}
					else if(fTools::less(fAngleBound, ANGLE_BOUND_MINIMUM_VALUE))
					{
						fAngleBound = 0.1;
					}

					for(sal_uInt32 a(0L); a < nEdgeCount; a++)
					{
						// get next and control points
						const sal_uInt32 nNextIndex((a + 1) % nPointCount);
						aBezier.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
						aBezier.setControlPointA(rCandidate.getNextControlPoint(a));
						aBezier.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
						aBezier.testAndSolveTrivialBezier();

						if(aBezier.isBezier())
						{
							// call adaptive subdivide
							aBezier.adaptiveSubdivideByAngle(aRetval, fAngleBound, true);
						}
						else
						{
							// add non-curved edge
							aRetval.append(aBezier.getEndPoint());
						}

						// prepare next step
						aBezier.setStartPoint(aBezier.getEndPoint());
					}

					if(rCandidate.isClosed())
					{
						// set closed flag and correct last point (which is added double now).
						closeWithGeometryChange(aRetval);
					}
				}

				return aRetval;
			}
			else
			{
				return rCandidate;
			}
		}

		B2DPolygon adaptiveSubdivideByCount(const B2DPolygon& rCandidate, sal_uInt32 nCount)
		{
			if(rCandidate.areControlPointsUsed())
			{
				const sal_uInt32 nPointCount(rCandidate.count());
				B2DPolygon aRetval;

				if(nPointCount)
				{
					// prepare edge-oriented loop
					const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
					B2DCubicBezier aBezier;
					aBezier.setStartPoint(rCandidate.getB2DPoint(0));

					// perf: try to avoid too many realloctions by guessing the result's pointcount
					aRetval.reserve(nPointCount*4);

					// add start point (always)
					aRetval.append(aBezier.getStartPoint());

					// #i37443# prepare convenient count if none was given
					if(0L == nCount)
					{
						nCount = COUNT_SUBDIVIDE_DEFAULT;
					}

					for(sal_uInt32 a(0L); a < nEdgeCount; a++)
					{
						// get next and control points
						const sal_uInt32 nNextIndex((a + 1) % nPointCount);
						aBezier.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
						aBezier.setControlPointA(rCandidate.getNextControlPoint(a));
						aBezier.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
						aBezier.testAndSolveTrivialBezier();

						if(aBezier.isBezier())
						{
							// call adaptive subdivide
							aBezier.adaptiveSubdivideByCount(aRetval, nCount);
						}
						else
						{
							// add non-curved edge
							aRetval.append(aBezier.getEndPoint());
						}

						// prepare next step
						aBezier.setStartPoint(aBezier.getEndPoint());
					}

					if(rCandidate.isClosed())
					{
						// set closed flag and correct last point (which is added double now).
						closeWithGeometryChange(aRetval);
					}
				}

				return aRetval;
			}
			else
			{
				return rCandidate;
			}
		}

		bool isInside(const B2DPolygon& rCandidate, const B2DPoint& rPoint, bool bWithBorder)
		{
			const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);

			if(bWithBorder && isPointOnPolygon(aCandidate, rPoint, true))
			{
				return true;
			}
			else
			{
				bool bRetval(false);
				const sal_uInt32 nPointCount(aCandidate.count());

				if(nPointCount)
				{
					B2DPoint aCurrentPoint(aCandidate.getB2DPoint(nPointCount - 1L));

					for(sal_uInt32 a(0L); a < nPointCount; a++)
					{
						const B2DPoint aPreviousPoint(aCurrentPoint);
						aCurrentPoint = aCandidate.getB2DPoint(a);

						// cross-over in Y?
						const bool bCompYA(fTools::more(aPreviousPoint.getY(), rPoint.getY()));
						const bool bCompYB(fTools::more(aCurrentPoint.getY(), rPoint.getY()));

						if(bCompYA != bCompYB)
						{
							// cross-over in X?
							const bool bCompXA(fTools::more(aPreviousPoint.getX(), rPoint.getX()));
							const bool bCompXB(fTools::more(aCurrentPoint.getX(), rPoint.getX()));

							if(bCompXA == bCompXB)
							{
								if(bCompXA)
								{
									bRetval = !bRetval;
								}
							}
							else
							{
								const double fCompare(
									aCurrentPoint.getX() - (aCurrentPoint.getY() - rPoint.getY()) *
									(aPreviousPoint.getX() - aCurrentPoint.getX()) /
									(aPreviousPoint.getY() - aCurrentPoint.getY()));

								if(fTools::more(fCompare, rPoint.getX()))
								{
									bRetval = !bRetval;
								}
							}
						}
					}
				}

				return bRetval;
			}
		}

		bool isInside(const B2DPolygon& rCandidate, const B2DPolygon& rPolygon, bool bWithBorder)
		{
			const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);
			const B2DPolygon aPolygon(rPolygon.areControlPointsUsed() ? rPolygon.getDefaultAdaptiveSubdivision() : rPolygon);
			const sal_uInt32 nPointCount(aPolygon.count());

			for(sal_uInt32 a(0L); a < nPointCount; a++)
			{
				const B2DPoint aTestPoint(aPolygon.getB2DPoint(a));

				if(!isInside(aCandidate, aTestPoint, bWithBorder))
				{
					return false;
				}
			}

			return true;
		}

		B2DRange getRangeWithControlPoints(const B2DPolygon& rCandidate)
		{
			const sal_uInt32 nPointCount(rCandidate.count());
			B2DRange aRetval;

			if(nPointCount)
			{
				const bool bControlPointsUsed(rCandidate.areControlPointsUsed());

				for(sal_uInt32 a(0); a < nPointCount; a++)
				{
					aRetval.expand(rCandidate.getB2DPoint(a));

					if(bControlPointsUsed)
					{
						aRetval.expand(rCandidate.getNextControlPoint(a));
						aRetval.expand(rCandidate.getPrevControlPoint(a));
					}
				}
			}

			return aRetval;
		}

		B2DRange getRange(const B2DPolygon& rCandidate)
		{
            // changed to use internally buffered version at B2DPolygon
            return rCandidate.getB2DRange();
		}

		double getSignedArea(const B2DPolygon& rCandidate)
		{
			const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);
			double fRetval(0.0);
			const sal_uInt32 nPointCount(aCandidate.count());

			if(nPointCount > 2)
			{
				for(sal_uInt32 a(0L); a < nPointCount; a++)
				{
					const B2DPoint aPreviousPoint(aCandidate.getB2DPoint((!a) ? nPointCount - 1L : a - 1L));
					const B2DPoint aCurrentPoint(aCandidate.getB2DPoint(a));

					fRetval += aPreviousPoint.getX() * aCurrentPoint.getY();
					fRetval -= aPreviousPoint.getY() * aCurrentPoint.getX();
				}

				fRetval /= 2.0;

				// correct to zero if small enough. Also test the quadratic
				// of the result since the precision is near quadratic due to
				// the algorithm
				if(fTools::equalZero(fRetval) || fTools::equalZero(fRetval * fRetval))
				{
					fRetval = 0.0;
				}
			}

			return fRetval;
		}

		double getArea(const B2DPolygon& rCandidate)
		{
			double fRetval(0.0);

			if(rCandidate.count() > 2 || rCandidate.areControlPointsUsed())
			{
				fRetval = getSignedArea(rCandidate);
				const double fZero(0.0);

				if(fTools::less(fRetval, fZero))
				{
					fRetval = -fRetval;
				}
			}

			return fRetval;
		}

		double getEdgeLength(const B2DPolygon& rCandidate, sal_uInt32 nIndex)
		{
			const sal_uInt32 nPointCount(rCandidate.count());
			OSL_ENSURE(nIndex < nPointCount, "getEdgeLength: Access to polygon out of range (!)");
			double fRetval(0.0);

            if(nPointCount)
            {
                const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);

                if(rCandidate.areControlPointsUsed())
                {
                    B2DCubicBezier aEdge;

                    aEdge.setStartPoint(rCandidate.getB2DPoint(nIndex));
                    aEdge.setControlPointA(rCandidate.getNextControlPoint(nIndex));
                    aEdge.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
                    aEdge.setEndPoint(rCandidate.getB2DPoint(nNextIndex));

                    fRetval = aEdge.getLength();
                }
                else
                {
					const B2DPoint aCurrent(rCandidate.getB2DPoint(nIndex));
					const B2DPoint aNext(rCandidate.getB2DPoint(nNextIndex));

                    fRetval = B2DVector(aNext - aCurrent).getLength();
                }
            }

			return fRetval;
		}

		double getLength(const B2DPolygon& rCandidate)
		{
			double fRetval(0.0);
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount)
			{
                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1L);

                if(rCandidate.areControlPointsUsed())
                {
                    B2DCubicBezier aEdge;
                    aEdge.setStartPoint(rCandidate.getB2DPoint(0));

                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
                    {
                        const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                        aEdge.setControlPointA(rCandidate.getNextControlPoint(a));
                        aEdge.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
                        aEdge.setEndPoint(rCandidate.getB2DPoint(nNextIndex));

                        fRetval += aEdge.getLength();
                        aEdge.setStartPoint(aEdge.getEndPoint());
                    }
                }
                else
                {
                    B2DPoint aCurrent(rCandidate.getB2DPoint(0));

                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
                    {
                        const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                        const B2DPoint aNext(rCandidate.getB2DPoint(nNextIndex));

                        fRetval += B2DVector(aNext - aCurrent).getLength();
                        aCurrent = aNext;
                    }
                }
			}

			return fRetval;
		}

		B2DPoint getPositionAbsolute(const B2DPolygon& rCandidate, double fDistance, double fLength)
		{
			B2DPoint aRetval;
			const sal_uInt32 nPointCount(rCandidate.count());

			if( 1L == nPointCount )
            {
                // only one point (i.e. no edge) - simply take that point
                aRetval = rCandidate.getB2DPoint(0);
            }
			else if(nPointCount > 1L)
			{
                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
				sal_uInt32 nIndex(0L);
				bool bIndexDone(false);

				// get length if not given
				if(fTools::equalZero(fLength))
				{
					fLength = getLength(rCandidate);
				}

				if(fTools::less(fDistance, 0.0))
				{
    				// handle fDistance < 0.0
					if(rCandidate.isClosed())
					{
						// if fDistance < 0.0 increment with multiple of fLength
						sal_uInt32 nCount(sal_uInt32(-fDistance / fLength));
						fDistance += double(nCount + 1L) * fLength;
					}
					else
					{
						// crop to polygon start
						fDistance = 0.0;
						bIndexDone = true;
					}
				}
				else if(fTools::moreOrEqual(fDistance, fLength))
				{
    				// handle fDistance >= fLength
					if(rCandidate.isClosed())
					{
						// if fDistance >= fLength decrement with multiple of fLength
						sal_uInt32 nCount(sal_uInt32(fDistance / fLength));
						fDistance -= (double)(nCount) * fLength;
					}
					else
					{
						// crop to polygon end
						fDistance = 0.0;
						nIndex = nEdgeCount;
						bIndexDone = true;
					}
				}

				// look for correct index. fDistance is now [0.0 .. fLength[
    			double fEdgeLength(getEdgeLength(rCandidate, nIndex));

                while(!bIndexDone)
                {
                    // edge found must be on the half-open range
                    // [0,fEdgeLength).
                    // Note that in theory, we cannot move beyond
                    // the last polygon point, since fDistance>=fLength
                    // is checked above. Unfortunately, with floating-
                    // point calculations, this case might happen.
                    // Handled by nIndex check below
                    if(nIndex < nEdgeCount && fTools::moreOrEqual(fDistance, fEdgeLength))
					{
						// go to next edge
						fDistance -= fEdgeLength;
						fEdgeLength = getEdgeLength(rCandidate, ++nIndex);
					}
					else
					{
						// it's on this edge, stop
						bIndexDone = true;
					}
                }

                // get the point using nIndex
				aRetval = rCandidate.getB2DPoint(nIndex);

				// if fDistance != 0.0, move that length on the edge. The edge
				// length is in fEdgeLength.
				if(!fTools::equalZero(fDistance))
				{
                    if(fTools::moreOrEqual(fDistance, fEdgeLength))
                    {
                        // end point of choosen edge
    			        const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
				        aRetval = rCandidate.getB2DPoint(nNextIndex);
                    }
                    else if(fTools::equalZero(fDistance))
                    {
                        // start point of choosen edge
                        aRetval = aRetval;
                    }
                    else
                    {
                        // inside edge
    			        const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
				        const B2DPoint aNextPoint(rCandidate.getB2DPoint(nNextIndex));
						bool bDone(false);

					    // add calculated average value to the return value
                        if(rCandidate.areControlPointsUsed())
                        {
                            // get as bezier segment
                            const B2DCubicBezier aBezierSegment(
                                aRetval, rCandidate.getNextControlPoint(nIndex),
                                rCandidate.getPrevControlPoint(nNextIndex), aNextPoint);

                            if(aBezierSegment.isBezier())
                            {
                                // use B2DCubicBezierHelper to bridge the non-linear gap between
                                // length and bezier distances
                                const B2DCubicBezierHelper aBezierSegmentHelper(aBezierSegment);
                                const double fBezierDistance(aBezierSegmentHelper.distanceToRelative(fDistance));

                                aRetval = aBezierSegment.interpolatePoint(fBezierDistance);
								bDone = true;
                            }
                        }

						if(!bDone)
                        {
						    const double fRelativeInEdge(fDistance / fEdgeLength);
    					    aRetval = interpolate(aRetval, aNextPoint, fRelativeInEdge);
                        }
                    }
				}
			}

			return aRetval;
		}

		B2DPoint getPositionRelative(const B2DPolygon& rCandidate, double fDistance, double fLength)
		{
			// get length if not given
			if(fTools::equalZero(fLength))
			{
				fLength = getLength(rCandidate);
			}

			// multiply fDistance with real length to get absolute position and
			// use getPositionAbsolute
			return getPositionAbsolute(rCandidate, fDistance * fLength, fLength);
		}

		B2DPolygon getSnippetAbsolute(const B2DPolygon& rCandidate, double fFrom, double fTo, double fLength)
		{
			const sal_uInt32 nPointCount(rCandidate.count());

            if(nPointCount)
            {
			    // get length if not given
			    if(fTools::equalZero(fLength))
			    {
				    fLength = getLength(rCandidate);
			    }

			    // test and correct fFrom
                if(fTools::less(fFrom, 0.0))
			    {
				    fFrom = 0.0;
			    }

			    // test and correct fTo
                if(fTools::more(fTo, fLength))
			    {
				    fTo = fLength;
			    }

			    // test and correct relationship of fFrom, fTo
                if(fTools::more(fFrom, fTo))
			    {
				    fFrom = fTo = (fFrom + fTo) / 2.0;
			    }

                if(fTools::equalZero(fFrom) && fTools::equal(fTo, fLength))
			    {
				    // no change, result is the whole polygon
				    return rCandidate;
			    }
			    else
			    {
                    B2DPolygon aRetval;
                    const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
				    double fPositionOfStart(0.0);
				    bool bStartDone(false);
				    bool bEndDone(false);

				    for(sal_uInt32 a(0L); !(bStartDone && bEndDone) && a < nEdgeCount; a++)
				    {
					    const double fEdgeLength(getEdgeLength(rCandidate, a));

					    if(!bStartDone)
					    {
                            if(fTools::equalZero(fFrom))
						    {
							    aRetval.append(rCandidate.getB2DPoint(a));

                                if(rCandidate.areControlPointsUsed())
                                {
                                    aRetval.setNextControlPoint(aRetval.count() - 1, rCandidate.getNextControlPoint(a));
                                }

							    bStartDone = true;
						    }
                            else if(fTools::moreOrEqual(fFrom, fPositionOfStart) && fTools::less(fFrom, fPositionOfStart + fEdgeLength))
						    {
							    // calculate and add start point
                                if(fTools::equalZero(fEdgeLength))
							    {
								    aRetval.append(rCandidate.getB2DPoint(a));

                                    if(rCandidate.areControlPointsUsed())
                                    {
                                        aRetval.setNextControlPoint(aRetval.count() - 1, rCandidate.getNextControlPoint(a));
                                    }
							    }
                                else
							    {
                                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
					                const B2DPoint aStart(rCandidate.getB2DPoint(a));
					                const B2DPoint aEnd(rCandidate.getB2DPoint(nNextIndex));
									bool bDone(false);

                                    if(rCandidate.areControlPointsUsed())
                                    {
                                        const B2DCubicBezier aBezierSegment(
                                            aStart, rCandidate.getNextControlPoint(a),
                                            rCandidate.getPrevControlPoint(nNextIndex), aEnd);

                                        if(aBezierSegment.isBezier())
                                        {
                                            // use B2DCubicBezierHelper to bridge the non-linear gap between
                                            // length and bezier distances
                                            const B2DCubicBezierHelper aBezierSegmentHelper(aBezierSegment);
                                            const double fBezierDistance(aBezierSegmentHelper.distanceToRelative(fFrom - fPositionOfStart));
                                            B2DCubicBezier aRight;

                                            aBezierSegment.split(fBezierDistance, 0, &aRight);
                                            aRetval.append(aRight.getStartPoint());
                                            aRetval.setNextControlPoint(aRetval.count() - 1, aRight.getControlPointA());
											bDone = true;
                                        }
                                    }

									if(!bDone)
                                    {
	                                    const double fRelValue((fFrom - fPositionOfStart) / fEdgeLength);
    								    aRetval.append(interpolate(aStart, aEnd, fRelValue));
                                    }
							    }

							    bStartDone = true;

							    // if same point, end is done, too.
							    if(fFrom == fTo)
							    {
								    bEndDone = true;
							    }
						    }
					    }

                        if(!bEndDone && fTools::moreOrEqual(fTo, fPositionOfStart) && fTools::less(fTo, fPositionOfStart + fEdgeLength))
					    {
						    // calculate and add end point
                            if(fTools::equalZero(fEdgeLength))
						    {
                                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
							    aRetval.append(rCandidate.getB2DPoint(nNextIndex));

                                if(rCandidate.areControlPointsUsed())
                                {
                                    aRetval.setPrevControlPoint(aRetval.count() - 1, rCandidate.getPrevControlPoint(nNextIndex));
                                }
						    }
                            else
                            {
                                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
				                const B2DPoint aStart(rCandidate.getB2DPoint(a));
				                const B2DPoint aEnd(rCandidate.getB2DPoint(nNextIndex));
								bool bDone(false);

                                if(rCandidate.areControlPointsUsed())
                                {
                                    const B2DCubicBezier aBezierSegment(
                                        aStart, rCandidate.getNextControlPoint(a),
                                        rCandidate.getPrevControlPoint(nNextIndex), aEnd);

                                    if(aBezierSegment.isBezier())
                                    {
                                        // use B2DCubicBezierHelper to bridge the non-linear gap between
                                        // length and bezier distances
                                        const B2DCubicBezierHelper aBezierSegmentHelper(aBezierSegment);
                                        const double fBezierDistance(aBezierSegmentHelper.distanceToRelative(fTo - fPositionOfStart));
                                        B2DCubicBezier aLeft;

                                        aBezierSegment.split(fBezierDistance, &aLeft, 0);
                                        aRetval.append(aLeft.getEndPoint());
                                        aRetval.setPrevControlPoint(aRetval.count() - 1, aLeft.getControlPointB());
										bDone = true;
                                    }
                                }

                                if(!bDone)
                                {
	                                const double fRelValue((fTo - fPositionOfStart) / fEdgeLength);
								    aRetval.append(interpolate(aStart, aEnd, fRelValue));
                                }
						    }

						    bEndDone = true;
					    }

					    if(!bEndDone)
					    {
						    if(bStartDone)
						    {
							    // add segments end point
                                const sal_uInt32 nNextIndex((a + 1) % nPointCount);
							    aRetval.append(rCandidate.getB2DPoint(nNextIndex));

                                if(rCandidate.areControlPointsUsed())
                                {
                                    aRetval.setPrevControlPoint(aRetval.count() - 1, rCandidate.getPrevControlPoint(nNextIndex));
                                    aRetval.setNextControlPoint(aRetval.count() - 1, rCandidate.getNextControlPoint(nNextIndex));
                                }
						    }

						    // increment fPositionOfStart
						    fPositionOfStart += fEdgeLength;
					    }
				    }
    			    return aRetval;
			    }
            }
            else
            {
                return rCandidate;
            }
		}

		B2DPolygon getSnippetRelative(const B2DPolygon& rCandidate, double fFrom, double fTo, double fLength)
		{
			// get length if not given
			if(fTools::equalZero(fLength))
			{
				fLength = getLength(rCandidate);
			}

			// multiply distances with real length to get absolute position and
			// use getSnippetAbsolute
			return getSnippetAbsolute(rCandidate, fFrom * fLength, fTo * fLength, fLength);
		}

		CutFlagValue findCut(
			const B2DPolygon& rCandidate,
			sal_uInt32 nIndex1, sal_uInt32 nIndex2,
			CutFlagValue aCutFlags,
			double* pCut1, double* pCut2)
		{
			CutFlagValue aRetval(CUTFLAG_NONE);
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nIndex1 < nPointCount && nIndex2 < nPointCount && nIndex1 != nIndex2)
			{
				sal_uInt32 nEnd1(getIndexOfSuccessor(nIndex1, rCandidate));
				sal_uInt32 nEnd2(getIndexOfSuccessor(nIndex2, rCandidate));

				const B2DPoint aStart1(rCandidate.getB2DPoint(nIndex1));
				const B2DPoint aEnd1(rCandidate.getB2DPoint(nEnd1));
				const B2DVector aVector1(aEnd1 - aStart1);

				const B2DPoint aStart2(rCandidate.getB2DPoint(nIndex2));
				const B2DPoint aEnd2(rCandidate.getB2DPoint(nEnd2));
				const B2DVector aVector2(aEnd2 - aStart2);

				aRetval = findCut(
					aStart1, aVector1, aStart2, aVector2,
					aCutFlags, pCut1, pCut2);
			}

			return aRetval;
		}

		CutFlagValue findCut(
			const B2DPolygon& rCandidate1, sal_uInt32 nIndex1,
			const B2DPolygon& rCandidate2, sal_uInt32 nIndex2,
			CutFlagValue aCutFlags,
			double* pCut1, double* pCut2)
		{
			CutFlagValue aRetval(CUTFLAG_NONE);
			const sal_uInt32 nPointCount1(rCandidate1.count());
			const sal_uInt32 nPointCount2(rCandidate2.count());

			if(nIndex1 < nPointCount1 && nIndex2 < nPointCount2)
			{
				sal_uInt32 nEnd1(getIndexOfSuccessor(nIndex1, rCandidate1));
				sal_uInt32 nEnd2(getIndexOfSuccessor(nIndex2, rCandidate2));

				const B2DPoint aStart1(rCandidate1.getB2DPoint(nIndex1));
				const B2DPoint aEnd1(rCandidate1.getB2DPoint(nEnd1));
				const B2DVector aVector1(aEnd1 - aStart1);

				const B2DPoint aStart2(rCandidate2.getB2DPoint(nIndex2));
				const B2DPoint aEnd2(rCandidate2.getB2DPoint(nEnd2));
				const B2DVector aVector2(aEnd2 - aStart2);

				aRetval = findCut(
					aStart1, aVector1, aStart2, aVector2,
					aCutFlags, pCut1, pCut2);
			}

			return aRetval;
		}

		CutFlagValue findCut(
			const B2DPoint& rEdge1Start, const B2DVector& rEdge1Delta,
			const B2DPoint& rEdge2Start, const B2DVector& rEdge2Delta,
			CutFlagValue aCutFlags,
			double* pCut1, double* pCut2)
		{
			CutFlagValue aRetval(CUTFLAG_NONE);
			double fCut1(0.0);
			double fCut2(0.0);
			bool bFinished(!((bool)(aCutFlags & CUTFLAG_ALL)));

			// test for same points?
			if(!bFinished
				&& (aCutFlags & (CUTFLAG_START1|CUTFLAG_END1))
				&& (aCutFlags & (CUTFLAG_START2|CUTFLAG_END2)))
			{
				// same startpoint?
				if(!bFinished && (aCutFlags & (CUTFLAG_START1|CUTFLAG_START2)) == (CUTFLAG_START1|CUTFLAG_START2))
				{
					if(rEdge1Start.equal(rEdge2Start))
					{
						bFinished = true;
						aRetval = (CUTFLAG_START1|CUTFLAG_START2);
					}
				}

				// same endpoint?
				if(!bFinished && (aCutFlags & (CUTFLAG_END1|CUTFLAG_END2)) == (CUTFLAG_END1|CUTFLAG_END2))
				{
					const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);
					const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);

					if(aEnd1.equal(aEnd2))
					{
						bFinished = true;
						aRetval = (CUTFLAG_END1|CUTFLAG_END2);
						fCut1 = fCut2 = 1.0;
					}
				}

				// startpoint1 == endpoint2?
				if(!bFinished && (aCutFlags & (CUTFLAG_START1|CUTFLAG_END2)) == (CUTFLAG_START1|CUTFLAG_END2))
				{
					const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);

					if(rEdge1Start.equal(aEnd2))
					{
						bFinished = true;
						aRetval = (CUTFLAG_START1|CUTFLAG_END2);
						fCut1 = 0.0;
						fCut2 = 1.0;
					}
				}

				// startpoint2 == endpoint1?
				if(!bFinished&& (aCutFlags & (CUTFLAG_START2|CUTFLAG_END1)) == (CUTFLAG_START2|CUTFLAG_END1))
				{
					const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);

					if(rEdge2Start.equal(aEnd1))
					{
						bFinished = true;
						aRetval = (CUTFLAG_START2|CUTFLAG_END1);
						fCut1 = 1.0;
						fCut2 = 0.0;
					}
				}
			}

			if(!bFinished && (aCutFlags & CUTFLAG_LINE))
			{
				if(!bFinished && (aCutFlags & CUTFLAG_START1))
				{
					// start1 on line 2 ?
					if(isPointOnEdge(rEdge1Start, rEdge2Start, rEdge2Delta, &fCut2))
					{
						bFinished = true;
						aRetval = (CUTFLAG_LINE|CUTFLAG_START1);
					}
				}

				if(!bFinished && (aCutFlags & CUTFLAG_START2))
				{
					// start2 on line 1 ?
					if(isPointOnEdge(rEdge2Start, rEdge1Start, rEdge1Delta, &fCut1))
					{
						bFinished = true;
						aRetval = (CUTFLAG_LINE|CUTFLAG_START2);
					}
				}

				if(!bFinished && (aCutFlags & CUTFLAG_END1))
				{
					// end1 on line 2 ?
					const B2DPoint aEnd1(rEdge1Start + rEdge1Delta);

					if(isPointOnEdge(aEnd1, rEdge2Start, rEdge2Delta, &fCut2))
					{
						bFinished = true;
						aRetval = (CUTFLAG_LINE|CUTFLAG_END1);
					}
				}

				if(!bFinished && (aCutFlags & CUTFLAG_END2))
				{
					// end2 on line 1 ?
					const B2DPoint aEnd2(rEdge2Start + rEdge2Delta);

					if(isPointOnEdge(aEnd2, rEdge1Start, rEdge1Delta, &fCut1))
					{
						bFinished = true;
						aRetval = (CUTFLAG_LINE|CUTFLAG_END2);
					}
				}

				if(!bFinished)
				{
					// cut in line1, line2 ?
					fCut1 = (rEdge1Delta.getX() * rEdge2Delta.getY()) - (rEdge1Delta.getY() * rEdge2Delta.getX());

					if(!fTools::equalZero(fCut1))
					{
						fCut1 = (rEdge2Delta.getY() * (rEdge2Start.getX() - rEdge1Start.getX())
							+ rEdge2Delta.getX() * (rEdge1Start.getY() - rEdge2Start.getY())) / fCut1;

						const double fZero(0.0);
						const double fOne(1.0);

						// inside parameter range edge1 AND fCut2 is calcable
						if(fTools::more(fCut1, fZero) && fTools::less(fCut1, fOne)
							&& (!fTools::equalZero(rEdge2Delta.getX()) || !fTools::equalZero(rEdge2Delta.getY())))
						{
							// take the mopre precise calculation of the two possible
							if(fabs(rEdge2Delta.getX()) > fabs(rEdge2Delta.getY()))
							{
								fCut2 = (rEdge1Start.getX() + fCut1
									* rEdge1Delta.getX() - rEdge2Start.getX()) / rEdge2Delta.getX();
							}
							else
							{
								fCut2 = (rEdge1Start.getY() + fCut1
									* rEdge1Delta.getY() - rEdge2Start.getY()) / rEdge2Delta.getY();
							}

							// inside parameter range edge2, too
							if(fTools::more(fCut2, fZero) && fTools::less(fCut2, fOne))
							{
								bFinished = true;
								aRetval = CUTFLAG_LINE;
							}
						}
					}
				}
			}

			// copy values if wanted
			if(pCut1)
			{
				*pCut1 = fCut1;
			}

			if(pCut2)
			{
				*pCut2 = fCut2;
			}

			return aRetval;
		}

		bool isPointOnEdge(
			const B2DPoint& rPoint,
			const B2DPoint& rEdgeStart,
			const B2DVector& rEdgeDelta,
			double* pCut)
		{
			bool bDeltaXIsZero(fTools::equalZero(rEdgeDelta.getX()));
			bool bDeltaYIsZero(fTools::equalZero(rEdgeDelta.getY()));
			const double fZero(0.0);
			const double fOne(1.0);

			if(bDeltaXIsZero && bDeltaYIsZero)
			{
				// no line, just a point
				return false;
			}
			else if(bDeltaXIsZero)
			{
				// vertical line
				if(fTools::equal(rPoint.getX(), rEdgeStart.getX()))
				{
					double fValue = (rPoint.getY() - rEdgeStart.getY()) / rEdgeDelta.getY();

					if(fTools::more(fValue, fZero) && fTools::less(fValue, fOne))
					{
						if(pCut)
						{
							*pCut = fValue;
						}

						return true;
					}
				}
			}
			else if(bDeltaYIsZero)
			{
				// horizontal line
				if(fTools::equal(rPoint.getY(), rEdgeStart.getY()))
				{
					double fValue = (rPoint.getX() - rEdgeStart.getX()) / rEdgeDelta.getX();

					if(fTools::more(fValue, fZero) && fTools::less(fValue, fOne))
					{
						if(pCut)
						{
							*pCut = fValue;
						}

						return true;
					}
				}
			}
			else
			{
				// any angle line
				double fTOne = (rPoint.getX() - rEdgeStart.getX()) / rEdgeDelta.getX();
				double fTTwo = (rPoint.getY() - rEdgeStart.getY()) / rEdgeDelta.getY();

				if(fTools::equal(fTOne, fTTwo))
				{
					// same parameter representation, point is on line. Take
					// middle value for better results
					double fValue = (fTOne + fTTwo) / 2.0;

					if(fTools::more(fValue, fZero) && fTools::less(fValue, fOne))
					{
						// point is inside line bounds, too
						if(pCut)
						{
							*pCut = fValue;
						}

						return true;
					}
				}
			}

			return false;
		}

		void applyLineDashing(const B2DPolygon& rCandidate, const ::std::vector<double>& rDotDashArray, B2DPolyPolygon* pLineTarget, B2DPolyPolygon* pGapTarget, double fDotDashLength)
        {
            const sal_uInt32 nPointCount(rCandidate.count());
            const sal_uInt32 nDotDashCount(rDotDashArray.size());

			if(fTools::lessOrEqual(fDotDashLength, 0.0))
            {
                fDotDashLength = ::std::accumulate(rDotDashArray.begin(), rDotDashArray.end(), 0.0);
            }

			if(fTools::more(fDotDashLength, 0.0) && (pLineTarget || pGapTarget) && nPointCount)
            {
				// clear targets
				if(pLineTarget)
				{
					pLineTarget->clear();
				}

				if(pGapTarget)
				{
					pGapTarget->clear();
				}

                // prepare current edge's start
				B2DCubicBezier aCurrentEdge;
                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
                aCurrentEdge.setStartPoint(rCandidate.getB2DPoint(0));

                // prepare DotDashArray iteration and the line/gap switching bool
                sal_uInt32 nDotDashIndex(0);
                bool bIsLine(true);
                double fDotDashMovingLength(rDotDashArray[0]);
				B2DPolygon aSnippet;

				// iterate over all edges
                for(sal_uInt32 a(0); a < nEdgeCount; a++)
                {
                    // update current edge (fill in C1, C2 and end point)
					double fLastDotDashMovingLength(0.0);
                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                    aCurrentEdge.setControlPointA(rCandidate.getNextControlPoint(a));
                    aCurrentEdge.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
                    aCurrentEdge.setEndPoint(rCandidate.getB2DPoint(nNextIndex));

					// check if we have a trivial bezier segment -> possible fallback to edge
					aCurrentEdge.testAndSolveTrivialBezier();

					if(aCurrentEdge.isBezier())
					{
						// bezier segment
						const B2DCubicBezierHelper aCubicBezierHelper(aCurrentEdge);
						const double fEdgeLength(aCubicBezierHelper.getLength());

						if(!fTools::equalZero(fEdgeLength))
						{
							while(fTools::less(fDotDashMovingLength, fEdgeLength))
							{
								// new split is inside edge, create and append snippet [fLastDotDashMovingLength, fDotDashMovingLength]
								const bool bHandleLine(bIsLine && pLineTarget);
								const bool bHandleGap(!bIsLine && pGapTarget);

								if(bHandleLine || bHandleGap)
								{
									const double fBezierSplitStart(aCubicBezierHelper.distanceToRelative(fLastDotDashMovingLength));
									const double fBezierSplitEnd(aCubicBezierHelper.distanceToRelative(fDotDashMovingLength));
									B2DCubicBezier aBezierSnippet(aCurrentEdge.snippet(fBezierSplitStart, fBezierSplitEnd));

									if(!aSnippet.count())
									{
										aSnippet.append(aBezierSnippet.getStartPoint());
									}

									aSnippet.appendBezierSegment(aBezierSnippet.getControlPointA(), aBezierSnippet.getControlPointB(), aBezierSnippet.getEndPoint());

									if(bHandleLine)
									{
										pLineTarget->append(aSnippet);
									}
									else
									{
										pGapTarget->append(aSnippet);
									}

									aSnippet.clear();
								}

								// prepare next DotDashArray step and flip line/gap flag
								fLastDotDashMovingLength = fDotDashMovingLength;
								fDotDashMovingLength += rDotDashArray[(++nDotDashIndex) % nDotDashCount];
								bIsLine = !bIsLine;
							}

							// append closing snippet [fLastDotDashMovingLength, fEdgeLength]
							const bool bHandleLine(bIsLine && pLineTarget);
							const bool bHandleGap(!bIsLine && pGapTarget);

							if(bHandleLine || bHandleGap)
							{
								B2DCubicBezier aRight;
								const double fBezierSplit(aCubicBezierHelper.distanceToRelative(fLastDotDashMovingLength));

								aCurrentEdge.split(fBezierSplit, 0, &aRight);

								if(!aSnippet.count())
								{
									aSnippet.append(aRight.getStartPoint());
								}

								aSnippet.appendBezierSegment(aRight.getControlPointA(), aRight.getControlPointB(), aRight.getEndPoint());
							}

							// prepare move to next edge
							fDotDashMovingLength -= fEdgeLength;
						}
					}
					else
					{
						// simple edge
						const double fEdgeLength(aCurrentEdge.getEdgeLength());

						if(!fTools::equalZero(fEdgeLength))
						{
							while(fTools::less(fDotDashMovingLength, fEdgeLength))
							{
								// new split is inside edge, create and append snippet [fLastDotDashMovingLength, fDotDashMovingLength]
								const bool bHandleLine(bIsLine && pLineTarget);
								const bool bHandleGap(!bIsLine && pGapTarget);

								if(bHandleLine || bHandleGap)
								{
									if(!aSnippet.count())
									{
										aSnippet.append(interpolate(aCurrentEdge.getStartPoint(), aCurrentEdge.getEndPoint(), fLastDotDashMovingLength / fEdgeLength));
									}

									aSnippet.append(interpolate(aCurrentEdge.getStartPoint(), aCurrentEdge.getEndPoint(), fDotDashMovingLength / fEdgeLength));

									if(bHandleLine)
									{
										pLineTarget->append(aSnippet);
									}
									else
									{
										pGapTarget->append(aSnippet);
									}

									aSnippet.clear();
								}

								// prepare next DotDashArray step and flip line/gap flag
								fLastDotDashMovingLength = fDotDashMovingLength;
								fDotDashMovingLength += rDotDashArray[(++nDotDashIndex) % nDotDashCount];
								bIsLine = !bIsLine;
							}

							// append snippet [fLastDotDashMovingLength, fEdgeLength]
							const bool bHandleLine(bIsLine && pLineTarget);
							const bool bHandleGap(!bIsLine && pGapTarget);

							if(bHandleLine || bHandleGap)
							{
								if(!aSnippet.count())
								{
									aSnippet.append(interpolate(aCurrentEdge.getStartPoint(), aCurrentEdge.getEndPoint(), fLastDotDashMovingLength / fEdgeLength));
								}

								aSnippet.append(aCurrentEdge.getEndPoint());
							}

							// prepare move to next edge
							fDotDashMovingLength -= fEdgeLength;
						}
					}

					// prepare next edge step (end point gets new start point)
                    aCurrentEdge.setStartPoint(aCurrentEdge.getEndPoint());
                }

                // append last intermediate results (if exists)
                if(aSnippet.count())
                {
                    if(bIsLine && pLineTarget)
                    {
                        pLineTarget->append(aSnippet);
                    }
                    else if(!bIsLine && pGapTarget)
                    {
                        pGapTarget->append(aSnippet);
                    }
                }

				// check if start and end polygon may be merged
				if(pLineTarget)
				{
					const sal_uInt32 nCount(pLineTarget->count());

					if(nCount > 1)
					{
						// these polygons were created above, there exists none with less than two points,
						// thus dircet point access below is allowed
						const B2DPolygon aFirst(pLineTarget->getB2DPolygon(0));
						B2DPolygon aLast(pLineTarget->getB2DPolygon(nCount - 1));

						if(aFirst.getB2DPoint(0).equal(aLast.getB2DPoint(aLast.count() - 1)))
						{
							// start of first and end of last are the same -> merge them
							aLast.append(aFirst);
							aLast.removeDoublePoints();
							pLineTarget->setB2DPolygon(0, aLast);
							pLineTarget->remove(nCount - 1);
						}
					}
				}

				if(pGapTarget)
				{
					const sal_uInt32 nCount(pGapTarget->count());

					if(nCount > 1)
					{
						// these polygons were created above, there exists none with less than two points,
						// thus dircet point access below is allowed
						const B2DPolygon aFirst(pGapTarget->getB2DPolygon(0));
						B2DPolygon aLast(pGapTarget->getB2DPolygon(nCount - 1));

						if(aFirst.getB2DPoint(0).equal(aLast.getB2DPoint(aLast.count() - 1)))
						{
							// start of first and end of last are the same -> merge them
							aLast.append(aFirst);
							aLast.removeDoublePoints();
							pGapTarget->setB2DPolygon(0, aLast);
							pGapTarget->remove(nCount - 1);
						}
					}
				}
            }
            else
            {
				// parameters make no sense, just add source to targets
                if(pLineTarget)
                {
                    pLineTarget->append(rCandidate);
                }

				if(pGapTarget)
				{
                    pGapTarget->append(rCandidate);
				}
            }
		}

		// test if point is inside epsilon-range around an edge defined
		// by the two given points. Can be used for HitTesting. The epsilon-range
		// is defined to be the rectangle centered to the given edge, using height
		// 2 x fDistance, and the circle around both points with radius fDistance.
		bool isInEpsilonRange(const B2DPoint& rEdgeStart, const B2DPoint& rEdgeEnd, const B2DPoint& rTestPosition, double fDistance)
		{
			// build edge vector
			const B2DVector aEdge(rEdgeEnd - rEdgeStart);
			bool bDoDistanceTestStart(false);
			bool bDoDistanceTestEnd(false);

			if(aEdge.equalZero())
			{
				// no edge, just a point. Do one of the distance tests.
				bDoDistanceTestStart = true;
			}
			else
			{
				// edge has a length. Create perpendicular vector.
				const B2DVector aPerpend(getPerpendicular(aEdge));
				double fCut(
					(aPerpend.getY() * (rTestPosition.getX() - rEdgeStart.getX())
					+ aPerpend.getX() * (rEdgeStart.getY() - rTestPosition.getY())) /
					(aEdge.getX() * aEdge.getX() + aEdge.getY() * aEdge.getY()));
				const double fZero(0.0);
				const double fOne(1.0);

				if(fTools::less(fCut, fZero))
				{
					// left of rEdgeStart
					bDoDistanceTestStart = true;
				}
				else if(fTools::more(fCut, fOne))
				{
					// right of rEdgeEnd
					bDoDistanceTestEnd = true;
				}
				else
				{
					// inside line [0.0 .. 1.0]
					const B2DPoint aCutPoint(interpolate(rEdgeStart, rEdgeEnd, fCut));
    			    const B2DVector aDelta(rTestPosition - aCutPoint);
					const double fDistanceSquare(aDelta.scalar(aDelta));

					if(fDistanceSquare <= fDistance * fDistance)
					{
						return true;
					}
					else
					{
						return false;
					}
				}
			}

			if(bDoDistanceTestStart)
			{
			    const B2DVector aDelta(rTestPosition - rEdgeStart);
				const double fDistanceSquare(aDelta.scalar(aDelta));

				if(fDistanceSquare <= fDistance * fDistance)
				{
					return true;
				}
			}
			else if(bDoDistanceTestEnd)
			{
			    const B2DVector aDelta(rTestPosition - rEdgeEnd);
				const double fDistanceSquare(aDelta.scalar(aDelta));

				if(fDistanceSquare <= fDistance * fDistance)
				{
					return true;
				}
			}

			return false;
		}

		// test if point is inside epsilon-range around the given Polygon. Can be used
		// for HitTesting. The epsilon-range is defined to be the tube around the polygon
		// with distance fDistance and rounded edges (start and end point).
		bool isInEpsilonRange(const B2DPolygon& rCandidate, const B2DPoint& rTestPosition, double fDistance)
		{
			// force to non-bezier polygon
			const B2DPolygon aCandidate(rCandidate.getDefaultAdaptiveSubdivision());
			const sal_uInt32 nPointCount(aCandidate.count());

			if(nPointCount)
			{
                const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1L);
				B2DPoint aCurrent(aCandidate.getB2DPoint(0));

				if(nEdgeCount)
				{
					// edges
					for(sal_uInt32 a(0); a < nEdgeCount; a++)
					{
						const sal_uInt32 nNextIndex((a + 1) % nPointCount);
						const B2DPoint aNext(aCandidate.getB2DPoint(nNextIndex));

						if(isInEpsilonRange(aCurrent, aNext, rTestPosition, fDistance))
						{
							return true;
						}

						// prepare next step
						aCurrent = aNext;
					}
				}
				else
				{
					// no edges, but points -> not closed. Check single point. Just
					// use isInEpsilonRange with twice the same point, it handles those well
					if(isInEpsilonRange(aCurrent, aCurrent, rTestPosition, fDistance))
					{
						return true;
					}
				}
			}

			return false;
		}

        B2DPolygon createPolygonFromRect( const B2DRectangle& rRect, double fRadius )
        {
			const double fZero(0.0);
			const double fOne(1.0);

			if(fTools::lessOrEqual(fRadius, fZero))
			{
				// no radius, use rectangle
				return createPolygonFromRect( rRect );
			}
			else if(fTools::moreOrEqual(fRadius, fOne))
			{
				// full radius, use ellipse
				const B2DPoint aCenter(rRect.getCenter());
				const double fRadiusX(rRect.getWidth() / 2.0);
				const double fRadiusY(rRect.getHeight() / 2.0);

				return createPolygonFromEllipse( aCenter, fRadiusX, fRadiusY );
			}
			else
			{
				// create rectangle with two radii between ]0.0 .. 1.0[
				return createPolygonFromRect( rRect, fRadius, fRadius );
			}
		}

        B2DPolygon createPolygonFromRect( const B2DRectangle& rRect, double fRadiusX, double fRadiusY )
        {
			const double fZero(0.0);
			const double fOne(1.0);

			// crop to useful values
			if(fTools::less(fRadiusX, fZero))
			{
				fRadiusX = fZero;
			}
			else if(fTools::more(fRadiusX, fOne))
			{
				fRadiusX = fOne;
			}

			if(fTools::less(fRadiusY, fZero))
			{
				fRadiusY = fZero;
			}
			else if(fTools::more(fRadiusY, fOne))
			{
				fRadiusY = fOne;
			}

			if(fZero == fRadiusX || fZero == fRadiusY)
			{
				B2DPolygon aRetval;

				// at least in one direction no radius, use rectangle.
				// Do not use createPolygonFromRect() here since original
				// creator (historical reasons) still creates a start point at the
				// bottom center, so do the same here to get the same line patterns.
				// Due to this the order of points is different, too.
				const B2DPoint aBottomCenter(rRect.getCenter().getX(), rRect.getMaxY());
				aRetval.append(aBottomCenter);

				aRetval.append( B2DPoint( rRect.getMinX(), rRect.getMaxY() ) );
				aRetval.append( B2DPoint( rRect.getMinX(), rRect.getMinY() ) );
				aRetval.append( B2DPoint( rRect.getMaxX(), rRect.getMinY() ) );
				aRetval.append( B2DPoint( rRect.getMaxX(), rRect.getMaxY() ) );

				// close
				aRetval.setClosed( true );

				return aRetval;
			}
			else if(fOne == fRadiusX && fOne == fRadiusY)
			{
				// in both directions full radius, use ellipse
				const B2DPoint aCenter(rRect.getCenter());
				const double fRectRadiusX(rRect.getWidth() / 2.0);
				const double fRectRadiusY(rRect.getHeight() / 2.0);

				return createPolygonFromEllipse( aCenter, fRectRadiusX, fRectRadiusY );
			}
			else
			{
				B2DPolygon aRetval;
				const double fBowX((rRect.getWidth() / 2.0) * fRadiusX);
				const double fBowY((rRect.getHeight() / 2.0) * fRadiusY);
	            const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0);

				// create start point at bottom center
				if(fOne != fRadiusX)
				{
					const B2DPoint aBottomCenter(rRect.getCenter().getX(), rRect.getMaxY());
					aRetval.append(aBottomCenter);
				}

				// create first bow
				{
					const B2DPoint aBottomRight(rRect.getMaxX(), rRect.getMaxY());
					const B2DPoint aStart(aBottomRight + B2DPoint(-fBowX, 0.0));
					const B2DPoint aStop(aBottomRight + B2DPoint(0.0, -fBowY));
					aRetval.append(aStart);
					aRetval.appendBezierSegment(interpolate(aStart, aBottomRight, fKappa), interpolate(aStop, aBottomRight, fKappa), aStop);
				}

				// create second bow
				{
					const B2DPoint aTopRight(rRect.getMaxX(), rRect.getMinY());
					const B2DPoint aStart(aTopRight + B2DPoint(0.0, fBowY));
					const B2DPoint aStop(aTopRight + B2DPoint(-fBowX, 0.0));
					aRetval.append(aStart);
					aRetval.appendBezierSegment(interpolate(aStart, aTopRight, fKappa), interpolate(aStop, aTopRight, fKappa), aStop);
				}

				// create third bow
				{
					const B2DPoint aTopLeft(rRect.getMinX(), rRect.getMinY());
					const B2DPoint aStart(aTopLeft + B2DPoint(fBowX, 0.0));
					const B2DPoint aStop(aTopLeft + B2DPoint(0.0, fBowY));
					aRetval.append(aStart);
					aRetval.appendBezierSegment(interpolate(aStart, aTopLeft, fKappa), interpolate(aStop, aTopLeft, fKappa), aStop);
				}

				// create forth bow
				{
					const B2DPoint aBottomLeft(rRect.getMinX(), rRect.getMaxY());
					const B2DPoint aStart(aBottomLeft + B2DPoint(0.0, -fBowY));
					const B2DPoint aStop(aBottomLeft + B2DPoint(fBowX, 0.0));
					aRetval.append(aStart);
					aRetval.appendBezierSegment(interpolate(aStart, aBottomLeft, fKappa), interpolate(aStop, aBottomLeft, fKappa), aStop);
				}

				// close
	            aRetval.setClosed( true );

				// remove double created points if there are extreme radii envolved
				if(fOne == fRadiusX || fOne == fRadiusY)
				{
					aRetval.removeDoublePoints();
				}

				return aRetval;
			}
		}

        B2DPolygon createPolygonFromRect( const B2DRectangle& rRect )
        {
            B2DPolygon aRetval;

            aRetval.append( B2DPoint( rRect.getMinX(), rRect.getMinY() ) );
            aRetval.append( B2DPoint( rRect.getMaxX(), rRect.getMinY() ) );
            aRetval.append( B2DPoint( rRect.getMaxX(), rRect.getMaxY() ) );
            aRetval.append( B2DPoint( rRect.getMinX(), rRect.getMaxY() ) );

			// close
			aRetval.setClosed( true );

            return aRetval;
        }

        B2DPolygon createUnitPolygon()
        {
            static B2DPolygon aRetval;

            if(!aRetval.count())
            {
                aRetval.append( B2DPoint( 0.0, 0.0 ) );
                aRetval.append( B2DPoint( 1.0, 0.0 ) );
                aRetval.append( B2DPoint( 1.0, 1.0 ) );
                aRetval.append( B2DPoint( 0.0, 1.0 ) );

			    // close
			    aRetval.setClosed( true );
            }

            return aRetval;
        }

        B2DPolygon createPolygonFromCircle( const B2DPoint& rCenter, double fRadius )
        {
            return createPolygonFromEllipse( rCenter, fRadius, fRadius );
        }

        B2DPolygon impCreateUnitCircle(sal_uInt32 nStartQuadrant)
        {
            B2DPolygon aUnitCircle;
	        const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0);
            const double fScaledKappa(fKappa * (1.0 / STEPSPERQUARTER));
            const B2DHomMatrix aRotateMatrix(createRotateB2DHomMatrix(F_PI2 / STEPSPERQUARTER));

            B2DPoint aPoint(1.0, 0.0);
            B2DPoint aForward(1.0, fScaledKappa);
            B2DPoint aBackward(1.0, -fScaledKappa);

            if(0 != nStartQuadrant)
            {
                const B2DHomMatrix aQuadrantMatrix(createRotateB2DHomMatrix(F_PI2 * (nStartQuadrant % 4)));
                aPoint *= aQuadrantMatrix;
                aBackward *= aQuadrantMatrix;
                aForward *= aQuadrantMatrix;
            }

            aUnitCircle.append(aPoint);

            for(sal_uInt32 a(0); a < STEPSPERQUARTER * 4; a++)
            {
                aPoint *= aRotateMatrix;
                aBackward *= aRotateMatrix;
                aUnitCircle.appendBezierSegment(aForward, aBackward, aPoint);
                aForward *= aRotateMatrix;
            }

            aUnitCircle.setClosed(true);
		    aUnitCircle.removeDoublePoints();

            return aUnitCircle;
        }

        B2DPolygon createPolygonFromUnitCircle(sal_uInt32 nStartQuadrant)
		{
            switch(nStartQuadrant % 4)
            {
                case 1 :
                {
        			static B2DPolygon aUnitCircleStartQuadrantOne;

                    if(!aUnitCircleStartQuadrantOne.count())
                    {
    		            ::osl::Mutex m_mutex;
                        aUnitCircleStartQuadrantOne = impCreateUnitCircle(1);
                    }

                    return aUnitCircleStartQuadrantOne;
                }
                case 2 :
                {
        			static B2DPolygon aUnitCircleStartQuadrantTwo;

                    if(!aUnitCircleStartQuadrantTwo.count())
                    {
    		            ::osl::Mutex m_mutex;
                        aUnitCircleStartQuadrantTwo = impCreateUnitCircle(2);
                    }

                    return aUnitCircleStartQuadrantTwo;
                }
                case 3 :
                {
        			static B2DPolygon aUnitCircleStartQuadrantThree;

                    if(!aUnitCircleStartQuadrantThree.count())
                    {
    		            ::osl::Mutex m_mutex;
                        aUnitCircleStartQuadrantThree = impCreateUnitCircle(3);
                    }

                    return aUnitCircleStartQuadrantThree;
                }
                default : // case 0 :
                {
        			static B2DPolygon aUnitCircleStartQuadrantZero;

                    if(!aUnitCircleStartQuadrantZero.count())
                    {
    		            ::osl::Mutex m_mutex;
                        aUnitCircleStartQuadrantZero = impCreateUnitCircle(0);
                    }

                    return aUnitCircleStartQuadrantZero;
                }
            }
		}

        B2DPolygon createPolygonFromEllipse( const B2DPoint& rCenter, double fRadiusX, double fRadiusY )
        {
			B2DPolygon aRetval(createPolygonFromUnitCircle());
			const B2DHomMatrix aMatrix(createScaleTranslateB2DHomMatrix(fRadiusX, fRadiusY, rCenter.getX(), rCenter.getY()));

			aRetval.transform(aMatrix);

            return aRetval;
        }

        B2DPolygon createPolygonFromUnitEllipseSegment( double fStart, double fEnd )
		{
	        B2DPolygon aRetval;

			// truncate fStart, fEnd to a range of [0.0 .. F_2PI[ where F_2PI
			// falls back to 0.0 to ensure a unique definition
			if(fTools::less(fStart, 0.0))
			{
				fStart = 0.0;
			}

			if(fTools::moreOrEqual(fStart, F_2PI))
			{
				fStart = 0.0;
			}

			if(fTools::less(fEnd, 0.0))
			{
				fEnd = 0.0;
			}

			if(fTools::moreOrEqual(fEnd, F_2PI))
			{
				fEnd = 0.0;
			}

		    if(fTools::equal(fStart, fEnd))
            {
                // same start and end angle, add single point
                aRetval.append(B2DPoint(cos(fStart), sin(fStart)));
            }
            else
            {
                const sal_uInt32 nSegments(STEPSPERQUARTER * 4);
                const double fAnglePerSegment(F_PI2 / STEPSPERQUARTER);
                const sal_uInt32 nStartSegment(sal_uInt32(fStart / fAnglePerSegment) % nSegments);
                const sal_uInt32 nEndSegment(sal_uInt32(fEnd / fAnglePerSegment) % nSegments);
    	        const double fKappa((M_SQRT2 - 1.0) * 4.0 / 3.0);
                const double fScaledKappa(fKappa * (1.0 / STEPSPERQUARTER));

                B2DPoint aSegStart(cos(fStart), sin(fStart));
                aRetval.append(aSegStart);

                if(nStartSegment == nEndSegment && fTools::more(fEnd, fStart))
                {
                    // start and end in one sector and in the right order, create in one segment
                    const B2DPoint aSegEnd(cos(fEnd), sin(fEnd));
                    const double fFactor(fScaledKappa * ((fEnd - fStart) / fAnglePerSegment));

                    aRetval.appendBezierSegment(
                        aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fFactor),
                        aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fFactor),
                        aSegEnd);
                }
                else
                {
                    double fSegEndRad((nStartSegment + 1) * fAnglePerSegment);
                    double fFactor(fScaledKappa * ((fSegEndRad - fStart) / fAnglePerSegment));
                    B2DPoint aSegEnd(cos(fSegEndRad), sin(fSegEndRad));

                    aRetval.appendBezierSegment(
                        aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fFactor),
                        aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fFactor),
                        aSegEnd);

                    sal_uInt32 nSegment((nStartSegment + 1) % nSegments);
                    aSegStart = aSegEnd;

                    while(nSegment != nEndSegment)
                    {
                        // No end in this sector, add full sector.
                        fSegEndRad = (nSegment + 1) * fAnglePerSegment;
                        aSegEnd = B2DPoint(cos(fSegEndRad), sin(fSegEndRad));

				        aRetval.appendBezierSegment(
                            aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fScaledKappa),
                            aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fScaledKappa),
                            aSegEnd);

                        nSegment = (nSegment + 1) % nSegments;
                        aSegStart = aSegEnd;
                    }

                    // End in this sector
                    const double fSegStartRad(nSegment * fAnglePerSegment);
                    fFactor = fScaledKappa * ((fEnd - fSegStartRad) / fAnglePerSegment);
                    aSegEnd = B2DPoint(cos(fEnd), sin(fEnd));

                    aRetval.appendBezierSegment(
                        aSegStart + (B2DPoint(-aSegStart.getY(), aSegStart.getX()) * fFactor),
                        aSegEnd - (B2DPoint(-aSegEnd.getY(), aSegEnd.getX()) * fFactor),
                        aSegEnd);
                }
            }

			// remove double points between segments created by segmented creation
			aRetval.removeDoublePoints();

			return aRetval;
		}

        B2DPolygon createPolygonFromEllipseSegment( const B2DPoint& rCenter, double fRadiusX, double fRadiusY, double fStart, double fEnd )
		{
	        B2DPolygon aRetval(createPolygonFromUnitEllipseSegment(fStart, fEnd));
			const B2DHomMatrix aMatrix(createScaleTranslateB2DHomMatrix(fRadiusX, fRadiusY, rCenter.getX(), rCenter.getY()));

			aRetval.transform(aMatrix);

			return aRetval;
		}

		bool hasNeutralPoints(const B2DPolygon& rCandidate)
		{
			OSL_ENSURE(!rCandidate.areControlPointsUsed(), "hasNeutralPoints: ATM works not for curves (!)");
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount > 2L)
			{
				B2DPoint aPrevPoint(rCandidate.getB2DPoint(nPointCount - 1L));
				B2DPoint aCurrPoint(rCandidate.getB2DPoint(0L));

				for(sal_uInt32 a(0L); a < nPointCount; a++)
				{
					const B2DPoint aNextPoint(rCandidate.getB2DPoint((a + 1) % nPointCount));
					const B2DVector aPrevVec(aPrevPoint - aCurrPoint);
					const B2DVector aNextVec(aNextPoint - aCurrPoint);
					const B2VectorOrientation aOrientation(getOrientation(aNextVec, aPrevVec));

					if(ORIENTATION_NEUTRAL == aOrientation)
					{
						// current has neutral orientation
						return true;
					}
					else
					{
						// prepare next
						aPrevPoint = aCurrPoint;
						aCurrPoint = aNextPoint;
					}
				}
			}

			return false;
		}

		B2DPolygon removeNeutralPoints(const B2DPolygon& rCandidate)
		{
			if(hasNeutralPoints(rCandidate))
			{
				const sal_uInt32 nPointCount(rCandidate.count());
				B2DPolygon aRetval;
				B2DPoint aPrevPoint(rCandidate.getB2DPoint(nPointCount - 1L));
				B2DPoint aCurrPoint(rCandidate.getB2DPoint(0L));

				for(sal_uInt32 a(0L); a < nPointCount; a++)
				{
					const B2DPoint aNextPoint(rCandidate.getB2DPoint((a + 1) % nPointCount));
					const B2DVector aPrevVec(aPrevPoint - aCurrPoint);
					const B2DVector aNextVec(aNextPoint - aCurrPoint);
					const B2VectorOrientation aOrientation(getOrientation(aNextVec, aPrevVec));

					if(ORIENTATION_NEUTRAL == aOrientation)
					{
						// current has neutral orientation, leave it out and prepare next
						aCurrPoint = aNextPoint;
					}
					else
					{
						// add current point
						aRetval.append(aCurrPoint);

						// prepare next
						aPrevPoint = aCurrPoint;
						aCurrPoint = aNextPoint;
					}
				}

				while(aRetval.count() && ORIENTATION_NEUTRAL == getOrientationForIndex(aRetval, 0L))
				{
					aRetval.remove(0L);
				}

				// copy closed state
				aRetval.setClosed(rCandidate.isClosed());

				return aRetval;
			}
			else
			{
				return rCandidate;
			}
		}

		bool isConvex(const B2DPolygon& rCandidate)
		{
			OSL_ENSURE(!rCandidate.areControlPointsUsed(), "isConvex: ATM works not for curves (!)");
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount > 2L)
			{
				const B2DPoint aPrevPoint(rCandidate.getB2DPoint(nPointCount - 1L));
				B2DPoint aCurrPoint(rCandidate.getB2DPoint(0L));
				B2DVector aCurrVec(aPrevPoint - aCurrPoint);
				B2VectorOrientation aOrientation(ORIENTATION_NEUTRAL);

				for(sal_uInt32 a(0L); a < nPointCount; a++)
				{
					const B2DPoint aNextPoint(rCandidate.getB2DPoint((a + 1) % nPointCount));
					const B2DVector aNextVec(aNextPoint - aCurrPoint);
					const B2VectorOrientation aCurrentOrientation(getOrientation(aNextVec, aCurrVec));

					if(ORIENTATION_NEUTRAL == aOrientation)
					{
						// set start value, maybe neutral again
						aOrientation = aCurrentOrientation;
					}
					else
					{
						if(ORIENTATION_NEUTRAL != aCurrentOrientation && aCurrentOrientation != aOrientation)
						{
							// different orientations found, that's it
							return false;
						}
					}

					// prepare next
					aCurrPoint = aNextPoint;
					aCurrVec = -aNextVec;
				}
			}

			return true;
		}

		B2VectorOrientation getOrientationForIndex(const B2DPolygon& rCandidate, sal_uInt32 nIndex)
		{
			OSL_ENSURE(nIndex < rCandidate.count(), "getOrientationForIndex: index out of range (!)");
			const B2DPoint aPrev(rCandidate.getB2DPoint(getIndexOfPredecessor(nIndex, rCandidate)));
			const B2DPoint aCurr(rCandidate.getB2DPoint(nIndex));
			const B2DPoint aNext(rCandidate.getB2DPoint(getIndexOfSuccessor(nIndex, rCandidate)));
			const B2DVector aBack(aPrev - aCurr);
			const B2DVector aForw(aNext - aCurr);

			return getOrientation(aForw, aBack);
		}

		bool isPointOnLine(const B2DPoint& rStart, const B2DPoint& rEnd, const B2DPoint& rCandidate, bool bWithPoints)
		{
			if(rCandidate.equal(rStart) || rCandidate.equal(rEnd))
			{
				// candidate is in epsilon around start or end -> inside
				return bWithPoints;
			}
			else if(rStart.equal(rEnd))
			{
				// start and end are equal, but candidate is outside their epsilon -> outside
				return false;
			}
			else
			{
				const B2DVector aEdgeVector(rEnd - rStart);
				const B2DVector aTestVector(rCandidate - rStart);

				if(areParallel(aEdgeVector, aTestVector))
				{
					const double fZero(0.0);
					const double fOne(1.0);
					const double fParamTestOnCurr(fabs(aEdgeVector.getX()) > fabs(aEdgeVector.getY())
						? aTestVector.getX() / aEdgeVector.getX()
						: aTestVector.getY() / aEdgeVector.getY());

					if(fTools::more(fParamTestOnCurr, fZero) && fTools::less(fParamTestOnCurr, fOne))
					{
						return true;
					}
				}

				return false;
			}
		}

		bool isPointOnPolygon(const B2DPolygon& rCandidate, const B2DPoint& rPoint, bool bWithPoints)
		{
			const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);
			const sal_uInt32 nPointCount(aCandidate.count());

			if(nPointCount > 1L)
			{
				const sal_uInt32 nLoopCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1L);
				B2DPoint aCurrentPoint(aCandidate.getB2DPoint(0L));

				for(sal_uInt32 a(0L); a < nLoopCount; a++)
				{
					const B2DPoint aNextPoint(aCandidate.getB2DPoint((a + 1L) % nPointCount));

					if(isPointOnLine(aCurrentPoint, aNextPoint, rPoint, bWithPoints))
					{
						return true;
					}

					aCurrentPoint = aNextPoint;
				}
			}
			else if(nPointCount && bWithPoints)
			{
				return rPoint.equal(aCandidate.getB2DPoint(0L));
			}

			return false;
		}

		bool isPointInTriangle(const B2DPoint& rA, const B2DPoint& rB, const B2DPoint& rC, const B2DPoint& rCandidate, bool bWithBorder)
		{
			if(arePointsOnSameSideOfLine(rA, rB, rC, rCandidate, bWithBorder))
			{
				if(arePointsOnSameSideOfLine(rB, rC, rA, rCandidate, bWithBorder))
				{
					if(arePointsOnSameSideOfLine(rC, rA, rB, rCandidate, bWithBorder))
					{
						return true;
					}
				}
			}

			return false;
		}

		bool arePointsOnSameSideOfLine(const B2DPoint& rStart, const B2DPoint& rEnd, const B2DPoint& rCandidateA, const B2DPoint& rCandidateB, bool bWithLine)
		{
			const B2DVector aLineVector(rEnd - rStart);
			const B2DVector aVectorToA(rEnd - rCandidateA);
			const double fCrossA(aLineVector.cross(aVectorToA));

			if(fTools::equalZero(fCrossA))
			{
				// one point on the line
				return bWithLine;
			}

			const B2DVector aVectorToB(rEnd - rCandidateB);
			const double fCrossB(aLineVector.cross(aVectorToB));

			if(fTools::equalZero(fCrossB))
			{
				// one point on the line
				return bWithLine;
			}

			// return true if they both have the same sign
			return ((fCrossA > 0.0) == (fCrossB > 0.0));
		}

		void addTriangleFan(const B2DPolygon& rCandidate, B2DPolygon& rTarget)
		{
			const sal_uInt32 nCount(rCandidate.count());

			if(nCount > 2L)
			{
				const B2DPoint aStart(rCandidate.getB2DPoint(0L));
				B2DPoint aLast(rCandidate.getB2DPoint(1L));

				for(sal_uInt32 a(2L); a < nCount; a++)
				{
					const B2DPoint aCurrent(rCandidate.getB2DPoint(a));
					rTarget.append(aStart);
					rTarget.append(aLast);
					rTarget.append(aCurrent);

					// prepare next
					aLast = aCurrent;
				}
			}
		}

        namespace
        {
            /// return 0 for input of 0, -1 for negative and 1 for positive input
            inline int lcl_sgn( const double n )
            {
                return n == 0.0 ? 0 : 1 - 2*::rtl::math::isSignBitSet(n);
            }
        }

        bool isRectangle( const B2DPolygon& rPoly )
        {
            // polygon must be closed to resemble a rect, and contain
            // at least four points.
            if( !rPoly.isClosed() ||
                rPoly.count() < 4 ||
                rPoly.areControlPointsUsed() )
            {
                return false;
            }

            // number of 90 degree turns the polygon has taken
            int nNumTurns(0);

            int  nVerticalEdgeType=0;
            int  nHorizontalEdgeType=0;
            bool bNullVertex(true);
            bool bCWPolygon(false);  // when true, polygon is CW
                                     // oriented, when false, CCW
            bool bOrientationSet(false); // when false, polygon
                                         // orientation has not yet
                                         // been determined.

            // scan all _edges_ (which involves coming back to point 0
            // for the last edge - thus the modulo operation below)
            const sal_Int32 nCount( rPoly.count() );
            for( sal_Int32 i=0; i<nCount; ++i )
            {
                const B2DPoint& rPoint0( rPoly.getB2DPoint(i % nCount) );
                const B2DPoint& rPoint1( rPoly.getB2DPoint((i+1) % nCount) );

                // is 0 for zero direction vector, 1 for south edge and -1
                // for north edge (standard screen coordinate system)
                int nCurrVerticalEdgeType( lcl_sgn( rPoint1.getY() - rPoint0.getY() ) );

                // is 0 for zero direction vector, 1 for east edge and -1
                // for west edge (standard screen coordinate system)
                int nCurrHorizontalEdgeType( lcl_sgn(rPoint1.getX() - rPoint0.getX()) );

                if( nCurrVerticalEdgeType && nCurrHorizontalEdgeType )
                    return false; // oblique edge - for sure no rect

                const bool bCurrNullVertex( !nCurrVerticalEdgeType && !nCurrHorizontalEdgeType );

                // current vertex is equal to previous - just skip,
                // until we have a real edge
                if( bCurrNullVertex )
                    continue;

                // if previous edge has two identical points, because
                // no previous edge direction was available, simply
                // take this first non-null edge as the start
                // direction. That's what will happen here, if
                // bNullVertex is false
                if( !bNullVertex )
                {
                    // 2D cross product - is 1 for CW and -1 for CCW turns
                    const int nCrossProduct( nHorizontalEdgeType*nCurrVerticalEdgeType -
                                             nVerticalEdgeType*nCurrHorizontalEdgeType );

                    if( !nCrossProduct )
                        continue; // no change in orientation -
                                  // collinear edges - just go on

                    // if polygon orientation is not set, we'll
                    // determine it now
                    if( !bOrientationSet )
                    {
                        bCWPolygon = nCrossProduct == 1;
                        bOrientationSet = true;
                    }
                    else
                    {
                        // if current turn orientation is not equal
                        // initial orientation, this is not a
                        // rectangle (as rectangles have consistent
                        // orientation).
                        if( (nCrossProduct == 1) != bCWPolygon )
                            return false;
                    }

                    ++nNumTurns;

                    // More than four 90 degree turns are an
                    // indication that this must not be a rectangle.
                    if( nNumTurns > 4 )
                        return false;
                }

                // store current state for the next turn
                nVerticalEdgeType	= nCurrVerticalEdgeType;
                nHorizontalEdgeType = nCurrHorizontalEdgeType;
                bNullVertex		    = false; // won't reach this line,
                                             // if bCurrNullVertex is
                                             // true - see above
            }

            return true;
        }

		B3DPolygon createB3DPolygonFromB2DPolygon(const B2DPolygon& rCandidate, double fZCoordinate)
		{
			if(rCandidate.areControlPointsUsed())
			{
				// call myself recursively with subdivided input
				const B2DPolygon aCandidate(adaptiveSubdivideByAngle(rCandidate));
				return createB3DPolygonFromB2DPolygon(aCandidate, fZCoordinate);
			}
			else
			{
				B3DPolygon aRetval;

				for(sal_uInt32 a(0L); a < rCandidate.count(); a++)
				{
					B2DPoint aPoint(rCandidate.getB2DPoint(a));
					aRetval.append(B3DPoint(aPoint.getX(), aPoint.getY(), fZCoordinate));
				}

				// copy closed state
				aRetval.setClosed(rCandidate.isClosed());

				return aRetval;
			}
		}

		B2DPolygon createB2DPolygonFromB3DPolygon(const B3DPolygon& rCandidate, const B3DHomMatrix& rMat)
		{
			B2DPolygon aRetval;
			const sal_uInt32 nCount(rCandidate.count());
			const bool bIsIdentity(rMat.isIdentity());

			for(sal_uInt32 a(0L); a < nCount; a++)
			{
				B3DPoint aCandidate(rCandidate.getB3DPoint(a));

				if(!bIsIdentity)
				{
					aCandidate *= rMat;
				}

				aRetval.append(B2DPoint(aCandidate.getX(), aCandidate.getY()));
			}

			// copy closed state
			aRetval.setClosed(rCandidate.isClosed());

			return aRetval;
		}

		double getDistancePointToEndlessRay(const B2DPoint& rPointA, const B2DPoint& rPointB, const B2DPoint& rTestPoint, double& rCut)
		{
			if(rPointA.equal(rPointB))
			{
				rCut = 0.0;
				const B2DVector aVector(rTestPoint - rPointA);
				return aVector.getLength();
			}
			else
			{
				// get the relative cut value on line vector (Vector1) for cut with perpendicular through TestPoint
				const B2DVector aVector1(rPointB - rPointA);
				const B2DVector aVector2(rTestPoint - rPointA);
				const double fDividend((aVector2.getX() * aVector1.getX()) + (aVector2.getY() * aVector1.getY()));
				const double fDivisor((aVector1.getX() * aVector1.getX()) + (aVector1.getY() * aVector1.getY()));

                rCut = fDividend / fDivisor;

				const B2DPoint aCutPoint(rPointA + rCut * aVector1);
				const B2DVector aVector(rTestPoint - aCutPoint);
				return aVector.getLength();
			}
		}

		double getSmallestDistancePointToEdge(const B2DPoint& rPointA, const B2DPoint& rPointB, const B2DPoint& rTestPoint, double& rCut)
		{
			if(rPointA.equal(rPointB))
			{
				rCut = 0.0;
				const B2DVector aVector(rTestPoint - rPointA);
				return aVector.getLength();
			}
			else
			{
				// get the relative cut value on line vector (Vector1) for cut with perpendicular through TestPoint
				const B2DVector aVector1(rPointB - rPointA);
				const B2DVector aVector2(rTestPoint - rPointA);
				const double fDividend((aVector2.getX() * aVector1.getX()) + (aVector2.getY() * aVector1.getY()));
				const double fDivisor((aVector1.getX() * aVector1.getX()) + (aVector1.getY() * aVector1.getY()));
				const double fCut(fDividend / fDivisor);

				if(fCut < 0.0)
				{
					// not in line range, get distance to PointA
					rCut = 0.0;
					return aVector2.getLength();
				}
				else if(fCut > 1.0)
				{
					// not in line range, get distance to PointB
					rCut = 1.0;
					const B2DVector aVector(rTestPoint - rPointB);
					return aVector.getLength();
				}
				else
				{
					// in line range
					const B2DPoint aCutPoint(rPointA + fCut * aVector1);
					const B2DVector aVector(rTestPoint - aCutPoint);
					rCut = fCut;
					return aVector.getLength();
				}
			}
		}

		double getSmallestDistancePointToPolygon(const B2DPolygon& rCandidate, const B2DPoint& rTestPoint, sal_uInt32& rEdgeIndex, double& rCut)
		{
			double fRetval(DBL_MAX);
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount > 1L)
			{
				const double fZero(0.0);
				const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1L);
				B2DCubicBezier aBezier;
				aBezier.setStartPoint(rCandidate.getB2DPoint(0));

				for(sal_uInt32 a(0L); a < nEdgeCount; a++)
				{
					const sal_uInt32 nNextIndex((a + 1) % nPointCount);
					aBezier.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
					double fEdgeDist;
					double fNewCut;
					bool bEdgeIsCurve(false);

					if(rCandidate.areControlPointsUsed())
					{
						aBezier.setControlPointA(rCandidate.getNextControlPoint(a));
						aBezier.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
						aBezier.testAndSolveTrivialBezier();
						bEdgeIsCurve = aBezier.isBezier();
					}

					if(bEdgeIsCurve)
					{
						fEdgeDist = aBezier.getSmallestDistancePointToBezierSegment(rTestPoint, fNewCut);
					}
					else
					{
						fEdgeDist = getSmallestDistancePointToEdge(aBezier.getStartPoint(), aBezier.getEndPoint(), rTestPoint, fNewCut);
					}

					if(DBL_MAX == fRetval || fEdgeDist < fRetval)
					{
						fRetval = fEdgeDist;
						rEdgeIndex = a;
						rCut = fNewCut;

						if(fTools::equal(fRetval, fZero))
						{
							// already found zero distance, cannot get better. Ensure numerical zero value and end loop.
							fRetval = 0.0;
							break;
						}
					}

					// prepare next step
					aBezier.setStartPoint(aBezier.getEndPoint());
				}

				if(1.0 == rCut)
				{
					// correct rEdgeIndex when not last point
					if(rCandidate.isClosed())
					{
						rEdgeIndex = getIndexOfSuccessor(rEdgeIndex, rCandidate);
						rCut = 0.0;
					}
					else
					{
						if(rEdgeIndex != nEdgeCount - 1L)
						{
							rEdgeIndex++;
							rCut = 0.0;
						}
					}
				}
			}

			return fRetval;
		}

		B2DPoint distort(const B2DPoint& rCandidate, const B2DRange& rOriginal, const B2DPoint& rTopLeft, const B2DPoint& rTopRight, const B2DPoint& rBottomLeft, const B2DPoint& rBottomRight)
		{
			if(fTools::equalZero(rOriginal.getWidth()) || fTools::equalZero(rOriginal.getHeight()))
			{
				return rCandidate;
			}
			else
			{
				const double fRelativeX((rCandidate.getX() - rOriginal.getMinX()) / rOriginal.getWidth());
				const double fRelativeY((rCandidate.getY() - rOriginal.getMinY()) / rOriginal.getHeight());
				const double fOneMinusRelativeX(1.0 - fRelativeX);
				const double fOneMinusRelativeY(1.0 - fRelativeY);
				const double fNewX((fOneMinusRelativeY) * ((fOneMinusRelativeX) * rTopLeft.getX() + fRelativeX * rTopRight.getX()) +
					fRelativeY * ((fOneMinusRelativeX) * rBottomLeft.getX() + fRelativeX * rBottomRight.getX()));
				const double fNewY((fOneMinusRelativeX) * ((fOneMinusRelativeY) * rTopLeft.getY() + fRelativeY * rBottomLeft.getY()) +
					fRelativeX * ((fOneMinusRelativeY) * rTopRight.getY() + fRelativeY * rBottomRight.getY()));

				return B2DPoint(fNewX, fNewY);
			}
		}

		B2DPolygon distort(const B2DPolygon& rCandidate, const B2DRange& rOriginal, const B2DPoint& rTopLeft, const B2DPoint& rTopRight, const B2DPoint& rBottomLeft, const B2DPoint& rBottomRight)
		{
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount && 0.0 != rOriginal.getWidth() && 0.0 != rOriginal.getHeight())
			{
				B2DPolygon aRetval;

				for(sal_uInt32 a(0L); a < nPointCount; a++)
				{
					aRetval.append(distort(rCandidate.getB2DPoint(a), rOriginal, rTopLeft, rTopRight, rBottomLeft, rBottomRight));

					if(rCandidate.areControlPointsUsed())
					{
						if(!rCandidate.getPrevControlPoint(a).equalZero())
						{
							aRetval.setPrevControlPoint(a, distort(rCandidate.getPrevControlPoint(a), rOriginal, rTopLeft, rTopRight, rBottomLeft, rBottomRight));
						}

						if(!rCandidate.getNextControlPoint(a).equalZero())
						{
							aRetval.setNextControlPoint(a, distort(rCandidate.getNextControlPoint(a), rOriginal, rTopLeft, rTopRight, rBottomLeft, rBottomRight));
						}
					}
				}

				aRetval.setClosed(rCandidate.isClosed());
				return aRetval;
			}
			else
			{
				return rCandidate;
			}
		}

		B2DPolygon rotateAroundPoint(const B2DPolygon& rCandidate, const B2DPoint& rCenter, double fAngle)
		{
			const sal_uInt32 nPointCount(rCandidate.count());
			B2DPolygon aRetval(rCandidate);

			if(nPointCount)
			{
                const B2DHomMatrix aMatrix(basegfx::tools::createRotateAroundPoint(rCenter, fAngle));

                aRetval.transform(aMatrix);
			}

			return aRetval;
		}

		B2DPolygon expandToCurve(const B2DPolygon& rCandidate)
		{
			B2DPolygon aRetval(rCandidate);

			for(sal_uInt32 a(0L); a < rCandidate.count(); a++)
			{
				expandToCurveInPoint(aRetval, a);
			}

			return aRetval;
		}

		bool expandToCurveInPoint(B2DPolygon& rCandidate, sal_uInt32 nIndex)
		{
			OSL_ENSURE(nIndex < rCandidate.count(), "expandToCurveInPoint: Access to polygon out of range (!)");
			bool bRetval(false);
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount)
			{
				// predecessor
				if(!rCandidate.isPrevControlPointUsed(nIndex))
				{
					if(!rCandidate.isClosed() && 0 == nIndex)
					{
						// do not create previous vector for start point of open polygon
					}
					else
					{
						const sal_uInt32 nPrevIndex((nIndex + (nPointCount - 1)) % nPointCount);
						rCandidate.setPrevControlPoint(nIndex, interpolate(rCandidate.getB2DPoint(nIndex), rCandidate.getB2DPoint(nPrevIndex), 1.0 / 3.0));
						bRetval = true;
					}
				}

				// successor
				if(!rCandidate.isNextControlPointUsed(nIndex))
				{
					if(!rCandidate.isClosed() && nIndex + 1 == nPointCount)
					{
						// do not create next vector for end point of open polygon
					}
					else
					{
						const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
						rCandidate.setNextControlPoint(nIndex, interpolate(rCandidate.getB2DPoint(nIndex), rCandidate.getB2DPoint(nNextIndex), 1.0 / 3.0));
						bRetval = true;
					}
				}
			}

			return bRetval;
		}

		B2DPolygon setContinuity(const B2DPolygon& rCandidate, B2VectorContinuity eContinuity)
		{
			B2DPolygon aRetval(rCandidate);

			for(sal_uInt32 a(0L); a < rCandidate.count(); a++)
			{
				setContinuityInPoint(aRetval, a, eContinuity);
			}

			return aRetval;
		}

		bool setContinuityInPoint(B2DPolygon& rCandidate, sal_uInt32 nIndex, B2VectorContinuity eContinuity)
		{
			OSL_ENSURE(nIndex < rCandidate.count(), "setContinuityInPoint: Access to polygon out of range (!)");
			bool bRetval(false);
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount)
			{
				const B2DPoint aCurrentPoint(rCandidate.getB2DPoint(nIndex));

				switch(eContinuity)
				{
					case CONTINUITY_NONE :
					{
						if(rCandidate.isPrevControlPointUsed(nIndex))
						{
							if(!rCandidate.isClosed() && 0 == nIndex)
							{
								// remove existing previous vector for start point of open polygon
								rCandidate.resetPrevControlPoint(nIndex);
							}
							else
							{
								const sal_uInt32 nPrevIndex((nIndex + (nPointCount - 1)) % nPointCount);
								rCandidate.setPrevControlPoint(nIndex, interpolate(aCurrentPoint, rCandidate.getB2DPoint(nPrevIndex), 1.0 / 3.0));
							}

							bRetval = true;
						}

						if(rCandidate.isNextControlPointUsed(nIndex))
						{
							if(!rCandidate.isClosed() && nIndex == nPointCount + 1)
							{
								// remove next vector for end point of open polygon
								rCandidate.resetNextControlPoint(nIndex);
							}
							else
							{
								const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
								rCandidate.setNextControlPoint(nIndex, interpolate(aCurrentPoint, rCandidate.getB2DPoint(nNextIndex), 1.0 / 3.0));
							}

							bRetval = true;
						}

						break;
					}
					case CONTINUITY_C1 :
					{
						if(rCandidate.isPrevControlPointUsed(nIndex) && rCandidate.isNextControlPointUsed(nIndex))
						{
							// lengths both exist since both are used
							B2DVector aVectorPrev(rCandidate.getPrevControlPoint(nIndex) - aCurrentPoint);
							B2DVector aVectorNext(rCandidate.getNextControlPoint(nIndex) - aCurrentPoint);
							const double fLenPrev(aVectorPrev.getLength());
							const double fLenNext(aVectorNext.getLength());
							aVectorPrev.normalize();
							aVectorNext.normalize();
							const B2VectorOrientation aOrientation(getOrientation(aVectorPrev, aVectorNext));

							if(ORIENTATION_NEUTRAL == aOrientation && aVectorPrev.scalar(aVectorNext) < 0.0)
							{
								// parallel and opposite direction; check length
								if(fTools::equal(fLenPrev, fLenNext))
								{
									// this would be even C2, but we want C1. Use the lengths of the corresponding edges.
									const sal_uInt32 nPrevIndex((nIndex + (nPointCount - 1)) % nPointCount);
									const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
									const double fLenPrevEdge(B2DVector(rCandidate.getB2DPoint(nPrevIndex) - aCurrentPoint).getLength() * (1.0 / 3.0));
									const double fLenNextEdge(B2DVector(rCandidate.getB2DPoint(nNextIndex) - aCurrentPoint).getLength() * (1.0 / 3.0));

									rCandidate.setControlPoints(nIndex,
										aCurrentPoint + (aVectorPrev * fLenPrevEdge),
										aCurrentPoint + (aVectorNext * fLenNextEdge));
									bRetval = true;
								}
							}
							else
							{
								// not parallel or same direction, set vectors and length
								const B2DVector aNormalizedPerpendicular(getNormalizedPerpendicular(aVectorPrev + aVectorNext));

								if(ORIENTATION_POSITIVE == aOrientation)
								{
									rCandidate.setControlPoints(nIndex,
										aCurrentPoint - (aNormalizedPerpendicular * fLenPrev),
										aCurrentPoint + (aNormalizedPerpendicular * fLenNext));
								}
								else
								{
									rCandidate.setControlPoints(nIndex,
										aCurrentPoint + (aNormalizedPerpendicular * fLenPrev),
										aCurrentPoint - (aNormalizedPerpendicular * fLenNext));
								}

								bRetval = true;
							}
						}
						break;
					}
					case CONTINUITY_C2 :
					{
						if(rCandidate.isPrevControlPointUsed(nIndex) && rCandidate.isNextControlPointUsed(nIndex))
						{
							// lengths both exist since both are used
							B2DVector aVectorPrev(rCandidate.getPrevControlPoint(nIndex) - aCurrentPoint);
							B2DVector aVectorNext(rCandidate.getNextControlPoint(nIndex) - aCurrentPoint);
							const double fCommonLength((aVectorPrev.getLength() + aVectorNext.getLength()) / 2.0);
							aVectorPrev.normalize();
							aVectorNext.normalize();
							const B2VectorOrientation aOrientation(getOrientation(aVectorPrev, aVectorNext));

							if(ORIENTATION_NEUTRAL == aOrientation && aVectorPrev.scalar(aVectorNext) < 0.0)
							{
								// parallel and opposite direction; set length. Use one direction for better numerical correctness
								const B2DVector aScaledDirection(aVectorPrev * fCommonLength);

								rCandidate.setControlPoints(nIndex,
									aCurrentPoint + aScaledDirection,
									aCurrentPoint - aScaledDirection);
							}
							else
							{
								// not parallel or same direction, set vectors and length
								const B2DVector aNormalizedPerpendicular(getNormalizedPerpendicular(aVectorPrev + aVectorNext));
								const B2DVector aPerpendicular(aNormalizedPerpendicular * fCommonLength);

								if(ORIENTATION_POSITIVE == aOrientation)
								{
									rCandidate.setControlPoints(nIndex,
										aCurrentPoint - aPerpendicular,
										aCurrentPoint + aPerpendicular);
								}
								else
								{
									rCandidate.setControlPoints(nIndex,
										aCurrentPoint + aPerpendicular,
										aCurrentPoint - aPerpendicular);
								}
							}

							bRetval = true;
						}
						break;
					}
				}
			}

			return bRetval;
		}

		B2DPolygon growInNormalDirection(const B2DPolygon& rCandidate, double fValue)
		{
			if(0.0 != fValue)
			{
				if(rCandidate.areControlPointsUsed())
				{
					// call myself recursively with subdivided input
					const B2DPolygon aCandidate(adaptiveSubdivideByAngle(rCandidate));
					return growInNormalDirection(aCandidate, fValue);
				}
				else
				{
					B2DPolygon aRetval;
					const sal_uInt32 nPointCount(rCandidate.count());

					if(nPointCount)
					{
						B2DPoint aPrev(rCandidate.getB2DPoint(nPointCount - 1L));
						B2DPoint aCurrent(rCandidate.getB2DPoint(0L));

						for(sal_uInt32 a(0L); a < nPointCount; a++)
						{
							const B2DPoint aNext(rCandidate.getB2DPoint(a + 1L == nPointCount ? 0L : a + 1L));
							const B2DVector aBack(aPrev - aCurrent);
							const B2DVector aForw(aNext - aCurrent);
							const B2DVector aPerpBack(getNormalizedPerpendicular(aBack));
							const B2DVector aPerpForw(getNormalizedPerpendicular(aForw));
							B2DVector aDirection(aPerpBack - aPerpForw);
							aDirection.normalize();
							aDirection *= fValue;
							aRetval.append(aCurrent + aDirection);

							// prepare next step
							aPrev = aCurrent;
							aCurrent = aNext;
						}
					}

					// copy closed state
					aRetval.setClosed(rCandidate.isClosed());

					return aRetval;
				}
			}
			else
			{
				return rCandidate;
			}
		}

		B2DPolygon reSegmentPolygon(const B2DPolygon& rCandidate, sal_uInt32 nSegments)
		{
			B2DPolygon aRetval;
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount && nSegments)
			{
				// get current segment count
				const sal_uInt32 nSegmentCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1L);

				if(nSegmentCount == nSegments)
				{
					aRetval = rCandidate;
				}
				else
				{
					const double fLength(getLength(rCandidate));
					const sal_uInt32 nLoopCount(rCandidate.isClosed() ? nSegments : nSegments + 1L);

					for(sal_uInt32 a(0L); a < nLoopCount; a++)
					{
						const double fRelativePos((double)a / (double)nSegments); // 0.0 .. 1.0
						const B2DPoint aNewPoint(getPositionRelative(rCandidate, fRelativePos, fLength));
						aRetval.append(aNewPoint);
					}

					// copy closed flag
					aRetval.setClosed(rCandidate.isClosed());
				}
			}

			return aRetval;
		}

		B2DPolygon reSegmentPolygonEdges(const B2DPolygon& rCandidate, sal_uInt32 nSubEdges, bool bHandleCurvedEdges, bool bHandleStraightEdges)
		{
			const sal_uInt32 nPointCount(rCandidate.count());

            if(nPointCount < 2 || nSubEdges < 2 || (!bHandleCurvedEdges && !bHandleStraightEdges))
            {
                // nothing to do:
                // - less than two points -> no edge at all
                // - less than two nSubEdges -> no resegment necessary
                // - neither bHandleCurvedEdges nor bHandleStraightEdges -> nothing to do
                return rCandidate;
            }
            else
            {
    			B2DPolygon aRetval;
                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
                B2DCubicBezier aCurrentEdge;

                // prepare first edge and add start point to target
                aCurrentEdge.setStartPoint(rCandidate.getB2DPoint(0));
                aRetval.append(aCurrentEdge.getStartPoint());

                for(sal_uInt32 a(0); a < nEdgeCount; a++)
                {
                    // fill edge
                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                    aCurrentEdge.setControlPointA(rCandidate.getNextControlPoint(a));
                    aCurrentEdge.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
                    aCurrentEdge.setEndPoint(rCandidate.getB2DPoint(nNextIndex));

                    if(aCurrentEdge.isBezier())
                    {
                        if(bHandleCurvedEdges)
                        {
                            for(sal_uInt32 b(nSubEdges); b > 1; b--)
                            {
                                const double fSplitPoint(1.0 / b);
                                B2DCubicBezier aLeftPart;

                                aCurrentEdge.split(fSplitPoint, &aLeftPart, &aCurrentEdge);
                                aRetval.appendBezierSegment(aLeftPart.getControlPointA(), aLeftPart.getControlPointB(), aLeftPart.getEndPoint());
                            }
                        }

                        // copy remaining segment to target
                        aRetval.appendBezierSegment(aCurrentEdge.getControlPointA(), aCurrentEdge.getControlPointB(), aCurrentEdge.getEndPoint());
                    }
                    else
                    {
                        if(bHandleStraightEdges)
                        {
                            for(sal_uInt32 b(nSubEdges); b > 1; b--)
                            {
                                const double fSplitPoint(1.0 / b);
                                const B2DPoint aSplitPoint(interpolate(aCurrentEdge.getStartPoint(), aCurrentEdge.getEndPoint(), fSplitPoint));

                                aRetval.append(aSplitPoint);
                                aCurrentEdge.setStartPoint(aSplitPoint);
                            }
                        }

                        // copy remaining segment to target
                        aRetval.append(aCurrentEdge.getEndPoint());
                    }

                    // prepare next step
                    aCurrentEdge.setStartPoint(aCurrentEdge.getEndPoint());
                }

                // copy closed flag and return
                aRetval.setClosed(rCandidate.isClosed());
                return aRetval;
            }
        }

		B2DPolygon interpolate(const B2DPolygon& rOld1, const B2DPolygon& rOld2, double t)
		{
			OSL_ENSURE(rOld1.count() == rOld2.count(), "B2DPolygon interpolate: Different geometry (!)");

			if(fTools::lessOrEqual(t, 0.0) || rOld1 == rOld2)
			{
				return rOld1;
			}
			else if(fTools::moreOrEqual(t, 1.0))
			{
				return rOld2;
			}
			else
			{
				B2DPolygon aRetval;
				const bool bInterpolateVectors(rOld1.areControlPointsUsed() || rOld2.areControlPointsUsed());
				aRetval.setClosed(rOld1.isClosed() && rOld2.isClosed());

				for(sal_uInt32 a(0L); a < rOld1.count(); a++)
				{
					aRetval.append(interpolate(rOld1.getB2DPoint(a), rOld2.getB2DPoint(a), t));

					if(bInterpolateVectors)
					{
						aRetval.setPrevControlPoint(a, interpolate(rOld1.getPrevControlPoint(a), rOld2.getPrevControlPoint(a), t));
						aRetval.setNextControlPoint(a, interpolate(rOld1.getNextControlPoint(a), rOld2.getNextControlPoint(a), t));
					}
				}

				return aRetval;
			}
		}

		bool isPolyPolygonEqualRectangle( const B2DPolyPolygon& rPolyPoly,
										  const B2DRange&	   rRect )
        {
            // exclude some cheap cases first
            if( rPolyPoly.count() != 1 )
                return false;

            // fill array with rectangle vertices
            const B2DPoint aPoints[] =
              {
				  B2DPoint(rRect.getMinX(),rRect.getMinY()),
				  B2DPoint(rRect.getMaxX(),rRect.getMinY()),
				  B2DPoint(rRect.getMaxX(),rRect.getMaxY()),
				  B2DPoint(rRect.getMinX(),rRect.getMaxY())
              };

			const B2DPolygon& rPoly( rPolyPoly.getB2DPolygon(0) );
			const sal_uInt32 nCount( rPoly.count() );
			const double epsilon = ::std::numeric_limits<double>::epsilon();

			for(unsigned int j=0; j<4; ++j)
			{
				const B2DPoint &p1 = aPoints[j];
				const B2DPoint &p2 = aPoints[(j+1)%4];
				bool bPointOnBoundary = false;
				for( sal_uInt32 i=0; i<nCount; ++i )
				{
					const B2DPoint p(rPoly.getB2DPoint(i));

					//	   1 | x0 y0 1 |
					// A = - | x1 y1 1 |
					//	   2 | x2 y2 1 |
					double fDoubleArea = p2.getX()*p.getY() -
										 p2.getY()*p.getX() -
										 p1.getX()*p.getY() +
										 p1.getY()*p.getX() +
										 p1.getX()*p2.getY() -
										 p1.getY()*p2.getX();

					if(fDoubleArea < epsilon)
					{
						bPointOnBoundary=true;
						break;
					}
				}
				if(!(bPointOnBoundary))
					return false;
			}

			return true;
        }


		// create simplified version of the original polygon by
		// replacing segments with spikes/loops and self intersections
		// by several trivial sub-segments
		B2DPolygon createSimplifiedPolygon( const B2DPolygon& rCandidate )
		{
			const sal_uInt32 nCount(rCandidate.count());

			if(nCount && rCandidate.areControlPointsUsed())
			{
				const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nCount : nCount - 1);
				B2DPolygon aRetval;
				B2DCubicBezier aSegment;

				aSegment.setStartPoint(rCandidate.getB2DPoint(0));
				aRetval.append(aSegment.getStartPoint());

				for(sal_uInt32 a(0); a < nEdgeCount; a++)
				{
					// fill edge
					const sal_uInt32 nNextIndex((a + 1) % nCount);
					aSegment.setControlPointA(rCandidate.getNextControlPoint(a));
					aSegment.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
					aSegment.setEndPoint(rCandidate.getB2DPoint(nNextIndex));

					if(aSegment.isBezier())
					{
						double fExtremumPos(0.0);
						sal_uInt32 nExtremumCounter(4);

						while(nExtremumCounter-- && aSegment.isBezier() && aSegment.getMinimumExtremumPosition(fExtremumPos))
						{
							// split off left, now extremum-free part and append
							B2DCubicBezier aLeft;

							aSegment.split(fExtremumPos, &aLeft, &aSegment);
		                    aLeft.testAndSolveTrivialBezier();
		                    aSegment.testAndSolveTrivialBezier();

							if(aLeft.isBezier())
							{
								aRetval.appendBezierSegment(aLeft.getControlPointA(), aLeft.getControlPointB(), aLeft.getEndPoint());
							}
							else
							{
								aRetval.append(aLeft.getEndPoint());
							}
						}

						// append (evtl. reduced) rest of Segment
						if(aSegment.isBezier())
						{
							aRetval.appendBezierSegment(aSegment.getControlPointA(), aSegment.getControlPointB(), aSegment.getEndPoint());
						}
						else
						{
							aRetval.append(aSegment.getEndPoint());
						}
					}
					else
					{
						// simple edge, append end point
						aRetval.append(aSegment.getEndPoint());
					}

					// prepare next edge
					aSegment.setStartPoint(aSegment.getEndPoint());
				}

				// copy closed flag and check for double points
				aRetval.setClosed(rCandidate.isClosed());
				aRetval.removeDoublePoints();

				return aRetval;
			}
			else
			{
				return rCandidate;
			}
		}

		// #i76891#
		B2DPolygon simplifyCurveSegments(const B2DPolygon& rCandidate)
		{
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount && rCandidate.areControlPointsUsed())
			{
				// prepare loop
				const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);
				B2DPolygon aRetval;
				B2DCubicBezier aBezier;
				aBezier.setStartPoint(rCandidate.getB2DPoint(0));

				// try to avoid costly reallocations
				aRetval.reserve( nEdgeCount+1);

				// add start point
				aRetval.append(aBezier.getStartPoint());

				for(sal_uInt32 a(0L); a < nEdgeCount; a++)
				{
					// get values for edge
					const sal_uInt32 nNextIndex((a + 1) % nPointCount);
					aBezier.setEndPoint(rCandidate.getB2DPoint(nNextIndex));
					aBezier.setControlPointA(rCandidate.getNextControlPoint(a));
					aBezier.setControlPointB(rCandidate.getPrevControlPoint(nNextIndex));
					aBezier.testAndSolveTrivialBezier();

					// still bezier?
					if(aBezier.isBezier())
					{
						// add edge with control vectors
						aRetval.appendBezierSegment(aBezier.getControlPointA(), aBezier.getControlPointB(), aBezier.getEndPoint());
					}
					else
					{
						// add edge
						aRetval.append(aBezier.getEndPoint());
					}

					// next point
					aBezier.setStartPoint(aBezier.getEndPoint());
				}

				if(rCandidate.isClosed())
				{
					// set closed flag, rescue control point and correct last double point
					closeWithGeometryChange(aRetval);
				}

				return aRetval;
			}
			else
			{
				return rCandidate;
			}
		}

		// makes the given indexed point the new polygon start point. To do that, the points in the
		// polygon will be rotated. This is only valid for closed polygons, for non-closed ones
		// an assertion will be triggered
		B2DPolygon makeStartPoint(const B2DPolygon& rCandidate, sal_uInt32 nIndexOfNewStatPoint)
		{
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount > 2 && nIndexOfNewStatPoint != 0 && nIndexOfNewStatPoint < nPointCount)
			{
				OSL_ENSURE(rCandidate.isClosed(), "makeStartPoint: only valid for closed polygons (!)");
				B2DPolygon aRetval;

				for(sal_uInt32 a(0); a < nPointCount; a++)
				{
					const sal_uInt32 nSourceIndex((a + nIndexOfNewStatPoint) % nPointCount);
					aRetval.append(rCandidate.getB2DPoint(nSourceIndex));

					if(rCandidate.areControlPointsUsed())
					{
						aRetval.setPrevControlPoint(a, rCandidate.getPrevControlPoint(nSourceIndex));
						aRetval.setNextControlPoint(a, rCandidate.getNextControlPoint(nSourceIndex));
					}
				}

				return aRetval;
			}

			return rCandidate;
		}

		B2DPolygon createEdgesOfGivenLength(const B2DPolygon& rCandidate, double fLength, double fStart, double fEnd)
		{
			B2DPolygon aRetval;

			if(fLength < 0.0)
			{
				fLength = 0.0;
			}

			if(!fTools::equalZero(fLength))
			{
				if(fStart < 0.0)
				{
					fStart = 0.0;
				}

				if(fEnd < 0.0)
				{
					fEnd = 0.0;
				}

				if(fEnd < fStart)
				{
					fEnd = fStart;
				}

				// iterate and consume pieces with fLength. First subdivide to reduce input to line segments
				const B2DPolygon aCandidate(rCandidate.areControlPointsUsed() ? rCandidate.getDefaultAdaptiveSubdivision() : rCandidate);
				const sal_uInt32 nPointCount(aCandidate.count());

				if(nPointCount > 1)
				{
					const bool bEndActive(!fTools::equalZero(fEnd));
					const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1);
					B2DPoint aCurrent(aCandidate.getB2DPoint(0));
					double fPositionInEdge(fStart);
					double fAbsolutePosition(fStart);

					for(sal_uInt32 a(0); a < nEdgeCount; a++)
					{
						const sal_uInt32 nNextIndex((a + 1) % nPointCount);
						const B2DPoint aNext(aCandidate.getB2DPoint(nNextIndex));
						const B2DVector aEdge(aNext - aCurrent);
						double fEdgeLength(aEdge.getLength());

						if(!fTools::equalZero(fEdgeLength))
						{
							while(fTools::less(fPositionInEdge, fEdgeLength))
							{
								// move position on edge forward as long as on edge
								const double fScalar(fPositionInEdge / fEdgeLength);
								aRetval.append(aCurrent + (aEdge * fScalar));
								fPositionInEdge += fLength;

								if(bEndActive)
								{
									fAbsolutePosition += fLength;

									if(fTools::more(fAbsolutePosition, fEnd))
									{
										break;
									}
								}
							}

							// substract length of current edge
							fPositionInEdge -= fEdgeLength;
						}

						if(bEndActive && fTools::more(fAbsolutePosition, fEnd))
						{
							break;
						}

						// prepare next step
						aCurrent = aNext;
					}

					// keep closed state
					aRetval.setClosed(aCandidate.isClosed());
				}
				else
				{
					// source polygon has only one point, return unchanged
					aRetval = aCandidate;
				}
			}

			return aRetval;
		}

		B2DPolygon createWaveline(const B2DPolygon& rCandidate, double fWaveWidth, double fWaveHeight)
		{
			B2DPolygon aRetval;

			if(fWaveWidth < 0.0)
			{
				fWaveWidth = 0.0;
			}

			if(fWaveHeight < 0.0)
			{
				fWaveHeight = 0.0;
			}

			const bool bHasWidth(!fTools::equalZero(fWaveWidth));
			const bool bHasHeight(!fTools::equalZero(fWaveHeight));

			if(bHasWidth)
			{
				if(bHasHeight)
				{
					// width and height, create waveline. First subdivide to reduce input to line segments
					// of WaveWidth. Last segment may be missing. If this turns out to be a problem, it
					// may be added here again using the original last point from rCandidate. It may
					// also be the case that rCandidate was closed. To simplify things it is handled here
					// as if it was opened.
					// Result from createEdgesOfGivenLength contains no curved segments, handle as straight
					// edges.
					const B2DPolygon aEqualLenghEdges(createEdgesOfGivenLength(rCandidate, fWaveWidth));
					const sal_uInt32 nPointCount(aEqualLenghEdges.count());

					if(nPointCount > 1)
					{
						// iterate over straight edges, add start point
						B2DPoint aCurrent(aEqualLenghEdges.getB2DPoint(0));
						aRetval.append(aCurrent);

						for(sal_uInt32 a(0); a < nPointCount - 1; a++)
						{
							const sal_uInt32 nNextIndex((a + 1) % nPointCount);
							const B2DPoint aNext(aEqualLenghEdges.getB2DPoint(nNextIndex));
							const B2DVector aEdge(aNext - aCurrent);
							const B2DVector aPerpendicular(getNormalizedPerpendicular(aEdge));
                            const B2DVector aControlOffset((aEdge * 0.467308) - (aPerpendicular * fWaveHeight));

							// add curve segment
							aRetval.appendBezierSegment(
								aCurrent + aControlOffset,
								aNext - aControlOffset,
								aNext);

							// prepare next step
							aCurrent = aNext;
						}
					}
				}
				else
				{
					// width but no height -> return original polygon
					aRetval = rCandidate;
				}
			}
			else
			{
				// no width -> no waveline, stay empty and return
			}

			return aRetval;
		}

        //////////////////////////////////////////////////////////////////////
		// comparators with tolerance for 2D Polygons

		bool equal(const B2DPolygon& rCandidateA, const B2DPolygon& rCandidateB, const double& rfSmallValue)
		{
			const sal_uInt32 nPointCount(rCandidateA.count());

			if(nPointCount != rCandidateB.count())
				return false;

			const bool bClosed(rCandidateA.isClosed());

			if(bClosed != rCandidateB.isClosed())
				return false;

			const bool bAreControlPointsUsed(rCandidateA.areControlPointsUsed());

			if(bAreControlPointsUsed != rCandidateB.areControlPointsUsed())
				return false;

			for(sal_uInt32 a(0); a < nPointCount; a++)
			{
				const B2DPoint aPoint(rCandidateA.getB2DPoint(a));

				if(!aPoint.equal(rCandidateB.getB2DPoint(a), rfSmallValue))
					return false;

				if(bAreControlPointsUsed)
				{
					const basegfx::B2DPoint aPrev(rCandidateA.getPrevControlPoint(a));

					if(!aPrev.equal(rCandidateB.getPrevControlPoint(a), rfSmallValue))
						return false;

					const basegfx::B2DPoint aNext(rCandidateA.getNextControlPoint(a));

					if(!aNext.equal(rCandidateB.getNextControlPoint(a), rfSmallValue))
						return false;
				}
			}

			return true;
		}

		bool equal(const B2DPolygon& rCandidateA, const B2DPolygon& rCandidateB)
		{
			const double fSmallValue(fTools::getSmallValue());

			return equal(rCandidateA, rCandidateB, fSmallValue);
		}

		// snap points of horizontal or vertical edges to discrete values
		B2DPolygon snapPointsOfHorizontalOrVerticalEdges(const B2DPolygon& rCandidate)
		{
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount > 1)
			{
				// Start by copying the source polygon to get a writeable copy. The closed state is
				// copied by aRetval's initialisation, too, so no need to copy it in this method
				B2DPolygon aRetval(rCandidate);

				// prepare geometry data. Get rounded from original
                B2ITuple aPrevTuple(basegfx::fround(rCandidate.getB2DPoint(nPointCount - 1)));
				B2DPoint aCurrPoint(rCandidate.getB2DPoint(0));
				B2ITuple aCurrTuple(basegfx::fround(aCurrPoint));

				// loop over all points. This will also snap the implicit closing edge
				// even when not closed, but that's no problem here
				for(sal_uInt32 a(0); a < nPointCount; a++)
				{
					// get next point. Get rounded from original
                    const bool bLastRun(a + 1 == nPointCount);
                    const sal_uInt32 nNextIndex(bLastRun ? 0 : a + 1);
					const B2DPoint aNextPoint(rCandidate.getB2DPoint(nNextIndex));
					const B2ITuple aNextTuple(basegfx::fround(aNextPoint));

					// get the states
					const bool bPrevVertical(aPrevTuple.getX() == aCurrTuple.getX());
					const bool bNextVertical(aNextTuple.getX() == aCurrTuple.getX());
					const bool bPrevHorizontal(aPrevTuple.getY() == aCurrTuple.getY());
					const bool bNextHorizontal(aNextTuple.getY() == aCurrTuple.getY());
					const bool bSnapX(bPrevVertical || bNextVertical);
					const bool bSnapY(bPrevHorizontal || bNextHorizontal);

					if(bSnapX || bSnapY)
					{
						const B2DPoint aSnappedPoint(
							bSnapX ? aCurrTuple.getX() : aCurrPoint.getX(),
							bSnapY ? aCurrTuple.getY() : aCurrPoint.getY());

						aRetval.setB2DPoint(a, aSnappedPoint);
					}

					// prepare next point
                    if(!bLastRun)
                    {
    					aPrevTuple = aCurrTuple;
	    				aCurrPoint = aNextPoint;
		    			aCurrTuple = aNextTuple;
                    }
				}

				return aRetval;
			}
			else
			{
				return rCandidate;
			}
		}

	} // end of namespace tools
} // end of namespace basegfx

//////////////////////////////////////////////////////////////////////////////
// eof