source/polygon/b3dpolygontools.cxx

/**************************************************************
 *
 * 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
 * under the License.
 *
 *************************************************************/


// MARKER(update_precomp.py): autogen include statement, do not remove
#include "precompiled_basegfx.hxx"
#include <osl/diagnose.h>
#include <basegfx/polygon/b3dpolygontools.hxx>
#include <basegfx/polygon/b3dpolygon.hxx>
#include <basegfx/numeric/ftools.hxx>
#include <basegfx/range/b3drange.hxx>
#include <basegfx/point/b2dpoint.hxx>
#include <basegfx/matrix/b3dhommatrix.hxx>
#include <basegfx/polygon/b2dpolygon.hxx>
#include <basegfx/polygon/b2dpolygontools.hxx>
#include <basegfx/tuple/b3ituple.hxx>
#include <numeric>

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

namespace basegfx
{
	namespace tools
	{
		// B3DPolygon tools
		void checkClosed(B3DPolygon& rCandidate)
		{
			while(rCandidate.count() > 1L
				&& rCandidate.getB3DPoint(0L).equal(rCandidate.getB3DPoint(rCandidate.count() - 1L)))
			{
				rCandidate.setClosed(true);
				rCandidate.remove(rCandidate.count() - 1L);
			}
		}

		// Get successor and predecessor indices. Returning the same index means there
		// is none. Same for successor.
		sal_uInt32 getIndexOfPredecessor(sal_uInt32 nIndex, const B3DPolygon& 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 B3DPolygon& rCandidate)
		{
			OSL_ENSURE(nIndex < rCandidate.count(), "getIndexOfPredecessor: Access to polygon out of range (!)");

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

		B3DRange getRange(const B3DPolygon& rCandidate)
		{
			B3DRange aRetval;
			const sal_uInt32 nPointCount(rCandidate.count());

			for(sal_uInt32 a(0L); a < nPointCount; a++)
			{
				const B3DPoint aTestPoint(rCandidate.getB3DPoint(a));
				aRetval.expand(aTestPoint);
			}

			return aRetval;
		}

		B3DVector getNormal(const B3DPolygon& rCandidate)
		{
			return rCandidate.getNormal();
		}

		B3DVector getPositiveOrientedNormal(const B3DPolygon& rCandidate)
		{
			B3DVector aRetval(rCandidate.getNormal());

			if(ORIENTATION_NEGATIVE == getOrientation(rCandidate))
			{
				aRetval = -aRetval;
			}

			return aRetval;
		}

		B2VectorOrientation getOrientation(const B3DPolygon& rCandidate)
		{
			B2VectorOrientation eRetval(ORIENTATION_NEUTRAL);

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

				if(fSignedArea > 0.0)
				{
					eRetval = ORIENTATION_POSITIVE;
				}
				else if(fSignedArea < 0.0)
				{
					eRetval = ORIENTATION_NEGATIVE;
				}
			}

			return eRetval;
		}

		double getSignedArea(const B3DPolygon& rCandidate)
		{
			double fRetval(0.0);
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount > 2)
			{
				const B3DVector aAbsNormal(absolute(getNormal(rCandidate)));
				sal_uInt16 nCase(3); // default: ignore z

				if(aAbsNormal.getX() > aAbsNormal.getY())
				{
					if(aAbsNormal.getX() > aAbsNormal.getZ())
					{
						nCase = 1; // ignore x
					}
				}
				else if(aAbsNormal.getY() > aAbsNormal.getZ())
				{
					nCase = 2; // ignore y
				}

				B3DPoint aPreviousPoint(rCandidate.getB3DPoint(nPointCount - 1L));

				for(sal_uInt32 a(0L); a < nPointCount; a++)
				{
					const B3DPoint aCurrentPoint(rCandidate.getB3DPoint(a));

					switch(nCase)
					{
						case 1: // ignore x
							fRetval += aPreviousPoint.getZ() * aCurrentPoint.getY();
							fRetval -= aPreviousPoint.getY() * aCurrentPoint.getZ();
							break;
						case 2: // ignore y
							fRetval += aPreviousPoint.getX() * aCurrentPoint.getZ();
							fRetval -= aPreviousPoint.getZ() * aCurrentPoint.getX();
							break;
						case 3: // ignore z
							fRetval += aPreviousPoint.getX() * aCurrentPoint.getY();
							fRetval -= aPreviousPoint.getY() * aCurrentPoint.getX();
							break;
					}

					// prepare next step
					aPreviousPoint = aCurrentPoint;
				}

				switch(nCase)
				{
					case 1: // ignore x
						fRetval /= 2.0 * aAbsNormal.getX();
						break;
					case 2: // ignore y
						fRetval /= 2.0 * aAbsNormal.getY();
						break;
					case 3: // ignore z
						fRetval /= 2.0 * aAbsNormal.getZ();
						break;
				}
			}

			return fRetval;
		}

		double getArea(const B3DPolygon& rCandidate)
		{
			double fRetval(0.0);

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

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

			return fRetval;
		}

		double getEdgeLength(const B3DPolygon& rCandidate, sal_uInt32 nIndex)
		{
			OSL_ENSURE(nIndex < rCandidate.count(), "getEdgeLength: Access to polygon out of range (!)");
			double fRetval(0.0);
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nIndex < nPointCount)
			{
				if(rCandidate.isClosed() || ((nIndex + 1L) != nPointCount))
				{
					const sal_uInt32 nNextIndex(getIndexOfSuccessor(nIndex, rCandidate));
					const B3DPoint aCurrentPoint(rCandidate.getB3DPoint(nIndex));
					const B3DPoint aNextPoint(rCandidate.getB3DPoint(nNextIndex));
					const B3DVector aVector(aNextPoint - aCurrentPoint);
					fRetval = aVector.getLength();
				}
			}

			return fRetval;
		}

		double getLength(const B3DPolygon& rCandidate)
		{
			double fRetval(0.0);
			const sal_uInt32 nPointCount(rCandidate.count());

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

				for(sal_uInt32 a(0L); a < nLoopCount; a++)
				{
					const sal_uInt32 nNextIndex(getIndexOfSuccessor(a, rCandidate));
					const B3DPoint aCurrentPoint(rCandidate.getB3DPoint(a));
					const B3DPoint aNextPoint(rCandidate.getB3DPoint(nNextIndex));
					const B3DVector aVector(aNextPoint - aCurrentPoint);
					fRetval += aVector.getLength();
				}
			}

			return fRetval;
		}

		B3DPoint getPositionAbsolute(const B3DPolygon& rCandidate, double fDistance, double fLength)
		{
			B3DPoint aRetval;
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount > 1L)
			{
				sal_uInt32 nIndex(0L);
				bool bIndexDone(false);
				const double fZero(0.0);
				double fEdgeLength(fZero);

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

				// handle fDistance < 0.0
				if(fTools::less(fDistance, fZero))
				{
					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 = fZero;
						bIndexDone = true;
					}
				}

				// handle fDistance >= fLength
				if(fTools::moreOrEqual(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 = fZero;
						nIndex = nPointCount - 1L;
						bIndexDone = true;
					}
				}

				// look for correct index. fDistance is now [0.0 .. fLength[
				if(!bIndexDone)
				{
					do
					{
						// get length of next edge
						fEdgeLength = getEdgeLength(rCandidate, nIndex);

						if(fTools::moreOrEqual(fDistance, fEdgeLength))
						{
							// go to next edge
							fDistance -= fEdgeLength;
							nIndex++;
						}
						else
						{
							// it's on this edge, stop
							bIndexDone = true;
						}
					} while (!bIndexDone);
				}

				// get the point using nIndex
				aRetval = rCandidate.getB3DPoint(nIndex);

				// if fDistance != 0.0, move that length on the edge. The edge
				// length is in fEdgeLength.
				if(!fTools::equalZero(fDistance))
				{
					sal_uInt32 nNextIndex(getIndexOfSuccessor(nIndex, rCandidate));
					const B3DPoint aNextPoint(rCandidate.getB3DPoint(nNextIndex));
					double fRelative(fZero);

					if(!fTools::equalZero(fEdgeLength))
					{
						fRelative = fDistance / fEdgeLength;
					}

					// add calculated average value to the return value
					aRetval += interpolate(aRetval, aNextPoint, fRelative);
				}
			}

			return aRetval;
		}

		B3DPoint getPositionRelative(const B3DPolygon& 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);
		}

		void applyLineDashing(const B3DPolygon& rCandidate, const ::std::vector<double>& rDotDashArray, B3DPolyPolygon* pLineTarget, B3DPolyPolygon* 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
				B3DPoint aCurrentPoint(rCandidate.getB3DPoint(0));
                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1);

                // prepare DotDashArray iteration and the line/gap switching bool
                sal_uInt32 nDotDashIndex(0);
                bool bIsLine(true);
                double fDotDashMovingLength(rDotDashArray[0]);
                B3DPolygon aSnippet;

                // iterate over all edges
                for(sal_uInt32 a(0); a < nEdgeCount; a++)
                {
                    // update current edge
                    double fLastDotDashMovingLength(0.0);
                    const sal_uInt32 nNextIndex((a + 1) % nPointCount);
                    const B3DPoint aNextPoint(rCandidate.getB3DPoint(nNextIndex));
                    const double fEdgeLength(B3DVector(aNextPoint - aCurrentPoint).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)
                            {
                                if(!aSnippet.count())
                                {
                                    aSnippet.append(interpolate(aCurrentPoint, aNextPoint, fLastDotDashMovingLength / fEdgeLength));
                                }

                                aSnippet.append(interpolate(aCurrentPoint, aNextPoint, 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(aCurrentPoint, aNextPoint, fLastDotDashMovingLength / fEdgeLength));
                            }

                            aSnippet.append(aNextPoint);
                        }

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

                    // prepare next edge step (end point gets new start point)
                    aCurrentPoint = aNextPoint;
                }

                // 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 B3DPolygon aFirst(pLineTarget->getB3DPolygon(0));
						B3DPolygon aLast(pLineTarget->getB3DPolygon(nCount - 1));

						if(aFirst.getB3DPoint(0).equal(aLast.getB3DPoint(aLast.count() - 1)))
						{
							// start of first and end of last are the same -> merge them
							aLast.append(aFirst);
							aLast.removeDoublePoints();
							pLineTarget->setB3DPolygon(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 B3DPolygon aFirst(pGapTarget->getB3DPolygon(0));
						B3DPolygon aLast(pGapTarget->getB3DPolygon(nCount - 1));

						if(aFirst.getB3DPoint(0).equal(aLast.getB3DPoint(aLast.count() - 1)))
						{
							// start of first and end of last are the same -> merge them
							aLast.append(aFirst);
							aLast.removeDoublePoints();
							pGapTarget->setB3DPolygon(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);
				}
            }
		}

		B3DPolygon applyDefaultNormalsSphere( const B3DPolygon& rCandidate, const B3DPoint& rCenter)
		{
			B3DPolygon aRetval(rCandidate);

			for(sal_uInt32 a(0L); a < aRetval.count(); a++)
			{
				B3DVector aVector(aRetval.getB3DPoint(a) - rCenter);
				aVector.normalize();
				aRetval.setNormal(a, aVector);
			}

			return aRetval;
		}

		B3DPolygon invertNormals( const B3DPolygon& rCandidate)
		{
			B3DPolygon aRetval(rCandidate);

			if(aRetval.areNormalsUsed())
			{
				for(sal_uInt32 a(0L); a < aRetval.count(); a++)
				{
					aRetval.setNormal(a, -aRetval.getNormal(a));
				}
			}

			return aRetval;
		}

		B3DPolygon applyDefaultTextureCoordinatesParallel( const B3DPolygon& rCandidate, const B3DRange& rRange, bool bChangeX, bool bChangeY)
		{
			B3DPolygon aRetval(rCandidate);

			if(bChangeX || bChangeY)
			{
				// create projection of standard texture coordinates in (X, Y) onto
				// the 3d coordinates straight
				const double fWidth(rRange.getWidth());
				const double fHeight(rRange.getHeight());
				const bool bWidthSet(!fTools::equalZero(fWidth));
				const bool bHeightSet(!fTools::equalZero(fHeight));
				const double fOne(1.0);

				for(sal_uInt32 a(0L); a < aRetval.count(); a++)
				{
					const B3DPoint aPoint(aRetval.getB3DPoint(a));
					B2DPoint aTextureCoordinate(aRetval.getTextureCoordinate(a));

					if(bChangeX)
					{
						if(bWidthSet)
						{
							aTextureCoordinate.setX((aPoint.getX() - rRange.getMinX()) / fWidth);
						}
						else
						{
							aTextureCoordinate.setX(0.0);
						}
					}

					if(bChangeY)
					{
						if(bHeightSet)
						{
							aTextureCoordinate.setY(fOne - ((aPoint.getY() - rRange.getMinY()) / fHeight));
						}
						else
						{
							aTextureCoordinate.setY(fOne);
						}
					}

					aRetval.setTextureCoordinate(a, aTextureCoordinate);
				}
			}

			return aRetval;
		}

		B3DPolygon applyDefaultTextureCoordinatesSphere( const B3DPolygon& rCandidate, const B3DPoint& rCenter, bool bChangeX, bool bChangeY)
		{
			B3DPolygon aRetval(rCandidate);

			if(bChangeX || bChangeY)
			{
				// create texture coordinates using sphere projection to cartesian coordinates,
				// use object's center as base
				const double fOne(1.0);
				const sal_uInt32 nPointCount(aRetval.count());
				bool bPolarPoints(false);
				sal_uInt32 a;

				// create center cartesian coordinates to have a possibility to decide if on boundary
				// transitions which value to choose
				const B3DRange aPlaneRange(getRange(rCandidate));
				const B3DPoint aPlaneCenter(aPlaneRange.getCenter() - rCenter);
				const double fXCenter(fOne - ((atan2(aPlaneCenter.getZ(), aPlaneCenter.getX()) + F_PI) / F_2PI));

				for(a = 0L; a < nPointCount; a++)
				{
					const B3DVector aVector(aRetval.getB3DPoint(a) - rCenter);
					const double fY(fOne - ((atan2(aVector.getY(), aVector.getXZLength()) + F_PI2) / F_PI));
					B2DPoint aTexCoor(aRetval.getTextureCoordinate(a));

					if(fTools::equalZero(fY))
					{
						// point is a north polar point, no useful X-coordinate can be created.
						if(bChangeY)
						{
							aTexCoor.setY(0.0);

							if(bChangeX)
							{
								bPolarPoints = true;
							}
						}
					}
					else if(fTools::equal(fY, fOne))
					{
						// point is a south polar point, no useful X-coordinate can be created. Set
						// Y-coordinte, though
						if(bChangeY)
						{
							aTexCoor.setY(fOne);

							if(bChangeX)
							{
								bPolarPoints = true;
							}
						}
					}
					else
					{
						double fX(fOne - ((atan2(aVector.getZ(), aVector.getX()) + F_PI) / F_2PI));

						// correct cartesinan point coordiante dependent from center value
						if(fX > fXCenter + 0.5)
						{
							fX -= fOne;
						}
						else if(fX < fXCenter - 0.5)
						{
							fX += fOne;
						}

						if(bChangeX)
						{
							aTexCoor.setX(fX);
						}

						if(bChangeY)
						{
							aTexCoor.setY(fY);
						}
					}

					aRetval.setTextureCoordinate(a, aTexCoor);
				}

				if(bPolarPoints)
				{
					// correct X-texture coordinates if polar points are contained. Those
					// coordinates cannot be correct, so use prev or next X-coordinate
					for(a = 0L; a < nPointCount; a++)
					{
						B2DPoint aTexCoor(aRetval.getTextureCoordinate(a));

						if(fTools::equalZero(aTexCoor.getY()) || fTools::equal(aTexCoor.getY(), fOne))
						{
							// get prev, next TexCoor and test for pole
							const B2DPoint aPrevTexCoor(aRetval.getTextureCoordinate(a ? a - 1L : nPointCount - 1L));
							const B2DPoint aNextTexCoor(aRetval.getTextureCoordinate((a + 1L) % nPointCount));
							const bool bPrevPole(fTools::equalZero(aPrevTexCoor.getY()) || fTools::equal(aPrevTexCoor.getY(), fOne));
							const bool bNextPole(fTools::equalZero(aNextTexCoor.getY()) || fTools::equal(aNextTexCoor.getY(), fOne));

							if(!bPrevPole && !bNextPole)
							{
								// both no poles, mix them
								aTexCoor.setX((aPrevTexCoor.getX() + aNextTexCoor.getX()) / 2.0);
							}
							else if(!bNextPole)
							{
								// copy next
								aTexCoor.setX(aNextTexCoor.getX());
							}
							else
							{
								// copy prev, even if it's a pole, hopefully it is already corrected
								aTexCoor.setX(aPrevTexCoor.getX());
							}

							aRetval.setTextureCoordinate(a, aTexCoor);
						}
					}
				}
			}

			return aRetval;
		}

		bool isInEpsilonRange(const B3DPoint& rEdgeStart, const B3DPoint& rEdgeEnd, const B3DPoint& rTestPosition, double fDistance)
		{
			// build edge vector
			const B3DVector 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
			{
                // calculate fCut in aEdge
    			const B3DVector aTestEdge(rTestPosition - rEdgeStart);
                const double fScalarTestEdge(aEdge.scalar(aTestEdge));
                const double fScalarStartEdge(aEdge.scalar(rEdgeStart));
                const double fScalarEdge(aEdge.scalar(aEdge));
                const double fCut((fScalarTestEdge - fScalarStartEdge) / fScalarEdge);
				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 B3DPoint aCutPoint(interpolate(rEdgeStart, rEdgeEnd, fCut));
    			    const B3DVector aDelta(rTestPosition - aCutPoint);
				    const double fDistanceSquare(aDelta.scalar(aDelta));

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

			if(bDoDistanceTestStart)
			{
    			const B3DVector aDelta(rTestPosition - rEdgeStart);
				const double fDistanceSquare(aDelta.scalar(aDelta));

				if(fDistanceSquare <= fDistance * fDistance * fDistance)
				{
					return true;
				}
			}
			else if(bDoDistanceTestEnd)
			{
    			const B3DVector aDelta(rTestPosition - rEdgeEnd);
				const double fDistanceSquare(aDelta.scalar(aDelta));

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

			return false;
		}

		bool isInEpsilonRange(const B3DPolygon& rCandidate, const B3DPoint& rTestPosition, double fDistance)
		{
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount)
			{
                const sal_uInt32 nEdgeCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1L);
				B3DPoint aCurrent(rCandidate.getB3DPoint(0));

				if(nEdgeCount)
				{
					// edges
					for(sal_uInt32 a(0); a < nEdgeCount; a++)
					{
						const sal_uInt32 nNextIndex((a + 1) % nPointCount);
						const B3DPoint aNext(rCandidate.getB3DPoint(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;
		}

		bool isInside(const B3DPolygon& rCandidate, const B3DPoint& rPoint, bool bWithBorder)
        {
			if(bWithBorder && isPointOnPolygon(rCandidate, rPoint, true))
			{
				return true;
			}
			else
			{
				bool bRetval(false);
				const B3DVector aPlaneNormal(rCandidate.getNormal());

				if(!aPlaneNormal.equalZero())
				{
				    const sal_uInt32 nPointCount(rCandidate.count());

				    if(nPointCount)
				    {
					    B3DPoint aCurrentPoint(rCandidate.getB3DPoint(nPointCount - 1));
					    const double fAbsX(fabs(aPlaneNormal.getX()));
					    const double fAbsY(fabs(aPlaneNormal.getY()));
					    const double fAbsZ(fabs(aPlaneNormal.getZ()));

					    if(fAbsX > fAbsY && fAbsX > fAbsZ)
					    {
						    // normal points mostly in X-Direction, use YZ-Polygon projection for check
                            // x -> y, y -> z
					        for(sal_uInt32 a(0); a < nPointCount; a++)
					        {
						        const B3DPoint aPreviousPoint(aCurrentPoint);
						        aCurrentPoint = rCandidate.getB3DPoint(a);

						        // cross-over in Z?
						        const bool bCompZA(fTools::more(aPreviousPoint.getZ(), rPoint.getZ()));
						        const bool bCompZB(fTools::more(aCurrentPoint.getZ(), rPoint.getZ()));

						        if(bCompZA != bCompZB)
						        {
							        // 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)
							        {
								        if(bCompYA)
								        {
									        bRetval = !bRetval;
								        }
							        }
							        else
							        {
								        const double fCompare(
									        aCurrentPoint.getY() - (aCurrentPoint.getZ() - rPoint.getZ()) *
									        (aPreviousPoint.getY() - aCurrentPoint.getY()) /
									        (aPreviousPoint.getZ() - aCurrentPoint.getZ()));

								        if(fTools::more(fCompare, rPoint.getY()))
								        {
									        bRetval = !bRetval;
								        }
							        }
						        }
					        }
					    }
					    else if(fAbsY > fAbsX && fAbsY > fAbsZ)
					    {
						    // normal points mostly in Y-Direction, use XZ-Polygon projection for check
                            // x -> x, y -> z
					        for(sal_uInt32 a(0); a < nPointCount; a++)
					        {
						        const B3DPoint aPreviousPoint(aCurrentPoint);
						        aCurrentPoint = rCandidate.getB3DPoint(a);

						        // cross-over in Z?
						        const bool bCompZA(fTools::more(aPreviousPoint.getZ(), rPoint.getZ()));
						        const bool bCompZB(fTools::more(aCurrentPoint.getZ(), rPoint.getZ()));

						        if(bCompZA != bCompZB)
						        {
							        // 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.getZ() - rPoint.getZ()) *
									        (aPreviousPoint.getX() - aCurrentPoint.getX()) /
									        (aPreviousPoint.getZ() - aCurrentPoint.getZ()));

								        if(fTools::more(fCompare, rPoint.getX()))
								        {
									        bRetval = !bRetval;
								        }
							        }
						        }
					        }
					    }
					    else
					    {
						    // normal points mostly in Z-Direction, use XY-Polygon projection for check
                            // x -> x, y -> y
					        for(sal_uInt32 a(0); a < nPointCount; a++)
					        {
						        const B3DPoint aPreviousPoint(aCurrentPoint);
						        aCurrentPoint = rCandidate.getB3DPoint(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 B3DPolygon& rCandidate, const B3DPolygon& rPolygon, bool bWithBorder)
        {
			const sal_uInt32 nPointCount(rPolygon.count());

			for(sal_uInt32 a(0L); a < nPointCount; a++)
			{
				const B3DPoint aTestPoint(rPolygon.getB3DPoint(a));

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

			return true;
        }

		bool isPointOnLine(const B3DPoint& rStart, const B3DPoint& rEnd, const B3DPoint& 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 B3DVector aEdgeVector(rEnd - rStart);
				const B3DVector aTestVector(rCandidate - rStart);

				if(areParallel(aEdgeVector, aTestVector))
				{
					const double fZero(0.0);
					const double fOne(1.0);
                    double fParamTestOnCurr(0.0);

                    if(aEdgeVector.getX() > aEdgeVector.getY())
                    {
                        if(aEdgeVector.getX() > aEdgeVector.getZ())
                        {
                            // X is biggest
                            fParamTestOnCurr = aTestVector.getX() / aEdgeVector.getX();
                        }
                        else
                        {
                            // Z is biggest
                            fParamTestOnCurr = aTestVector.getZ() / aEdgeVector.getZ();
                        }
                    }
                    else
                    {
                        if(aEdgeVector.getY() > aEdgeVector.getZ())
                        {
                            // Y is biggest
                            fParamTestOnCurr = aTestVector.getY() / aEdgeVector.getY();
                        }
                        else
                        {
                            // Z is biggest
                            fParamTestOnCurr = aTestVector.getZ() / aEdgeVector.getZ();
                        }
                    }

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

				return false;
			}
        }

		bool isPointOnPolygon(const B3DPolygon& rCandidate, const B3DPoint& rPoint, bool bWithPoints)
        {
			const sal_uInt32 nPointCount(rCandidate.count());

			if(nPointCount > 1L)
			{
				const sal_uInt32 nLoopCount(rCandidate.isClosed() ? nPointCount : nPointCount - 1L);
				B3DPoint aCurrentPoint(rCandidate.getB3DPoint(0));

				for(sal_uInt32 a(0); a < nLoopCount; a++)
				{
					const B3DPoint aNextPoint(rCandidate.getB3DPoint((a + 1) % nPointCount));

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

					aCurrentPoint = aNextPoint;
				}
			}
			else if(nPointCount && bWithPoints)
			{
				return rPoint.equal(rCandidate.getB3DPoint(0));
			}

			return false;
        }

        bool getCutBetweenLineAndPlane(const B3DVector& rPlaneNormal, const B3DPoint& rPlanePoint, const B3DPoint& rEdgeStart, const B3DPoint& rEdgeEnd, double& fCut)
        {
            if(!rPlaneNormal.equalZero() && !rEdgeStart.equal(rEdgeEnd))
            {
			    const B3DVector aTestEdge(rEdgeEnd - rEdgeStart);
                const double fScalarEdge(rPlaneNormal.scalar(aTestEdge));

				if(!fTools::equalZero(fScalarEdge))
				{
					const B3DVector aCompareEdge(rPlanePoint - rEdgeStart);
					const double fScalarCompare(rPlaneNormal.scalar(aCompareEdge));

					fCut = fScalarCompare / fScalarEdge;
					return true;
				}
            }

            return false;
        }

        bool getCutBetweenLineAndPolygon(const B3DPolygon& rCandidate, const B3DPoint& rEdgeStart, const B3DPoint& rEdgeEnd, double& fCut)
        {
            const sal_uInt32 nPointCount(rCandidate.count());

            if(nPointCount > 2 && !rEdgeStart.equal(rEdgeEnd))
            {
                const B3DVector aPlaneNormal(rCandidate.getNormal());

                if(!aPlaneNormal.equalZero())
                {
                    const B3DPoint aPointOnPlane(rCandidate.getB3DPoint(0));

                    return getCutBetweenLineAndPlane(aPlaneNormal, aPointOnPlane, rEdgeStart, rEdgeEnd, fCut);
                }
            }

            return false;
        }

		//////////////////////////////////////////////////////////////////////
		// comparators with tolerance for 3D Polygons

		bool equal(const B3DPolygon& rCandidateA, const B3DPolygon& 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;

			for(sal_uInt32 a(0); a < nPointCount; a++)
			{
				const B3DPoint aPoint(rCandidateA.getB3DPoint(a));

				if(!aPoint.equal(rCandidateB.getB3DPoint(a), rfSmallValue))
					return false;
			}

			return true;
		}

		bool equal(const B3DPolygon& rCandidateA, const B3DPolygon& rCandidateB)
		{
			const double fSmallValue(fTools::getSmallValue());

			return equal(rCandidateA, rCandidateB, fSmallValue);
		}

		// snap points of horizontal or vertical edges to discrete values
		B3DPolygon snapPointsOfHorizontalOrVerticalEdges(const B3DPolygon& 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
				B3DPolygon aRetval(rCandidate);

				// prepare geometry data. Get rounded from original
                B3ITuple aPrevTuple(basegfx::fround(rCandidate.getB3DPoint(nPointCount - 1)));
				B3DPoint aCurrPoint(rCandidate.getB3DPoint(0));
				B3ITuple 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 B3DPoint aNextPoint(rCandidate.getB3DPoint(nNextIndex));
					const B3ITuple 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 B3DPoint aSnappedPoint(
							bSnapX ? aCurrTuple.getX() : aCurrPoint.getX(),
							bSnapY ? aCurrTuple.getY() : aCurrPoint.getY(),
							aCurrPoint.getZ());

						aRetval.setB3DPoint(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