xref: /AOO41X/main/basegfx/source/polygon/b2dsvgpolypolygon.cxx (revision cdf0e10c4e3984b49a9502b011690b615761d4a3)

/*************************************************************************
 *
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * Copyright 2000, 2010 Oracle and/or its affiliates.
 *
 * OpenOffice.org - a multi-platform office productivity suite
 *
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 *
 * OpenOffice.org is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License version 3
 * only, as published by the Free Software Foundation.
 *
 * OpenOffice.org is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License version 3 for more details
 * (a copy is included in the LICENSE file that accompanied this code).
 *
 * You should have received a copy of the GNU Lesser General Public License
 * version 3 along with OpenOffice.org.  If not, see
 * <http://www.openoffice.org/license.html>
 * for a copy of the LGPLv3 License.
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// MARKER(update_precomp.py): autogen include statement, do not remove
#include "precompiled_basegfx.hxx"

#include <basegfx/polygon/b2dpolygontools.hxx>
#include <basegfx/polygon/b2dpolypolygontools.hxx>
#include <basegfx/polygon/b2dpolygontools.hxx>
#include <basegfx/polygon/b2dpolypolygon.hxx>
#include <basegfx/matrix/b2dhommatrix.hxx>
#include <basegfx/matrix/b2dhommatrixtools.hxx>
#include <rtl/ustring.hxx>
#include <rtl/math.hxx>

namespace basegfx
{
	namespace tools
	{
        namespace
        {
            void lcl_skipSpaces(sal_Int32& 				io_rPos,
                                const ::rtl::OUString& 	rStr,
                                const sal_Int32 		nLen)
            {
                while( io_rPos < nLen &&
                       sal_Unicode(' ') == rStr[io_rPos] )
                {
                    ++io_rPos;
                }
            }

            void lcl_skipSpacesAndCommas(sal_Int32& 			io_rPos,
                                         const ::rtl::OUString& rStr,
                                         const sal_Int32 		nLen)
            {
                while(io_rPos < nLen
                      && (sal_Unicode(' ') == rStr[io_rPos] || sal_Unicode(',') == rStr[io_rPos]))
                {
                    ++io_rPos;
                }
            }

            inline bool lcl_isOnNumberChar(const sal_Unicode aChar, bool bSignAllowed = true)
            {
                const bool bPredicate( (sal_Unicode('0') <= aChar && sal_Unicode('9') >= aChar)
                                       || (bSignAllowed && sal_Unicode('+') == aChar)
                                       || (bSignAllowed && sal_Unicode('-') == aChar) );

                return bPredicate;
            }

            inline bool lcl_isOnNumberChar(const ::rtl::OUString& rStr, const sal_Int32 nPos, bool bSignAllowed = true)
            {
                return lcl_isOnNumberChar(rStr[nPos],
                                          bSignAllowed);
            }

            bool lcl_getDoubleChar(double& 					o_fRetval,
                                   sal_Int32& 				io_rPos,
                                   const ::rtl::OUString& 	rStr,
                                   const sal_Int32 			/*nLen*/)
            {
                sal_Unicode aChar( rStr[io_rPos] );
                ::rtl::OUStringBuffer sNumberString;

                if(sal_Unicode('+') == aChar || sal_Unicode('-') == aChar)
                {
                    sNumberString.append(rStr[io_rPos]);
                    aChar = rStr[++io_rPos];
                }

                while((sal_Unicode('0') <= aChar && sal_Unicode('9') >= aChar)
                      || sal_Unicode('.') == aChar)
                {
                    sNumberString.append(rStr[io_rPos]);
                    aChar = rStr[++io_rPos];
                }

                if(sal_Unicode('e') == aChar || sal_Unicode('E') == aChar)
                {
                    sNumberString.append(rStr[io_rPos]);
                    aChar = rStr[++io_rPos];

                    if(sal_Unicode('+') == aChar || sal_Unicode('-') == aChar)
                    {
                        sNumberString.append(rStr[io_rPos]);
                        aChar = rStr[++io_rPos];
                    }

                    while(sal_Unicode('0') <= aChar && sal_Unicode('9') >= aChar)
                    {
                        sNumberString.append(rStr[io_rPos]);
                        aChar = rStr[++io_rPos];
                    }
                }

                if(sNumberString.getLength())
                {
                    rtl_math_ConversionStatus eStatus;
                    o_fRetval = ::rtl::math::stringToDouble( sNumberString.makeStringAndClear(),
                                                             (sal_Unicode)('.'),
                                                             (sal_Unicode)(','),
                                                             &eStatus,
                                                             NULL );
                    return ( eStatus == rtl_math_ConversionStatus_Ok );
                }

                return false;
            }

            bool lcl_importDoubleAndSpaces( double& 				o_fRetval,
                                            sal_Int32& 				io_rPos,
                                            const ::rtl::OUString& 	rStr,
                                            const sal_Int32 		nLen )
            {
                if( !lcl_getDoubleChar(o_fRetval, io_rPos, rStr, nLen) )
                    return false;

                lcl_skipSpacesAndCommas(io_rPos, rStr, nLen);

                return true;
            }

            bool lcl_importNumberAndSpaces(sal_Int32&                o_nRetval,
                                           sal_Int32& 				io_rPos,
                                           const ::rtl::OUString& 	rStr,
                                           const sal_Int32 		nLen)
            {
                sal_Unicode aChar( rStr[io_rPos] );
                ::rtl::OUStringBuffer sNumberString;

                if(sal_Unicode('+') == aChar || sal_Unicode('-') == aChar)
                {
                    sNumberString.append(rStr[io_rPos]);
                    aChar = rStr[++io_rPos];
                }

                while(sal_Unicode('0') <= aChar && sal_Unicode('9') >= aChar)
                {
                    sNumberString.append(rStr[io_rPos]);
                    aChar = rStr[++io_rPos];
                }

                if(sNumberString.getLength())
                {
                    o_nRetval = sNumberString.makeStringAndClear().toInt32();
                    lcl_skipSpacesAndCommas(io_rPos, rStr, nLen);

                    return true;
                }

                return false;
            }

            void lcl_skipNumber(sal_Int32& 				io_rPos,
                                const ::rtl::OUString& 	rStr,
                                const sal_Int32 		nLen)
            {
                bool bSignAllowed(true);

                while(io_rPos < nLen && lcl_isOnNumberChar(rStr, io_rPos, bSignAllowed))
                {
                    bSignAllowed = false;
                    ++io_rPos;
                }
            }

            void lcl_skipDouble(sal_Int32& 				io_rPos,
                                const ::rtl::OUString& 	rStr,
                                const sal_Int32 		/*nLen*/)
            {
                sal_Unicode aChar( rStr[io_rPos] );

                if(sal_Unicode('+') == aChar || sal_Unicode('-') == aChar)
                    aChar = rStr[++io_rPos];

                while((sal_Unicode('0') <= aChar && sal_Unicode('9') >= aChar)
                      || sal_Unicode('.') == aChar)
                {
                    aChar = rStr[++io_rPos];
                }

                if(sal_Unicode('e') == aChar || sal_Unicode('E') == aChar)
                {
                    aChar = rStr[++io_rPos];

                    if(sal_Unicode('+') == aChar || sal_Unicode('-') == aChar)
                        aChar = rStr[++io_rPos];

                    while(sal_Unicode('0') <= aChar && sal_Unicode('9') >= aChar)
                    {
                        aChar = rStr[++io_rPos];
                    }
                }
            }
            void lcl_skipNumberAndSpacesAndCommas(sal_Int32& 				io_rPos,
                                                  const ::rtl::OUString& 	rStr,
                                                  const sal_Int32 			nLen)
            {
                lcl_skipNumber(io_rPos, rStr, nLen);
                lcl_skipSpacesAndCommas(io_rPos, rStr, nLen);
            }

			// #100617# Allow to skip doubles, too.
            void lcl_skipDoubleAndSpacesAndCommas(sal_Int32& 				io_rPos,
                                                  const ::rtl::OUString& 	rStr,
                                                  const sal_Int32 			nLen)
            {
                lcl_skipDouble(io_rPos, rStr, nLen);
                lcl_skipSpacesAndCommas(io_rPos, rStr, nLen);
            }

            void lcl_putNumberChar( ::rtl::OUStringBuffer& rStr,
                                    double 		 	       fValue )
            {
                rStr.append( fValue );
            }

            void lcl_putNumberCharWithSpace( ::rtl::OUStringBuffer& rStr,
                                             double 		        fValue,
                                             double 		        fOldValue,
                                             bool 			        bUseRelativeCoordinates )
            {
                if( bUseRelativeCoordinates )
                    fValue -= fOldValue;

                const sal_Int32 aLen( rStr.getLength() );
                if(aLen)
                {
                    if( lcl_isOnNumberChar(rStr.charAt(aLen - 1), false) &&
                        fValue >= 0.0 )
                    {
                        rStr.append( sal_Unicode(' ') );
                    }
                }

                lcl_putNumberChar(rStr, fValue);
            }

            inline sal_Unicode lcl_getCommand( sal_Char cUpperCaseCommand,
                                               sal_Char cLowerCaseCommand,
                                               bool 	bUseRelativeCoordinates )
            {
                return bUseRelativeCoordinates ? cLowerCaseCommand : cUpperCaseCommand;
            }
        }

        bool importFromSvgD(B2DPolyPolygon& o_rPolyPolygon, const ::rtl::OUString& 	rSvgDStatement)
        {
            o_rPolyPolygon.clear();
            const sal_Int32 nLen(rSvgDStatement.getLength());
            sal_Int32 nPos(0);
            bool bIsClosed(false);
            double nLastX( 0.0 );
            double nLastY( 0.0 );
			B2DPolygon aCurrPoly;

			// skip initial whitespace
            lcl_skipSpaces(nPos, rSvgDStatement, nLen);

            while(nPos < nLen)
            {
                bool bRelative(false);
                bool bMoveTo(false);
                const sal_Unicode aCurrChar(rSvgDStatement[nPos]);

                switch(aCurrChar)
                {
                    case 'z' :
                    case 'Z' :
                    {
                        nPos++;
                        lcl_skipSpaces(nPos, rSvgDStatement, nLen);

                        // remember closed state of current polygon
                        bIsClosed = true;
                        break;
                    }

                    case 'm' :
                    case 'M' :
                    {
                        bMoveTo = true;
                        // FALLTHROUGH intended
                    }
                    case 'l' :
                    case 'L' :
                    {
                        if('m' == aCurrChar || 'l' == aCurrChar)
						{
                            bRelative = true;
						}

                        if(bMoveTo)
                        {
							// new polygon start, finish old one
                            if(aCurrPoly.count())
                            {
								// add current polygon
								if(bIsClosed)
								{
									closeWithGeometryChange(aCurrPoly);
								}

								o_rPolyPolygon.append(aCurrPoly);

								// reset import values
								bIsClosed = false;
                                aCurrPoly.clear();
                            }
                        }

                        nPos++;
                        lcl_skipSpaces(nPos, rSvgDStatement, nLen);

                        while(nPos < nLen && lcl_isOnNumberChar(rSvgDStatement, nPos))
                        {
                            double nX, nY;

                            if(!lcl_importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;

                            if(bRelative)
                            {
                                nX += nLastX;
                                nY += nLastY;
                            }

                            // set last position
                            nLastX = nX;
                            nLastY = nY;

                            // add point
                            aCurrPoly.append(B2DPoint(nX, nY));
                        }
                        break;
                    }

                    case 'h' :
                    {
                        bRelative = true;
                        // FALLTHROUGH intended
                    }
                    case 'H' :
                    {
                        nPos++;
                        lcl_skipSpaces(nPos, rSvgDStatement, nLen);

                        while(nPos < nLen && lcl_isOnNumberChar(rSvgDStatement, nPos))
                        {
                            double nX, nY(nLastY);

                            if(!lcl_importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;

                            if(bRelative)
							{
                                nX += nLastX;
							}

                            // set last position
                            nLastX = nX;

                            // add point
                            aCurrPoly.append(B2DPoint(nX, nY));
                        }
                        break;
                    }

                    case 'v' :
                    {
                        bRelative = true;
                        // FALLTHROUGH intended
                    }
                    case 'V' :
                    {
                        nPos++;
                        lcl_skipSpaces(nPos, rSvgDStatement, nLen);

                        while(nPos < nLen && lcl_isOnNumberChar(rSvgDStatement, nPos))
                        {
                            double nX(nLastX), nY;

                            if(!lcl_importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;

                            if(bRelative)
							{
                                nY += nLastY;
							}

                            // set last position
                            nLastY = nY;

                            // add point
                            aCurrPoly.append(B2DPoint(nX, nY));
                        }
                        break;
                    }

                    case 's' :
                    {
                        bRelative = true;
                        // FALLTHROUGH intended
                    }
                    case 'S' :
                    {
                        nPos++;
                        lcl_skipSpaces(nPos, rSvgDStatement, nLen);

                        while(nPos < nLen && lcl_isOnNumberChar(rSvgDStatement, nPos))
                        {
                            double nX, nY;
                            double nX2, nY2;

                            if(!lcl_importDoubleAndSpaces(nX2, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nY2, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;

                            if(bRelative)
                            {
                                nX2 += nLastX;
                                nY2 += nLastY;
                                nX += nLastX;
                                nY += nLastY;
                            }

							// ensure existance of start point
							if(!aCurrPoly.count())
							{
                                aCurrPoly.append(B2DPoint(nLastX, nLastY));
							}

							// get first control point. It's the reflection of the PrevControlPoint
							// of the last point. If not existent, use current point (see SVG)
							B2DPoint aPrevControl(B2DPoint(nLastX, nLastY));
							const sal_uInt32 nIndex(aCurrPoly.count() - 1);

							if(aCurrPoly.areControlPointsUsed() && aCurrPoly.isPrevControlPointUsed(nIndex))
							{
								const B2DPoint aPrevPoint(aCurrPoly.getB2DPoint(nIndex));
								const B2DPoint aPrevControlPoint(aCurrPoly.getPrevControlPoint(nIndex));

								// use mirrored previous control point
								aPrevControl.setX((2.0 * aPrevPoint.getX()) - aPrevControlPoint.getX());
								aPrevControl.setY((2.0 * aPrevPoint.getY()) - aPrevControlPoint.getY());
							}

							// append curved edge
							aCurrPoly.appendBezierSegment(aPrevControl, B2DPoint(nX2, nY2), B2DPoint(nX, nY));

                            // set last position
                            nLastX = nX;
                            nLastY = nY;
                        }
                        break;
                    }

                    case 'c' :
                    {
                        bRelative = true;
                        // FALLTHROUGH intended
                    }
                    case 'C' :
                    {
                        nPos++;
                        lcl_skipSpaces(nPos, rSvgDStatement, nLen);

                        while(nPos < nLen && lcl_isOnNumberChar(rSvgDStatement, nPos))
                        {
                            double nX, nY;
                            double nX1, nY1;
                            double nX2, nY2;

                            if(!lcl_importDoubleAndSpaces(nX1, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nY1, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nX2, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nY2, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;

                            if(bRelative)
                            {
                                nX1 += nLastX;
                                nY1 += nLastY;
                                nX2 += nLastX;
                                nY2 += nLastY;
                                nX += nLastX;
                                nY += nLastY;
                            }

							// ensure existance of start point
							if(!aCurrPoly.count())
							{
                                aCurrPoly.append(B2DPoint(nLastX, nLastY));
							}

							// append curved edge
							aCurrPoly.appendBezierSegment(B2DPoint(nX1, nY1), B2DPoint(nX2, nY2), B2DPoint(nX, nY));

                            // set last position
                            nLastX = nX;
                            nLastY = nY;
                        }
                        break;
                    }

                    // #100617# quadratic beziers are imported as cubic ones
                    case 'q' :
                    {
                        bRelative = true;
                        // FALLTHROUGH intended
                    }
                    case 'Q' :
                    {
                        nPos++;
                        lcl_skipSpaces(nPos, rSvgDStatement, nLen);

                        while(nPos < nLen && lcl_isOnNumberChar(rSvgDStatement, nPos))
                        {
                            double nX, nY;
                            double nX1, nY1;

                            if(!lcl_importDoubleAndSpaces(nX1, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nY1, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;

                            if(bRelative)
                            {
                                nX1 += nLastX;
                                nY1 += nLastY;
                                nX += nLastX;
                                nY += nLastY;
                            }

                            // calculate the cubic bezier coefficients from the quadratic ones
                            const double nX1Prime((nX1 * 2.0 + nLastX) / 3.0);
                            const double nY1Prime((nY1 * 2.0 + nLastY) / 3.0);
                            const double nX2Prime((nX1 * 2.0 + nX) / 3.0);
                            const double nY2Prime((nY1 * 2.0 + nY) / 3.0);

							// ensure existance of start point
							if(!aCurrPoly.count())
							{
                                aCurrPoly.append(B2DPoint(nLastX, nLastY));
							}

							// append curved edge
							aCurrPoly.appendBezierSegment(B2DPoint(nX1Prime, nY1Prime), B2DPoint(nX2Prime, nY2Prime), B2DPoint(nX, nY));

                            // set last position
                            nLastX = nX;
                            nLastY = nY;
                        }
                        break;
                    }

                    // #100617# relative quadratic beziers are imported as cubic
                    case 't' :
                    {
                        bRelative = true;
                        // FALLTHROUGH intended
                    }
                    case 'T' :
                    {
                        nPos++;
                        lcl_skipSpaces(nPos, rSvgDStatement, nLen);

                        while(nPos < nLen && lcl_isOnNumberChar(rSvgDStatement, nPos))
                        {
                            double nX, nY;

                            if(!lcl_importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;

                            if(bRelative)
                            {
                                nX += nLastX;
                                nY += nLastY;
                            }

							// ensure existance of start point
							if(!aCurrPoly.count())
							{
                                aCurrPoly.append(B2DPoint(nLastX, nLastY));
							}

							// get first control point. It's the reflection of the PrevControlPoint
							// of the last point. If not existent, use current point (see SVG)
							B2DPoint aPrevControl(B2DPoint(nLastX, nLastY));
							const sal_uInt32 nIndex(aCurrPoly.count() - 1);
							const B2DPoint aPrevPoint(aCurrPoly.getB2DPoint(nIndex));

							if(aCurrPoly.areControlPointsUsed() && aCurrPoly.isPrevControlPointUsed(nIndex))
							{
								const B2DPoint aPrevControlPoint(aCurrPoly.getPrevControlPoint(nIndex));

								// use mirrored previous control point
								aPrevControl.setX((2.0 * aPrevPoint.getX()) - aPrevControlPoint.getX());
								aPrevControl.setY((2.0 * aPrevPoint.getY()) - aPrevControlPoint.getY());
							}

							if(!aPrevControl.equal(aPrevPoint))
							{
								// there is a prev control point, and we have the already mirrored one
								// in aPrevControl. We also need the quadratic control point for this
								// new quadratic segment to calculate the 2nd cubic control point
								const B2DPoint aQuadControlPoint(
									((3.0 * aPrevControl.getX()) - aPrevPoint.getX()) / 2.0,
									((3.0 * aPrevControl.getY()) - aPrevPoint.getY()) / 2.0);

								// calculate the cubic bezier coefficients from the quadratic ones.
								const double nX2Prime((aQuadControlPoint.getX() * 2.0 + nX) / 3.0);
								const double nY2Prime((aQuadControlPoint.getY() * 2.0 + nY) / 3.0);

								// append curved edge, use mirrored cubic control point directly
								aCurrPoly.appendBezierSegment(aPrevControl, B2DPoint(nX2Prime, nY2Prime), B2DPoint(nX, nY));
							}
							else
							{
								// when no previous control, SVG says to use current point -> straight line.
								// Just add end point
								aCurrPoly.append(B2DPoint(nX, nY));
							}

                            // set last position
                            nLastX = nX;
                            nLastY = nY;
                        }
                        break;
                    }

                    case 'a' :
                    {
                        bRelative = true;
                        // FALLTHROUGH intended
                    }
                    case 'A' :
                    {
                        nPos++;
                        lcl_skipSpaces(nPos, rSvgDStatement, nLen);

                        while(nPos < nLen && lcl_isOnNumberChar(rSvgDStatement, nPos))
                        {
                            double nX, nY;
                            double fRX, fRY, fPhi;
                            sal_Int32 bLargeArcFlag, bSweepFlag;

                            if(!lcl_importDoubleAndSpaces(fRX, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(fRY, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(fPhi, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importNumberAndSpaces(bLargeArcFlag, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importNumberAndSpaces(bSweepFlag, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nX, nPos, rSvgDStatement, nLen)) return false;
                            if(!lcl_importDoubleAndSpaces(nY, nPos, rSvgDStatement, nLen)) return false;

                            if(bRelative)
                            {
                                nX += nLastX;
                                nY += nLastY;
                            }

							const B2DPoint aPrevPoint(aCurrPoly.getB2DPoint(aCurrPoly.count() - 1));

                            if( nX == nLastX && nY == nLastY )
                                continue; // start==end -> skip according to SVG spec

                            if( fRX == 0.0 || fRY == 0.0 )
                            {
                                // straight line segment according to SVG spec
                                aCurrPoly.append(B2DPoint(nX, nY));
                            }
                            else
                            {
                                // normalize according to SVG spec
                                fRX=fabs(fRX); fRY=fabs(fRY);

                                // from the SVG spec, appendix F.6.4

                                // |x1'|   |cos phi   sin phi|  |(x1 - x2)/2|
                                // |y1'| = |-sin phi  cos phi|  |(y1 - y2)/2|
                                const B2DPoint p1(nLastX, nLastY);
                                const B2DPoint p2(nX, nY);
                                B2DHomMatrix aTransform(basegfx::tools::createRotateB2DHomMatrix(-fPhi*M_PI/180));

                                const B2DPoint p1_prime( aTransform * B2DPoint(((p1-p2)/2.0)) );

                                //           ______________________________________       rx y1'
                                // |cx'|  + /  rx^2 ry^2 - rx^2 y1'^2 - ry^2 x1^2           ry
                                // |cy'| =-/       rx^2y1'^2 + ry^2 x1'^2               - ry x1'
                                //                                                          rx
                                // chose + if f_A != f_S
                                // chose - if f_A  = f_S
                                B2DPoint aCenter_prime;
                                const double fRadicant(
                                    (fRX*fRX*fRY*fRY - fRX*fRX*p1_prime.getY()*p1_prime.getY() - fRY*fRY*p1_prime.getX()*p1_prime.getX())/
                                    (fRX*fRX*p1_prime.getY()*p1_prime.getY() + fRY*fRY*p1_prime.getX()*p1_prime.getX()));
                                if( fRadicant < 0.0 )
                                {
                                    // no solution - according to SVG
                                    // spec, scale up ellipse
                                    // uniformly such that it passes
                                    // through end points (denominator
                                    // of radicant solved for fRY,
                                    // with s=fRX/fRY)
                                    const double fRatio(fRX/fRY);
                                    const double fRadicant2(
                                        p1_prime.getY()*p1_prime.getY() +
                                        p1_prime.getX()*p1_prime.getX()/(fRatio*fRatio));
                                    if( fRadicant2 < 0.0 )
                                    {
                                        // only trivial solution, one
                                        // of the axes 0 -> straight
                                        // line segment according to
                                        // SVG spec
                                        aCurrPoly.append(B2DPoint(nX, nY));
                                        continue;
                                    }

                                    fRY=sqrt(fRadicant2);
                                    fRX=fRatio*fRY;

                                    // keep center_prime forced to (0,0)
                                }
                                else
                                {
                                    const double fFactor(
                                        (bLargeArcFlag==bSweepFlag ? -1.0 : 1.0) *
                                        sqrt(fRadicant));

                                    // actually calculate center_prime
                                    aCenter_prime = B2DPoint(
                                        fFactor*fRX*p1_prime.getY()/fRY,
                                        -fFactor*fRY*p1_prime.getX()/fRX);
                                }

                                //              +           u - v
                                // angle(u,v) =  arccos( ------------ )     (take the sign of (ux vy - uy vx))
                                //              -        ||u|| ||v||

                                //                  1    | (x1' - cx')/rx |
                                // theta1 = angle((   ), |                | )
                                //                  0    | (y1' - cy')/ry |
                                const B2DPoint aRadii(fRX,fRY);
                                double fTheta1(
                                    B2DVector(1.0,0.0).angle(
                                        (p1_prime-aCenter_prime)/aRadii));

                                //                 |1|    |  (-x1' - cx')/rx |
                                // theta2 = angle( | | ,  |                  | )
                                //                 |0|    |  (-y1' - cy')/ry |
                                double fTheta2(
                                    B2DVector(1.0,0.0).angle(
                                        (-p1_prime-aCenter_prime)/aRadii));

                                // map both angles to [0,2pi)
                                fTheta1 = fmod(2*M_PI+fTheta1,2*M_PI);
                                fTheta2 = fmod(2*M_PI+fTheta2,2*M_PI);

                                // make sure the large arc is taken
                                // (since
                                // createPolygonFromEllipseSegment()
                                // normalizes to e.g. cw arc)
                                const bool bFlipSegment( (bLargeArcFlag!=0) ==
                                    (fmod(fTheta2+2*M_PI-fTheta1,
                                          2*M_PI)<M_PI) );
                                if( bFlipSegment )
                                    std::swap(fTheta1,fTheta2);

                                // finally, create bezier polygon from this
                                B2DPolygon aSegment(
                                    tools::createPolygonFromUnitEllipseSegment(
                                        fTheta1, fTheta2 ));

                                // transform ellipse by rotation & move to final center
                                aTransform = basegfx::tools::createScaleB2DHomMatrix(fRX, fRY);
                                aTransform.translate(aCenter_prime.getX(),
                                                     aCenter_prime.getY());
                                aTransform.rotate(fPhi*M_PI/180);
                                const B2DPoint aOffset((p1+p2)/2.0);
                                aTransform.translate(aOffset.getX(),
                                                     aOffset.getY());
                                aSegment.transform(aTransform);

                                // createPolygonFromEllipseSegment()
                                // always creates arcs that are
                                // positively oriented - flip polygon
                                // if we swapped angles above
                                if( bFlipSegment )
                                    aSegment.flip();
                                aCurrPoly.append(aSegment);
                            }

                            // set last position
                            nLastX = nX;
                            nLastY = nY;
                        }
                        break;
                    }

                    default:
                    {
                        OSL_ENSURE(false, "importFromSvgD(): skipping tags in svg:d element (unknown)!");
                        OSL_TRACE("importFromSvgD(): skipping tags in svg:d element (unknown: \"%c\")!", aCurrChar);
                        ++nPos;
                        break;
                    }
                }
            }

            if(aCurrPoly.count())
            {
                // end-process last poly
				if(bIsClosed)
				{
					closeWithGeometryChange(aCurrPoly);
				}

				o_rPolyPolygon.append(aCurrPoly);
            }

            return true;
        }

        bool importFromSvgPoints( B2DPolygon&            o_rPoly,
                                  const ::rtl::OUString& rSvgPointsAttribute )
        {
            o_rPoly.clear();
            const sal_Int32 nLen(rSvgPointsAttribute.getLength());
            sal_Int32 nPos(0);
            double nX, nY;

            // skip initial whitespace
            lcl_skipSpaces(nPos, rSvgPointsAttribute, nLen);

            while(nPos < nLen)
            {
                if(!lcl_importDoubleAndSpaces(nX, nPos, rSvgPointsAttribute, nLen)) return false;
                if(!lcl_importDoubleAndSpaces(nY, nPos, rSvgPointsAttribute, nLen)) return false;

                // add point
                o_rPoly.append(B2DPoint(nX, nY));

                // skip to next number, or finish
                lcl_skipSpaces(nPos, rSvgPointsAttribute, nLen);
            }

            return true;
        }

        ::rtl::OUString exportToSvgD(
			const B2DPolyPolygon& rPolyPolygon,
			bool bUseRelativeCoordinates,
			bool bDetectQuadraticBeziers)
        {
            const sal_uInt32 nCount(rPolyPolygon.count());
            ::rtl::OUStringBuffer aResult;
            B2DPoint aCurrentSVGPosition(0.0, 0.0); // SVG assumes (0,0) as the initial current point

            for(sal_uInt32 i(0); i < nCount; i++)
            {
                const B2DPolygon aPolygon(rPolyPolygon.getB2DPolygon(i));
                const sal_uInt32 nPointCount(aPolygon.count());

				if(nPointCount)
				{
					const bool bPolyUsesControlPoints(aPolygon.areControlPointsUsed());
					const sal_uInt32 nEdgeCount(aPolygon.isClosed() ? nPointCount : nPointCount - 1);
					sal_Unicode aLastSVGCommand(' '); // last SVG command char
					B2DPoint aLeft, aRight; // for quadratic bezier test

					// handle polygon start point
					B2DPoint aEdgeStart(aPolygon.getB2DPoint(0));
                    aResult.append(lcl_getCommand('M', 'm', bUseRelativeCoordinates));
					lcl_putNumberCharWithSpace(aResult, aEdgeStart.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates);
					lcl_putNumberCharWithSpace(aResult, aEdgeStart.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates);
					aLastSVGCommand =  lcl_getCommand('L', 'l', bUseRelativeCoordinates);
					aCurrentSVGPosition = aEdgeStart;

					for(sal_uInt32 nIndex(0); nIndex < nEdgeCount; nIndex++)
					{
						// prepare access to next point
						const sal_uInt32 nNextIndex((nIndex + 1) % nPointCount);
						const B2DPoint aEdgeEnd(aPolygon.getB2DPoint(nNextIndex));

						// handle edge from (aEdgeStart, aEdgeEnd) using indices (nIndex, nNextIndex)
						const bool bEdgeIsBezier(bPolyUsesControlPoints
							&& (aPolygon.isNextControlPointUsed(nIndex) || aPolygon.isPrevControlPointUsed(nNextIndex)));

						if(bEdgeIsBezier)
						{
							// handle bezier edge
							const B2DPoint aControlEdgeStart(aPolygon.getNextControlPoint(nIndex));
							const B2DPoint aControlEdgeEnd(aPolygon.getPrevControlPoint(nNextIndex));
							bool bIsQuadraticBezier(false);

							// check continuity at current edge's start point. For SVG, do NOT use an
							// existing continuity since no 'S' or 's' statement should be written. At
							// import, that 'previous' control vector is not available. SVG documentation
							// says for interpretation:
							//
							// "(If there is no previous command or if the previous command was
							// not an C, c, S or s, assume the first control point is coincident
							// with the current point.)"
							//
							// That's what is done from our import, so avoid exporting it as first statement
							// is necessary.
							const bool bSymmetricAtEdgeStart(
								0 != nIndex
								&& CONTINUITY_C2 == aPolygon.getContinuityInPoint(nIndex));

							if(bDetectQuadraticBeziers)
							{
								// check for quadratic beziers - that's
								// the case if both control points are in
								// the same place when they are prolonged
								// to the common quadratic control point
								//
								// Left: P = (3P1 - P0) / 2
								// Right: P = (3P2 - P3) / 2
								aLeft = B2DPoint((3.0 * aControlEdgeStart - aEdgeStart) / 2.0);
								aRight= B2DPoint((3.0 * aControlEdgeEnd - aEdgeEnd) / 2.0);
								bIsQuadraticBezier = aLeft.equal(aRight);
							}

							if(bIsQuadraticBezier)
							{
								// approximately equal, export as quadratic bezier
								if(bSymmetricAtEdgeStart)
								{
									const sal_Unicode aCommand(lcl_getCommand('T', 't', bUseRelativeCoordinates));

									if(aLastSVGCommand != aCommand)
									{
                                        aResult.append(aCommand);
										aLastSVGCommand = aCommand;
									}

									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates);
									aLastSVGCommand = aCommand;
									aCurrentSVGPosition = aEdgeEnd;
								}
								else
								{
									const sal_Unicode aCommand(lcl_getCommand('Q', 'q', bUseRelativeCoordinates));

									if(aLastSVGCommand != aCommand)
									{
                                        aResult.append(aCommand);
										aLastSVGCommand = aCommand;
									}

									lcl_putNumberCharWithSpace(aResult, aLeft.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aLeft.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates);
									aLastSVGCommand = aCommand;
									aCurrentSVGPosition = aEdgeEnd;
								}
							}
							else
							{
								// export as cubic bezier
								if(bSymmetricAtEdgeStart)
								{
									const sal_Unicode aCommand(lcl_getCommand('S', 's', bUseRelativeCoordinates));

									if(aLastSVGCommand != aCommand)
									{
                                        aResult.append(aCommand);
										aLastSVGCommand = aCommand;
									}

									lcl_putNumberCharWithSpace(aResult, aControlEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aControlEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates);
									aLastSVGCommand = aCommand;
									aCurrentSVGPosition = aEdgeEnd;
								}
								else
								{
									const sal_Unicode aCommand(lcl_getCommand('C', 'c', bUseRelativeCoordinates));

									if(aLastSVGCommand != aCommand)
									{
                                        aResult.append(aCommand);
										aLastSVGCommand = aCommand;
									}

									lcl_putNumberCharWithSpace(aResult, aControlEdgeStart.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aControlEdgeStart.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aControlEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aControlEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates);
									aLastSVGCommand = aCommand;
									aCurrentSVGPosition = aEdgeEnd;
								}
							}
						}
						else
						{
							// straight edge
							if(0 == nNextIndex)
							{
								// it's a closed polygon's last edge and it's not a bezier edge, so there is
								// no need to write it
							}
							else
							{
								const bool bXEqual(aEdgeStart.getX() == aEdgeEnd.getX());
								const bool bYEqual(aEdgeStart.getY() == aEdgeEnd.getY());

								if(bXEqual && bYEqual)
								{
									// point is a double point; do not export at all
								}
								else if(bXEqual)
								{
									// export as vertical line
									const sal_Unicode aCommand(lcl_getCommand('V', 'v', bUseRelativeCoordinates));

									if(aLastSVGCommand != aCommand)
									{
                                        aResult.append(aCommand);
										aLastSVGCommand = aCommand;
									}

									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates);
									aCurrentSVGPosition = aEdgeEnd;
								}
								else if(bYEqual)
								{
									// export as horizontal line
									const sal_Unicode aCommand(lcl_getCommand('H', 'h', bUseRelativeCoordinates));

									if(aLastSVGCommand != aCommand)
									{
                                        aResult.append(aCommand);
										aLastSVGCommand = aCommand;
									}

									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates);
									aCurrentSVGPosition = aEdgeEnd;
								}
								else
								{
									// export as line
									const sal_Unicode aCommand(lcl_getCommand('L', 'l', bUseRelativeCoordinates));

									if(aLastSVGCommand != aCommand)
									{
                                        aResult.append(aCommand);
										aLastSVGCommand = aCommand;
									}

									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getX(), aCurrentSVGPosition.getX(), bUseRelativeCoordinates);
									lcl_putNumberCharWithSpace(aResult, aEdgeEnd.getY(), aCurrentSVGPosition.getY(), bUseRelativeCoordinates);
									aCurrentSVGPosition = aEdgeEnd;
								}
							}
						}

						// prepare edge start for next loop step
						aEdgeStart = aEdgeEnd;
					}

					// close path if closed poly (Z and z are equivalent here, but looks nicer when case is matched)
					if(aPolygon.isClosed())
					{
                        aResult.append(lcl_getCommand('Z', 'z', bUseRelativeCoordinates));
					}
				}
            }

            return aResult.makeStringAndClear();
        }
    }
}

// eof