Adding upstream version 1:7.0.4.upstream/1%7.0.4upstream

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 817 insertions, 0 deletions

diff --git a/basegfx/source/polygon/b2dpolygonclipper.cxx b/basegfx/source/polygon/b2dpolygonclipper.cxx
new file mode 100644
index 000000000..246d5a10a
--- /dev/null
+++ b/basegfx/source/polygon/b2dpolygonclipper.cxx
@@ -0,0 +1,817 @@
+/* -*- Mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
+/*
+ * This file is part of the LibreOffice project.
+ *
+ * This Source Code Form is subject to the terms of the Mozilla Public
+ * License, v. 2.0. If a copy of the MPL was not distributed with this
+ * file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ *
+ * This file incorporates work covered by the following license notice:
+ *
+ *   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 .
+ */
+
+#include <basegfx/polygon/b2dpolygonclipper.hxx>
+#include <basegfx/polygon/b2dpolygontools.hxx>
+#include <basegfx/numeric/ftools.hxx>
+#include <basegfx/polygon/b2dpolypolygoncutter.hxx>
+#include <basegfx/polygon/b2dpolygoncutandtouch.hxx>
+#include <basegfx/polygon/b2dpolypolygontools.hxx>
+#include <basegfx/curve/b2dcubicbezier.hxx>
+#include <basegfx/utils/rectcliptools.hxx>
+
+namespace basegfx::utils
+{
+        B2DPolyPolygon clipPolygonOnParallelAxis(const B2DPolygon& rCandidate, bool bParallelToXAxis, bool bAboveAxis, double fValueOnOtherAxis, bool bStroke)
+        {
+            B2DPolyPolygon aRetval;
+
+            if(rCandidate.count())
+            {
+                const B2DRange aCandidateRange(getRange(rCandidate));
+
+                if(bParallelToXAxis && fTools::moreOrEqual(aCandidateRange.getMinY(), fValueOnOtherAxis))
+                {
+                    // completely above and on the clip line. also true for curves.
+                    if(bAboveAxis)
+                    {
+                        // add completely
+                        aRetval.append(rCandidate);
+                    }
+                }
+                else if(bParallelToXAxis && fTools::lessOrEqual(aCandidateRange.getMaxY(), fValueOnOtherAxis))
+                {
+                    // completely below and on the clip line. also true for curves.
+                    if(!bAboveAxis)
+                    {
+                        // add completely
+                        aRetval.append(rCandidate);
+                    }
+                }
+                else if(!bParallelToXAxis && fTools::moreOrEqual(aCandidateRange.getMinX(), fValueOnOtherAxis))
+                {
+                    // completely right of and on the clip line. also true for curves.
+                    if(bAboveAxis)
+                    {
+                        // add completely
+                        aRetval.append(rCandidate);
+                    }
+                }
+                else if(!bParallelToXAxis && fTools::lessOrEqual(aCandidateRange.getMaxX(), fValueOnOtherAxis))
+                {
+                    // completely left of and on the clip line. also true for curves.
+                    if(!bAboveAxis)
+                    {
+                        // add completely
+                        aRetval.append(rCandidate);
+                    }
+                }
+                else
+                {
+                    // add cuts with axis to polygon, including bezier segments
+                    // Build edge to cut with. Make it a little big longer than needed for
+                    // numerical stability. We want to cut against the edge seen as endless
+                    // ray here, but addPointsAtCuts() will limit itself to the
+                    // edge's range ]0.0 .. 1.0[.
+                    const double fSmallExtension((aCandidateRange.getWidth() + aCandidateRange.getHeight()) * (0.5 * 0.1));
+                    const B2DPoint aStart(
+                        bParallelToXAxis ? aCandidateRange.getMinX() - fSmallExtension : fValueOnOtherAxis,
+                        bParallelToXAxis ? fValueOnOtherAxis : aCandidateRange.getMinY() - fSmallExtension);
+                    const B2DPoint aEnd(
+                        bParallelToXAxis ? aCandidateRange.getMaxX() + fSmallExtension : fValueOnOtherAxis,
+                        bParallelToXAxis ? fValueOnOtherAxis : aCandidateRange.getMaxY() + fSmallExtension);
+                    const B2DPolygon aCandidate(addPointsAtCuts(rCandidate, aStart, aEnd));
+                    const sal_uInt32 nPointCount(aCandidate.count());
+                    const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                    B2DCubicBezier aEdge;
+                    B2DPolygon aRun;
+
+                    for(sal_uInt32 a(0); a < nEdgeCount; a++)
+                    {
+                        aCandidate.getBezierSegment(a, aEdge);
+                        const B2DPoint aTestPoint(aEdge.interpolatePoint(0.5));
+                        const bool bInside(bParallelToXAxis ?
+                            fTools::moreOrEqual(aTestPoint.getY(), fValueOnOtherAxis) == bAboveAxis :
+                            fTools::moreOrEqual(aTestPoint.getX(), fValueOnOtherAxis) == bAboveAxis);
+
+                        if(bInside)
+                        {
+                            if(!aRun.count() || !aRun.getB2DPoint(aRun.count() - 1).equal(aEdge.getStartPoint()))
+                            {
+                                aRun.append(aEdge.getStartPoint());
+                            }
+
+                            if(aEdge.isBezier())
+                            {
+                                aRun.appendBezierSegment(aEdge.getControlPointA(), aEdge.getControlPointB(), aEdge.getEndPoint());
+                            }
+                            else
+                            {
+                                aRun.append(aEdge.getEndPoint());
+                            }
+                        }
+                        else
+                        {
+                            if(bStroke && aRun.count())
+                            {
+                                aRetval.append(aRun);
+                                aRun.clear();
+                            }
+                        }
+                    }
+
+                    if(aRun.count())
+                    {
+                        if(bStroke)
+                        {
+                            // try to merge this last and first polygon; they may have been
+                            // the former polygon's start/end point
+                            if(aRetval.count())
+                            {
+                                const B2DPolygon aStartPolygon(aRetval.getB2DPolygon(0));
+
+                                if(aStartPolygon.count() && aStartPolygon.getB2DPoint(0).equal(aRun.getB2DPoint(aRun.count() - 1)))
+                                {
+                                    // append start polygon to aRun, remove from result set
+                                    aRun.append(aStartPolygon); aRun.removeDoublePoints();
+                                    aRetval.remove(0);
+                                }
+                            }
+
+                            aRetval.append(aRun);
+                        }
+                        else
+                        {
+                            // set closed flag and correct last point (which is added double now).
+                            closeWithGeometryChange(aRun);
+                            aRetval.append(aRun);
+                        }
+                    }
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon clipPolyPolygonOnParallelAxis(const B2DPolyPolygon& rCandidate, bool bParallelToXAxis, bool bAboveAxis, double fValueOnOtherAxis, bool bStroke)
+        {
+            const sal_uInt32 nPolygonCount(rCandidate.count());
+            B2DPolyPolygon aRetval;
+
+            for(sal_uInt32 a(0); a < nPolygonCount; a++)
+            {
+                const B2DPolyPolygon aClippedPolyPolygon(clipPolygonOnParallelAxis(rCandidate.getB2DPolygon(a), bParallelToXAxis, bAboveAxis, fValueOnOtherAxis, bStroke));
+
+                if(aClippedPolyPolygon.count())
+                {
+                    aRetval.append(aClippedPolyPolygon);
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon clipPolygonOnRange(const B2DPolygon& rCandidate, const B2DRange& rRange, bool bInside, bool bStroke)
+        {
+            const sal_uInt32 nCount(rCandidate.count());
+            B2DPolyPolygon aRetval;
+
+            if(!nCount)
+            {
+                // source is empty
+                return aRetval;
+            }
+
+            if(rRange.isEmpty())
+            {
+                if(bInside)
+                {
+                    // nothing is inside an empty range
+                    return aRetval;
+                }
+                else
+                {
+                    // everything is outside an empty range
+                    return B2DPolyPolygon(rCandidate);
+                }
+            }
+
+            const B2DRange aCandidateRange(getRange(rCandidate));
+
+            if(rRange.isInside(aCandidateRange))
+            {
+                  // candidate is completely inside given range
+                if(bInside)
+                {
+                    // nothing to do
+                    return B2DPolyPolygon(rCandidate);
+                }
+                else
+                {
+                    // nothing is outside, then
+                    return aRetval;
+                }
+            }
+
+            if(!bInside)
+            {
+                // cutting off the outer parts of filled polygons at parallel
+                // lines to the axes is only possible for the inner part, not for
+                // the outer part which means cutting a hole into the original polygon.
+                // This is because the inner part is a logical AND-operation of
+                // the four implied half-planes, but the outer part is not.
+                // It is possible for strokes, but with creating unnecessary extra
+                // cuts, so using clipPolygonOnPolyPolygon is better there, too.
+                // This needs to be done with the topology knowledge and is unfortunately
+                // more expensive, too.
+                const B2DPolygon aClip(createPolygonFromRect(rRange));
+
+                return clipPolygonOnPolyPolygon(rCandidate, B2DPolyPolygon(aClip), bInside, bStroke);
+            }
+
+            // clip against the four axes of the range
+            // against X-Axis, lower value
+            aRetval = clipPolygonOnParallelAxis(rCandidate, true, bInside, rRange.getMinY(), bStroke);
+
+            if(aRetval.count())
+            {
+                // against Y-Axis, lower value
+                if(aRetval.count() == 1)
+                {
+                    aRetval = clipPolygonOnParallelAxis(aRetval.getB2DPolygon(0), false, bInside, rRange.getMinX(), bStroke);
+                }
+                else
+                {
+                    aRetval = clipPolyPolygonOnParallelAxis(aRetval, false, bInside, rRange.getMinX(), bStroke);
+                }
+
+                if(aRetval.count())
+                {
+                    // against X-Axis, higher value
+                    if(aRetval.count() == 1)
+                    {
+                        aRetval = clipPolygonOnParallelAxis(aRetval.getB2DPolygon(0), true, false, rRange.getMaxY(), bStroke);
+                    }
+                    else
+                    {
+                        aRetval = clipPolyPolygonOnParallelAxis(aRetval, true, false, rRange.getMaxY(), bStroke);
+                    }
+
+                    if(aRetval.count())
+                    {
+                        // against Y-Axis, higher value
+                        if(aRetval.count() == 1)
+                        {
+                            aRetval = clipPolygonOnParallelAxis(aRetval.getB2DPolygon(0), false, false, rRange.getMaxX(), bStroke);
+                        }
+                        else
+                        {
+                            aRetval = clipPolyPolygonOnParallelAxis(aRetval, false, false, rRange.getMaxX(), bStroke);
+                        }
+                    }
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon clipPolyPolygonOnRange(const B2DPolyPolygon& rCandidate, const B2DRange& rRange, bool bInside, bool bStroke)
+        {
+            const sal_uInt32 nPolygonCount(rCandidate.count());
+            B2DPolyPolygon aRetval;
+
+            if(!nPolygonCount)
+            {
+                // source is empty
+                return aRetval;
+            }
+
+            if(rRange.isEmpty())
+            {
+                if(bInside)
+                {
+                    // nothing is inside an empty range
+                    return aRetval;
+                }
+                else
+                {
+                    // everything is outside an empty range
+                    return rCandidate;
+                }
+            }
+
+            if(bInside)
+            {
+                for(sal_uInt32 a(0); a < nPolygonCount; a++)
+                {
+                    const B2DPolyPolygon aClippedPolyPolygon(clipPolygonOnRange(rCandidate.getB2DPolygon(a), rRange, bInside, bStroke));
+
+                    if(aClippedPolyPolygon.count())
+                    {
+                        aRetval.append(aClippedPolyPolygon);
+                    }
+                }
+            }
+            else
+            {
+                // for details, see comment in clipPolygonOnRange for the "cutting off
+                // the outer parts of filled polygons at parallel lines" explanations
+                const B2DPolygon aClip(createPolygonFromRect(rRange));
+
+                return clipPolyPolygonOnPolyPolygon(rCandidate, B2DPolyPolygon(aClip), bInside, bStroke);
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon clipPolyPolygonOnPolyPolygon(const B2DPolyPolygon& rCandidate, const B2DPolyPolygon& rClip, bool bInside, bool bStroke)
+        {
+            B2DPolyPolygon aRetval;
+
+            if(rCandidate.count() && rClip.count())
+            {
+                // one or both are no rectangle - go the hard way and clip PolyPolygon
+                // against PolyPolygon...
+                if(bStroke)
+                {
+                    // line clipping, create line snippets by first adding all cut points and
+                    // then marching along the edges and detecting if they are inside or outside
+                    // the clip polygon
+                    for(sal_uInt32 a(0); a < rCandidate.count(); a++)
+                    {
+                        // add cuts with clip to polygon, including bezier segments
+                        const B2DPolygon aCandidate(addPointsAtCuts(rCandidate.getB2DPolygon(a), rClip));
+                        const sal_uInt32 nPointCount(aCandidate.count());
+                        const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1);
+                        B2DCubicBezier aEdge;
+                        B2DPolygon aRun;
+
+                        for(sal_uInt32 b(0); b < nEdgeCount; b++)
+                        {
+                            aCandidate.getBezierSegment(b, aEdge);
+                            const B2DPoint aTestPoint(aEdge.interpolatePoint(0.5));
+                            const bool bIsInside(utils::isInside(rClip, aTestPoint) == bInside);
+
+                            if(bIsInside)
+                            {
+                                if(!aRun.count())
+                                {
+                                    aRun.append(aEdge.getStartPoint());
+                                }
+
+                                if(aEdge.isBezier())
+                                {
+                                    aRun.appendBezierSegment(aEdge.getControlPointA(), aEdge.getControlPointB(), aEdge.getEndPoint());
+                                }
+                                else
+                                {
+                                    aRun.append(aEdge.getEndPoint());
+                                }
+                            }
+                            else
+                            {
+                                if(aRun.count())
+                                {
+                                    aRetval.append(aRun);
+                                    aRun.clear();
+                                }
+                            }
+                        }
+
+                        if(aRun.count())
+                        {
+                            // try to merge this last and first polygon; they may have been
+                            // the former polygon's start/end point
+                            if(aRetval.count())
+                            {
+                                const B2DPolygon aStartPolygon(aRetval.getB2DPolygon(0));
+
+                                if(aStartPolygon.count() && aStartPolygon.getB2DPoint(0).equal(aRun.getB2DPoint(aRun.count() - 1)))
+                                {
+                                    // append start polygon to aRun, remove from result set
+                                    aRun.append(aStartPolygon); aRun.removeDoublePoints();
+                                    aRetval.remove(0);
+                                }
+                            }
+
+                            aRetval.append(aRun);
+                        }
+                    }
+                }
+                else
+                {
+                    // check for simplification with ranges if !bStroke (handling as stroke is more simple),
+                    // but also only when bInside, else the simplification may lead to recursive calls (see
+                    // calls to clipPolyPolygonOnPolyPolygon in clipPolyPolygonOnRange and clipPolygonOnRange)
+                    if (bInside && basegfx::utils::isRectangle(rClip))
+                    {
+                        // #i125349# detect if both given PolyPolygons are indeed ranges
+                        if (basegfx::utils::isRectangle(rCandidate))
+                        {
+                            // both are rectangle
+                            if(rCandidate.getB2DRange().equal(rClip.getB2DRange()))
+                            {
+                                // if both are equal -> no change
+                                return rCandidate;
+                            }
+                            else
+                            {
+                                // not equal -> create new intersection from both ranges,
+                                // but much cheaper based on the ranges
+                                basegfx::B2DRange aIntersectionRange(rCandidate.getB2DRange());
+
+                                aIntersectionRange.intersect(rClip.getB2DRange());
+
+                                if(aIntersectionRange.isEmpty())
+                                {
+                                    // no common IntersectionRange -> the clip will be empty
+                                    return B2DPolyPolygon();
+                                }
+                                else
+                                {
+                                    // use common aIntersectionRange as result, convert
+                                    // to expected utils::PolyPolygon form
+                                    return basegfx::B2DPolyPolygon(
+                                        basegfx::utils::createPolygonFromRect(aIntersectionRange));
+                                }
+                            }
+                        }
+                        else
+                        {
+                            // rClip is rectangle -> clip rCandidate on rRectangle, use the much
+                            // cheaper and numerically more stable clipping against a range
+                            return clipPolyPolygonOnRange(rCandidate, rClip.getB2DRange(), bInside, bStroke);
+                        }
+                    }
+
+                    // area clipping
+
+                    // First solve all polygon-self and polygon-polygon intersections.
+                    // Also get rid of some not-needed polygons (neutral, no area -> when
+                    // no intersections, these are tubes).
+                    // Now it is possible to correct the orientations in the cut-free
+                    // polygons to values corresponding to painting the utils::PolyPolygon with
+                    // a XOR-WindingRule.
+                    B2DPolyPolygon aMergePolyPolygonA = solveCrossovers(rClip);
+                    aMergePolyPolygonA = stripNeutralPolygons(aMergePolyPolygonA);
+                    aMergePolyPolygonA = correctOrientations(aMergePolyPolygonA);
+
+                    if(!bInside)
+                    {
+                        // if we want to get the outside of the clip polygon, make
+                        // it a 'Hole' in topological sense
+                        aMergePolyPolygonA.flip();
+                    }
+
+
+                    // prepare 2nd source polygon in same way
+                    B2DPolyPolygon aMergePolyPolygonB = solveCrossovers(rCandidate);
+                    aMergePolyPolygonB = stripNeutralPolygons(aMergePolyPolygonB);
+                    aMergePolyPolygonB = correctOrientations(aMergePolyPolygonB);
+
+                    // to clip against each other, concatenate and solve all
+                    // polygon-polygon crossovers. polygon-self do not need to
+                    // be solved again, they were solved in the preparation.
+                    aRetval.append(aMergePolyPolygonA);
+                    aRetval.append(aMergePolyPolygonB);
+                    aRetval = solveCrossovers(aRetval);
+
+                    // now remove neutral polygons (closed, but no area). In a last
+                    // step throw away all polygons which have a depth of less than 1
+                    // which means there was no logical AND at their position. For the
+                    // not-inside solution, the clip was flipped to define it as 'Hole',
+                    // so the removal rule is different here; remove all with a depth
+                    // of less than 0 (aka holes).
+                    aRetval = stripNeutralPolygons(aRetval);
+                    aRetval = stripDispensablePolygons(aRetval, bInside);
+                }
+            }
+
+            return aRetval;
+        }
+
+        B2DPolyPolygon clipPolygonOnPolyPolygon(const B2DPolygon& rCandidate, const B2DPolyPolygon& rClip, bool bInside, bool bStroke)
+        {
+            B2DPolyPolygon aRetval;
+
+            if(rCandidate.count() && rClip.count())
+            {
+                aRetval = clipPolyPolygonOnPolyPolygon(B2DPolyPolygon(rCandidate), rClip, bInside, bStroke);
+            }
+
+            return aRetval;
+        }
+
+        namespace {
+
+        /*
+        * let a plane be defined as
+        *
+        *     v.n+d=0
+        *
+        * and a ray be defined as
+        *
+        *     a+(b-a)*t=0
+        *
+        * substitute and rearranging yields
+        *
+        *     t = -(a.n+d)/(n.(b-a))
+        *
+        * if the denominator is zero, the line is either
+        * contained in the plane or parallel to the plane.
+        * in either case, there is no intersection.
+        * if numerator and denominator are both zero, the
+        * ray is contained in the plane.
+        *
+        */
+        struct scissor_plane {
+            double nx,ny;           // plane normal
+            double d;               // [-] minimum distance from origin
+            sal_uInt32 clipmask;    // clipping mask, e.g. 1000 1000
+        };
+
+        }
+
+        /*
+        *
+        * polygon clipping rules  (straight out of Foley and Van Dam)
+        * ===========================================================
+        * current   |next       |emit
+        * ____________________________________
+        * inside    |inside     |next
+        * inside    |outside    |intersect with clip plane
+        * outside   |outside    |nothing
+        * outside   |inside     |intersect with clip plane followed by next
+        *
+        */
+        static sal_uInt32 scissorLineSegment( ::basegfx::B2DPoint           *in_vertex,    // input buffer
+                                       sal_uInt32                     in_count,     // number of verts in input buffer
+                                       ::basegfx::B2DPoint           *out_vertex,   // output buffer
+                                       scissor_plane const           *pPlane,       // scissoring plane
+                                       const ::basegfx::B2DRectangle &rR )          // clipping rectangle
+        {
+
+            sal_uInt32 out_count=0;
+
+            // process all the verts
+            for(sal_uInt32 i=0; i<in_count; i++) {
+
+                // vertices are relative to the coordinate
+                // system defined by the rectangle.
+                ::basegfx::B2DPoint *curr = &in_vertex[i];
+                ::basegfx::B2DPoint *next = &in_vertex[(i+1)%in_count];
+
+                // perform clipping judgement & mask against current plane.
+                sal_uInt32 clip = pPlane->clipmask & ((getCohenSutherlandClipFlags(*curr,rR)<<4)|getCohenSutherlandClipFlags(*next,rR));
+
+                if(clip==0) { // both verts are inside
+                    out_vertex[out_count++] = *next;
+                }
+                else if((clip&0x0f) && (clip&0xf0)) { // both verts are outside
+                }
+                else if((clip&0x0f) && (clip&0xf0)==0) { // curr is inside, next is outside
+
+                    // direction vector from 'current' to 'next', *not* normalized
+                    // to bring 't' into the [0<=x<=1] interval.
+                    ::basegfx::B2DPoint dir((*next)-(*curr));
+
+                    double denominator = pPlane->nx*dir.getX() +
+                                         pPlane->ny*dir.getY();
+                    double numerator =  pPlane->nx*curr->getX() +
+                                        pPlane->ny*curr->getY() +
+                                        pPlane->d;
+                    double t = -numerator/denominator;
+
+                    // calculate the actual point of intersection
+                    ::basegfx::B2DPoint intersection( curr->getX()+t*dir.getX(),
+                                                    curr->getY()+t*dir.getY() );
+
+                    out_vertex[out_count++] = intersection;
+                }
+                else if((clip&0x0f)==0 && (clip&0xf0)) { // curr is outside, next is inside
+
+                    // direction vector from 'current' to 'next', *not* normalized
+                    // to bring 't' into the [0<=x<=1] interval.
+                    ::basegfx::B2DPoint dir((*next)-(*curr));
+
+                    double denominator = pPlane->nx*dir.getX() +
+                                         pPlane->ny*dir.getY();
+                    double numerator =  pPlane->nx*curr->getX() +
+                                        pPlane->ny*curr->getY() +
+                                        pPlane->d;
+                    double t = -numerator/denominator;
+
+                    // calculate the actual point of intersection
+                    ::basegfx::B2DPoint intersection( curr->getX()+t*dir.getX(),
+                                                    curr->getY()+t*dir.getY() );
+
+                    out_vertex[out_count++] = intersection;
+                    out_vertex[out_count++] = *next;
+                }
+            }
+
+            return out_count;
+        }
+
+        B2DPolygon clipTriangleListOnRange( const B2DPolygon& rCandidate,
+                                            const B2DRange&   rRange )
+        {
+            B2DPolygon aResult;
+
+            if( !(rCandidate.count()%3) )
+            {
+                const int scissor_plane_count = 4;
+
+                scissor_plane sp[scissor_plane_count];
+
+                sp[0].nx = +1.0;
+                sp[0].ny = +0.0;
+                sp[0].d = -(rRange.getMinX());
+                sp[0].clipmask = (RectClipFlags::LEFT << 4) | RectClipFlags::LEFT; // 0001 0001
+                sp[1].nx = -1.0;
+                sp[1].ny = +0.0;
+                sp[1].d = +(rRange.getMaxX());
+                sp[1].clipmask = (RectClipFlags::RIGHT << 4) | RectClipFlags::RIGHT; // 0010 0010
+                sp[2].nx = +0.0;
+                sp[2].ny = +1.0;
+                sp[2].d = -(rRange.getMinY());
+                sp[2].clipmask = (RectClipFlags::TOP << 4) | RectClipFlags::TOP; // 0100 0100
+                sp[3].nx = +0.0;
+                sp[3].ny = -1.0;
+                sp[3].d = +(rRange.getMaxY());
+                sp[3].clipmask = (RectClipFlags::BOTTOM << 4) | RectClipFlags::BOTTOM; // 1000 1000
+
+                // retrieve the number of vertices of the triangulated polygon
+                const sal_uInt32 nVertexCount = rCandidate.count();
+
+                if(nVertexCount)
+                {
+                    // Upper bound for the maximal number of vertices when intersecting an
+                    // axis-aligned rectangle with a triangle in E2
+
+                    // The rectangle and the triangle are in general position, and have 4 and 3
+                    // vertices, respectively.
+
+                    //   Lemma: Since the rectangle is a convex polygon ( see
+                    //   http://mathworld.wolfram.com/ConvexPolygon.html for a definition), and
+                    //   has no holes, it follows that any straight line will intersect the
+                    //   rectangle's border line at utmost two times (with the usual
+                    //   tie-breaking rule, if the intersection exactly hits an already existing
+                    //   rectangle vertex, that this intersection is only attributed to one of
+                    //   the adjoining edges). Thus, having a rectangle intersected with
+                    //   a half-plane (one side of a straight line denotes 'inside', the
+                    //   other 'outside') will at utmost add _one_  vertex to the resulting
+                    //   intersection polygon (adding two intersection vertices, and removing at
+                    //   least one rectangle vertex):
+
+                    //         *
+                    //     +--+-----------------+
+                    //     | *                  |
+                    //     |*                   |
+                    //     +                    |
+                    //    *|                    |
+                    //   * |                    |
+                    //     +--------------------+
+
+                    //   Proof: If the straight line intersects the rectangle two
+                    //   times, it does so for distinct edges, i.e. the intersection has
+                    //   minimally one of the rectangle's vertices on either side of the straight
+                    //   line (but maybe more). Thus, the intersection with a half-plane has
+                    //   minimally _one_ rectangle vertex removed from the resulting clip
+                    //   polygon, and therefore, a clip against a half-plane has the net effect
+                    //   of adding at utmost _one_ vertex to the resulting clip polygon.
+
+                    // Theorem: The intersection of a rectangle and a triangle results in a
+                    // polygon with at utmost 7 vertices.
+
+                    // Proof: The inside of the triangle can be described as the consecutive
+                    // intersection with three half-planes. Together with the lemma above, this
+                    // results in at utmost 3 additional vertices added to the already existing 4
+                    // rectangle vertices.
+
+                    // This upper bound is attained with the following example configuration:
+
+                    //                               *
+                    //                             ***
+                    //                           ** *
+                    //                         **  *
+                    //                       **   *
+                    //                     **    *
+                    //                   **     *
+                    //                 **      *
+                    //               **       *
+                    //             **        *
+                    //           **         *
+                    //     ----*2--------3 *
+                    //     | **          |*
+                    //     1*            4
+                    //   **|            *|
+                    // **  |           * |
+                    //   **|          *  |
+                    //     7*        *   |
+                    //     --*6-----5-----
+                    //         **  *
+                    //           **
+
+                    // As we need to scissor all triangles against the
+                    // output rectangle we employ an output buffer for the
+                    // resulting vertices.  the question is how large this
+                    // buffer needs to be compared to the number of
+                    // incoming vertices.  this buffer needs to hold at
+                    // most the number of original vertices times '7'. see
+                    // figure above for an example.  scissoring triangles
+                    // with the cohen-sutherland line clipping algorithm
+                    // as implemented here will result in a triangle fan
+                    // which will be rendered as separate triangles to
+                    // avoid pipeline stalls for each scissored
+                    // triangle. creating separate triangles from a
+                    // triangle fan produces (n-2)*3 vertices where n is
+                    // the number of vertices of the original triangle
+                    // fan.  for the maximum number of 7 vertices of
+                    // resulting triangle fans we therefore need 15 times
+                    // the number of original vertices.
+
+                    //const size_t nBufferSize = sizeof(vertex)*(nVertexCount*16);
+                    //vertex *pVertices = (vertex*)alloca(nBufferSize);
+                    //sal_uInt32 nNumOutput = 0;
+
+                    // we need to clip this triangle against the output rectangle
+                    // to ensure that the resulting texture coordinates are in
+                    // the valid range from [0<=st<=1]. under normal circumstances
+                    // we could use the BORDERCOLOR renderstate but some cards
+                    // seem to ignore this feature.
+                    ::basegfx::B2DPoint stack[3];
+                    unsigned int clipflag = 0;
+
+                    for(sal_uInt32 nIndex=0; nIndex<nVertexCount; ++nIndex)
+                    {
+                        // rotate stack
+                        stack[0] = stack[1];
+                        stack[1] = stack[2];
+                        stack[2] = rCandidate.getB2DPoint(nIndex);
+
+                        // clipping judgement
+                        clipflag |= unsigned(!(rRange.isInside(stack[2])));
+
+                        if(nIndex > 1)
+                        {
+                            // consume vertices until a single separate triangle has been visited.
+                            if(!((nIndex+1)%3))
+                            {
+                                // if any of the last three vertices was outside
+                                // we need to scissor against the destination rectangle
+                                if(clipflag & 7)
+                                {
+                                    ::basegfx::B2DPoint buf0[16];
+                                    ::basegfx::B2DPoint buf1[16];
+
+                                    sal_uInt32 vertex_count = 3;
+
+                                    // clip against all 4 planes passing the result of
+                                    // each plane as the input to the next using a double buffer
+                                    vertex_count = scissorLineSegment(stack,vertex_count,buf1,&sp[0],rRange);
+                                    vertex_count = scissorLineSegment(buf1,vertex_count,buf0,&sp[1],rRange);
+                                    vertex_count = scissorLineSegment(buf0,vertex_count,buf1,&sp[2],rRange);
+                                    vertex_count = scissorLineSegment(buf1,vertex_count,buf0,&sp[3],rRange);
+
+                                    if(vertex_count >= 3)
+                                    {
+                                        // convert triangle fan back to triangle list.
+                                        ::basegfx::B2DPoint v0(buf0[0]);
+                                        ::basegfx::B2DPoint v1(buf0[1]);
+                                        for(sal_uInt32 i=2; i<vertex_count; ++i)
+                                        {
+                                            ::basegfx::B2DPoint v2(buf0[i]);
+                                            aResult.append(v0);
+                                            aResult.append(v1);
+                                            aResult.append(v2);
+                                            v1 = v2;
+                                        }
+                                    }
+                                }
+                                else
+                                {
+                                    // the last triangle has not been altered, simply copy to result
+                                    for(const basegfx::B2DPoint & i : stack)
+                                        aResult.append(i);
+                                }
+                            }
+                        }
+
+                        clipflag <<= 1;
+                    }
+                }
+            }
+
+            return aResult;
+        }
+
+} // end of namespace
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */