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+/* -*- 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>
+#include <sal/log.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, size_t* pPointLimit)
+ {
+ 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, pPointLimit);
+
+ if (pPointLimit && !*pPointLimit)
+ {
+ SAL_WARN("basegfx", "clipPolyPolygonOnPolyPolygon hit point limit");
+ return aRetval;
+ }
+
+ 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: */