Adding upstream version 4:7.4.7.upstream/4%7.4.7upstream

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

1 files changed, 200 insertions, 0 deletions

diff --git a/basegfx/source/workbench/convexhull.cxx b/basegfx/source/workbench/convexhull.cxx
new file mode 100644
index 000000000..ddcb04046
--- /dev/null
+++ b/basegfx/source/workbench/convexhull.cxx
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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 <algorithm>
+#include <vector>
+
+#include <bezierclip.hxx>
+
+/* Implements the theta function from Sedgewick: Algorithms in XXX, chapter 24 */
+template <class PointType> double theta( const PointType& p1, const PointType& p2 )
+{
+    typename PointType::value_type dx, dy, ax, ay;
+    double t;
+
+    dx = p2.x - p1.x; ax = absval( dx );
+    dy = p2.y - p1.y; ay = absval( dy );
+    t = (ax+ay == 0) ? 0 : (double) dy/(ax+ay);
+    if( dx < 0 )
+        t = 2-t;
+    else if( dy < 0 )
+        t = 4+t;
+
+    return t*90.0;
+}
+
+/* Model of LessThanComparable for theta sort.
+ * Uses the theta function from Sedgewick: Algorithms in XXX, chapter 24
+ */
+template <class PointType> class ThetaCompare
+{
+public:
+    explicit ThetaCompare( const PointType& rRefPoint ) : maRefPoint( rRefPoint ) {}
+
+    bool operator() ( const PointType& p1, const PointType& p2 )
+    {
+        // return true, if p1 precedes p2 in the angle relative to maRefPoint
+        return theta(maRefPoint, p1) < theta(maRefPoint, p2);
+    }
+
+    double operator() ( const PointType& p ) const
+    {
+        return theta(maRefPoint, p);
+    }
+
+private:
+    PointType maRefPoint;
+};
+
+/* Implementation of the predicate 'counter-clockwise' for three points, from Sedgewick: Algorithms in XXX, chapter 24 */
+template <class PointType, class CmpFunctor> typename PointType::value_type ccw( const PointType& p0, const PointType& p1, const PointType& p2, CmpFunctor& thetaCmp )
+{
+    typename PointType::value_type dx1, dx2, dy1, dy2;
+    typename PointType::value_type theta0( thetaCmp(p0) );
+    typename PointType::value_type theta1( thetaCmp(p1) );
+    typename PointType::value_type theta2( thetaCmp(p2) );
+
+#if 0
+    if( theta0 == theta1 ||
+        theta0 == theta2 ||
+        theta1 == theta2 )
+    {
+        // cannot reliably compare, as at least two points are
+        // theta-equal. See bug description below
+        return 0;
+    }
+#endif
+
+    dx1 = p1.x - p0.x; dy1 = p1.y - p0.y;
+    dx2 = p2.x - p0.x; dy2 = p2.y - p0.y;
+
+    if( dx1*dy2 > dy1*dx2 )
+        return +1;
+
+    if( dx1*dy2 < dy1*dx2 )
+        return -1;
+
+    if( (dx1*dx2 < 0) || (dy1*dy2 < 0) )
+        return -1;
+
+    if( (dx1*dx1 + dy1*dy1) < (dx2*dx2 + dy2*dy2) )
+        return +1;
+
+    return 0;
+}
+
+/*
+ Bug
+ ===
+
+ Sometimes, the resulting polygon is not the convex hull (see below
+ for an edge configuration to reproduce that problem)
+
+ Problem analysis:
+ =================
+
+ The root cause of this bug is the fact that the second part of
+ the algorithm (the 'wrapping' of the point set) relies on the
+ previous theta sorting. Namely, it is required that the
+ generated point ordering, when interpreted as a polygon, is not
+ self-intersecting. This property, although, cannot be
+ guaranteed due to limited floating point accuracy. For example,
+ for two points very close together, and at the same time very
+ far away from the theta reference point p1, can appear on the
+ same theta value (because floating point accuracy is limited),
+ although on different rays to p1 when inspected locally.
+
+ Example:
+
+                    /
+             P3    /
+               |\ /
+               | /
+               |/ \
+             P2    \
+                    \
+      ...____________\
+     P1
+
+ Here, P2 and P3 are theta-equal relative to P1, but the local
+ ccw measure always says 'left turn'. Thus, the convex hull is
+ wrong at this place.
+
+ Solution:
+ =========
+
+ If two points are theta-equal and checked via ccw, ccw must
+ also classify them as 'equal'. Thus, the second stage of the
+ convex hull algorithm sorts the first one out, effectively
+ reducing a cluster of theta-equal points to only one. This
+ single point can then be treated correctly.
+*/
+
+/* Implementation of Graham's convex hull algorithm, see Sedgewick: Algorithms in XXX, chapter 25 */
+Polygon2D convexHull( const Polygon2D& rPoly )
+{
+    const Polygon2D::size_type N( rPoly.size() );
+    Polygon2D result( N + 1 );
+    std::copy(rPoly.begin(), rPoly.end(), result.begin()+1 );
+    Polygon2D::size_type min, i;
+
+    // determine safe point on hull (smallest y value)
+    for( min=1, i=2; i<=N; ++i )
+    {
+        if( result[i].y < result[min].y )
+            min = i;
+    }
+
+    // determine safe point on hull (largest x value)
+    for( i=1; i<=N; ++i )
+    {
+        if( result[i].y == result[min].y &&
+            result[i].x > result[min].x )
+        {
+            min = i;
+        }
+    }
+
+    // TODO: add inner elimination optimization from Sedgewick: Algorithms in XXX, chapter 25
+    // TODO: use radix sort instead of std::sort(), calc theta only once and store
+
+    // setup first point and sort
+    std::swap( result[1], result[min] );
+    ThetaCompare<Point2D> cmpFunc(result[1]);
+    std::sort( result.begin()+1, result.end(), cmpFunc );
+
+    // setup sentinel
+    result[0] = result[N];
+
+    // generate convex hull
+    Polygon2D::size_type M;
+    for( M=3, i=4; i<=N; ++i )
+    {
+        while( ccw(result[M], result[M-1], result[i], cmpFunc) >= 0 )
+            --M;
+
+        ++M;
+        std::swap( result[M], result[i] );
+    }
+
+    // copy range [1,M] to output
+    return Polygon2D( result.begin()+1, result.begin()+M+1 );
+}
+
+/* vim:set shiftwidth=4 softtabstop=4 expandtab: */