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| -rw-r--r-- | basegfx/source/workbench/convexhull.cxx | 200 |
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 @@ -0,0 +1,200 @@ +/* -*- 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: */ |